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RESEARCH ARTICLE

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Stimulated Raman Scattering (SRS) in 𝜶-AlOOH (Diaspore)

Ladislav Bohatý,* Oliver Lux, Hans-Joachim Eichler, Hanjo Rhee, Alexander A. Kaminskii†,

and Petra Becker*

In single crystals of orthorhombic 𝜶-AlOOH, known also as mineral diaspore,

𝝌(3)-nonlinear lasing by stimulated Raman scattering (SRS) and

Raman-induced four-wave mixing (RFWM) is investigated. Picosecond

pumping at 1.064 μm wavelength produces a broadband Stokes and

anti-Stokes frequency comb with up to 25 SRS- and RFWM-generated

emission lines. All observed Stokes and anti-Stokes lasing components in the

visible and near-IR are identiﬁed and attributed to a single SRS-promoting

vibration mode with 𝝎SRS ≈445 cm−1. The ﬁrst Stokes steady-state Raman

gain coeﬃcient in the visible spectral range is estimated to a value not less

than 0.36 cm GW−1.

1. Introduction

Nonlinear 𝜒(3)-lasing processes by stimulated Raman scattering

(SRS) and Raman-induced four-wave mixing (RFWM) have been

studied in a large variety of crystals in the last two decades (for

an overview see, e.g., ref. [1]). The generated SRS emission lines

cover the broad region from ≈0.2 to ≈2μm and result from SRS-

active vibration modes with energies that range between ≈50

L. Bohatý, P. Becker

Section Crystallography

Institute of Geology and Mineralogy, University of Cologne

50939 Köln, Germany

E-mail: ladislav[email protected]; [email protected]

O. Lux, H.-J. Eichler, H. Rhee

Institute of Optics and Atomic Physics

Technical University of Berlin

10623 Berlin, Germany

O. Lux

Deutsches Zentrum für Luft- und Raumfahrt

Institut für Physik der Atmosphäre

82234 Oberpfaﬀenhofen, Germany

A. A.

Institute of Crystallography, Federal Scientiﬁc Center “Crystallography

and Photonics”

Russian Academy of Sciences

Moscow 119333, Russia

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

can be found under https://doi.org/10.1002/crat.202100055

†A. A. Kaminskii passed away during the present work.

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

Creative Commons Attribution-NonCommercial-NoDerivs License,

which permits use and distribution in any medium, provided the original

work is properly cited, the use is non-commercial and no modiﬁcations

or adaptations are made.

DOI: 10.1002/crat.202100055

and ≈3400 cm−1. The Raman shifts of

these SRS-active Raman modes, how-

ever, are not distributed equally within

the so far realized energy range and

there are only few materials, e.g., 𝛼-

quartz (𝜔SRS ≈465 cm−1[2]

)and𝛼-Al2O3

(𝜔SRS ≈419 cm−1 [3,4]), that possess SRS-

promoting vibration modes of around

450 cm−1. Here, 𝛼-AlOOH, which shows

a strong, sharp, and isolated vibration

mode at 446 cm−1in its spontaneous Ra-

man spectra,[5] appears to be a promis-

ing further material which could com-

plement the set of SRS materials in this

region. In addition, among the variety of studied SRS crystals,

materials which possess large Raman shifts of around 3000 cm−1

are of interest, since they are able to generate the ﬁrst Stokes

component in the eye-safe region starting from 1 μm pumping

wavelengths. Here, the question arises, whether O─H stretching

vibrations of intermediate hydrogen bonds, that have typical en-

ergy values of 2800–3100 cm−1,[6] can act as SRS-active vibration

modes in crystals. To the best of our knowledge neither for or-

ganic, for semi-organic nor for inorganic crystals, that have been

studied by SRS so far, SRS-promoting modes of O─H stretching

vibrations has been detected.

As has been shown in detailed investigations based on exper-

imental data (IR and spontaneous Raman spectroscopy, inelas-

tic X-ray scattering) and theoretical calculations[6–9] 𝛼-AlOOH is

a suitable model system to study O─Hgroupsinintermediate

hydrogen bonds due to its rather simple chemistry and crys-

tal structure.[6] A possible limitation of the applicability of this

model system to the study of potential SRS-activity of O─Hvi-

bration modes is given by the broadness of O─H stretching vi-

brations in 𝛼-AlOOH found in spontaneous Raman spectra by

ref. [5], since the Raman gain coeﬃcient for generation of the

ﬁrst Stokes components via SRS is proportional to the inverse of

the linewidth of the SRS-promoting vibration mode in the spon-

taneous Raman spectrum.[10] However, this precept is not exclu-

sionary, as has been shown, e.g., in ref. [11], where also weak and

broad vibration modes of the spontaneous Raman spectrum gave

rise to stimulated Raman scattering. In this work, we present an

experimental study of stimulated Raman scattering in single crys-

tals of 𝛼-AlOOH, also known as mineral diaspore.

2. Crystals of 𝜶-AlOOH

Diaspore (𝛼-AlOOH) had been subject of structural investiga-

tions by X-ray diﬀraction already since the early 1930s.[12–17] Cor-

rect localization of hydrogen atoms in the crystal structure us-

ing neutron diﬀraction was ﬁrst achieved by ref. [18]. In the

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Figure 1. Graphical representation of the crystal structure of 𝛼-AlOOH, structure data are taken from ref. [20]. Al is given by gray spheres; O ligands are

given by blue spheres and H is given by small red spheres. Distorted octahedral coordination polyhedra [AlO3(OH)3] are indicated. a) View approximately

along the c-axis showing the connection scheme of double chains, running along the c-axis, of [AlO3(OH)3] octahedra. b) View approximately along the

a-axis, visualizing the linkage of [AlO3(OH)3] to double chains by sharing common edges.

Figure 2. Left: Gem-quality natural single crystal of 𝛼-AlOOH (diaspore) used for preparation of samples for the investigations in this work. (Small

squares give 1 ×1mm

2). Right: Sample of 𝛼-AlOOH, prepared from the crystal on the left and used for SRS and RFWM measurements. Sample faces

were polished but without antireﬂection coating.

following, a number of structural reﬁnements and structural in-

vestigations under nonambient conditions have been performed

(for a compilation see ref. [19]). In the present work, we use struc-

ture data taken from ref. [20].

Crystals of 𝛼-AlOOH crystallize with orthorhombic space

group symmetry Pbnm (setting cab), with lattice constants

a=4.4007(6) Å, b=9.4253(13) Å, and c=2.8452(3) Å.[20]

The main structural feature of 𝛼-AlOOH is double-chains of

[AlO3(OH)3] octahedra, where each aluminum coordination octa-

hedron shares common edges with four adjacent octahedra (see

Figure 1b). The double chains that run along the c-axis are linked

via common corners (i.e., oxygen atoms) to a 3D network, as it is

illustrated in Figure 1a.

Because of its relevance for both, geo-sciences and technical

applications, the system Al2O3–H2O has been studied intensively

already many years ago, see, e.g., refs. [21–25]. Therefore, the range

of thermodynamic stability as well as the possibility of crystalliza-

tion of 𝛼-AlOOH under hydrothermal conditions is well known.

While the preparation of small (sub-mm size) crystals has been

performed, see, e.g., ref. [26], the growth of large (≥1cm

3)single

crystals of 𝛼-AlOOH, which would require considerable expendi-

ture, is not reported in literature so far. Fortunately, large crystals

of 𝛼-AlOOH (mineral diaspore) of optical (gem-stone) quality can

be found in some localities in nature. For the present work we

used a single crystal of gem-quality diaspore (see Figure 2,left)

from Turkey, Mu˘

gla Province, which is described as locality in

ref. [27].

Gem-quality crystals from this locality typically contain up

to ≈0.1% of Fe3+,[28,29] which substitutes Al3+in the crystal

structure. Low iron content in 𝛼-AlOOH and similarly in 𝛼-

Al2O3(corundum) is known to cause weak absorption bands at

≈384 nm and ≈398 nm in 𝛼-AlOOH and ≈377 nm and ≈388 nm

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Figure 3. Transmission spectrum of the used natural single crystal of 𝛼-AlOOH in orientation (001) with 1.37 mm thickness. The inset gives a magni-

ﬁcation of the short wavelength region, with indicated UV transmission limit at 50% of maximum transmission (dashed lines). The arrows mark two

absorption peaks that, according to ref. [28], can be attributed to Fe3+in diaspore.

in 𝛼-Al2O3, respectively.[28,30,31] Nonpolarized optical transmis-

sion data of our crystal were collected using a polished plate of

orientation (001) of 1.37 mm thickness and a spectrophotome-

ter Perkin Elmer Lambda 950. The transmission spectrum is

given in Figure 3. Optical transmission of 𝛼-AlOOH ranges from

≈0.35 μm (50% of maximum transmission level) to ≈1.5 μm. The

transmission data show weak absorption bands in the near UV

similar to those reported in ref. [28] (see inset of Figure 3), which

signalize a small content of Fe3+in our used crystal. Due to its or-

thorhombic symmetry 𝛼-AlOOH is optically biaxial and, as calcu-

lated from refractive indices, possesses positive character of bire-

fringence with an angle 2V𝛾between the optic axes ranging be-

tween 83.5°(𝜆=0.4358 μm) and 82.8°(𝜆=0.6438 μm). Refractive

index data of diaspore are given in literature for wavelengths in

the visible range (𝜆=0.4358–0.6438 μm)[29,32] and are compiled

in Table 1, together with selected further physical properties of

𝛼-AlOOH crystals.

For the measurement of SRS and RFWM spectra a rectangular

parallel-epipedal sample was prepared with face normals along

the orthorhombic axes a,b,andcand with dimensions 5.74 ×

5.79 ×11.09 mm3( see Figure 2, right). All sample faces were

polished but without antireﬂection coating.

3. Stimulated Raman Scattering

3.1. Experimental Setup

The spectroscopic investigation of 𝜒(3)-nonlinear processes in 𝛼-

AlOOH was performed using a mode-locked Nd3+:Y3Al5O12 mas-

ter oscillator power ampliﬁer system in combination with a spec-

trometric setup, as described in previous publications (see, e.g.,

refs. [35, 36]). The pump laser system operated at 1 Hz repetition

rate, providing single pulses at 𝜆f1 =1.06415 μm wavelength with

pulse energy of up to 40 mJ and pulse duration of about 80 ps.

The pump beam was guided to the registration part of the ex-

perimental setup which is shown in Figure 4a. Here, continuous

attenuation of the pump was realized with the combination of

a revolving half-wave-plate (𝜆f1/2) and a Glan-laser polarizer (P),

while the pump energy incident on the 𝛼-AlOOH sample was

monitored by measuring a small portion of the radiation using

a pyroelectric energy meter (Polytec RjP-735). The linearly polar-

ized and collimated, nearly Gaussian beam was then focused into

the 𝛼-AlOOH crystal using a planoconvex lens with a focal length

of fL1 =250 mm. The sample could be aligned at any angle with

respect to the pump beam direction and polarization by means

of a customized 3D-adjustable holder. A lens system consisting

of a spherical biconvex lens (fL2 =100 mm) and a planoconvex

cylindrical lens (fL3 =100 mm) was employed to collimate the

divergent output radiation and to image it onto the variable en-

trance slit of a monochromator in Czerny-Turner arrangement

(McPherson Model 270, 6.8 Å pixel−1dispersion, 150 lines mm−1

grating). The spectral composition of the scattered emission was

ﬁnally recorded by a silicon (Si)-CCD sensor (Hamamatsu S3924-

1024Q with 1024 pixels) for the UV and visible spectral region

and an InGaAs sensor (Hamamatsu G9204-512D with 512 pix-

els) for the range between 0.9 and 1.7 μm, respectively (see

Figure 4b). For the energy calibration of the recorded Stokes

and anti-Stokes components the laser emission wavelengths at

0.63282 and 0.54337 μm (He-Ne laser) in the visible range, and

at 1.06415 μm(Nd

3+:YAG), 1.3166 μm(Ba(NO

3)2Raman laser),

and 1.5987 μm (Er3+:GdVO4) in the IR region were used.

3.2. Results

All registered Stokes and anti-Stokes sidebands in the measured

spectra were identiﬁed and attributed to a single SRS-promoting

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Table 1. Selected physical properties of 𝛼-AlOOH (diaspore) at room temperature.

Property Value

Chemical composition[28,29] AlOOH (synthetic), gem

diaspore from Turkey with

traces of Fe3+

Space group[13] Pbmn –D16

2h(No. 62)

Unit cell parameters[20] [Å] a=4.4007(6)

b=9.4253(13)

c=2.8452(3)

Formula units per unit cell[13] Z=4

Fractional coordinates x, y, z, and site symmetry (ss)[20] xyzss

Al 0.04472(8) −0.14450(4) −0.25 4c(m)

O1 0.71234(17) 0.19892(9) −0.25 4c(m)

O2 0.19714(18) 0.05338(9) −0.25 4c(m)

H 0.4095 0.0876 −0.25 4c(m)

Density[33] [g cm−3] 3.388(2)

Cleavage (see, e.g.,[25,34]) {010} perfect

Hardness (Mohs scale; see, e.g.,[25,34]) 6.5–7

Thermal expansion at 293 K[33] [10−6K−1]𝛼11 =7.5 (5) 𝛼22 =6.5 (5) 𝛼33 =6.0 (5)

Optical transparency range [μm] ≈0.35 to ≈1.50

Refractive indices (Sellmeier coeﬃcients)a) D1D2D3D4𝜉2

𝜉2is the sum of the squares of the residuals n𝛼=nc2.84(3) 0.020(9) −0.01(4) −0.002(4) 8.2 ×10−9

n𝛽=nb2.78(8) 0.08(4) −0.16(8) −0.12(7) 6.1 ×10−9

n𝛾=na2.99(2) 0.028(6) −0.03(2) 0.008(2) 2.1 ×10−9

Optical nonlinearity 𝜒(3)

Energy of SRS-promoting vibration modes at room

temperature 𝜔SRS [cm−1]

≈445

FWHM linewidth Δ𝜈Rfor the Raman shifted line

related to SRS-promoting vibration mode [cm−1]

Steady-state Raman gain coeﬃcient for ﬁrst Stokes

generation [cm GW−1] at a pump wavelength

𝜆f=1.06415 μm

≥0.36

a) Sellmeier coeﬃcients with respect to the modiﬁed Sellmeier equation (𝜆is in μm) n2(𝜆)=D1+D2

(𝜆2−D3)−D4𝜆2, calculated using refractive index data in the visible range

given in ref. [32].

phonon mode. The Raman shift 𝜔SRS of this SRS-active vibration

mode was determined as the mean value resulting from all ana-

lyzed SRS and RFWM spectra of the used 𝛼-AlOOH single crystal

and amounts to 𝜔SRS =445(2) cm−1. Selected 𝜒(3)-nonlinear las-

ing spectra, recorded at room temperature with 1 μm picosecond

pumping in diﬀerent excitation geometries, together with the re-

sults of their spectral analysis are presented in Figures 5–7.The

attribution of all observed Stokes and anti-Stokes components to

SRS and RFWM processes are summarized in Tables 2 and 3.

As can be seen from Figure 5, picosecond pumping at

𝜆f1 =1.06415 μm wavelength of the AlOOH crystal, with an SRS

active length of ≈11 mm in excitation geometry c(a,a)c(for the

used notation see footnote a) in Table 2), gave rise to single-

phonon 𝜒(3)-nonlinear lasing with 𝜔SRS ≈445 cm−1.Asmanyas

17 anti-Stokes and four Stokes sidebands were recorded under

these excitation conditions (see Table 2). Using excitation geom-

etry c(b,b)c(see Figures 6 and 7) the SRS-active mode with 𝜔SRS

≈445 cm−1led to the generation of an even broader frequency

comb consisting of 21 anti-Stokes and six Stokes components

(see Table 3). The latter was produced by cascaded 𝜒(3) interac-

tions (most probably RFWM processes) and covers nearly one

spectral octave (more than 12 000 cm−1). In Tables 2 and 3, the

most likely RFWM processes for each observed spectral compo-

nent are given.

The spatial distribution of the broadband anti-Stokes emission

generated with pumping at 𝜆f1 =1.06415 μm wavelength in exci-

tation geometry c(b,b)c and given in Figure 7 was analyzed using

a CCD photocamera (Panasonic, model Lumix DMC-TZ7). The

camera recorded the radiation reﬂected from a screen which was

inserted behind the 𝛼-AlOOH sample. As shown in Figure 8, the

anti-Stokes components, which are predominantly originated by

RFWM, are emitted along cones whose opening angles increase

with the anti-Stokes order as a result of momentum conserva-

tion in the presence of normal dispersion. The corresponding

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Figure 4. a) Schematic diagram of the experimental setup used for the spectroscopic analysis of SRS and nonlinear mixing interactions in 𝛼-AlOOH

single crystals (P: polarizer; L1–L3: lenses; see also text). b) Spectral sensitivity of the used Si- and InGaAs line sensors (data taken from Hamamatsu

Photonics K.K. datasheet).

Figure 5. Selected parts of SRS and RFWM lasing spectra of a single crystal of 𝛼-AlOOH, recorded at room temperature in excitation geometry c(a,a)c

with single-wavelength picosecond pumping at 𝜆f1 =1.06415 μm. The wavelength of all lines (pump line is asterisked) is given in μm, their intensity is

shown without correction for the spectral sensitivity of the used recording spectrometric system. Part (a) is recorded with a silicon-CCD sensor, part (b)

with an InGaAs sensor. All generated Stokes and anti-Stokes components are related to the SRS-active vibration mode with 𝜔SRS ≈445 cm−1.

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Figure 6. Infrared Stokes generation in an 𝛼-AlOOH single crystal under picosecond pumping at 𝜆f1 =1.06415 μm wavelength (pumping wavelength

marked with asterisk), using excitation geometry c(b,b)c. Wavelengths of all generated Stokes (and anti-Stokes) components are given in μm. Part (a)

and (b) are recorded with an InGaAs sensor. All generated components are related to the SRS-active vibration mode with 𝜔SRS ≈445 cm−1.

Figure 7. Selected parts of SRS and RFWM lasing spectra of a single crystal of 𝛼-AlOOH, recorded at room temperature in excitation geometry c(b,b)c

with single-wavelength picosecond pumping at 𝜆f1 =1.06415 μm. The wavelength of all lines (pump line is asterisked) is given in μm, their intensity is

shown without correction for the spectral sensitivity of the used recording spectrometric system. Part (a) is recorded with a silicon-CCD sensor and part

(b) is recorded with an InGaAs-CCD sensor. All generated Stokes and anti-Stokes components are related to the SRS-active vibration mode with 𝜔SRS ≈

445 cm−1.

phase-matching conditions lead to a coaxial ring pattern on a

screen perpendicular to the propagation direction with the color

changing from inside to outside from red via orange, yellow, and

green to blue (“anti-Stokes rainbow”).

Within the framework of our SRS experiments, we com-

pared the SRS threshold for the ﬁrst Stokes generation at

𝜆St1 =1.1170 μmin𝛼-AlOOH with that of GdVO4at

𝜆St1–1 =1.1744 μm, in order to determine the steady-state Ra-

man gain coeﬃcient gSt1

ssR for the title crystal under pump-

ing at 𝜆f1 =1.06415 μm. This procedure is based on the

relation[38,39]gSt1

ssR Ith

plSRS≈30, with land Ith

pdenoting the sample

length and threshold pump intensity that has to be applied for a

reliable detection of the ﬁrst-Stokes signal, respectively. In our

experiments we used an 𝛼-AlOOH sample of ≈11 mm length

in excitation geometry c(b,b)c and a crystal of GdVO4of sim-

ilar length (l=8 mm) as a reference. The gSt1−1

ssR value of the

latter accounts for ≥4.5 cm GW−1.[40] Comparative measure-

ments yielded an about ninefold higher threshold for ﬁrst Stokes

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Table 2. Room-temperature spectral composition of Stokes and anti-Stokes generation components in an 𝛼-AlOOH single crystal recorded under pi-

cosecond Nd3+:Y3Al5O12 laser excitation at the fundamental wavelength 𝜆f1 =1.06415 μm.

Excitation

geometry

c(a,a)ca)

SRS and RFWM lasing

Wavelengthb) [μm] Lasing component Line attribution SRS and RFWM attributionc)

Figure 5a 0.5895 ASt17 𝜔f1 +17𝜔SRS 𝜔f1 +17𝜔SRS =[𝜔f1 +(𝜔f1 +16𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt16 –𝜔St1]=𝜔ASt17

0.6054 ASt16 𝜔f1 +16𝜔SRS 𝜔f1 +16𝜔SRS =[𝜔f1 +(𝜔f1 +15𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt15 –𝜔St1]=𝜔ASt16

0.6222 ASt15 𝜔f1 +15𝜔SRS 𝜔f1 +15𝜔SRS =[𝜔f1 +(𝜔f1 +14𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt14 –𝜔St1]=𝜔ASt15

0.6399 ASt14 𝜔f1 +14𝜔SRS 𝜔f1 +14𝜔SRS =[𝜔f1 +(𝜔f1 +13𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt13 –𝜔St1]=𝜔ASt14

0.6587 ASt13 𝜔f1 +13𝜔SRS 𝜔f1 +13𝜔SRS =[𝜔f1 +(𝜔f1 +12𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt12 –𝜔St1]=𝜔ASt13

0.6786 ASt12 𝜔f1 +12𝜔SRS 𝜔f1 +12𝜔SRS =[𝜔f1 +(𝜔f1 +11𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt11 –𝜔St1]=𝜔ASt12

0.6997 ASt11 𝜔f1 +11𝜔SRS 𝜔f1 +11𝜔SRS =[𝜔f1 +(𝜔f1 +10𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt10 –𝜔St1]=𝜔ASt11

0.7222 ASt10 𝜔f1 +10𝜔SRS 𝜔f1 +10𝜔SRS =[𝜔f1 +(𝜔f1 +9𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt9 –𝜔St1]=𝜔ASt10

0.7461 ASt9𝜔f1 +9𝜔SRS 𝜔f1 +9𝜔SRS =[𝜔f1 +(𝜔f1 +8𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt8 –𝜔St1]=𝜔ASt9

0.7718 ASt8𝜔f1 +8𝜔SRS 𝜔f1 +8𝜔SRS =[𝜔f1 +(𝜔f1 +7𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt7 –𝜔St1]=𝜔ASt8

0.7992 ASt7𝜔f1 +7𝜔SRS 𝜔f1 +7𝜔SRS =[𝜔f1 +(𝜔f1 +6𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt6 –𝜔St1]=𝜔ASt7

0.8287 ASt6𝜔f1 +6𝜔SRS 𝜔f1 +6𝜔SRS =[𝜔f1 +(𝜔f1 +5𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt5 –𝜔St1]=𝜔ASt6

0.8604 ASt5𝜔f1 +5𝜔SRS 𝜔f1 +5𝜔SRS =[𝜔f1 +(𝜔f1 +4𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt4 –𝜔St1]=𝜔ASt5

0.8947 ASt4𝜔f1 +4𝜔SRS 𝜔f1 +4𝜔SRS =[𝜔f1 +(𝜔f1 +3𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt3 –𝜔St1]=𝜔ASt4

0.9318 ASt3𝜔f1 +3𝜔SRS 𝜔f1 +3𝜔SRS =[𝜔f1 +(𝜔f1 +2𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt2 –𝜔St1]=𝜔ASt3

Figure 5b 1.0160 ASt1𝜔f1 +𝜔SRS 𝜔f1 +𝜔SRS =[𝜔f1 +𝜔f1 –(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔f1 –𝜔St1]=𝜔ASt1

1.06415 𝜆f1 𝜔f1 𝜔f1

1.1170 St1𝜔f1 −𝜔SRS 𝜔f1 –𝜔SRS =𝜔St1

1.1755 St2𝜔f1 −2𝜔SRS 𝜔f1 –2𝜔SRS =[(𝜔f1 –𝜔SRS)–𝜔SRS]=𝜔St2

1.2404 St3𝜔f1 −3𝜔SRS 𝜔f1 –3𝜔SRS =[(𝜔f1 –2𝜔SRS)–𝜔SRS]=𝜔St3

1.3128 St4𝜔f1 −4𝜔SRS 𝜔f1 –4𝜔SRS =[(𝜔f1 –3𝜔SRS)–𝜔SRS]=𝜔St4

a) Notation is used in analogy to that in ref. [37]: Characters to the left and to the right of the parentheses denote the direction of the wave normal of the incident and of the

generated light, respectively, characters within the parentheses give the polarization direction of the incident and the generated light, respectively; b) Measurement accuracy

is ±0.0003 μm; c) Lines related to cascaded 𝜒(3)-lasing transitions, in square brackets possibilities for nonlinear-laser components of the RFWM process are given; d) Note

that the second anti-Stokes component is not given in Figure 5.

generation in the title crystal. Considering the shorter sample

length of the reference crystal, we conclude that the lower limit of

the steady-state Raman gain coeﬃcient for ﬁrst Stokes generation

in 𝛼-AlOOH at 𝜆St1 =1.1170 μm is not less than 0.36 cm GW−1.

Here, it should be noted that the generation of Stokes and anti-

Stokes frequency combs was accomplished for pump energies

only slightly above the ﬁrst Stokes threshold. In particular, higher

order anti-Stokes emission was already observed if the pump en-

ergy was increased above Ith

pby only 5%.

3.3. SRS-Promoting Vibration Mode

A spontaneous Raman spectrum with the same crystal of 𝛼-

AlOOH, that was used for the SRS investigations, was measured

in geometry c(b,b)c, using a distributed feedback laser at 𝜆exc =

0.785 μm as excitation source. The spectrum given in Figure 9

was recorded in backscattering geometry by means of a ﬁber-

coupled Raman spectrometer (Princeton Instruments, model PI

320) in combination with a Si-CCD detector (Princeton Instru-

ments, model LN/CCD-1024-EHRB/1). The energy axis of the Ra-

man shift was calibrated using polystyrene. The estimated error

of the determination of the Raman line positions is 3 cm−1.

The primitive unit cell of the crystal structure of 𝛼-AlOOH with

symmetry Pbmn – D16

2hwith Z=4contains16atoms,whichgives

3NZ =48 vibration modes (k≈0): 8 A1g +4A

1u +8B

1g +4

B1u +4B

2g +8B

2u +4B

3g +8B3u. Among them, 24 modes

are Raman-active (8 A1g +8B

1g +4B

2g +4B

3g) and 17 modes

are IR-active (3 B1u +7B

2u +7B

3u), three translation modes

(1B1u +1B2u +1B3u) and four “silent” modes (4 A1u), see also

ref. [7]. 𝛼-AlOOH has been subject to several spontaneous Ra-

man studies including both, experimental investigations and ab

initio calculations.[5,7,8,9] The most intense vibration mode of 𝛼-

AlOOH in these studies, as well as in our spectrum given in Fig-

ure 9, is found in the range between 446 and 449 cm−1.Ascanbe

seen from Figure 9 in our spontaneous Raman investigation we

determined the Raman shift for this mode to 449(3) cm−1.This

mode is assigned in literature to an A1g mode, most probably an

Al─O─Al bending mode.[5,7] In our SRS investigation this sharp,

strong vibration mode turned out to be the SRS-promoting mode.

4. Conclusion

The present study of nonlinear laser generation via SRS and

RFWM processes in natural crystals of 𝛼-AlOOH (diaspore)

shows that 𝛼-AlOOH is a promising material for eﬃcient

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Table 3. Room-temperature spectral composition of Stokes and anti-Stokes generation components in an 𝛼-AlOOH single crystal recorded under pi-

cosecond Nd3+:Y3Al5O12 laser excitation at the fundamental wavelength 𝜆f1 =1.06415 μm.

Excitation

geometry

c(b,b)ca)

SRS and RFWM lasing

Wavelengthb) [μm] Lasing component Line attribution SRS and RFWM attributionc)

Figure 6a 1.0160 ASt1𝜔f1 +𝜔SRS 𝜔f1 +𝜔SRS =[𝜔f1 +𝜔f1 –(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔f1 –𝜔St1]=𝜔ASt1

1.06415 𝜆f1 𝜔f1 𝜔f1

1.1170 St1𝜔f1 −𝜔SRS 𝜔f1 –𝜔SRS =𝜔St1

1.1755 St2𝜔f1 −2𝜔SRS 𝜔f1 –2𝜔SRS =[(𝜔f1 –𝜔SRS)–𝜔SRS]=𝜔St2

1.2404 St3𝜔f1 −3𝜔SRS 𝜔f1 –3𝜔SRS =[(𝜔f1 –2𝜔SRS)–𝜔SRS]=𝜔St3

Figure 6b 1.3128 St4𝜔f1 −4𝜔SRS 𝜔f1 –4𝜔SRS =[(𝜔f1 –3𝜔SRS)–𝜔SRS]=𝜔St4

1.3943 St5𝜔f1 −5𝜔SRS 𝜔f1 –5𝜔SRS =[(𝜔f1 –4𝜔SRS)–𝜔SRS]=𝜔St5

1.4865 St6𝜔f1 −6𝜔SRS 𝜔f1 –6𝜔SRS =[(𝜔f1 –4𝜔SRS)–𝜔SRS]=𝜔St6

Figure 7a 0.5336 ASt21 𝜔f1 +21𝜔SRS 𝜔f1 +21𝜔SRS =[𝜔f1 +(𝜔f1 +20𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt20 –𝜔St1]=𝜔ASt21

0.5465 ASt20 𝜔f1 +20𝜔SRS 𝜔f1 +20𝜔SRS =[𝜔f1 +(𝜔f1 +19𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt19 –𝜔St1]=𝜔ASt20

0.5602 ASt19 𝜔f1 +19𝜔SRS 𝜔f1 +19𝜔SRS =[𝜔f1 +(𝜔f1 +18𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt18 –𝜔St1]=𝜔ASt19

0.5745 ASt18 𝜔f1 +18𝜔SRS 𝜔f1 +18𝜔SRS =[𝜔f1 +(𝜔f1 +17𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt17 –𝜔St1]=𝜔ASt18

0.5895 ASt17 𝜔f1 +17𝜔SRS 𝜔f1 +17𝜔SRS =[𝜔f1 +(𝜔f1 +16𝜔SRS)–(𝜔f1 –𝜔SRS)] =[𝜔f1 +𝜔ASt16 –𝜔St1]=𝜔ASt17