Nonreciprocal components are essential in photonic systems for protecting light sources and for signal routing functions. Acousto-optic methods to produce nonreciprocal devices offer a foundry-compatible alternative to magneto-optic solutions and are especially important for photonic integration. In this paper, we experimentally demonstrate a dynamically reconfigurable nonreciprocal acousto-optic modulator at the telecom wavelength with a peak contrast of 8 dB and a 3 dB bandwidth of 1.1 GHz. The modulator can be arranged in a multitude of reciprocal and nonreciprocal configurations by means of an external RF input. The dynamic reconfigurability of the device is enabled by a new cross-finger interdigitated piezoelectric transducer that can change the directionality of the reciprocity-breaking acoustic excitation based on the phase of the RF input. The methodology we demonstrate here may enable new avenues for direction dependent signal processing and optical isolation.

Optical isolators and circulators are crucial components in photonic circuits for protecting light sources from backscattering and for achieving direction dependent signal routing.1–3 These functions can be only achieved by components that are nonreciprocal, i.e., that have asymmetric scattering matrices that imply different port-to-port propagation in opposing directions. The traditional approach to produce nonreciprocal components employs the Faraday rotation effect in magneto-optic media and has recently been implemented for chip-scale photonics through heterogeneous bonding of ferrites.4–6 However, this approach is not yet feasible in foundries due to material limitations and challenges with the generation and confinement of magnetic fields on-chip. As a result, while foundry-based integrated photonic systems have made tremendous progress, developments in foundry-compatible integrated nonreciprocal devices have been relatively slow.

An alternative approach is to use spatiotemporal modulation or momentum-biasing of the medium to produce magnetless nonreciprocity. This class of method, of which specific approaches employ synthetic magnetism,7–9 interband photonic transition,10–19 angular momentum biasing,20–22 and phase modulation,23–28 is particularly attractive since it leverages common dielectrics and can produce linear nonreciprocal responses. Moreover, since these methods employ optical and electrical modulations, the nonreciprocity can be activated and deactivated when needed.

In this context, we previously demonstrated an on-chip nonreciprocal modulator17 that uses a traveling acoustic wave to produce indirect interband transitions in a photonic resonator. The photoelastic perturbations of the dielectric material caused by the acoustic wave possess high momentum and low frequency, which is essential for the momentum biasing technique.12,14–18 The underlying phase matching requirement only permits this optical coupling in one direction, depending on the propagation momentum of the acoustic wave, and hence produces a nonreciprocal modulation response. Since the device geometry, e.g., the interdigitated transducer that actuates the acoustic wave, cannot be changed once fabricated, the direction of nonreciprocity is fixed. In this work, we introduce a new design for on-chip nonreciprocal modulators that permit dynamic direction reconfigurability of the nonreciprocal effect. With the approach demonstrated here, the level of transparency (in terms of whether or not the signal is modulated) or opacity in the forward and backward directions can be set independently.

A nonreciprocal modulator can be obtained through intermodal scattering between two optical modes of the photonic system that are distinct in both frequency and momentum space.11,17,18 In this work, we employ an optical racetrack resonator that supports two (four if we count opposite direction partners) distinct circulating optical modes—the quasi-TE00 (ω1, ±k1) and quasi-TE10 (ω2, ±k2) modes, as shown in Fig. 1(a). For compactness of notation, we drop the “quasi” prefix in further description. The principle of intermodal scattering in this resonator is illustrated in the ωk diagram in Fig. 1(b). We consider the specific case where the resonance frequency of the TE10 mode is higher than that of the TE00 mode [Fig. 1(b)]. An acoustic wave with frequency and momentum (Ω, q) can photoelastically modulate the resonator to enable intermodal scattering between the optical modes. This scattering of course requires that the phase matching conditions Ω = ω1ω2 and q = k1k2 are satisfied. In the example here, if the acoustic wave propagates in the forward direction (i.e., with positive wave vector), only the backward propagating (i.e., negative wave vector) optical modes are coupled as illustrated in Fig. 1(c-i). This coupling allows the mode conversion from the TE00 mode to the TE10 mode through anti-Stokes scattering or from the TE10 mode to TE00 mode through Stokes scattering. However, this same acoustic wave does not satisfy the phase matching condition for the forward propagating optical modes due to momentum mismatch. On the other hand, if the acoustic wave direction is reversed, i.e., the acoustic wave propagates in the backward direction [Fig. 1(c-ii)], only the forward propagating optical modes would be coupled but the backward propagating optical modes remain unaffected. Thus, the direction of the nonreciprocal scattering can in principle be controlled by dynamically adjusting the direction of the acoustic wave.

FIG. 1.

Conceptual schematic of the direction reconfigurable nonreciprocal acousto-optic modulator. (a) The device is composed of a racetrack resonator supporting two optical modes (TE00 and TE10) that is evanescently coupled to a single mode waveguide. The acousto-optic intermodal scattering is enabled over the linear part of the racetrack resonator. (b) Phase-matching requirements between the optical fields and acoustic excitation represented in frequency momentum space enable the nonreciprocal modulation. Here, we illustrate a case where the resonance frequency of the TE10 (ω1, k1) mode is higher than that of the TE00 (ω2, k2) mode. The existence of a forward (backward) propagating acoustic wave at (Ω, q) satisfies the phase matching condition for only the backward (forward) circulating optical modes. (c) Illustration of the acousto-optic interaction in the linear region of the racetrack, with (i) forward and (ii) backward propagating acoustic waves. When the light and the acoustic wave counterpropagate, the intermode photonic transition can occur. However, when the light and the acoustic wave copropagate, the scattering is suppressed since the phase matching condition is not satisfied.

FIG. 1.

Conceptual schematic of the direction reconfigurable nonreciprocal acousto-optic modulator. (a) The device is composed of a racetrack resonator supporting two optical modes (TE00 and TE10) that is evanescently coupled to a single mode waveguide. The acousto-optic intermodal scattering is enabled over the linear part of the racetrack resonator. (b) Phase-matching requirements between the optical fields and acoustic excitation represented in frequency momentum space enable the nonreciprocal modulation. Here, we illustrate a case where the resonance frequency of the TE10 (ω1, k1) mode is higher than that of the TE00 (ω2, k2) mode. The existence of a forward (backward) propagating acoustic wave at (Ω, q) satisfies the phase matching condition for only the backward (forward) circulating optical modes. (c) Illustration of the acousto-optic interaction in the linear region of the racetrack, with (i) forward and (ii) backward propagating acoustic waves. When the light and the acoustic wave counterpropagate, the intermode photonic transition can occur. However, when the light and the acoustic wave copropagate, the scattering is suppressed since the phase matching condition is not satisfied.

Close modal

In our previous study on this topic,17 we employed an interdigitated transducer (IDT) patterned on a piezoelectric film to launch the acoustic wave. IDTs are typically structured as a periodic array of paired electrodes, each carrying one polarity of an RF drive signal. This RF electrical stimulus mechanically deforms the material due to the piezoelectric effect and launches acoustic waves that match the acoustic dispersion relation, with the wave vector magnitude |q| being set through the physical periodicity of the IDT. When stimulated, the IDT necessarily launches acoustic waves outward with both +q and −q wave vectors in opposite directions. Depending on the physical placement of the photonic device in relation to the IDT, only one of these wave vectors may be utilized,17,29–31 or a standing wave may be utilized,32,33 either of which cannot be changed once fabricated. Moreover, while unidirectional IDT designs (i.e., only +q or only −q) have been developed previously,34 these IDT variants also cannot be reconfigured once fabricated. Since our goal in this work is to be able to dynamically reconfigure the nonreciprocity without having to make physical changes to the structure, a new transducer design is needed.

Here, we explore a different approach to synthesize an acoustic wave with dynamically reconfigurable momentum through the superposition of two standing acoustic waves with relative spatial and temporal phase offsets. To understand this approach, let us consider two frequency degenerate coaxial standing waves having a quarter wavelength relative shift in space and define the z as the axis on which these standing waves are formed. We can represent these two waves mathematically as u1 = ψ(x, y) cos(qz) cos(Ωt) and u2 = ψ(x, y) sin(qz) cos(Ωt + θt) with θt being a phase that we can assign based on driving. Here, ψ(x, y) is the cross-sectional mode shape of the acoustic wave including its amplitude, and θt represents the relative temporal phase of the acoustic wave u2 with respect to the acoustic wave u1. The superposition of these two standing waves produces the acoustic excitation

u=u1+u2=14ψ(x,y)(1+ei(θt+π/2))ei(qzΩt)+(1+ei(θtπ/2))ei(qzΩt)+c.c.,
(1)

where the first term on the RHS is a forward propagating acoustic wave (+q wave vector) and the second term is a backward propagating acoustic wave (−q wave vector). The most interesting cases appear when the relative temporal phase is either set to θt = π/2 or θt = 3π/2, at which point the excitation becomes a pure traveling wave. For θt = π/2, the synthesized acoustic wave propagates only in the backward direction, and Eq. (1) simplifies to

uθt=π/2=ψ(x,y)cos(qzΩt).
(2)

Similarly, for θt = 3π/2, the synthesized acoustic wave propagates in the forward direction, and Eq. (1) simplifies to

uθt=3π/2=ψ(x,y)cos(qzΩt).
(3)

This means that by simply adjusting the relative temporal phase, we can dynamically reconfigure the fraction of forward or backward propagating wave contributions, and therefore, dynamically reconfigure a nonreciprocal modulator or optical isolator based on this platform. Note that the equations above imply that an error in the spatial phase offset cannot be compensated by a suitable change in the temporal offset.

We now analyze the acousto-optic intermodal interaction with the above synthesized traveling acoustic wave using the coupled equations of motion,

tAm=(iWΓGm)Am+Ksin,meiωlt,
(4)

where the subscript m can represent either forward (f) or backward (b) propagation and indicates a defined directionality of light propagating through the system. Other system parameters are represented by matrices

Am=a1,ma2,m,   W=ω100ω2,Γ=κ100κ2,   K=κex1κex2.

Here, a1,m and a2,m are the intracavity field amplitudes within the TE10 and TE00 modes, respectively, ω1 and ω2 are the corresponding resonance frequencies, κex1 and κex2 are the corresponding external coupling rates between the waveguide and the resonator modes, and κ1 and κ2 are the corresponding loaded loss rates. The variable ωl represents the input laser frequency, and sin,m is the input field to the waveguide. Most of variables of interest are illustrated in Fig. 1(a). The output field amplitude sout can then be expressed as

sout,m=sin,mKTAm.
(5)

Due to the phase matching condition, the coupling between the forward propagating optical modes is only induced by the backward propagating component of the acoustic excitation [see Fig. 1(b)]. Thus, the corresponding coupling term becomes

Gf=0g(1+ei(θt+π/2))eiΩtg(1+ei(θt+π/2))eiΩt0,
(6)

where g is the optomechanical coupling coefficient proportional to the cross-sectional overlap integral of the two optical and acoustic waves, which will be discussed in detail later. Similarly, the coupling between the backward propagating optical modes is only induced by the forward propagating component of the acoustic excitation. Thus, the corresponding coupling term becomes

Gb=0g(1+ei(θtπ/2))eiΩtg(1+ei(θtπ/2))eiΩt0.
(7)

As shown in the equations above, the intermodal coupling Gm between the optical modes is always a function of the relative temporal phase θt. Specifically, when the phase is θt = π/2, only the forward propagating light experiences the intermodal scattering since the backward coupling term Gb = 0. Similarly, when the phase is θt = 3π/2 only the backward propagating light experiences the intermodal scattering, since Gf = 0.

In order to couple two distinct optical modes in a photonic system, the photoelastic perturbation should not only satisfy the phase matching condition in the propagating direction but also must break the orthogonality in the transverse direction. As shown in Fig. 2(f), the cross-sectional shapes of the TE00 mode ϕ1(x, y) and the TE10 mode ϕ2(x, y), respectively, have symmetric and antisymmetric electric field profiles relative to the center of the waveguide. Since the optomechanical coupling g is proportional to the cross-sectional overlap integral ∫∫(ϕ1 · ϕ2)(∇ · ψ)dxdy,17 the cross-sectional shape of the acoustic wave ψ(x, y) should have an asymmetric density profile to ensure that the overlap integral is nonzero.

FIG. 2.

Direction reconfigurable nonreciprocal modulator. (a) Schematic of a cross-finger interdigitated transducer (CFIDT) and (b) the corresponding S0 Lamb acoustic mode shape simulated by the finite-element method (FEM). Color represents mechanical density variation with red indicating high and blue indicating low. (c) Schematic of the acousto-optic interaction region. Two CFIDTs are employed with quarter wavelength physical offset in the light propagating direction. Two “free edge” acoustic reflectors are designed in the transverse direction to confine the acoustic mode. An additional finite element simulation showing the synthetic traveling acoustic wave actuated by this dual-CFIDT actuator is provided in the supplementary material, Sec. S1. (d) True-color microscope image of the fabricated device. The orange region is AlN on air, and the green region is AlN on silicon. (e) Cross-sectional schematic of the acousto-optic interaction region. (f) Finite element simulated mode shapes of the TE10 and TE00 optical modes (electric field intensity), and the S0 acoustic wave (density variation with red high and blue low).

FIG. 2.

Direction reconfigurable nonreciprocal modulator. (a) Schematic of a cross-finger interdigitated transducer (CFIDT) and (b) the corresponding S0 Lamb acoustic mode shape simulated by the finite-element method (FEM). Color represents mechanical density variation with red indicating high and blue indicating low. (c) Schematic of the acousto-optic interaction region. Two CFIDTs are employed with quarter wavelength physical offset in the light propagating direction. Two “free edge” acoustic reflectors are designed in the transverse direction to confine the acoustic mode. An additional finite element simulation showing the synthetic traveling acoustic wave actuated by this dual-CFIDT actuator is provided in the supplementary material, Sec. S1. (d) True-color microscope image of the fabricated device. The orange region is AlN on air, and the green region is AlN on silicon. (e) Cross-sectional schematic of the acousto-optic interaction region. (f) Finite element simulated mode shapes of the TE10 and TE00 optical modes (electric field intensity), and the S0 acoustic wave (density variation with red high and blue low).

Close modal

To generate an acoustic wave that produces the requisite photoelastic perturbation in both propagating and transverse directions, we have developed a new cross-finger interdigitated transducer (CFIDT) illustrated in Fig. 2(a). Unlike conventional IDTs, CFIDTs have electrode finger pair periodicities in two orthogonal directions. This permits the electrical actuation of an acoustic wave that has a 2D profile on the propagation plane [Fig. 2(b)] with antinodal points located at the electrode fingers. The CFIDT pitch in the propagating direction is designed to satisfy the phase matching condition, while the transverse pitch is independently designed to maximize the overlap integral between the optical modes and the acoustic wave. In past work,17 the propagating and transverse wave vectors were necessarily coupled since they were set by the delicate tuning of the angle and the pitch of a conventional IDT, which significantly complicated the design and the iteration cycle. Finally, since the acoustic wave generated by one CFIDT alone is a standing wave, two CFIDTs are needed to produce a traveling wave as described in Eqs. (1)–(3). In this work, we combine two CFIDTs having a quarter wavelength physical offset in the direction of the optical waveguide [Fig. 2(c)]. With an appropriate reconfiguration of the temporal phase θt, this arrangement enables generation of a propagating acoustic wave in either direction, while simultaneously forming a standing acoustic wave in the transverse direction. The transverse standing wave is supported by “free edge” acoustic reflectors on both sides of the interaction region that also resonantly enhance the acoustic wave.

We fabricated the reconfigurable nonreciprocal modulator using 350 nm sputter deposited c-axis oriented aluminum nitride (AlN) on a silicon handling wafer [Figs. 2(d) and 2(e)]. AlN is an excellent material for integrated acousto-optics due to its low intrinsic loss for both acoustics and optics, and it has an appreciable piezoelectric coefficient.29,32,35–38 We first pattern the two-mode racetrack resonator, along with adjacent single-mode waveguide and grating couplers using electron-beam lithography on ZEP-520 E-beam resist. The widths of the racetrack waveguide and the single-mode waveguide are selected as 2.2 μm and 0.8 μm, respectively. The waveguide is evanescently coupled to the racetrack resonator with a 1.2 μm gap over a 170 μm coupling length. Both the racetrack resonator and waveguide have a ridge structure formed by partially etching 230 nm of the AlN layer through Cl2-based inductively coupled plasma reactive ion etch (ICP-RIE). Next, we pattern the “free edge” acoustic reflectors and release holes on double-spin coated ZEP-520 resist followed by complete etching of 350 nm AlN through Cl2 based ICP-RIE. Two CFIDTs are then patterned by E-beam lithography followed by E-beam deposition of 60 nm of aluminum and lift off. Finally, the device is released using XeF2 dry etching of Si for improving the confinement of both acoustic and optical modes in the AlN waveguide.

We designed the separation of the two optical modes in ωk space with the help of finite element (Comsol) simulation (both frequency-matching and momentum-matching are critical as stated in Sec. II). This design is then experimentally confirmed by iterative testing using a range of fabricated devices with swept parameters around the design point. Once the device design and modal separation are finalized, we can produce a series of devices that exhibit very small variation from the ideal mode separation. Since the TE10 and TE00 modes have slightly different dispersion, the frequency difference between consecutive mode pairs varies, even as the momentum difference remains fixed. As shown previously,17 this implies that the same device can show different phase-matching conditions using different mode pairs.

The two CFIDTs are designed with the required quarter wavelength offset in the propagating direction along the resonator. The required acoustic wavenumber q, which is the wavevector difference between the two optical modes, is calculated through COMSOL simulation based on the measured dimensions of the waveguide of the racetrack resonator. In our case, the pitch of the CFIDT in the propagating direction is set to Λpropagating = 2π/q = 18.3 μm. The pitch in the transverse direction is set to Λtransverse = 2.2 μm, which matches with the racetrack width, to maximize the overlap integral.

We begin experiments by first characterizing the acoustic and optical properties of the system. The CFIDTs are characterized by means of the RF reflection (s11) measurement using a vector network analyzer (VNA). As shown in Fig. 3(b), both CFIDTs exhibit the same resonant frequency for the acoustic mode located at 4.98 GHz. This resonant frequency shows good agreement with the S0 Lamb acoustic mode frequency simulated by finite element method (FEM) (details are given in the supplementary material, Sec. S2). The baseline of the electrical s11 measurement is around −13 dB caused by resistive losses from the Al electrodes and the Si substrate. The optical transmission spectrum through the waveguide allows the measurement of the optical modes of the racetrack resonator. Here, we select a resonator mode pair located near 1540 nm with a frequency separation of 4.97 GHz as shown in Fig. 3(c), which is very similar to the acoustic resonance frequency. The measured optical transmission spectrum [Fig. 3(c)] is plotted relative to the TE10 resonance frequency (Δ = ωlω1 = 0). The loaded quality factor of the TE00 mode is measured at ∼176 000 and of the TE10 mode is ∼133 000. Both of the resonator modes are undercoupled to the single-mode waveguide.

FIG. 3.

Experimental setup and characterization. (a) Light from a continuous 1520–1570 nm fiber-coupled laser is split into two branches for optical heterodyne detection. The light in the reference path is offset by Ωr = 100 MHz using an acousto-optic frequency shifter (AOFS) to enable separate measurement of Stokes and anti-Stokes sidebands. Fiber polarization controllers (FPCs) are used to manipulate the polarization of the input and the output to orient correctly with the on-chip grating couplers. The output light from the device is amplified using an erbium-doped fiber amplifier (EDFA) to compensate for the loss from the grating couplers (i.e., minimum 5 dB loss for each grating coupler). A tunable optical bandpass filter is placed to minimize the additional broad spectrum noise added by the EDFA. The light from the reference path and the device is combined and generates beat notes at a photodetector (PD). The RF signal from the PD is measured using a RF spectrum analyzer (RFSA). An optical switch is used to control the direction of the light going into the device. The RF stimulus signal—which controls the nonreciprocity—is produced by a signal generator and split into two paths connected to each CFIDT. Phase shifters are placed at each path to independently control the phase of the two RF inputs to the CFIDTs. (b) Measured RF reflection coefficients (S11) of the two CFIDTs obtained with a vector network analyzer. Both CFIDTs efficiently generate the acoustic excitation at 4.98 GHz; however, they do have slightly different electromechanical transduction efficiencies. (c) Measured (dots) and fitted (solid) optical transmission spectra through the waveguide show the optical mode pair with the frequency separation of 4.97 GHz located around 1540 nm. The left dip is the resonance of the TE00 mode, and the right dip is the TE10 mode.

FIG. 3.

Experimental setup and characterization. (a) Light from a continuous 1520–1570 nm fiber-coupled laser is split into two branches for optical heterodyne detection. The light in the reference path is offset by Ωr = 100 MHz using an acousto-optic frequency shifter (AOFS) to enable separate measurement of Stokes and anti-Stokes sidebands. Fiber polarization controllers (FPCs) are used to manipulate the polarization of the input and the output to orient correctly with the on-chip grating couplers. The output light from the device is amplified using an erbium-doped fiber amplifier (EDFA) to compensate for the loss from the grating couplers (i.e., minimum 5 dB loss for each grating coupler). A tunable optical bandpass filter is placed to minimize the additional broad spectrum noise added by the EDFA. The light from the reference path and the device is combined and generates beat notes at a photodetector (PD). The RF signal from the PD is measured using a RF spectrum analyzer (RFSA). An optical switch is used to control the direction of the light going into the device. The RF stimulus signal—which controls the nonreciprocity—is produced by a signal generator and split into two paths connected to each CFIDT. Phase shifters are placed at each path to independently control the phase of the two RF inputs to the CFIDTs. (b) Measured RF reflection coefficients (S11) of the two CFIDTs obtained with a vector network analyzer. Both CFIDTs efficiently generate the acoustic excitation at 4.98 GHz; however, they do have slightly different electromechanical transduction efficiencies. (c) Measured (dots) and fitted (solid) optical transmission spectra through the waveguide show the optical mode pair with the frequency separation of 4.97 GHz located around 1540 nm. The left dip is the resonance of the TE00 mode, and the right dip is the TE10 mode.

Close modal

We experimentally test nonreciprocal modulation by measuring the Stokes and anti-Stokes optical sidebands produced independently for forward and backward optical inputs, for which the optical heterodyne measurement [Fig. 3(a)] is employed. During this measurement, the input optical power is kept below 50 μW so that the device does not experience any thermal or nonlinear effects. For this, we first produce a 100 MHz frequency-shifted optical reference from the input laser signal using an acousto-optic frequency shifter (AOFS). The photocurrent beat notes formed between this reference signal and either the Stokes or anti-Stokes sidebands of the original input are therefore frequency-separated and can be measured independently. The electrode drive stimulus from a signal generator is split into two paths—the input to one CFIDT is provided through an RF phase shifter which allows the control of the temporal phase θt, while the input to the second CFIDT is unmodified. During this experiment, the RF drive frequency is set at 4.97 GHz so that the acoustic wave is most efficiently generated for both CFIDTs, and the RF input power provided to each CFIDT is 2 dBm.

In Fig. 4(a), we present a theoretical prediction of the output power of Stokes and anti-Stokes sidebands as a function of detuning of the input laser Δ and the temporal phase applied on RF stimulus θt. In Fig. 4(b), we present the experimentally measured Stokes and anti-Stokes sidebands that exhibit the nonreciprocal modulation.

FIG. 4.

Experimental demonstration of direction reconfigurable nonreciprocal modulation. (a) Theoretical and (b) experimentally measured Stokes and anti-Stokes modulation efficiencies (ratio of output sideband power to input optical power) with respect to the input laser optical detuning (Δ) and RF driving stimulus phase difference (θt). This experiment used 5 dBm of RF driving power. Note that the modulation efficiency increases linearly with increasing RF drive power. Colors represent modulation efficiency on a linear scale. The theoretical plot is based on the parameters extracted from the carrier transmission data [Fig. 3(c)] and the predictive Eq. (5). Note that the detuning Δ is defined relative to the higher frequency, i.e., the TE10, optical mode in this experiment. As a result, Δ = 0 implies that the laser is on resonance with the higher frequency mode and that only a Stokes sideband should be observable when scattering takes place. Similarly, Δ = −5 GHz implies that the laser is on resonance with the lower frequency mode and that only the anti-Stokes sideband should be observed.

FIG. 4.

Experimental demonstration of direction reconfigurable nonreciprocal modulation. (a) Theoretical and (b) experimentally measured Stokes and anti-Stokes modulation efficiencies (ratio of output sideband power to input optical power) with respect to the input laser optical detuning (Δ) and RF driving stimulus phase difference (θt). This experiment used 5 dBm of RF driving power. Note that the modulation efficiency increases linearly with increasing RF drive power. Colors represent modulation efficiency on a linear scale. The theoretical plot is based on the parameters extracted from the carrier transmission data [Fig. 3(c)] and the predictive Eq. (5). Note that the detuning Δ is defined relative to the higher frequency, i.e., the TE10, optical mode in this experiment. As a result, Δ = 0 implies that the laser is on resonance with the higher frequency mode and that only a Stokes sideband should be observable when scattering takes place. Similarly, Δ = −5 GHz implies that the laser is on resonance with the lower frequency mode and that only the anti-Stokes sideband should be observed.

Close modal

Let us first examine intermodal scattering at θt = 0 where a standing acoustic wave is generated. This corresponds to the left-most edge of each of the subplots in Fig. 4. Since the acoustic excitation is nonpropagating, the intermodal scattering occurs in both forward and backward directions symmetrically. When the light enters the TE10 mode (at Δ = 0 GHz) in either direction, only a single Stokes sideband is generated. This is because Stokes scattering from the TE10 mode is resonantly enhanced by the TE00 resonance located at Δ = −4.97 GHz. However, anti-Stokes scattering is suppressed since there is no optical mode that is phase matched. Similarly, if the light enters the TE00 mode, only the anti-Stokes sideband is generated due to the TE10 resonance located at Δ = 0. Using these data, we measured a maximum modulation efficiency (output sideband power vs input optical power) of 0.0025% when the system is driven with 5 dBm of RF input power. With higher RF input power, a larger modulation efficiency is expected.

We now test for the reconfiguration of this nonreciprocal behavior by analyzing the sideband response as a function of the temporal phase difference θt. We focus on the specific cases θt = 0, π/2, π, 3π/2, where the acoustic excitations have properties of interest: at θt = 0 and π, the excitation is a purely standing acoustic wave; at θt = π/2, the excitation is a pure backward propagating acoustic wave, and at θt = 3π/2, the excitation is a pure forward propagating acoustic wave.

In both experimental data and theoretical simulation, there is a clear distinction in the sidebands produced depending on whether the light enters in the backward or forward direction. In the theoretical plot, when θt = 0 and π, the sideband amplitudes in the backward and forward directions are identical. When the phase difference is set to θt = π/2, the backward sideband generation is suppressed, while the sideband amplitude in the forward direction is maximized. This is exactly as expected since θt = π/2 only launches an acoustic wave in the backward direction, implying that only the forward optical modes are correctly phase matched. Conversely, when θt = 3π/2, the forward sideband generation is suppressed, while scattering in the backward direction is maximized.

The experimental data show very similar trends. However, the sideband amplitude peaks and nulls are slightly misaligned on the θt axis relative to the theoretical prediction. For example, the peak of anti-Stokes sideband power in the forward direction is located at θt ≈ 3π/4, whereas the null of the anti-Stokes sideband power in the backward direction is located near θt = π/2. This shift in the nulls is caused by a small quantity of undesired intramodal scattering that takes place within the resonator. Since both the intermodal scattered light and the intramodal scattered light exit the resonator from the same single-mode waveguide, they experience interference that shifts the apparent null points. Additional factors that contribute to this shift may be a slight physical misalignment of the two CFIDTs or the physical phases of the acoustic waves produced by them, either of which may be due to fabrication imperfection. Resolution of this question is not possible with the capabilities of the current devices and is left for future work.

The largest Stokes sideband nonreciprocal contrast that we experimentally observed is ∼8 dB with θt = π/2 and is also primarily limited by the nonideality of the experiment. Specifically, if the amplitudes of the two acoustic waves generated by the CFIDTs are slightly different, the synthesized acoustic wave cannot be a pure traveling wave and does contain a standing wave term. This would create a little extra scattering that might be possible to calibrate out by setting different drive amplitudes at the two CFIDTs. In practice, this inequality is readily caused by differences in electromechanical couplings of the CFIDTs as shown in the s11 measurement [Fig. 3(b)], or from different RF losses in the transmission lines connecting the RF power splitter to the CFIDTs.

In this work, we have demonstrated a dynamically reconfigurable nonreciprocal acousto-optic modulator at the telecom wavelength that can be set in a variety of reciprocal and nonreciprocal configurations. The nonreciprocal modulation is achieved by biasing the optical resonator with a synthesized traveling acoustic wave, with the direction and magnitude of nonreciprocity simply controlled by adjusting the temporal phase of an RF stimulus. Using this synthesized acoustic wave, we achieve a peak nonreciprocal contrast of 8 dB and a 3 dB bandwidth of 1.1 GHz that is limited by the optical mode linewidth. This reconfigurable functionality can potentially enable new signal processing capabilities for integrated communications and sensing systems. Moreover, this work showcases a fully lithographically defined approach to producing nonreciprocal components that is not strictly material dependent and that can be adapted for different wavelength regimes. We expect that the performance of this nonreciprocal acousto-optic modulator can be further improved by enhancing electromechanical coupling, acousto-optic coupling, and optical quality factors of the subcomponents. In the long term, this type of approach could be adapted to produce linear optical isolators and circulators in integrated photonics.

See the supplementary material for a simulation of the traveling acoustic wave launched by the dual-CFIDT and for identification of the experimentally measured acoustic mode.

This material was based on research sponsored by the Air Force Research Laboratory (AFRL) under agreement No. FA9453-16-1-0025. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of Air Force Research Laboratory (AFRL) and (DARPA) or the U.S. Government. D.B.S. would also like to acknowledge support from a U.S. National Science Foundation Graduate Research Fellowship. Experiments were carried out in part in the Frederick Seitz Materials Research Laboratory Central Research Facilities and Holonyak Micro and Nanotechnology Laboratory at the University of Illinois at Urbana, Champaign.

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Supplementary Material