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Review

Physics and Applications of High-β Micro- and Nanolasers

Hui Deng, Gian Luca Lippi, Jesper Mørk, Jan Wiersig, and Stephan Reitzenstein*

DOI: 10.1002/adom.202100415

1. Introduction

The revolutionary development of con-

ventional semiconductor lasers toward

micro- and nanolasers has made it pos-

sible in the past few years to explore

the ultimate physical limits of these

photonic devices.[1,2] Above all, the signifi-

cantly increased light–matter interaction

strength, in resonators with low mode vol-

umes in the range of the cube-wavelength,

allows micro- and nanolasers to break new

ground. For example, the effects of cavity

quantum electrodynamics (cQED) open

up the possibility of realizing lasers that

are based mainly on the gain of a single

quantum emitter.[3] In addition, optical

resonators with a low mode volume and

high quality (Q)-factor also ensure effi-

cient control of the spontaneous emission

of the integrated gain medium. The Pur-

cell effect or suitable mode engineering

makes it possible to couple spontaneously

emitted photons with high probability into

the laser mode. This important process

in micro- and nanolasers is quantified in terms of the β-factor

which describes the fraction of spontaneous emission that is

coupled into the considered laser mode.[4] The physical limit is

reached for β= 1, the so-called thresholdless laser.[5] In addition

to the exciting physics of high-β lasers, these devices are also

extremely interesting for energy-efficient applications, since the

lasing threshold can be reduced by orders of magnitude.

In this progress report, we present an overview of the current

state of development of high-β micro- and nanolasers and dis-

cuss open questions as well as future challenges and prospects

for these exciting devices. The addressed topics include the

latest investigations of small scale vertical-cavity surface-emit-

ting lasers (VCSELs) in the limit of the smallest light intensities

at the laser threshold in Section2, where the description of the

emission processes using semiclassical rate equations reaches

its limits and stochastic methods are required for successful

modeling. Building on this, Section3 presents the fundamen-

tals and current developments in high-β lasers leading to the

“holy grail” of laser physics: the thresholdless laser. In this con-

text, we review the challenges in characterizing high-β devices

and emphasize the need for quantum optical measurement

methods for the clear identification of coherent light emission.

An interesting sub-class is represented by bimodal microlasers,

where coupling through the gain medium leads to intriguing

effects such as super-thermal light emission and unconven-

tional normal mode coupling (Section4). Looking beyond con-

ventional devices, emerging nanolaser concepts are discussed in

Micro- and nanolasers are emerging optoelectronic components with many

properties still to be explored and understood. On the one hand, they make

it possible to address fundamental physical questions in the border area

between classical physics and quantum physics, on the other hand, they

open up new application perspectives in many areas of photonics. This

progress report provides an overview of the exciting developments from

conventional semiconductor lasers toward nanoscale lasers, whose function

relies on increased light–matter interaction in low-mode-volume resona-

tors and unconventional gain concepts. The latest advances in the physical

understanding of light emission from high-β lasers, in which a large part of

the spontaneous emission is coupled into the laser mode, are highlighted.

In the limit of β= 1, this leads to thresholdless lasing and it is shown that

quantum optical characterization is required to fully explore the underlying

emission processes. In addition, emerging nanolaser concepts based on Fano

resonators, topological photonics, and 2D materials are presented. Open

questions, future prospects, and application scenarios of high-β lasers in

integrated photonics, quantum nanophotonics, and neuromorphic computing

arediscussed.

Prof. H. Deng

Department of Physics

University of Michigan

Ann Arbor, MI 48109-1040, USA

Prof. G. L. Lippi

Université Côte d’Azur, Institut de Physique de Nice (INPHYNI)

UMR 7010 CNRS

1361 Route des Lucioles, Valbonne F-06560, France

Prof. J. Mørk

DTU Fotonik

Technical University of Denmark

Kongens Lyngby DK-2800, Denmark

Prof. J. Wiersig

Institut für Physik

Otto-von-Guericke-Universität Magdeburg

Postfach 4120, Universitätsplatz 2, D-39016 Magdeburg, Germany

Prof. S. Reitzenstein

Institut für Festkörperphysik

Technische Universität Berlin

Hardenbergstraße 36, 10623 Berlin, Germany

E-mail: [email protected]

The ORCID identification number(s) for the author(s) of this article

can be found under https://doi.org/10.1002/adom.202100415.

VCH GmbH. This is an open access article under the terms of the

Creative Commons Attribution License, which permits use, distribution

and reproduction in any medium, provided the original work is properly

cited.

Adv. Optical Mater. 2021, 9, 2100415

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Section5, providing an outlook on realizations with great devel-

opment potential. On the one hand, Fano lasers, based on very

interesting physics, are particularly attractive for ultra-fast on-

chip applications. On the other hand, topological lasers and new

devices based on novel 2D gain materials open up entirely new

perspectives. Interestingly, work on high-β lasers has focused

on technological development and on the study of their emis-

sion properties. Only recently have the first “real” applications

been conceptually suggested and experimentally demonstrated.

Before offering a short conclusion, we thus highlight (Section6)

this important aspect of nanolasers, stressing their high applica-

tion potential in the field of optical interconnects, in quantum

nanophotonics, and in optical neuromorphiccomputing.

2. Exploring the Limits of Small Scale VCSELs

at Low Light Levels

The exploration of laser physics at the microscale[6,7] can be

traced back to the quest for reduced cavity volume,[8–15] well-dis-

cussed in an early review,[16] and to the consequent technolog-

ical benefits coming from improved efficiency, reduced thermal

load, and smaller footprint in telecommunications. Concomi-

tant work on spontaneous emission in atomic physics[17–23]

provided the support for the early development of dye microla-

sers[24–27] and of VCSELs.[28–32] Cavity engineering, based on the

Purcell effect,[33–35] enabled the construction of resonators where

the β-factor is increased,[36,37] as discussed in more detail in Sec-

tion3. At this scale, however, the standard Maxwell–Bloch laser

description,[38–40] excellent for modeling macroscopic lasers,

fails because it neglects spontaneous emission. For micro- and

nanolasers comprising a single or a few emitters in the active

region, it is feasible to solve full quantum mechanical models of

the laser dynamics.[41–43] Such models show the intricate transi-

tion from below-threshold operation featuring dressed states to

the emergence of a single dominant peak in the lasing region.[41]

For microlasers with extended gain media comprising many

emitters, rate equations have been tremendously successful.[44]

In these, the fraction of spontaneous emission feeding into the

photon population of the lasing cavity mode is explicitly taken

into account. It was shown that the photon number predicted

by properly derived effective rate equations agrees quantitatively

with the outcome of full quantum mechanical models, below as

well as above threshold.[43] The inclusion of spontaneous emis-

sion in the rate equations enables the description of the below-

threshold regime and the smooth growth of the emission as a

function of growing pump power,[31] but it leads to questioning

the concept of laser threshold, best illustrated by the paradox-

ical identification of the β= 1 case with a thresholdless.[45,46] or

zero threshold laser[25] (see Section3). Although the β= 1 case

provides a strictly linear input-output laser response only in the

absence of non-radiative losses (cf.[29] for a rate-equation based

proof and[47,48] for photoluminescent measurements), it repre-

sents a sufficient reason for calling into question the principle

of lasingthreshold.

Aside from niche technological applications, micro-VCSELs

have become today the main source of information on the

physical interaction between electromagnetic field and emit-

ters. Their privileged bridging position between the macro- and

the nanoscale, enables a sufficiently detailed analysis of the

physics of light–matter interaction. Figure1 offers a synopsis of

the evolution (top arrow) from the macro- to the nanoscale with

the accompanying level of model description. The distinction

among the three scales is qualitative and can be best pictured

on the basis of (inverse) cavity volume (V−1), as a surrogate

for several indicators which quantify the device’s characteris-

tics (β-factor, Purcell factor and cavity Q-factor[49]). One way of

loosely quantifying a border between scales makes use of the

relative fluctuations at threshold as defined on the basis of a

quantum statistical theory of the laser.[50] Thus, microscopic

devices (or mesolasers) are characterized by 10−4≤β≤ 10−2,

followed by nanolasers β≤ 1.[51] Macroscopic devices (β< 10−4)

are a good approximation of a thermodynamic optical system,

which ideally requires an infinite number of electromagnetic

cavity modes. The large-size system description satisfactorily

describes the laser threshold as a second-order phase transi-

tion,[52–55] thus occurring at a precise value of the pump rate

(control parameter). Here, radiation changes its nature from

entirely incoherent to purely coherent at a precise pump rate

value (in practice over a negligibly small interval), thus masking

any possible intermediate steps in the evolution of the light–

matter interaction. At the extreme nanoscale end, on the other

hand, the interaction is best described quantum-mechanically,

as long as the number of emitters and modes involved in the

interaction is small (typically less than 10). Presently, techno-

logical constraints related to the responsivity of fast detectors

strongly limit its investigation to mostly statistical properties of

the emission. The intermediate, very extended range presents

features of finite-size systems and benefits from a stochastic

description, stemming from the discreteness of the physical

processes which characterize the exchange between emitter

excitations and photons, and from the impossibility of consid-

ering large size averages. While microlasers also cover part of

this intermediate scale range, nanolasers represent the hinge

which bridges the gap between the two extreme regimes. In

particular, they marry a larger photon flux—improving the

experimental accessibility to information—to surviving finite-

size features, in addition to a broader pump range interval over

Adv. Optical Mater. 2021, 9, 2100415

Figure 1. Graphical illustration of the transition from macroscopic to nanolasers with accompanying physical characteristics.

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which the threshold is stretched. This unique and fortunate

combination of attributes enables the detailed observation of

the evolution of the interaction between radiation and matter

on the way towardlasing.

A two-level micromaser with strong coupling to a single

cavity mode [11] emits coherent light even at the lowest power

levels (fraction of a photon present in the cavity, in average).

This remarkable configuration, however, does not shed useful

light onto the much more complex laser behavior [37], where the

questions raised by the smoothness of the transition between

incoherent and coherent emission in small-sized devices [32, 38,

39] still remain. Quantum statistical considerations[50] explain

the origin of a threshold in the thermodynamic limit and of its

disappearance at the micro- and nanoscale. Although conceptu-

ally correct, this result neither advances our understanding of

micro- and nanolaser physics, nor does it offer practical advice

for the realization of devices whose coherence properties must

be ensured for applications (e.g., Mach–Zehnder-based all-

optical operations for on-chip photonics[56,57]). Yet, since experi-

mental evidence for Poissonian photon statistics exists even in

nanolasers,[58–66] what is sorely missing is a fundamental under-

standing of the transition toward coherence: The simple collec-

tion of existing experimental observations leads indeed to an

extremely complex and confusing picture. A practical approach

used by micro-VCSEL manufacturers to circumvent the problem

is to specify a threshold current high enough to ensure coherence

(compare, e.g., ref. [67] with the measured response in ref. [68]).

Although pragmatic, this approach does not answer the funda-

mental thresholdquestion.

As mentioned above, micro-VCSELs (β> 10−4 with an upper

limit approaching 10−2) represent an ideal compromise between

the emergence of complex threshold physics—rather than a

sudden transition—and the technological constraints which

restrict nanolaser investigation to photon statistical measure-

ments. Wide-bandwidth detectors (up to 10 GHz) have sensitivity

as low as a μW, thus permitting time-resolved measurements

with a photon flux about three orders of magnitude below the

lasing edge, or about one order of magnitude below the “standard

threshold” defined in ref. [50] for a β= 10−4 laser. This perfor-

mance enables the collection of a complete set of data which can

be analyzed with dynamical, as well as statistical indicators[68,69]

offering a much better set of tools to characterize the laser

dynamics during the transition between incoherent and coherent

emission. In addition, fast oscilloscopes with large memory depth

permit the collection of very large datasets over sufficiently short

time intervals to ensure good experiment stability. The commer-

cial availability of a number of robust and durable devices with dif-

ferent characteristics eases the technological side of the investiga-

tions, without excluding the realization of custom-madesamples.

Although the great potential of optical microcavities was

already seen in the early 1990s[70] and experimentally some

threshold properties were observed (in micro-VCSELs,[31,71,72]

as well as in microdisk lasers[73,74]), most of the early reports

focused on obtaining ever decreasing pump power and coher-

ence properties. At the end of the 1990s, detection systems were

not as advanced as to allow the good characterization that we

can now obtain, thus fundamental work on microlasers was

vigorously pursued on custom-built solid-state microlasers

with “relatively high” β-factors (≈10−5).[75] Although some of the

conclusions reached at the time[76] have been recently revised

in light of micro-VCSEL measurements[51] and models,[77] these

surrogate investigations allowed for conceptual inroads into

nanolaser threshold physics and represent the first major con-

tribution in establishing connections across laser scales.[78]

More recent micro-VCSEL experimental contributions to

the description of the transition from incoherent to coherent

laser emission come from experimental evidence which can

be summarized as follows. The observed smooth transition, in

the average laser response, hides a wealth of information on

the physics which develops in the various stages.[68] The first

observation is the appearance of photon bursts which precede

the establishment of a continuous coherent field. These bursts,

easily obtained also with the stochastic simulations (cf. discus-

sion below) and interpretable on the basis of topological con-

siderations,[79] had not been previously reported, but indirect

traces can be found in the nonzero average, below-threshold

oscillation of two orthogonal polarizations.[72] Their features

are illustrated in Figure2a,b which shows the stochastically

computed bursts for a β= 10−4 (a) and β= 10−3 (b) laser. Their

Adv. Optical Mater. 2021, 9, 2100415

Figure 2. a,b) Stochastically computed photon bursts for microlasers

with different β-factor (adapted with permission from Figure7 of ref. [51],

sample traces (insets) obtained from measurements in a micro-VCSEL

American Physical Society). The injected current values are i= 1.26 mA (c),

1.30 mA (d), 1.45 mA (e), and 3.0 mA (f). “Threshold” is estimated to be

close to the injection current of panel (e).

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main feature is a peak amplitude which can be more than

two orders of magnitude larger than the average photon flux

(β= 10−4), with frequency (and shape) which increase at the

expense of amplitude as βgrows.

Up until now, aside from micro-VCSELs, no other system

probably possesses the needed stability, and a sufficiently

broad pump interval over which the photon bursts appear,

to allow for their systematic observation. The height and fre-

quency of the bursts can give rise to strong photon bunching

with superthermal statistical properties[51] in the single-mode

regime. The frequency of the photon bunches increases,

while their height (photon number) decreases, to eventually

give rise to an initially strongly noisy continuous-wave (cw)

coherent laser emission. The experimentally measured prob-

ability density function (PDF) shown in Figure2c–f illustrates

the evolution through the threshold region starting from below

threshold.[68] Panel (c) shows a peaked PDF—measured below

threshold—with a long tail at large photon numbers, which

matches the spikes exemplified in the corresponding inset

(photon burst—only the tip is visible due to the detector sen-

sitivity; electrical noise ranges between approximately 5 and 8

mV). This PDF strongly differs from the one of macroscopic

lasers below threshold.[80] As the current injection increases

(remaining below threshold) the PDF deforms (panel (d)) to

something more symmetrical, due to a burst amplitude reduc-

tion and frequency increase, which start forming an irregular

signal (inset of panel (d)), to eventually give rise to only occa-

sional drops of power to the noise level (PDF of panel (e), with

a power drop illustrated in the inset). Finally, a PDF compat-

ible with regular lasing appears in panel (f). It is interesting

to notice that true lasing (i.e., the photon statistics is well

described by Poisson statistics) lies well beyond the manufac-

turer-specified threshold[67] (typical specified threshold current

ith= 2.2 mA with maximum 3 mA), at least for the devices that

were studied[68] (Poisson statistics reached at ith≈ 4.5 mA[51]).

The second-order zero-delay autocorrelation function for the

photon number n

gnn

=−

(0)

(2)

(1)

shows plateaus of (nearly) constant autocorrelation,[68] whose

origin can be reconduced to a complex dynamical interaction

between carrier density (i.e., the energy reservoir) and the

photon field. It is interesting to notice that similar structures

have recently been observed in a metallic nanolaser:[81] While

the complex procedure to reconstruct the autocorrelation may

induce one to think that not too much weight should be placed

on this resemblance, it is nonetheless worth pointing out the

similarities, for a purely random likeness seems improbable.

Further work is needed to prove whether the route observed in

the micro-VCSEL[68] extends to nanolasers aswell.

The resulting understanding of the threshold region’s struc-

ture and of the transition between photon bursts and cw oscil-

lation has enabled the establishment of a technique for experi-

mentally identifying lasing.[82] It is based on a modulation of

the pump current with a frequency close to the inverse of the

typical repetition rate of the photon bursts before the transi-

tion to cw operation:[83] The latter precedes the emergence of

the well-known relaxation oscillations, which only exist in the

presence of the coherent field. A resonance between the modu-

lation and the photon emission is detected by the autocorrela-

tion function. Numerical predictions show that, although less

pronounced, the effect holds for nanolasers and should provide

a simple experimental technique for detecting the onset of cw,

superpoissonian (weakly) coherent emission[82] as a possible

alternative to quantum optical studies on the photon statistics

of emission (see Section3).

The improved insights into the threshold physics at the

microlaser scale have suggested the possibility for alternative

information encoding schemes, with lower power consumption

and without changes in device construction, where reasonably

regular photon bursts can be induced near threshold.[84] Simi-

larly, trains of photon bursts, with increased regularity, appear

thanks to optical feedback when a micro-VCSEL is biased close

to its threshold.[85]

Although current efforts are mostly devoted to nanolaser

development, as detailed in the following sections, a great deal of

attention is currently being paid to the technological applications

of micro-VCSELs, especially in the telecom sector. High-speed,

low-energy consumption devices have been developed over the

past decade[86–89] for high-speed modulation and optical link

implementation, extensively reviewed in.[90] Similarly, VCSEL

designs, although not capable of providing true nanolaser char-

acteristics, continue to attract attention in the development of

small sources.[91] An extensive reference list can be found in

ref.[92].

A number of the previous observations have been guided

and/or explained with the help of a fully stochastic mod-

eling approach, a necessary support for providing a funda-

mental understanding of the transition between incoherent

and coherent emission. The model is based on Einstein’s

semiclassical theory for the interaction between radiation and

matter[93] and has been implemented into different schemes,

for example, in ref. [94,95] (after a proposal in[50]), and in

ref. [96] (following previous work[97]), both using a Monte Carlo

approach; in ref. [98] as a discretization of rate equations; and

in ref. [99–101] on individual trajectories over which averages

are then taken. All physical processes (pump, absorption, emis-

sion—both spontaneous and stimulated—, and photon trans-

mission through the cavity mirror) are evaluated as probabil-

istic events which involve integer number of exchanges (pho-

tons and excitation). Thus, not only are the times at which each

process occurs random—as well as the number of events—but

the discreteness introduces a granularity which differentiates it

substantially from the differential representation[98] and gives

rise to intrinsic noise, which is otherwise introduced as a Lan-

gevin process in continuous models. The mostly numerical pre-

dictive power stems from the intrinsic granularity in time and

events (photons and excitations) which automatically account

for a poissonian “noise”. Quantities can be computed to match

experimental observations and provide predictions in excellent

agreement with the observations.[102]

The physical meaning of the photon bursts is not yet entirely

clarified, but may play a conceptually fundamental role in the

establishment of coherence. Photon-statistical work on early

lasers[80,103] established that the transition between incoherent

and coherent emission takes place through a statistical mixture

Adv. Optical Mater. 2021, 9, 2100415

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of the two kinds of radiations.[102] Photon bursts may enlarge

the picture by describing the temporal evolution which was

summarized in those statistical considerations.[102]

To conclude this section, it is important to remark the appear-

ance of a new model (extending work aimed at the description

of semiconductor-based nanolasers[104–108]) which—at variance

with rate equations — introduces the incoherent and coherent

field as separate variables, and univocally identifies the position

of the growth of the coherent component through a bifurcation

analysis.[109] This picture provides the first clear definition of the

laser threshold, regardless of laser size and solves the problem

raised by the rate-equation picture,[4,45,110] circumventing the

thermodynamical constraints which prevent the identification

of a threshold in small systems.[50]

3. Ultra-High-β Nanolasers: Entering the

Thresholdless Lasing Regime

A significant impetus for the development of micro- and nano-

lasers, beyond the small scale VCSELs discussion of the pre-

vious section, was and is still provided by the perspective of

realizing lasers with high β-factors. With regard to possible

applications, this opens up the opportunity for reducing the

laser threshold by orders of magnitude,[111] thus increasing the

lasers’ energy efficiency. In addition, high-β lasers can be used

to explore the thresholdless lasing regime, which is extremely

interesting from a fundamental point of view. In the following,

current developments from high-β lasers to the regime of

thresholdless lasing are presented and discussed in thiscontext.

3.1. The Foundations and Development of High-β Lasers

Research in high-β lasers, including the thresholdless case, dates

back to the beginning of the 1990, as already mentioned. On

the basis of experimental results in a microcavity[25] and early

rate-equation modeling,[45] Bjork, Karlsson, and Yamamoto in

1994 dealt with the question of a suitable definition of the laser

threshold of microlasers.[111] In the extreme case of one unique

cavity mode resonating with the gain medium, no threshold can

be identified on the basis of the output characteristics as the

latter is a straight line, whence the term “thresholdless”. This

early work, however, identified the need for a finite amount of

pump to achieve coherent laser emission, based on the require-

ment of at least one photon in the lasing mode (on average)[111]

to reach threshold, thus already invalidating the “zero-threshold”

denomination. Furthermore, an analysis of the quantum Lan-

gevin rate equations showed that the threshold pump value

would be reduced by orders of magnitude, going from mac-

roscopic (β< 10−4) to thresholdless devices (β= 1) and that in

the latter, lasing could occur without population inversion. The

β-factor itself can be influenced by cQED effects and in micro-

pillar resonators can be expressed, through an effective Purcell

factor FP, by β≈ FP/(FP+ 1), that is, taking into account the con-

tributions from all emitters.[112] The further proportionality FP∝

Q/Vmode directly relates β to the Q-factor and, inversely, to the

mode volume Vmode. The latter expression explains the great sci-

entific interest in laser resonators with high-Q and low-volume

modes to decrease the threshold pump power and to enter the

regime of thresholdless lasing. We would like to note that the

impact of the Purcell Factor, the Q-factor, and the β-factor are

discussed in detail in a recent review article dedicated to the

memory of M. I. Stockman.[113]

Based on the enthusiasm arising from early theoretical work

on high-β lasers, great technological efforts were directed at

manufacturing and experimentally investigating such devices,

with major advances, at the turn of the millennium, especially

in the area of quantum dot (QD)-based microlasers. High-β

lasing was demonstrated in QD microdisks,[74,114] QD micropil-

lars,[115] and also in QD photonic crystal (PhC) cavities,[58,116] with

the latter reaching a β-factor up to 0.85. It is interesting to note

that the underlying technological advances in resonator fabrica-

tion also enabled the investigation of single-QD lasing effects

in microdisks,[117] micropillar cavities,[118] and PhC cavities[3] in

the cQED regime of weak coupling and later also in regime of

strong coupling in PhC cavities[119] and micropillars.[120]

Plasmonic nanolasers[2] constitute a different interesting

class of devices where light is confined—at least partly—by a

metallic mirror. As a result, the modal volume can be substan-

tially restricted to values even well below the cubic wavelength

of the emitted light. Typically, the gain medium consists of a

3D semiconductor material or of 2D multiple quantum wells

(QWs). Prominent representatives of this class are nanolasers

based on a metal-insulator-semiconductor-insulator-metal plas-

monic gap mode[121] and plasmonic nanolaser based on a two-

dimensionally confined nanowire plasmonic mode[122] with a

β-factor of up to80%.

The first thresholdless semiconductor laser was demon-

strated in 2012.[5] It is a so-called coaxial nanolaser with a QW

gain medium. In this type of plasmonic nanolaser with dimen-

sions of a few 100 nm, the mode confinement is implemented,

as shown in the inset of Figure3a, via a central rod surrounded

by the semiconductor gain medium with a metallic outer shell.

A SiO2 plug between the upper part of the semiconductor and

the metallic resonator prevents the creation of undesired (dis-

sipating) plasmonic modes. Optical excitation and emission

take place via the lower opening of the resonator. Due to the

small mode volume of the coaxial nanolaser (ideally) only one

resonator mode overlaps with the gain medium, which here

consists of six InGaAsP QWs. This, together with a moderately

high Q-factor (in the range of 200–300), promises a β-factor of

0.99 and, accordingly, virtually thresholdless lasing. The experi-

mental data (red dots), which are shown in Figure 3a for a

measurement with optical excitation at 4.5 K, confirm the ultra-

high β-factor and the virtually threshold-free lasing behavior. In

fact, the output power here rises almost linearly with the input

pump power, as indicated by the blue line. Figure3b shows the

corresponding linewidth of the emission at a wavelength of

1.5 μm as a function of the pump power. The power-dependent

decrease in the linewidth above about 2 × 10−7 W, which cor-

responds to the threshold pump power of this laser, indicates

the transition from spontaneous to stimulated emission with

increased temporal coherence. This behavior also illustrates the

aforementioned point that a thresholdless laser also needs a

finite pumping power to produce laseremission.

After this milestone result, (near) thresholdless lasing was

also achieved in other resonator types and gain configurations.

Adv. Optical Mater. 2021, 9, 2100415

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This includes demonstrations in PhC cavities with buried QW

gain medium[123] and InGaAs QDs[124] at cryogenic tempera-

ture, and laser demonstration at room temperature in PhC

cavities with InAsSb QDs[125] and GaN nanobeam cavities with

an InGaN/GaN QW.[126] These advances in the field of high-β

lasers have initiated a vivid debate about the emission proper-

ties that characterize a thresholdless laser and how laser opera-

tion can be clearly demonstrated in such a laser. This aspect is

discussed in the followingsection.

3.2. How to Verify High-β and Thresholdless Lasing?

In conventional semiconductor lasers, the detection of the laser

emission is usually done by simply recording the input-output

characteristic, whereby the transition from spontaneous to

stimulated emission at the laser threshold is clearly noticeable

in a pronounced non-linearity. In addition, the increased tem-

poral coherence of lasing emission above threshold shows the

characteristic P−1 dependence, where P is the optical power, of

the linewidth reduction predicted by Schawlow and Townes.[127]

In contrast, it is difficult (impossible) in high β (threshold-

less) lasers to determine the transition to stimulated emission

via the input-output characteristic. A lively debate around lasing

characterization in high-β devices proved that linewidth reduc-

tion is usually insufficient to prove lasing.[110] Against this back-

ground, the quantum optical measurement of the emission

statistics has established itself in recent years as proof of laser

operation in high-β micro- and nanolasers.[1,58–60,62,119]

We now discuss the correct and unambiguous detection of

laser emission in high-β devices, pointing out possible pitfalls

in the interpretation of experimental data. A family of microres-

onators with different optical amplification and otherwise very

similar optical properties lends itself to this discussion.[63] The

selected structures are AlGaAs/GaAs micropillar cavities with a

single active layer of InGaAs QDs. The number of QDs effec-

tively coupled to the relevant optical mode can be controlled

through the pillar diameter (here between 2.0 and 2.5 μm) and

the position in the wafer. Operation of each device either as a

laser or a LED, emitting photons exclusively spontaneously, can

be mastered thisway.

In the present case, three QD micropillars, A, B, and C, with a

diameter of 2.0, 2.0, and 2.5 μm, respectively, were selected and

their emission was examined. The corresponding input–output

characteristics are shown in Figure4a. Here, the ordinate shows

Adv. Optical Mater. 2021, 9, 2100415

Figure 3. Thresholdless coaxial nanolaser. a) Input–output characteris-

tics of coaxial nanolaser with a gain medium composed of six InGaAsP

QWs at 4.5K. The linear power dependence (indicated by the blue line)

is characteristic for the thresholdless operation of the laser. As shown in

the inset, the coaxial resonator consists of a metallic (silver) rod which is

enclosed by a metal coated semiconductor ring. Typical dimensions are

r= 100 − 200 nm and Δ= 75 − 100 nm. b) Corresponding dependence

of the emission linewidth. The decrease of linewidth for pump power

values above 10−7 W indicates the transition from spontaneous emission

to stimulated emission with enhanced temporal coherence. Adapted with

Figure 4. Emission properties of a family of optically pumped QD micropillars with a diameter of 2.0 μm (pillar A and B) and 2.5 μm (pillar C), respec-

tively. a) Input-output characteristics indicating LED-like behavior for pillar A, high-β lasing for pillar C, and possibly thresholdless lasing operation for

pillar B. b) Corresponding emission linewidth as function of excitation power. c) Photon autocorrelation function at zero time delay g(2)(0) as function

of intracavity photon number for the three considered micropillars A, B, C. The measured g(2)(0) values indicate LED-like behavior for micropillar A,

www.advancedsciencenews.com www.advopticalmat.de

the intracavity photon number, nPh, determined via a theoretical

modeling of the experimental characteristics. The optical gain

of microresonator A is not large enough to reach the threshold

(nPh= 1) for laser emission; the intracavity photon number

saturates therefore at nPh≈ 0.5. Consistent with this finding,

the emission linewidth (panel (b)) decreases only slightly over

the considered pump power range, a reduction attributed to the

saturation of optical absorption channels. In contrast, micro-

pillar C shows an s-shaped power characteristic typical of a

laser combined with nPh of up to 200, a laser threshold at about

600 μW (at nPh= 1), and a significant decrease in the emission

linewidth, as shown in panel (b). The behavior of micropillar B

is very interesting, as it has an almost linear performance char-

acteristic together with a strong and almost identical decrease

in linewidth compared to micropillar C. According to these cri-

teria, this could be a thresholdlesslaser.

In order to substantiate this “classic” interpretation of the

experimental data, quantum-optical studies of the emission

statistics were carried out on the three micropillars. Corre-

sponding measurements of the second-order autocorrelation

function (g(2)(τ )) via a Hanbury-Brown and Twiss configu-

ration provide important insight into the underlying emis-

sion processes. In particular, the value g(2)(τ = 0) can be used

to distinguish between thermal emission with g(2)(0) = 2 and

coherent emission with g(2)(0) = 1.[128] The experimental g(2)(0)

values are plotted in Figure4c for the three considered micro-

resonators as a function of the intracavity photon number. For

the LED-like micropillar in the spontaneous emission regime,

the autocorrelation remains, as expected, around 2. For micro-

pillar C, there is a transition from thermal (below threshold)

to coherent light (above threshold), as expected in a laser. In

contrast, micropillar B—previously considered as a possible

thresholdless laser—shows a slight decrease in autocorrelation,

around nPh= 1, from its thermal value, g(2)(0) = 2, to then return

to the emission of (pure) thermal light (g(2)(0) = 2) at larger

photon numbers. We would like to note that in the thermal

regime, the experimental g(2)(0) values are usually lower than

expected from theory because of the limited time resolution

of the used detectors.[58,59] For the data presented inFigure4c,

the Siegert relation, which links the normalized first-order cor-

relation function to the second-order photon autocorrelation

function, was applied to overcome this limitation.[63] Interest-

ingly, superthermal bunching with g(2)(0) > 2 is observed for

micropillar C below threshold which can be attributed to super-

radiant emission.[129] Superthermal bunching can also occur

above threshold pump power in bimodal cavities,[130] where it

indicates temporal mode switching in (Section4).

This analysis reveals that micropillar B is a thermal emitter,

rather than a thresholdless laser, which, despite a high intra-

cavity photon number, does not reach the lasing threshold.

This evidence proves that photon statistics is essential, particu-

larly for high-β devices, in determining the presence of lasing.

Against this background, all experimental work on the devel-

opment of high-β micro- and nanolasers should be backed up

by power dependent measurements of the photon statistics,

as recently done in refs.[81,124,126]. Even deeper insight into

the photon statistics can be obtained with a photon number

resolving detector, as it provides access to higher order photon

correlations (see Section4.4).

3.3. Open Questions and Prospects

The last two decades of developments in the field of high-β lasers

have enabled the exploration of the physical limits of threshold-

less and single-QD lasing, while exposing new questions which

require further investigation. The prospect of single-QD lasing

was first introduced in ref.[131] and discussed in an instructive

way in ref.[132], where it was concluded that single-QD lasing

could be possible in the good-cavity limit of weak coupling in

which the emission linewidth of the resonator is smaller than

that of the QD. Until now, this regime, which requires ultra-

high Q-factors, has not been realized in experiment, and

attempts to demonstrate the single-QD lasing have been made

in the boundary of the bad-cavity limit, for which the cavity has

a higher linewidth than the emitter (see ref. [3,117–120]). In this

bad-cavity limit, it has been shown that although the optical

amplification in single-QD lasers was provided dominantly by

a resonant emitter, the gain contribution from further non-

resonant QDs is necessary to enter the lasing regime.[133] For

a real single-QD laser, the question arises as to whether it can

(only) function in the regime of strong cQED coupling and how

lasing and the climbing the Jaynes–Cummings ladder differ. In

the area of high-β single-QD lasers, deterministic fabrication

technologies are interesting, since they permit a precise con-

trol of the position and number of the QDs in the laser’s active

area. The buried-stressor growth method is predestined for this

objective. With this method, the number of QDs in the active

medium can be set in the range of about 1–20 during growth,[65]

which can pave the way for a systematic study of few-QD laser

toward the thresholdless single-QD limit in the future. Thresh-

oldless lasing was achieved with optical excitation and with

conventional QW and QD material. In addition, 2D quantum

materials are considered as active media for nanolasers[134] (see

Section 5.3), and the question arises whether threshold-free

lasing can also be achieved in such structures. From an applica-

tion point of view, it will be interesting to develop thresholdless

lasers under electrical excitation. Questions about the modula-

tion bandwidth, energy efficiency and the possible integration of

high-β and threshold-free lasers in optoelectronic circuits occupy

a special place in the list of topics which needaddressing.

4. Physics and Prospects of Bimodal Microlasers

Bimodal lasing is a well-known phenomenon in macroscopic

lasers such as ring lasers[135,136] and VCSELs.[72] In the realm of

microlasers and nanophotonics, micropillars are good candi-

dates for bimodal lasing as a slight ellipticity of the cross sec-

tion lifts the spectral degeneracy of the fundamental mode (see

inset of Figure5d) leading to two modes with orthogonal linear

polarizations.[137,138] Bimodal microlasers also naturally emerge

in the context of evanescently coupled microcavities supporting

two supermodes.[139–141]

There are a number of intriguing effects in bimodal microla-

sers associated with mode competition for the limited available

gain. This includes bistability and hysteresis,[139] superthermal

light emission,[138] stochastic mode hopping,[130] unconventional

normal-mode coupling,[142] spontaneous symmetry breaking,[143]

and pump-power-driven mode switching.[140,144]

Adv. Optical Mater. 2021, 9, 2100415

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4.1. Input–Output Characteristics and Intensity Fluctuations

A typical input–output curve of a bimodal microlaser is pre-

sented in Figure 5a. One mode (henceforth called the strong

mode) exhibits an “s”-shaped input-output curve known from

high-β single-mode microlasers (see Section3 and Figure4). In

contrast, the intensity of the weak mode saturates and finally

drops down for large injection currents. This mode loses the

competition for the common gainmaterial.

This interpretation is underpinned by the behavior of the

linewidths in Figure 5b. Both linewidths first decrease dra-

matically due to the bleaching of the absorption of the active

medium. While the linewidth of the strong mode stays at a res-

olution-limited value of about 25 μeV, indicating an enhanced

temporal coherence due to stimulated emission, a slight

increase of the linewidth can be observed for the weak mode

above a current of three times the threshold current, indicating

a growing contribution of spontaneous emission, but still, the

linewidth is remarkablysmall.

The intensity fluctuations of bimodal lasers are described by

the set of second-order equal-time correlation functions

ξζ

ξζζξ

ξξζζ

gbbbb

bb bb

(0)

(2)

††

(2)

with ξ, ξ= s, w, delay time τ, and photon annihilation opera-

tors bs and bw of the strong and weak mode, correspondingly.

Figure 5c shows the HBT-setup measurement of the autocor-

relation functions g(0

)

(2) and g(0)

(2) as function of the injec-

tion current. Below threshold, the values of the autocorrelation

functions are significantly below the expected value of 2 for

thermal emission due to the limited temporal resolution of the

HBT configuration.[59] Around threshold, g(0)

(2) shows a small

maximum and approaches the value 1 for Poisson-distributed

light, which indicates the transition from spontaneous emis-

sion to stimulated emission. In contrast, g(0

)

(2) demonstrates

a large maximum well above 2, proving superthermal emis-

sion. It is noteworthy that this superthermal light source is

different from superthermal light sources based on sub- and

superradiance (see, e.g., ref. [129]). Figure 5d shows that the

crosscorrelation function g(0)

(2) exhibits a well-pronounced

minimum, which is an evidence for a strong anticorrelation of

the mode’sintensities.

The experimental findings have been confirmed by full

quantum calculations based on a microscopic semiconductor

Hamiltonian[138] and by semiclassical calculations.[130] Both

approaches support a two-state model:[130,138,145] In state 1, the

strong mode is lasing with large intensity and the weak mode is

nonlasing with relatively small intensity (not necessarily emit-

ting thermal light[146]); in state 2, it is the other way round. This

model is most intuitive in the semiclassical approach which

predicts a mode hopping dynamics resulting from a dynamical

bistability of the classical electric field subject to spontaneous

emission noise.[130] The two-state model is an extension of the

on–off model for macroscopic lasers (see, e.g., refs.[135,136]).

The hopping dynamics and the laser characteristics can be con-

trolled via selective optical injection into either the strong or the

weak mode[147] or by time-delayed self-feedback.[148,149]

4.2. Unconventional Normal-Mode Coupling

Normal-mode coupling is an important topic in cQED. In the

regime of strong (weak) coupling, the energies (linewidths) of

the involved eigenmodes split. The indirect coupling of the

two modes in a bimodal laser via the common gain medium

can be understood as an unconventional normal-mode

coupling.[142]

In the strong coupling regime, the eigenmodes of the total

active system exhibit frequency locking (the well-known laser

frequency locking), and the linewidths of the eigenmodes

exhibit a splitting. On the contrary, in the weak coupling

regime, the spectrum consists of two separated peaks with

similar linewidths.[142] This explains the long coherence times

of the weak mode observed experimentally in Figure5b.

Adv. Optical Mater. 2021, 9, 2100415

Figure 5. Measured characteristics of a bimodal In0.3Ga0.3As QD-micro-

pillar laser with a diameter of 3 μm and slightly elliptical cross section.

The threshold current is estimated to be Ith= 5.1 μA. a) Input–output

characteristic, b) emission mode linewidth and the photon c) auto- and

d) crosscorrelation functions

)

(2), (0

)

(2)

g, and (0)

(2)

g of emission

from the strong and the weak mode, respectively. The inset in (d) shows

a polarization-resolved μEL emission spectrum. Adapted with permis-

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4.3. Mode Switching

Experiments on bimodal lasers have demonstrated a possible

switching of the mode properties occurring when the pump

power is increased beyond the laser threshold[140,144] (not seen

in Figure 5a). This phenomenon is known from VCSELs as

“polarization switching.”[72]

At the switching point the intensity anticorrelation is most

distinct, whereas the strongest bunching appears just before

and after the switching point. For micropillar lasers, the effect

has been discussed in terms of the competition between effec-

tive gain and the intermode kinetics with asymmetric inter-

mode transitions.[144] This mechanism is formally identical to

the one leading to equilibrium Bose–Einstein condensation of

massive bosons. In experiments on coupled PhC nanolasers,

the asymmetric intermode transitions resulted from stimu-

lated scattering due to carrier population oscillations.[140] Cross-

gain saturation is another mechanism to create pump-power-

driven mode switching.[150] A further scheme to achieve a mode

switching is based on injection seeding.[151,152]

4.4. Photon Number-Resolved Measurements

The individual photon-number distributions Pi and Pj for the

strong and the weak mode have been measured in the few-

photon regime using a superconducting transition edge sensor

(TES).[153] Good agreement has been observed with a bimodal

birth-death model introduced in ref. [138]. The most efficient

way to solve the model are Monte Carlo simulations based on

the Gillespie algorithm.[144]

More recently, a two-channel TES has been introduced that

can simultaneously detect the photon number-resolved light

emission of the two orthogonal modes.[146] An example of the

resulting joint photon-number distribution Pij is depicted in

Figure6. The presence of two well-separated peaks is the basis

of the two-state model.[145] The peak with small j corresponds to

state 1 (the strong mode is lasing and the weak mode is non-

lasing), whereas the peak with small i corresponds to state 2.

The faint “bridge” between these two peaks corresponds to

transitions between state 1 and 2. If the transition time is suf-

ficiently large, then the bimodal laser shows bistability and

hysteresis.[139] The two peaks in Pij carry over to a double-peak

structure of the individual photon-number distributionsPi and

Pj, demonstrating that both modes have a Poisson-like and a

thermal-like contribution. The experimental results agree very

well with an extended birth-death model including external

degrees of freedom.[146]

4.5. Prospects

The bimodal high-β microcavity laser can be considered as an

ideal superthermal light source as i) the coherence time is large

(as opposed to a conventional thermal light source) and ii) the

intensity fluctuations can be tuned simply by adjusting the

injection current. The large intensity fluctuations and the cor-

responding high probability of photon pairs can be very useful

for thermal ghost imaging,[154,155] photon-statistics excitation

spectroscopy,[156] two-photon subwavelength lithography,[157]

and two-photon luminescence microscopy.[158,159] Moreover, the

superthermal light may improve the phase sensitivity in inter-

ferometry experiments,[160] help to detect subwavelength inter-

ference,[161] and improve the reconstruction of photon-number

distributions.[162]

Mode switching in bimodal microlasers might be exploited

in the context of all-optical switching and low-power optical

storage (see, e.g., refs. [151,152]).

Bimodal microlasers with time-delayed self-feedback provide

a convenient platform to study nonlinear dynamics including

chaos in the few-photon regime.[148,149] We expect that this

merging of chaos and nanophotonics will result in a number

of applications such as ultra-fast random bit generators, secure

data communication with chaotic pulses, and novel schemes

for informationprocessing.

Micropillar cavities with elliptical cross section exhibit lin-

early polarized emission.[137] The coupling between carrier spin

and light polarization can be exploited to generate fast polari-

zation oscillations. This feature can render micropillar lasers

excellent candidates for spin lasers, which promise low-energy

ultrafast optical communication.[163]

5. Emerging Nanolaser Concepts

Going beyond the traditional scaling of microlasers toward

nanolasers, very interesting concepts have emerged in recent

years for new types of high-β lasers as well as lasers with unu-

sual properties. These are based, among other things, on new

Adv. Optical Mater. 2021, 9, 2100415

Figure 6. The joint photon-number distribution of a bimodal QD-micro-

pillar laser far above threshold close to the switching point measured by

a two-channel TES. Shown is also the individual photon-number distribu-

tion for the strong mode at the bottom and for the weak mode at the left

axis calculated via a sum over the respective columns and rows. Adapted

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types of resonator geometries and new types of gain media, but

also on unconventional physical principles. Against this back-

ground, the three following sections are dedicated to particu-

larly promising newconcepts.

5.1. Fano Lasers

The development of ultra-small in-plane lasers that emit light

into on-chip waveguides is important for the development of a

number of applications, like on-chip communication between

the cores of a computer,[164] sensors, and quantum applica-

tions[165] (see Section 6.2). Recent years have seen impressive

development of such lasers, in particular based on the PhC plat-

form.[166,167] The development of electrical pumping schemes[168]

and PhC buried heterostructure technology[169] are particularly

important. The latter enables the integration of active and pas-

sive sections in the same waveguide layer. Evanescent coupling

to silicon waveguides is also an important technology allowing

to power silicon photonics circuits with ultrasmall lasers.[166]

Further progress in the field requires the development of

lasers with many of the same features as found in macroscopic

lasers, that is, high modulation bandwidth, low-noise, high

quantum and wall-plug efficiency, robustness toward optical

feedback, and different functionalities, such as generation of

short optical pulses. The semiconductor Fano laser, theoreti-

cally suggested in ref. [171] and experimentally demonstrated

in ref. [170], shows promise in meeting many of these require-

ments as well as displaying rich physics. This laser structure

uses Fano interference effects to realize at least one of the mir-

rors. Fano interference is a general wave-interference phenom-

enon observed in many different physical systems, including

quantum mechanics, optics, and plasmonics.[172,173] The Fano

mirror in combination with nonlinearities gives the possibility

to perform a range of optical signal processing functionalities,

including wavelength conversion, pulse shortening, signal

regeneration, and non-reciprocal diode characteristics.[174] In

the context of lasers, the use of Fano interference allows for

the implementation of a frequency-dependent mirror that only

features a high reflectivity in a narrow frequency interval. This

gives rise to fundamentally new laser dynamics, with several

possible applications, such as strong frequency-selectivity, ultra-

high modulation bandwidth, pulse-generation, suppression of

quantum noise, and increased resilience toward optical feed-

back.[175] The lasing mode in the Fano laser may be classified

as a so-called bound-state-in-the-continuum,[176] relying on an

intricate interference mechanism which produces a very sen-

sitive mode-dependence on laser parameters[177] and imparts

the laser with its characteristic features. The first experimental

demonstration of a laser based on a bound-state-in-the-con-

tinuum was not achieved until recently.[178] The Fano laser rep-

resents another design for a bound-state-in-the-continuum and

has the further advantage of in-planeemission.

Figure7 shows a schematic of the Fano laser as it may be

implemented in a PhC platform.[179,180] The figure shows a top

view of a PhC membrane, where blue areas denote InP and

white areas are airholes. Within the optical bandgap of the sur-

rounding periodic PhC structure, in-plane confinement can

be realized by defects, that is, missing or displaced airholes

making up waveguides (line defects) or localized cavities (point

defects). Out-of plane confinement is realized by total internal

reflection in the membrane, which has a height of the order of

a few hundred nanometer. The left mirror of the laser cavity,

with frequency-dependent reflectivity rL(ω), is obtained by the

conventional bandgap effect and has a relatively broad band-

width.[181] The right mirror, with reflectivity rR(ω), is instead

due to Fano interference, realized by side-coupling a nanocavity

to the waveguide.[182] Excited by light right-propagating in the

Adv. Optical Mater. 2021, 9, 2100415

Figure 7. Upper: Schematic of a Fano laser. The left mirror is a con-

ventional broadband photonic crystal mirror. The reflection of the right

mirror is due to Fano interference between the field in the waveguide and

the field in the side-coupled nanocavity, which here is implemented by

omission of an air-hole. Middle: Frequency-dependent reflectivity of the

Fano mirror. Lower: Comparison of measured mode resonances for Fano

lasers (blue square markers) and line defect lasers (red circle markers)

versus cavity length measured in number of “missing” holes between left

and right mirror. Lower figure: Reproduced with permission.[170] Copyright

2017, Springer Nature.

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waveguide, the nanocavity’s resonant field component destruc-

tively interferes with the waveguide’s, thus preventing trans-

mission and reflecting back the radiation in a bandwidth deter-

mined by the Q-factor.

The reflectivity of the Fano mirror, shown in Figure7, can

easily be calculated using coupled-mode-theory.[175,182] If QT

denotes the total Q-factor of the nanocavity (including its

coupling to the waveguide) and Qi is the so-called intrinsic

Q-factor (devoid of waveguide coupling, thus dominated by ver-

tical diffraction losses), the maximum reflectivity of the Fano

mirror is obtained at the resonance frequency ωc and given by

|rR(ωc)|= 1 − QT/Qi. Thus, achieving near-unity reflectivity for

the Fano mirror only requires that the nanocavity’s loss rate be

dominated by coupling to the waveguide. The Fano mirror’s

3-dB bandwidth is given by 2γ T=ωc/QT. Notice that the addi-

tion of an airhole in the waveguide below the nanocavity allows

controlling the amplitude of the continuum path.[183] This turns

the symmetric reflectivity profile seen in Figure7 into an asym-

metric one, useful for lowering switching energies.[174,183]

The lasing oscillation condition for the laser can be

expressed as rLrRexp (ikL), where L is the distance between the

left and right mirror and k is the complex wavenumber, the

imaginary part of which accounts for the gain. The strong fre-

quency dependence of the amplitude and phase of the Fano

mirror reflectivity (see Figure 7) implies that the oscillation

condition only is fulfilled when the laser oscillates very close to

the resonance frequency of the nanocavity and simultaneously

fulfills the phase condition at that frequency. This has the con-

sequence that the laser only meets the oscillation condition for

cavity lengths L that are within a few tens of nanometers from

the optimum positions.[175]

In the experimental demonstration of the Fano laser,[170] the

active gain material was composed of three layers of InAs QDs

contained in the middle of the 250 nm thick InP membrane.

The laser was optically pumped, at room temperature, by a

continuous-wave laser beam focused to the laser cavity region

between the two mirrors, while the nanocavity was unpumped.

Figure7 shows the measured lasing wavelength for Fano lasers

with different lengths, obtained by changes of integer numbers

of PhC periods. In all cases, the Fano laser operates on a single

mode and oscillates close to the resonance of the nanocavity. In

contrast, conventional line defect PhC lasers with two bandgap

mirrors display a number of longitudinal optical modes, whose

wavelengths change with cavity length, approaching the PhC

bandedge where slow light effects lower the threshold gain.[184]

In the experiments,[170] the laser could operate both in a

regime showing cw emission as well as in a regime where it

emits a self-sustained train of short pulses at a repetition rate

of a few gigahertz. Pulsing is explained as an example of pas-

sive Q-switching, promoted by un-pumped QDs in the nano-

cavity region of the Fano laser, which leads to a Fano mirror

reflectivity that grows with laser intensity.[170,185] This is not

unlike the use of semiconductor saturable mirrors to achieve

pulse generation in VCSELs,[186] but in contrast to these, the

Fano mirror is ultrasmall and monolithically integrated. The

Fano laser dynamics can be modeled[171,185] by combining a

general transmission line description of lasers[187] with dynam-

ical coupled mode theory. Mathematically, the onset of self-

pulsing can be understood as a generalized Hopf (Bautin)

bifurcation[188] and the parameter region where it occurs has

been identified.[185,188]

By using buried heterostructure technology[169] to limit the

gain region to the waveguide region, the appearance of self-

pulsing can be avoided and the nanocavity can instead be used

to modulate the laser. It has been predicted[171,189] that the Fano

laser can be directly modulated at frequencies up to several

hundred gigahertz, without the usual limitation to a few tens of

gigahertz imposed by the excitation of relaxation oscillations.[190]

This modulation scheme uses the adiabatic wavelength conver-

sion effect of an optical nanocavity,[180] where the wavelength of

a field stored in a cavity may be changed dynamically by varying

the refractive index of the cavity. By modulating the nanocavity

of the Fano laser, preferentially through an applied electrical

field, the laser signal thus becomes frequency modulated (FM-

modulation). Since there is no, or little, variation of the laser

intensity, the carrier density in the active laser waveguide is not

modulated and accordingly the bandwidth is only limited by the

ability to modulate the refractive index of the nanocavity. This

is illustrated by the calculation in Figure8,[175] which shows

the amplitude of the FM modulation response and the corre-

sponding modulation index. The experimental demonstration

of this novel approach for laser modulation requires develop-

ment of nanoelectrode technology, which is of general interest

for further integrating optics andelectronics.

It is well-known that semiconductor lasers can turn unstable

due to even extremely small fractions of optical feedback. This is

most important for practical applications, and usually demands

the use of an optical isolator at the output of the laser. To date,

however, there is no technology available for realizing inte-

grated and ultra-small optical isolators, and therefore feedback-

induced instabilities pose a challenge for on-chip micro- and

nanolasers. One solution may be to use QD active material, so

engineered as to reduce the linewidth enhancement factor α to

Adv. Optical Mater. 2021, 9, 2100415

Figure 8. Frequency-modulation (FM) response (black) and modulation

index (blue) for small-signal modulation of the the nanocavity resonance

frequency. The modulated signal is extracted from a cross-port (CP) cou-

pled to the nanocavity.[175] The dashed line indicates the characteristic

frequency corresponding to the nanocavity decay rate, γT, and the dotted

line is for the sum of the nanocavity decay rate and the inverse roundtrip

time in the laser cavity, γL). Reproduced with permission.[175] Copyright

2019, IEEE.

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a value close to zero, which strongly reduces the instability.[191]

It was recently shown that the use of the Fano laser geometry

provides another attractive solution for strongly improving the

resilience of the laser towards optical feedback.[192] The feed-

back sensitivity was thus theoretically shown to be reduced by

more than two orders of magnitude, an effect that can be traced

back to an effective strong damping of relaxation oscillations

due to temporal storage-effects of the nanocavity.[192]

5.2. Topological Microlasers

Topological insulators have attracted tremendous attention in

the condensed matter community and beyond. Such a mate-

rial is insulating in the bulk but exhibits conducting surface

states that are protected by finite bulk band gaps and symme-

tries. In 2008 the concept was expanded into photonics,[193] see

also.[194–197] The application to lasers was proposed and theo-

retically studied in 2013[198] and first realized experimentally in

2017.[199] Topological micro- and nanolasers promise to combine

the robustness against disorder, defects, and sharp corners with

single-mode lasing, an improved slope efficiency, a small foot-

print, and a low laserthreshold.

5.2.1. 1D Systems

The original proposal of topological lasers[198] and its recent

1D realizations are based on the Su–Schrieffer–Hegger (SSH)

chain. This tight-binding chain of dimers with alternating

bonds between nearest-neighbor elements possesses two

bands. A finite chain can host a midgap mode localized at the

end of the chain or at domain walls. This mode, in contrast to

conventional edge or defect modes, is not only protected by

the finite bulk band gap that suppresses scattering into bulk

modes, but also by a sublattice symmetry that ensures that the

mode remains exactly in the middle of thegap.

A proper non-uniform distribution of gain and loss

selects the edge mode,[198] as demonstrated in the microwave

regime.[200] The first experiment on topological microlasers

mimicked the SSH chain by a zigzag arrangement of coupled

GaAlAs polariton micropillars with embedded GaAs QWs as

gain material[201] (see Figure9a). Further experiments were

performed on coupled microrings containing InGaAsP QWs

and supporting whispering-gallery modes (WGMs).[202,203] In

ref. [203], the topological robustness was verified via struc-

tural deformations of the microring array. The same work also

demonstrated large-area single-mode lasing resulting from the

overlap of the edge mode with the inner part of the array. Topo-

logical lasing in exciton-polariton microcavity traps containing

InGaAs QWs was realized in ref.[204].

The recent fabrication of topological nanolasers were based

on high-β PhC structures.[205,206] Ref. [205] reported single-

mode lasing in a GaAs PhC nanobeam containing InAs QDs,

with small mode volume of 0.23(λ/n)3, an experimental (simu-

lated) Q of ≈9 600 (60 000), and a spontaneous emission factor

β of 0.03. In ref.[206], a PhC nanocavity with InAsP/InP QWs

(Figure9b) showed single-mode lasing with a simulated Q of

≈35 000 and β= 0.15.

5.2.2. 2D Systems with Broken Time-Reversal Symmetry

2D topological photonic systems with broken time-reversal sym-

metry are the photonic analogues of the quantum Hall systems

in condensed matter physics. The first experimental realization

Adv. Optical Mater. 2021, 9, 2100415

Figure 9. One- (top) and 2D (bottom) topological lasers. a) Scanning electron microscopy (SEM) image of a SSH chain of coupled micropillars. Repro-

Nature. c) SEM image of a cavity made of the USA-shaped boundary between two topologically inequivalent PhCs. The inner one has a star-shaped unit

www.advancedsciencenews.com www.advopticalmat.de

employed a PhC with embedded InGaAsP QWs[199] emitting at

telecommunication wavelengths and at room temperature (see

Figure 9c). A yttrium iron garnet (YIG) substrate was used to

break time-reversal symmetry under a static external magnetic

field. Even though the resulting topological band gap was narrow

and the gain distribution was uniform, lasing on chiral modes

has been observed. These tightly confined modes propagate uni-

directionally along the edge being insensitive to its shape and to

disorder. Such a unidirectional propagation allows an efficient

phase locking and a reduction of spatial-holeburning.

5.2.3. 2D Systems with Time-Reversal Symmetry

2D topological photonic systems with time-reversal symmetry

are the photonic analogues of quantum spin Hall systems. No

external magnetic field is required here, but instead an internal

symmetry, related to a pseudospin degree of freedom. The edge

modes are helical, that is, they occur in counterpropagating

pairs with equal frequency but opposite pseudospin. These

modes are protected from backscattering into each other only

if the above symmetry is preserved, that is, only for disorder of

certaintypes.

The first demonstration used microring arrays on an InGaAsP

QW platform,[207] with gain on the edges only (see Figure9d).

The pseudospin was here the orbital angular momentum in the

rotational symmetric microrings. The nonlinear laser dynamics

and the chosen excitation conditions selected one of the pseu-

dospins resulting in unidirectional lasing. The pseudospin

selection can be also biased by introducing asymmetric back-

scattering (see, e.g., ref.[208]) in the microrings.[207]

Most of the experiments on topological lasers have utilized

optical pumping rather than electrical injection needed for

applications. A recent experiment succeeded in electrically

pumping THz quantum cascade lasers (GaAs/AlGaAs) using a

valley PhC.[209] The latter is the photonic analogue of 2D gapped

valleytronic materials. Negligible inter-valley scattering and

therefore uncoupled valley pseudospins ensure that the helical

edge modes are topologically protected. Numerical Q-factors of

up to 10 000 were achieved. Another experiment demonstrated

single-mode (simulated Q≈20 000) topological lasing in a valley

PhC with InGaAsP QWs at telecommunication wavelength

under optical pumping.[210]

Higher-order topological states, such as corner modes, can

provide sufficiently strong confinement needed for nanolasers.

This was established for a GaAs PhC containing a single layer

of InGaAs QDs.[211] A β-factor of 0.25 was measured, a mode

volume of 0.61(λ/n)3 and a Q-factor up to 50 000 was calcu-

lated and an experimental Q-factor around 1 700 was obtained.

Room-temperature lasing of corner modes was demonstrated

in a PhC slab accommodating InGaAsP QWs[212] with a simu-

lated Q of ≈4000.

5.2.4. Prospects

The theoretical understanding of the coherence and the sta-

bility of topological lasers is still not well developed. While

lasers with instantaneous gain saturation (class-A lasers) allow

for dynamical stability,[213] there are indications that lasers

with slow carrier dynamics (class-B lasers) can be dynamically

unstable.[214] Recent theoretical studies showed that topological

lasers in comparison to conventional laser arrays have a sig-

nificantly improved temporal coherence in the presence of spa-

tial disorder,[215] while in its absence, the temporal coherence

is slightly below the conventional case, but the second-order

photon autocorrelation function is still close to unity.[216] The

latter was experimentally verified in refs. [204,217].

Even though large-area single-mode lasing is realized in top-

ological lasers,[203] in most cases, the edge modes are exponen-

tially localized in a few cavities of the array. There are a number

of exciting new ideas to cure this problem, such as topological

bulk lasing using an artificial imaginary gauge field[218,219] and

frequency-selective band-inversion-induced reflection,[220] as

well as exploiting synthetic dimensions.[221]

Further fascinating developments are the generation

and multiplexing of light beams carrying orbital angular

momentum,[217] and the in situ control of topological modes by

non-Hermiticity, that is, gain and loss,[222] which for example,

allows for the flexible reconfiguration of topological edge

modes.[223] It can be anticipated that the rapidly advancing field

of topological lasers hold further great opportunities for basic

research andapplications.

5.3. Nanolasers Based on 2D Quantum Materials

2D materials have emerged as a new class of crystalline gain

media, following the discovery in 2010 that transition metal

dichalcogenides (TMDs) become direct band-gap semiconduc-

tors in the monolayer limit.[224,225] The reduced dimensionality

leads to reduced screening, large exciton binding energies, and

strong optical transition dipole moment. Each monolayer is

only about 0.7nm thick but can absorb a few to a few tens of

percent of light on a single pass, which suggests the potential

of achieving high gain with a small number of injected carriers.

Due to the absence of dangling bonds at the surface and weak

inter-molecular layer van der Waals binding, 2D heterostruc-

tures can be crafted layer by layer, and integrated with different

substrate without requiring lattice matching.[226] Thereby, new

systems may be created where the media, the cavity modes, or

both possess unusual properties, providing opportunities for

new types of high-β factornanolaser.

Taking advantage of the flexibility in integration, lasers have

been built with monolayer TMDs directly placed on a variety of

cavity architectures, including 2D PhC[227] and 1D nanobeam[228]

cavities, micro-disks with WGMs,[229] and plasmonic nano-

resonator arrays.[230] Lasing was identified by a super-linear

increase in the emission intensity of the resonant mode as a

function of the excitation intensity. These systems showed rela-

tively low photon fluxes, large background from spontaneous

emission, and a small linewidth reduction at the threshold.

These properties have led to some skepticism of the nature of

the observed super-linear power dependence.[231] On the other

hand, these systems have similar configurations as those of QD

lasers made of conventional materials. An interesting question

is whether carrier localization has played an important role in

thesesystems.

Adv. Optical Mater. 2021, 9, 2100415

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While a monolayer forms the thinnest gain medium, it is

insensitive to vertical electrical field and cannot form a vertical

p-n junction. Each material typically has a preferred doping

type, so it is often difficult to create high-quality lateral p- and

n-contacts on the same monolayer. These difficulties can be

circumvented using heterostructures. The simplest type of

2D heterostructures are formed by stacking two monolayers

together. Laser emission, largely free from background spon-

taneous emission, was observed in a MoSe2/WSe2 hetero-

bilayer placed directly on a 1D grating with guided-wave reso-

nances[232] (Figure10). The MoSe2/WSe2 hetero-bilayer has

type-II band alignment. When the twist angle θ between the

monolayer crystal orientations is close to the commensurate

angles of 0° or 60°, a direct bandgap is formed. Carriers can

be injected through the intralayer exciton resonance, followed

by ultrafast charge transfer to the lower energy conduction

band, while carrier losses due to radiative emission is sup-

pressed. This allows efficient carrier build-up and popula-

tion inversion. The 1D grating supports a spatially extended

mode that couples to the full area of the 2D heterostruc-

ture. Therefore lasing leads to narrowing of the emission in

the Fourier space near zero in-plane wavenumber, in addi-

tion to a super-linear increase of the emission intensity and

linewidth reduction. A sharp increase in spatial coherence

length above threshold pump power was observed, showing

the formation of extended spatial coherence, supported by a

2D gainmedium.

In the same type of hetero-bilayer, 1D and 2D moiré lat-

tices have been reported.[233–236] It is therefore intriguing to ask

whether a moiré lattice existed and played a key role in the het-

ero-bilayer laser. It is also important to understand the interplay

between energy relaxation and radiative decay of the intra- and

inter-layer transitions. A promising system for these studies is

the MoSe2/WS2 hetero-bilayers. In MoSe2/WS2 hetero-bilayers,

moiré lattices have been shown to form over a wide range of

twist angles,[237,238] and the oscillator strength of the resulting

moiré excitons are tunable via the twist angle.[238] Recent work

shows that each moiré cell functions as a zero-dimensional QD

with fully localized excitons of discrete energy levels.[239] The

size of the moiré cell, corresponding to the period of the moiré

lattice, is typically a few to a few tens of nanometers, similar

to typical QDs. Compared to self-assembled QDs, such moiré

“dots” are densely packed and do not have intrinsic structural

or compositional inhomogeneities. As a result, the moiré-dot

array can collectively couple with a cavity field, with a total oscil-

lator strength comparable to that of a QW.[239] Therefore, the 2D

moiré system may offer a new types of ensemble QD medium,

which may be integrated with high-β factor nano-cavities devel-

oped for QD(s) as discussed in previous sections to enable

high-beta factor lasers with high gain andefficiency.

Adv. Optical Mater. 2021, 9, 2100415

Figure 10. a) Schematic of the laser device consisting of a hetero-bilayer on a grating cavity. The TE-polarized guided wave resonance of the grating

is near the interlayer exciton resonance of the hetero-bilayer. b) Illustration of the rotationally aligned hetero-bilayer with twist angle θ= 0° (left), and

the corresponding band structure with extrema at the K-valleys (right). Depending on the twist angle θ, the hetero-bilayer has a direct or indirect band-

gap. c) Band alignment and carrier dynamics of the hetero-bilayer. d) Angle-resolved spectra of the TE emission above lasing threshold, with overlaid

simulated dispersions of the empty cavity (crosses) and cavity with bilayer (stars). e) The intensity (red) and linewidth (blue) of the TE emission from

the hetero-bilayer versus input pump power. The emission intensity is integrated over |kx|< 0.7 μm−1 and |ky|< 0.13 μm−1. The dot-dashed line indicates

a linear line, the vertical red line marks Pth, and the horizontal purple line indicates Ip= 1. f) The coherence length λc of the emission versus the pump

www.advancedsciencenews.com www.advopticalmat.de

While the science of 2D materials as a gain medium is still at

infancy, future development of 2D material laser will also ben-

efit greatly from the intense efforts on improving the quantum

yield and fabrication technology of 2D material systems.

Despite initial reports of less than 1% of quantum yield in

TMD monolayers, recent work have shown proper passivation

procedures may lead to near unity quantum yield in exfoliated

monolayers[240] and over 60% in CVD-grown monolayers[241]

at the room temperature. As technologies mature for scalable

fabrication of 2D material heterostructures with high quantum

yield, 2D material lasers may allow energy efficient, electrically

injected, room temperature semiconductor nanolasers that are

easily integrable with existing silicon-basedphotonics.

6. Applications of High-β Micro- and Nanolasers

In addition to their fundamental interest, high-β micro- and

nanolasers hold great promise for applications thanks to their

small component size and reduced threshold power. In addi-

tion, their tight mode confinement potentially enables the

design of properties optimally tailored to specific applications.

Three such areas are discussed here, asexamples.

6.1. On-Chip Interconnects

It is well-known that photonics is a key enabling technology for

the internet. Were it not for low-loss high-speed transmission of

data in optical fibers as well as the efficient conversion between

electrical and optical signals using semiconductor lasers and

photodetectors, we would not have developed the information

society and the global interconnectivity to nearly the level we

are at today. Photonics is also being used for data communi-

cations inside data centers and there is increasing motivation

for using optics even inside computer chips. Today, most of the

energy dissipated inside computers is used to communicate

rather than for logical operations.[164] Not only does this repre-

sent a significant fraction of global energy consumption, the

generated heat limits the processor speed itself. The obvious

solution is the of use optical interconnects, in the form of wave-

guides connecting different parts of the processor architecture.

The advantages of using optics for interconnects are summa-

rized in the following four points formulated by Miller:[164] 1) it

can reduce interconnect energy by eliminating the charging of

electrical lines; 2) it can send information over large distances

at high rates without additional loss or distortion; 3) it can allow

very high densities of high-bandwidth connections; 4) it can

offer very precise timing and retiming ofsignals.

In order to benefit from the replacement of an electrical

wire with an optical waveguide interconnect, the required

energy per bit may have to be as low as a few tens of atto-

joules,[164] depending on the architecture. This condition puts

stricts demands on the conversion efficiency from electronic to

photonic bits (the laser) and vice versa (the photodetector). Fur-

thermore, for such low-energy bits, shot noise becomes impor-

tant and leads to bit-errors. Figure11, following ref. [242] shows

the calculated Bit-Error-Ratio (BER) versus number of photons

in the bit for different noise distributions. As discussed earlier

in this article (see Sections 2 and 3), a laser operating above

threshold has Poissonian photon number statistics and the

purple markers in Figure11 show that in order to reach a BER

of 10−20, about 300 photons per bit are needed on average, cor-

responding to a bit energy of about 40 aJ at a wavelength of

1.55 μm. Notice that the requirement on the BER is much more

stringent for communications between the cores of a computer

than for normal internet traffic, where a BER of 10−9 often is

considered “error-free” and where advanced error-correcting

schemes may beemployed.

This energy can be significantly reduced if one employs

intensity-squeezed signals with sub-Poissonian statistics.[243]

For a device generating a pure photon number state in the con-

sidered bit slot, no errors due to shot noise would be encoun-

tered if the effective loss of the link, including generation and

detection efficiencies, were zero. It has been known since the

work of Yamamoto etal. [244,245] that the output intensity noise

of lasers can be reduced below the standard quantum limit by

driving the laser with a so-called “quiet” electron stream. The

combined effect of the degree of laser noise squeezing and the

loss of the link can be described by a so-called Fano factor F,

with F= 1 corresponding to Poisson statistics and F= 0 to a pure

number state at the output of the link.[243] The corresponding

effective efficiency in converting from the quiet electron stream

to the photon stream is given by η= 1 − F. Figure11 shows

the calculated BER for different values of η,[242] showing the

large potential reduction of required photon number by using

squeezedlight.

The squeezing achieved in semiconductor lasers and

LEDs[246–249] is limited by a number of factors, including side

modes, intrinsic losses in the laser cavity,[250] and current

leakage,[251] and the squeezing demonstrated so far has been

limited to relatively small bandwidths that are typically insuf-

ficient for transmission of data. These limitations may to a

large degree be overcome if the fundamental light–matter

coupling in the device can be significantly enhanced. Recent

designs[252–254] for achieving deep subwavelength confinement

in an optical semiconductor cavity may provide a new approach

for realizing such devices. Thus, while the Purcell factor in the

conventional “good cavity limit,” where the cavity bandwidth is

Adv. Optical Mater. 2021, 9, 2100415

Figure 11. Bit-error-ratio (BER) versus average bit photon number for dif-

ferent noise distributions. The parameter η is related to the Fano factor

by F= 1 −η, and is a measure of how well a quiet electrical pump current

at the input is converted to a quiet photon stream at the output within

the considered signal bandwidth.

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smaller than the homogeneous emitter broadening, does not

depend on the Q-factor, but it does depend on the inverse of

the effective mode volume.[100,255] It was recently shown that by

employing such a design for “extreme dielectric confinement,”

it should be feasible to realize a nanoLED featuring a high

degree of squeezing in a large bandwidth.[242] The experimental

realization of such novel deep-subwavelength laser cavities,

without resorting to metal cavities and the strong losses that

they bring,[256] is an important futurechallenge.

6.2. Quantum Nanophotonics

A second very interesting and suitable application scenario

for high-β lasers is their use in the field of quantum nanopho-

tonics. Here, these devices can act as coherent light sources for

the resonant excitation of quantum emitters in order to gen-

erate single photons with high indistinguishability (in prin-

ciple) on demand. Corresponding sources of indistinguishable

photons are basic building blocks in photonic quantum tech-

nology. For instance, indistinguishable photons are required in

long-distance quantum communication, which is based on the

entanglement distribution via Bell state measurements.[257] Fur-

thermore, indistinguishable photons are of high relevance as

information carriers for boson sampling in the field of photonic

quantum computing.[258,259]

In this context, it is important to mention that quantum

emitters such as QDs can in principle be excited in pin-diode

structures by electrical charge carrier injection to emit indi-

vidual photons. However, the large number of free charge car-

riers in this intrinsically non-resonant type of excitation limits

the indistinguishability of generated photons to values well

below 50% even in state-of-the-art electrically driven single-

photon sources.[260] Higher photon indistinguishability can be

achieved by means of resonant excitation schemes, as has been

shown many times in experiments in conventional laboratory

setups under optical excitation with bulky (and expensive) com-

mercial lasers. Particularly interesting is the strictly resonant

excitation directly into the s-shell of the relevant QD, through

which values of photon indistinguishability of over 99% were

achieved.[261,262]

It is therefore extremely attractive to use monolithically

integrated microlasers for the resonant optical excitation

of quantum emitters. In this concept, compact sources of

indistinguishable photons can be realized in a scalable way,

for example, to provide modular quantum light sources in

quantum communication and photonic state generators in

photonic quantumcomputing.

The first application of a high-β laser in quantum nanopho-

tonics was reported by Kreinberg etal.[263]. The aim of the work

was to show that an electrically operated QD micropillar can be

used for pulsed, strictly resonant excitation of a QD. This is a

first step toward compact on-demand sources indistinguishable

from the above concept. Its implementation is very challenging

and places high demands on the optical quality of the microlaser.

In fact, the laser must have an emission linewidth well below the

homogeneous linewidth of the QD (typically 1 GHz), emit light

pulses with a width well below the spontaneous life of the QD

(typically 1 ns in a homogeneous medium and reduced to 100–200

ps for usual Purcell factors of 5–10 in micropillar systems[265]), and

has to deliver a sufficiently high emission power to saturate the

QD (typically 1 μW). Furthermore, the microlaser must be able to

be sensitively brought into spectral resonance with theQD.

In the corresponding experiment, an electrically operated

QD-micropillar laser in one cryostat was used to excite a single

QD in a second cryostat via single-mode fiber coupling. The

emission properties of the laser are presented in Figure12.

The single-mode device emits at around 919 nm and its

Adv. Optical Mater. 2021, 9, 2100415

Figure 12. Application of an electrically driven QD-micropillar laser in quantum nanophotonics. a) Input–output characteristics of the monomode

laser delivering up to 1 μW at 919 nm. b) Emission linewidth and equal-time second-order photon autocorrelation function as function of applied

bias voltage. Laser emission with a linewidth as low as 50 MHz and is evidenced by the pronounced bias voltage dependent linewidth narrowing and

the transition of g(2)(0) toward unity at high excitation strength. c) Resonance fluorescence intensity map indicating spectral resonance between the

microlaser (L) and the QD s-shell (X) at a laser temperature of 66 K. d) SEM image of an integrated WGM-microlaser–SPS-micropillar configuration.

e) Corresponding second-order photon autocorrelation function demonstrating triggered single-photon of the SPS-micropillar excited by the on-chip

American Chemical Society.

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input–output characteristic shows the typical s-shaped behavior

of a high-β emitter and an output power up to 1 μW (panel (a)).

Furthermore, in panel (b), a clear excitation-strength dependent

decrease in the emission linewidth down to around 50 MHz

can be observed. These features indicate lasing behavior with

a threshold in the range of 7–8 volts bias voltage which is con-

firmed by measurements on the photon statistics with a char-

acteristic maximum of (the convoluted) g(2)(0) dependence at

threshold.[58,59]

These emission properties make the high-β microlaser a

very attractive candidate for resonant excitation of a quantum

emitter in quantum nanophotonics. In particular, the output

power and the emission linewidth are in the necessary range

for strict resonant excitation of a QD in order to observe reso-

nance fluorescence and to generate individual photons with

excellent quantum properties. In fact, in ref.[263], it was pos-

sible for the first time to use a high-β microlaser as coherent

excitation source for a quantum optical experiment. As shown

in Figure12c, the laser was used to excite a QD (in the second

cryostat) into its s-shell and thus to generate resonance fluo-

rescence. The temperature of the laser was varied in the range

from 64 to 68 K for the necessary spectral fine tuning between

microlaser and QD. In spectral resonance at about 66 K, there

is a significant increase in intensity, with the double peak fea-

ture in resonance fluorescence being attributed to the fine

structure splitting of the QD. In this microlaser-QD configura-

tion, the emission of individual photons with g(2)(0) = 0.02 and

an indistinguishability of 0.57(9) was achieved under pulsed-

resonant excitation. The indistinguishability was limited on the

one hand by a comparatively large pulse length of 200 ps (com-

pared to an ideal pulse length of about 10 ps[261]) but also by the

non-ideal properties of the QD itself, and it is expected to reach

significantly higher indistinguishability values by technological

improvements in thefuture.

While the application discussed is to be understood as

an experimentally very complex proof-of-principle demon-

stration, it is interesting to mention that the underlying

approach has already been implemented in a fully integrated

concept.[264,266,267] A corresponding device is presented in

Figure 12d. The SEM image shows an electrically operated

WGM microlaser, which excites a single QD in a micropillar

15 μm away acting as single-photon source (SPS). Interestingly,

the fact that micropillar cavities can emit also via WGMs was

first reported in ref.[268], and first laser emission of WGMs in

micropillar cavities was demonstrated in ref.[269], both under

optical pumping. In the SPS micropillar, the Purcell effect is

used to increase the photon extraction efficiency and the rel-

evant QD-transition can be tuned in spectral resonance with

the fundamental resonator mode by the quantum confined

Stark effect using the electrical contact of the SPS-micropillar.

It is interesting to note that this contact has a local aperture

to separate the individual photons emitted from the stray light

of the microlaser. In this configuration, with a repetition fre-

quency of 165 MHz, it was possible to generate single photons

with a g(2)(0) = 0.07 under wetting-layer excitation as shown in

Figure 12e.[264] In the future, it will be interesting to further

optimize the integrated approach for strict resonant excitation

and also to develop a waveguide coupling for microlaser inte-

gration in integrated quantum photonic circuits.[165]

All in all, the results presented in this section show the great

potential of high-β micro- and nanolasers in a targeted and

suitable manner to find an attractive application in the field of

quantumnanophotonics.

6.3. Neuromorphic Computing

Instead of improving established von-Neumann-type com-

puter architectures, for example, by using optical intercon-

nects as discussed earlier, a radically different approach is to

use neural network approaches, where weighted interactions

between nodes and processing or decision-making at nodes are

interweaved. Such schemes may, for example, be particularly

useful for applications such as real-time data handling, com-

puter vision and natural-language processing. In particular, it

appears that neuromorphic computing schemes[270] may be able

to exploit some of the key characteristic features of photonics,

leading to promises of increasing the computation speed by

several orders of magnitude, while simultaneously achieving

excellent energyefficiencies.

Neuromorphic computing or signal processing schemes are

inspired by the way neurons are used for processing informa-

tion in our brains and one of the key challenges for photonics

implementations is to develop photonic structures that can play

the equivalent role of neurons.[270] The artificial photonic neu-

rons making up the networks consist of two essential building

blocks, illustrated in Figure13, that is, a linear weighting and

integration operation, where inputs from other neurons are

accumulated with certain weighting functions, as well as a

non-linear activation function, which determines whether that

particular neuron should “fire” and generate an optical pulse

for further transmission and processing in the network. The

latter is essentially a thresholding characteristic, with demands

on the pulse generated at the output and the period between

pulses. These devices must be ultra-compact, compatible with

dense integration, energy-efficient and fast, thus providing a

very challenging overall task.[271]

There have been a number of suggestions for realizing the

nonlinear activation function, which is key to the photonic

neuron, including use of electro-absorption modulators,[272]

micro-ring modulators,[273] as well as all-optical realizations like

photonic reservoir computing.[274,275] A promising opportunity

Adv. Optical Mater. 2021, 9, 2100415

Figure 13. Schematic illustration of functionality needed in an artificial

neuron-node in a neuromorphic computing scheme. Inputs from various

nodes are weighted, summed, and sent as input to a thresholding device,

where a nonlinear activation function decides whether the neuron should

“fire” and generate an output pulse. Excitable semiconductor nanolasers

may serve as the nonlinear element in such photonic neurons. The figure

was inspired by ref. [270].

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is to use excitable semiconductor lasers, which are reviewed in

ref. [270]. The development of nanolasers for these functionali-

ties are particularly attractive, given the need to integrate many

nodes and the low energy available for each of those nodes. As

an example, it has been theoretically shown that a semicon-

ductor Fano laser (see Section5.1) features intrinsic excitability

and can be operated to give such a nonlinear thresholding

functionality.[276] In this scheme, the nanocavity resonance is

detuned from its optimal position such that the laser is oper-

ating in a below-threshold off-state. An optical pulse, repre-

senting the weighted input of other “spiking neurons”, excites

the nanocavity, and if the power is above the threshold level,

the laser releases a new spike. The Fano laser features low

threshold energy, gigahertz repetition rates, and orders of mag-

nitude suppression between the on- and off-states.[276]

A related processing scheme is that of reservoir computing,

where the network of interacting nodes is treated as a “black

box”, that is, the reservoir.[277] The training of the network is

instead performed at the output to map many examples of

inputs to desired outputs by invoking the right combination of

reservoir states. The reservoir has to be “dynamic enough”[278]

to sustain the desired processing complexity, but one has to

avoid instabilities. Reservoir computing has been experimen-

tally demonstrated on a silicon photonics chip, where the net-

work itself is linear and the nonlinearity is implemented in the

readout layer.[278]

A network of mutually coupled lasers appear as a particu-

larly attractive way of implementing reservoir computing. This

can for instance be achieved by optically coupling an array of

VCSELS though an external diffractive element and using a spa-

tial modulator for controlling individual coupling strengths.[275]

The use of relatively large VCSELs as the individual elements

of the array, however, imposes limitations on the reservoir

dimension that can be achieved. Another approach is to use

a dense array of energy efficient high-β micropillars.[279] Since

the coupling relies on mutual injection locking between the

lasers, the approach demands a high spectral homogeneity

between the micropillar lasers. Promising progress in this

direction was recently achieved through the demonstration

of an array of 8 × 8 microlasers with spectral inhomogeneity

below 200 μeV. This was achieved through the development of

a nanoprocessing platform allowing for individual adjustments

of laser wavelengths, and with the potential to be scaled to the

coupling of hundreds ofmicrolasers.

7. Conclusion

In summary, high-β micro- and nanolasers are innovative nano-

photonic components with interesting physical properties and

enormous application potential. Their development in the last

two decades has benefited greatly from advances in modern

nanotechnology, so that it was possible, for example, to reach

the limiting case of thresholdless lasing. Furthermore, as we

presented in this progress report, these miniaturized lasers

provide a fertile basis for innovative ideas in order to explore

new functional principles, based for instance on Fano resona-

tors, topological effects, and 2D heterostructures, and to open

up attractive areas of application in quantum photonics and

neuromorphic computing. We hope that our article will not only

provide an overview of the current status of micro- and nano-

lasers, but also stimulate further work and kick-start develop-

ments in order to tap the full potential of these exciting devices

in an interdisciplinary and innovative researchenvironment.

Acknowledgements

The authors acknowledge financial support by the German Research

Foundation via projects Re2974/20-1, Re2974/21-1, Re2974/29-1,

WI1986/11-1, by the Volkswagen Foundation via projects NeuroQNet1

and NeuroQNet2, and by the European Research Council under the

European Union’s Seventh Framework ERC Grant Agreement No.

615613 and No. 834410. Funding and support has also been provided

by the Région PACA and Investments for the Future programme under

the Université Côte d’Azur UCA-JEDI project managed by the ANR

(ANR-15-IDEX-01) as well as the Danish National Research Foundation

(DNRF147). The authors also acknowledge support by the United

States Army Research Office Award W911NF-17-1-0312, Air Force Office

of Scientific Research Award FA2386-18-1-4086, and the Humboldt

Foundation’s Friedrich Wilhelm Bessel Research Award. The authors

would like to thank H. Schomerus fordiscussions.

Open access funding enabled and organized by Projekt DEAL.

Conflict of interest

The authors declare no conflict ofinterest.

Keywords

Fano lasers, high-β lasers, microlasers, nanolasers, neuromorphic

computing, quantum nanophotonics, thresholdless lasing

Received: February 26, 2021

Revised: May 21, 2021

Published online: June 23, 2021

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Hui Deng received her Ph.D. from Stanford University in 2006. After a postdoctoral position at

the California Institute of Technology, she joined the faculty of University of Michigan, Ann Arbor,

in 2008, where she is currently a full professor. Her current research interests include light-matter

interactions and phase transition physics in micro- and nano-photonic structures and van der

Waals materials. H. Deng is a Fellow of the American Physical Society and the Optical Society

ofAmerica.

Gian Luca Lippi received his Ph.D. in Physics from Bryn Mawr College (USA) in 1990. After a

Humboldt-Fellowship Post-Doc at the University of Münster (Germany), and positions at the

Université de Nice-Sophia Antipolis, he is currently Distinguished Professor at the Université

Côte d’Azur. His current research interests revolve around experiments and models in the physics

and dynamics of micro- and nanolasers, and biophotonics. G.L. Lippi is a member of the Optical

Society of America and former director of two doctoralschools.

Jesper Mork received his Ph.D. in Applied Mathematical Physics from The Technical University

of Denmark in 1988. Since 2002, he has been full professor at the Department of Photonics

Engineering. His current research interests revolve around light−matter interaction in nanopho-

tonic structures, including nanolasers, de-coherence in cavity QED, quantum noise and nonlinear

dynamics. J. Mork is a Fellow of the Optical Society of America and is director of a newly estab-

lished Center for Nanophotonics -NanoPhoton.

Adv. Optical Mater. 2021, 9, 2100415

www.advancedsciencenews.com www.advopticalmat.de

Jan Wiersig received his Ph.D. from the University of Bremen in 1998. He was a postdoctoral

researcher at the Queen Mary and Westfield College in London, at the Max Planck Institute for

the Physics of Complex Systems in Dresden, and at the University of Bremen. In 2008, he became

a full Professor at the Otto von Guericke University Magdeburg. His current research interests

include light–matter interaction in semiconductor micro- and nanostructures, wave chaos and

non-Hermitian effects in opticalmicrocavities.

Stephan Reitzenstein received his Ph.D. degree in physics (summa cum laude) from the

University of Würzburg, Germany, in 2005. In 2010, he habilitated with studies regarding optical

properties of low-dimensional semiconductor systems. Since September 2011, he has been a

full Professor at the Technical University of Berlin, Germany, holds the Chair of Optoelectronics

and Quantum Devices, and is director of the Center of Nanophotonics. His research interests

are in the area of micro-/nanolasers and quantum optics in semiconductor nanostructures.

S. Reitzenstein is member of the German Physical Society where he is presently the spokesman

of the Semiconductor Division.

Adv. Optical Mater. 2021, 9, 2100415