Electro-optic non-reciprocal polarization rotation in lithium niobate O gulcan E. Orsel1 Gaurav Bahl2

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Electro-optic non-reciprocal polarization rotation

in lithium niobate

O˘gulcan E. ¨

Orsel 1, Gaurav Bahl 2

1Department of Electrical & Computer Engineering,

2Department of Mechanical Science & Engineering,

University of Illinois at Urbana–Champaign, Urbana, IL 61801 USA

Abstract

Polarization is a fundamental degree of freedom for light and is widely

leveraged in free space and ﬁber optics. Non-reciprocal polarization rota-

tion, enabled via the magneto-optic Faraday eﬀect, has been essentially

unbeatable for broadband isolators and circulators. For integrated pho-

tonics foundries, however, there is still no good path to producing low-loss

magneto-optic components, which has prompted a search for alternatives

that do not use polarization rotation. Moreover, magneto-optic materials

tend to be highly lossy, and while large (10 −100 rad/cm) polarization

rotation can be achieved, the key ﬁgure of merit (rotation-per-loss) is typ-

ically <1 rad/dB. Here, we demonstrate that broadband non-reciprocal

polarization rotation can be produced using electro-optics in nanophotonic

devices. Our demonstration leverages electro-optic inter-polarization scat-

tering around 780 nm in lithium niobate, in which the reciprocity is broken

with the help of a radiofrequency stimulus that carries synthetic momen-

tum. While the demonstrated electro-optic polarization rotation rate is

≈1 rad/cm, the exceptionally low loss of lithium niobate enables non-

reciprocal polarization rotators with ﬁgures of merit that are 1-2 orders-

of-magnitude better than what is possible with magneto-optics. This

approach can be replicated in III-V platforms paving the way for high-

performance lasers with co-integrated monolithic isolators.

The Magneto-optic Faraday rotation eﬀect (MOFE) is the foundation for

all commercially-ﬁelded isolator and circulator devices available today. Its pri-

mary action is to induce directional non-reciprocity in the polarization degree

of freedom for photons [1–3], which when combined with polarization ﬁlters

can produce a direction dependent power-transmission function [4–6]. The key

feature that enables the dominance of the MOFE in non-reciprocal technolo-

gies is the very wide operating bandwidth over which it acts, and the strength

of the polarization rotation (expressed as the Verdet constant in rad/T·cm) in

magneto-optic materials, e.g. terbium gallium garnet (TGG) being a prominent

arXiv:2210.01064v2 [physics.optics] 4 Oct 2022

example. For these reasons, MOFE-based circulators are found in all complex

optical systems, and isolators are considered essential for laser stabilization.

MOFE-based nonreciprocal devices do come with limitations, however, as

they require specialized materials and magnetic biasing, neither of which are

typically available in integrated photonics platforms. The eﬀect also tends to

be strongly chromatic, which forces changes to material selection and adjust-

ment of the magnetic bias in order to tune the operational wavelength. Finally,

magneto-optic materials also tend to be quite lossy with typical propagation

loss approaching 50-70 dB/cm [7,8]. This compels designers to only use the

minimum amount of material and requires careful management between the

strength of the polarization non-reciprocity generated (rad/cm) and the signal

attenuation incurred (dB/cm), with the central ﬁgure of merit being their ratio

(rad/dB). While a number of successful attempts have been made in produc-

ing on-chip MOFE isolators [7–14], the common theme is to use the minimum

allowable magneto-optic material to minimize the accompanying losses.

Because of these limitations, multiple alternative approaches have been ex-

plored that would improve foundry compatibility, that rely on lithographical

patterning for wavelength tuning rather than on materials changes, and that

avoid magnetic ﬁelds for sensitive applications. The most notable alternatives

leverage spatio-temporal modulations or momentum biasing through optome-

chanical interactions [15], acousto-optics [16–22], and electro-optics [23–28]. A

few of these approaches can produce near-ideal isolation behavior with simulta-

neously very low insertion loss and large contrast [19,22], and are therefore quite

competitive with magneto-optics (for a recent detailed comparison we refer the

reader to the Supplementary Information of Ref. [22]). Even so, the interac-

tion that generates the non-reciprocity is usually weak, and resonant structures

are often used to enhance the non-reciprocal eﬀect but inadvertently limit the

isolation bandwidth. Magneto-optics still remain unbeatable on the bandwidth

metric.

In this work, we show that an MOFE-like nonreciprocal polarization rotation

eﬀect can be achieved on-chip using electro-optic materials, without the use of

magneto-optics. Electro-optic materials such as lithium niobate (LiNbO3) have

been rising to prominence due to their wide band gaps, extreme low loss [22,29],

and the possibility of producing active devices [22,30–33]. Indeed, these ma-

terials can be turned into dynamic polarization rotators via external pertur-

bations [34–36]. Unlike the MOFE, however, the physics of the electro-optic

polarization rotation eﬀect is reciprocal and cannot be used directly to produce

non-reciprocal devices. We show here that this reciprocity issue is resolvable by

introducing a large synthetic momentum bias into the electro-optic modulation.

As with previous approaches that use synthetic momenta [19,23,25], here we

demonstrate that this approach produces a very strong non-reciprocity in the

polarization conversion. Importantly, since high quality electro-optic materials

can exhibit ultra-low propagation loss (<0.1 dB/cm) [22,29], we show that the

ﬁgure of merit for electro-optic non-reciprocal polarization rotators can be 1-2

orders of magnitude greater than what is possible with the best MOFE-based

on-chip devices to date [7,8].

Figure 1: Principle of non-reciprocal polarization rotation via travelling wave induced interband scatter-

ing. (a) We consider here the fundamental TE00 and TM00 modes of a waveguide with linear dispersion. A spatial

modulation with large momentum applied to the waveguide has the ability to scatter photons between the modes and

achieve polarization rotation. If this modulation additionally has a time-domain component, i.e. results in a traveling

wave with frequency Ω and momentum q, the phase-matching is only satisﬁed for one direction of propagation at a selected

optical probing frequency. (b) The group velocities for the modes are not matched in the general case, which results in a

sinc2spectral dependence of the scattering process, and a propagation direction-dependent spectral shift in the scattering

proﬁles. Here we illustrate the anti-Stokes case only. (c) The applied modulation must utilize suitable electro-optic

coeﬃcients r that break the orthogonality of the polarizations. (d) One illustrative example of the resulting behavior of

the electro-optic non-reciprocal polarization rotator (EO-NPR) is presented.

The principle of our broadband nonreciprocal polarization rotator is de-

scribed in Fig. 1.d We consider an optical waveguide that supports two modes

of types TE00 and TM00, i.e. with mutually transverse polarization. These

guided modes are orthogonal and have distinct dispersions that are separated

in momentum-frequency space by a non-zero momentum. We can induce cou-

pling between these modes by introducing a spatial perturbation that shifts the

momentum for guided photons, such as a specialized grating, though the re-

sulting polarization rotation is completely reciprocal [37,38]. Non-reciprocal

behavior can now be introduced by adding a time-dependent component to the

perturbation, that is, by using a traveling wave modulation that shifts both

frequency and momentum for light [16,22,39–41]. With this type of pertur-

bation applied, light injected into either the TM00 or TE00 mode can only be

converted into the transverse polarization partner mode as long as the phase

matching relations hold true, that is, both frequency and momentum match-

ing conditions are satisﬁed (see Supplement §S1 &§S2) In the speciﬁc example

shown in Fig. 1a, we apply a traveling wave modulation at frequency Ω with

a forward-directed momentum such that it only permits conversion from TM

polarization to TE for forward-propagating light via anti-Stokes scattering from

input frequency ωfto ωf+ Ω. Conversely, forward-propagating light in the TE

polarization can only be converted to TM via Stokes scattering from ωf+ Ω

down to ωf. On the other hand, for backward-propagating light, the phase

matching is satisﬁed diﬀerently and the frequency shift during scattering is re-

versed such that conversion from TM to TE polarization can only take place

between frequencies ωb+ Ω (for TM) and ωb(for TE). As a general principle

this asymmetric frequency shift eﬀect is broadband, i.e. works for any ωfand

ωb, and extends over a frequency range where the group velocities of the optical

modes are matched.

In practice, however, these group velocities are rarely matched due to the

dispersive nature of the material and the waveguide geometry. In order to

understand the implications, we consider the anti-Stokes process in Fig. 1a

although identical dynamics are produced for the Stokes process. For light

injected into the TM00 mode in the forward direction, the anti-Stokes polar-

ization conversion is maximized at ωfwhere perfect phase matching occurs,

and as a function of detuning the conversion exhibits a sinc2proﬁle that orig-

inates due to phase accumulation (Fig. 1b). A detailed discussion is provided

in the Supplement §S2. On the other hand, due to the mismatched disper-

sion, light entering the TE00 mode in the backward direction can only opti-

mally undergo anti-Stokes scattering back into the TM00 mode at a diﬀerent

frequency ωb. This produces a direction-dependent spectral shift in the sinc2

proﬁle (Fig. 1b) and results in a nonreciprocal conversion process for the for-

ward and backward directions. The spectral shift can be analytically evaluated

as ωf−ωb= Ω (nTM

g+nTE

g)/(nTM

g−nTE

g), and increases with larger values of

the applied modulation frequency Ω and with better matching of the group in-

dices. In fact, if the group indices are exactly matched then the phase matching

in the opposite direction is never satisﬁed and the bandwidth becomes inﬁnite

in theory with limits imposed by other practical constraints. In the cases where

this shift ωf−ωbis well resolved, i.e. (nTM

g+nTE

g)ΩL/ πc 1 (see Supplement

§S3 ), where Lis the total interaction length, the device can exhibit large mode

conversion in the forward direction but negligible conversion in the backward

direction over some frequency bands (Fig. 1d). Furthermore, this non-reciprocal

behaviour is maximized if the spectral shift aligns the peak of the sinc2in one di-

rection with a null in the opposite direction of propagation. The above analyses

are discussed in detail in the Supplement §S3.

In addition to the above phase matching requirements, we must ensure a non-

zero overlap integral between the transverse polarization modes and the travel-

ing wave modulation that provides the rotation action. Such inter-polarization

scattering can be achieved electro-optically [34,42,43], i.e. using the second or-

der optical nonlinearity which produces refractive index change under an applied

radio-frequency (RF) electric ﬁeld. The overlap integral requirement can then be

summarized as RPijk ETM

i(r⊥)ETE

j(r⊥) rijk ERF

k(r⊥)dr⊥6= 0 where ETE(r⊥),

ETM(r⊥), and ERF(r⊥) are the transverse ﬁeld distribution of optical and ap-

plied RF modes respectively (see Supplement §S1) and the subscripts (ijk) refer

to coordinate axes for material’s electro-optic tensor. This requirement is visu-

ally depicted in Fig. 1c. The overlap integral can be interpreted into a speciﬁc

requirement of non-zero electro-optic coeﬃcients rijk for i6=j[44,45], which are

signiﬁcant in many electro-optic materials, such as LiNbO3[34,42,43], GaAs

[46,47], InP [47] and InGaP [48]. These materials therefore give us a path

to realize non-reciprocal polarization rotation in foundry compatible processes

without requiring magneto-optics, by just applying appropriately designed RF

stimuli. As an important observation, the best chip-scale magnetless optical

isolators to date have used materials that are not easy to co-integrate with ac-

tive III-V photonics, and this electro-optic approach could help traverse that

barrier.

In order to bridge the momentum gap between the optical modes, as de-

scribed above, the spatiotemporally propagating RF ﬁeld proﬁle needs to ex-

hibit a low group velocity, that is, large momentum for low frequency. This is

relatively simple if using acoustic phonons as in past studies [16–18,20–22] as

they can carry signiﬁcant momentum. Unfortunately, RF modes are not capable

of providing suﬃcient momentum for modest frequencies [30,33,49] which sets

a practical constraint to this approach. To circumvent this issue we generate a

synthetic momentum for the RF excitation along the waveguide by engineering

a split electrode structure [19,23,25,50]. Each electrode (of pitch L) is pro-

vided a single tone RF stimulus at frequency Ω with a relative phase shift of

∆φbetween electrodes (see Fig. 2a). The dominant component of the resulting

spatial phase proﬁle produces an eﬀective momentum at q= ∆φ/L that can

bridge the momentum gap and, in principle, could be tuned dynamically with

a suitably adaptive design. A detailed discussion on this synthetic momentum,

along with its primary and higher order Fourier components, is provided in the

Supplement §S4. For this work, we employed a 3-phase periodicity to produce

the required synthetic momentum.

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Electro-opticnon-reciprocalpolarizationrotationinlithiumniobateOgulcanE.Orsel1,GauravBahl21DepartmentofElectrical&ComputerEngineering,2DepartmentofMechanicalScience&Engineering,UniversityofIllinoisatUrbana{Champaign,Urbana,IL61801USAAbstractPolarizationisafundamentaldegreeoffreedomforlightandiswid...

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Electro-optic non-reciprocal polarization rotation in lithium niobate O gulcan E. Orsel1 Gaurav Bahl2

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