Non-reciprocal electrooptic intermodal scattering with momentum engineered RF waves

Abstract

Spatiotemporal modulation approaches have been often employed as alternatives for producing optical non-reciprocity without magneto-optic materials. Unidirectional inter-modal scattering, enabled by either acousto-optic or electro-optic (EO) modulation, is a promising method in this category as it can directly modify optical dispersions and even enables linear non-reciprocal photonic devices in the strong coupling limit. While EO approaches are often preferred for their practicality, it is challenging to generate the large spatiotemporal momentum required for inter-modal phase matching without EO drive schemes involving multiple drive stimuli. Here, we demonstrate highly selective non-reciprocal inter-modal EO scattering enabled by a single high-index radiofrequency (RF) traveling wave stimulus. Our experimental demonstration is performed on a thin-film lithium niobate integrated photonics platform, in which we engineer a slow-wave radiofrequency (SWRF) transmission line with an effective RF index > 9 that natively generates the required RF momentum while simultaneously maintaining strong RF-optical mode overlap. By additionally engineering the interaction length, we achieve a directional ~20 dB non-reciprocal scattering contrast. The SWRF architecture provides a scalable route to magnetic-free non-reciprocity and establishes momentum-engineered RF waves as a powerful tool for next-generation, fully integrated non-reciprocal photonic systems.

Figures (11)

• Figure 1: Principle of non-reciprocal inter-modal scattering by slow RF waves.(a) Diagram for direction-dependent phase matching of inter-modal scattering. Two optical modes can be coupled when their frequency difference $\Delta\omega_{\text{opt}}$ and momentum difference $\Delta k_{\text{opt}}$ match the frequency $\Omega_\textrm{m}$ and momentum $q_\textrm{m}$ of the RF wave, respectively. In the specific configuration shown here, the directionality of the RF wave is only phase-matched with optical modes in the counter-propagating direction. In the co-propagating case, the phase-matching condition is not satisfied, and the scattering is suppressed. (b) Spectral scattering efficiency at a fixed frequency as a function of modulation momentum for a finite-length low-index CPW (orange) and a finite-length slow RF wave (blue). (c) Same as (b), but plotted on a logarithmic scale, highlighting that the interaction length of slow RF wave can be intentionally designed such that the scattering efficiency exhibits a null at $-q_\textrm{m}$, thereby maximizing non-reciprocity.
• Figure 2: Design and implementation of our experimental device.(a) Cross-section schematic of the double optical waveguide system and the electro-optic modulation electrodes. (b) Simulated electric-field profiles ($E_z$) of the TEodd and TEeven optical modes supported in the waveguide. (c) Simulated radiofrequency field distribution from the electrodes. (d) Schematic of the SWRF electrode. The insets (i)–(iii) illustrate the intermediate design steps of the SWRF electrode (bottom). The structure has periodicity of $p=10$$\mu\mathrm{m}$. The ground lines (G) have lateral slots of width $l_\textrm{g}=170$$\mu\mathrm{m}$. The signal lines (S) have lateral extensions of width $l_\textrm{s}=36$$\mu\mathrm{m}$. The black solid line indicates the location of the cross-section whose RF field distribution is shown in Fig. \ref{['fig2']}c.
• Figure 3: Images of the test device and RF characterization results.(a) Schematic for the device consisting of a racetrack resonator and two modulators (SWRF and CPW electrodes) on two straight sections of the resonator. The optical signal enters through Port 1 and exits through Port 2, while the RF signals are launched from the ends of the electrodes. (b) Optical microscope image of the fabricated device. Ground-Signal-Ground (GSG) pads are implemented at the ends of the electrodes via adiabatic tapers to interface with the RF input and output signals. (c) Zoomed-in microscope images of the fabricated electrodes. The left panel shows the SWRF electrode with a periodic interdigitated structure, while the right panel shows the CPW. (d) Extracted RF effective index as a function of RF frequency $\Omega_m$, showing that the SWRF waveguide achieves a significantly higher index (above 9) compared to the CPW (around 2) over the 10--20 GHz range.
• Figure 4: Experimental characterization of non-reciprocal scattering.(a) Measured optical transmission spectrum of the racetrack resonator, showing two mode pairs (Mode pair (1) and Mode pair (2)) separated by one FSR. The inner mode pair TEeven(1) and TEodd(2) are separated by $16.8~\mathrm{GHz}$, corresponding to the RF modulation frequency $\Omega_\textrm{m}$ used in this study. (b) The inferred positioning of the optical modes is indicated in this diagram, along with inter-modal scatterings enabled by the RF stimulus. (c) Measured and normalized scattered optical power under SWRF modulation. When the optical and RF signals are counter-propagating (top), strong non-reciprocal inter-modal scattering is observed, with well-resolved anti-Stokes (AS) and Stokes (S) sidebands. AS$_{(+1)}$ is the anti-Stokes scattering to the next FSR, and S$_{(-1)}$ is the Stokes scattering to the previous FSR. When the optical and RF signals are co-propagating (bottom), scattered power is suppressed to the noise floor, demonstrating $\sim 20~\mathrm{dB}$ non-reciprocity. (d) Measured and normalized scattered power using the CPW modulator. In both counter- and co-propagating cases, we observe a cluttered spectrum with indications of mixture of inter-modal and intra-modal scattering.
• Figure 5: Experimental characterization of non-reciprocal scattering via the SWRF waveguide at different optical wavelengths.(a) Measured Stokes (red) and anti-Stokes (blue) sidebands when optical and RF waves are counter-propagating. (b) Measured Stokes (red) and anti-Stokes (blue) sidebands when optical and RF waves are co-propagating. Scattered power remains significantly suppressed, confirming robust non-reciprocal behavior across all tested wavelengths.