Magne ically Con olled Op ical Logic Ga es Based on he Fa aday
E ec
and he Th ee–Pola ize Pa adox
Rica do Adonis Ca accioli Ab ego∗Michael Joel Spilsbu y Fuen es†
Ma co An onio Reyes Pagoada‡
Uni e sidad Nacional Au ónoma de Hondu as (UNAH)
Campus Co és, Hondu as
Feb ua y 24, 2025
Abs ac
We p opose and analyze a econ igu able op ical logic ga e a chi ec u e ha combines he
Fa aday o a ion e ec wi h he classical h ee–pola ize pa adox. By dynamically o a ing
he pola iza ion plane o ligh be ween wo c ossed pola ize s, he sys em enables magne ic
con ol o logical s a es, suppo ing AND, OR, NOT and mul i–le el logic ope a ions. The
app oach sugges s new pa hways owa d magne o–op ical logic, op ical memo y elemen s, and
p og ammable pho onic/quan um ci cui s.
Keywo ds: Magne o-op ics, Op ical logic, Fa aday e ec , Pola iza ion, Pho onic compu ing
1 In oduc ion
Op ical logic is a cen al componen in ad anced pho onic compu a ion, low–la ency signal p o-
cessing, and quan um in o ma ion sys ems. A undamen al bu coun e in ui i e phenomenon in
pola iza ion op ics is he h ee–pola ize pa adox, whe e inse ing an in e media e pola ize be-
ween wo c ossed pola ize s allows nonze o ansmission. In his wo k, we ex end his concep
by in oducing a magne ically con olled Fa aday o a o as he in e media e elemen . Because
he Fa aday e ec o a es he pola iza ion p opo ionally o an applied magne ic ield, i na u ally
enables econ igu able logical s a es and analog/mul i–le el logic ansi ions.
2 Physical P inciples
2.1 Th ee–Pola ize T ansmission
Two ideal pola ize s o ien ed a 0◦and 90◦ ully supp ess ansmission. I a o a ion θoccu s
be ween hem, he ou pu in ensi y ollows he cascaded Malus law:
Iou =I0cos2(θ) sin2(θ) = I0
4sin2(2θ).(1)
∗[email p o ec ed]
†[email p o ec ed]
‡[email p o ec ed]
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This p o ides a na u al nonlinea ansmission cu e, wi h a maximum a θ= 45◦.
45 90
0.25
0.5
θ(◦)
I/I0
I/I0=1
4sin2(2θ)
Figu e 1: No malized ansmi ed in ensi y o he h ee–pola ize con igu a ion, ollowing Eq. (1).
2.2 Fa aday Ro a ion
In a Fa aday medium, he plane o pola iza ion o a es by
θF=V BL, (2)
whe e Vis he Ve de cons an , B he axial magne ic ield, and L he in e ac ion leng h. Thus,
he magne ic ield ac s as a unable con ol pa ame e o op ical ansmission.
3 P oposed A chi ec u e
Figu e 2 illus a es he p oposed de ice: a linea ly pola ized lase passes h ough a i s pola ize
(P1), a Fa aday o a o , and a c ossed analyze (P2). A pho odiode measu es he inal in ensi y.
Lase Pola ize
(P1)
Fa aday
Ro a o
Pola ize
(P2) Pho odiode
Figu e 2: Schema ic o he magne ically con olled op ical logic ga e: linea ly pola ized lase ,
pola ize P1, Fa aday o a o , c ossed pola ize P2 and pho odiode.
3.1 Logical In e p e a ion
Logical s a es a e de ined as:
•Logical 0: B= 0 ⇒θF= 0◦⇒Iou ≈0.
•Logical 1: B=B45 such ha θF= 45◦, yielding maximal ansmission.
•Analog / Mul ile el: Con inuous a ia ion o Bp oduces g aded in ensi y le els be ween
0 and he maximum.
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3.2 S a e Table
Inpu Ligh Magne ic Field BRo a ion θFIou /I0
P esen 0 0◦0
P esen B45 45◦0.25
P esen B90 90◦0
Absen Any — 0
Table 1: S a e able o he magne ically con olled op ical logic ga e.
4 Implemen a ion o Logic Ga es
4.1 NOT Ga e
A NOT ope a ion can be implemen ed by in e p e ing he magne ic ield as logical inpu while
eading he op ical in ensi y as ou pu . Fo ins ance, i we de ine a high ou pu (logical 1) as he
absence o magne ic ield and a low ou pu (logical 0) when he ield d i es he sys em o maximum
ansmission, we can w i e:
B= 0 ⇒1ou , B =B45 ⇒0ou .
Al e na i e con en ions (e.g. in ensi y in e sion using an addi ional pola ize ) can be adop ed
depending on he a ge logic amily.
4.2 AND / OR Ga es
To implemen wo–inpu logic ga es, we conside magne ic ields B1and B2 ep esen ing he inpu s.
AND ga e. A simple ealiza ion uses a single Fa aday o a o wi h o al magne ic ield
B=B1+B2.
By choosing he indi idual inpu le els such ha B1=B2=B45/2 o logical 1 and 0 o logical
0, one can se an in ensi y h eshold I h so ha
Iou > I h only when B1=B2=B45/2,
ha is, only when bo h inpu s a e a logical 1.
OR ga e. Fo an OR ope a ion, wo pa allel op ical pa hs can be used, each wi h i s own Fa aday
o a o and analyze , gene a ing no malized in ensi ies I1and I2(each mapped o he in e al [0,1]
a e sui able no maliza ion and biasing). The o al ou pu in ensi y can be in e p e ed as
Iou ≈I1+I2−I1I2,
which ac s as a smoo h op ical analogue o he logical OR ope a ion (equal o 1 when ei he I1
o I2is 1, and 0 only when bo h a e 0). P ac ical implemen a ions can use beam combine s and
sui able scaling o app oxima e his beha io in a obus way.
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4.3 Op ical Memo y
I he Fa aday medium exhibi s magne ic hys e esis (e.g. ce ain e imagne ic ga ne s), hen a
nonze o o a ion can pe sis e en a e emo ing he ex e nal ield, p o iding an op ical s o age
mechanism. In such a con igu a ion, a w i e pulse se s he o a ion (and hus he logical s a e),
while a weake ead beam p obes he s o ed s a e wi hou signi ican ly dis u bing i .
5 Discussion and Feasibili y
To es ima e ealis ic ope a ing pa ame e s, conside e bium gallium ga ne (TGG) wi h a Ve de
cons an o app oxima ely
V≈40 ad/(T ·m)
nea a wa eleng h o 1064 nm. Fo a a ge Fa aday o a ion o θF= 45◦=π/4and an in e ac ion
leng h L= 5 cm, he equi ed magne ic ield magni ude is
B=θF
V L ≈π/4
40 ×0.05 ≈0.39 T.
This is wi hin each o compac elec omagne s o in eg a ed magne o–op ical s uc u es wi h
pe manen magne s.
The ex inc ion a io o ypical high–quali y pola ize s in a c ossed con igu a ion can exceed
30 dB, ensu ing a well de ined logical “ze o” le el. On he o he hand, he maximum ansmi ed
in ensi y a θF= 45◦is Iou =I0/4, which can be u he ampli ied o no malized in subsequen
op ical o elec onic s ages.
The swi ching speed o he de ice is p ima ily limi ed by he dynamics o he magne ic ield,
which can ange om mic oseconds o milliseconds wi h con en ional d i e s. Howe e , he use
o high–speed cu en d i e s, esonan magne ic s uc u es, o magne o–op ical esona o s could
signi ican ly educe he e ec i e swi ching ime, opening he doo o as e op ical logic and memo y
elemen s.
6 Conclusion
We ha e p esen ed a magne ically unable op ical logic ga e based on he Fa aday e ec and he
h ee–pola ize pa adox. The de ice suppo s digi al, analog and mul i–le el logic, and admi s
na u al ex ensions owa d mo e complex a chi ec u es. In pa icula , his scheme can be ex ended
o:
•Recon igu able logic ga es whose ans e unc ion is uned in si u ia magne ic con ol.
•Non– ola ile op ical memo y elemen s using magne o–op ical ma e ials wi h p onounced hys-
e esis.
•Analog op ical compu ing blocks o ma ix ope a ions and weigh ed summa ion.
•Hyb id in e aces be ween classical pho onic p ocessing and eme ging quan um o spin onic
pla o ms.
These ea u es illus a e a p omising di ec ion o magne o–op ical compu ing and o he in eg a-
ion o logic, memo y and p ocessing wi hin a uni ied pho onic amewo k.
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Acknowledgmen s
The au ho s hank colleagues a UNAH Campus Co és o help ul discussions on magne o–op ical
ma e ials and pho onic implemen a ions.
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