Programmable on-chip nonlinear photonics

TL;DR

This work addresses the rigidity of conventional nonlinear photonic devices by introducing a planar waveguide with a two-dimensional, programmable distribution of $\chi^{(2)}(x,z)$ realized via electric-field-induced nonlinearity in a $\chi^{(3)}$ host. A photoconductive SRN layer and patterned optical programming generate a spatially programmable bias field $E_{\text{bias}}(x,z)$, yielding $\chi^{(2)}(x,z)=3\chi^{(3)}E_{\text{bias}}(x,z)$ and enabling arbitrary two-dimensional QPM structures. The authors demonstrate real-time SHG control across spectral, spatial, and spatio-spectral domains, including in situ inverse design to shape SH spectra (e.g., a real-time promotion of target spectra) and the creation of complex spatial profiles such as Airy beams, all within a single device. Although the demonstrated nonlinearity is modest ($\approx 0.47\ \text{pm/V}$) and update rates are limited by RC time constants and hardware, the platform offers a path to high-throughput, reconfigurable nonlinear photonics with potential applications in programmable quantum gates, adaptive optical processing, and structured-light sensing, with prospects to reach higher nonlinearities and DC operation through material and device optimizations.

Abstract

Nonlinear photonics uses coherent interactions between optical waves to engineer functionality that is not possible with purely linear optics. Traditionally, the function of a nonlinear-optical device is determined during design and fixed during fabrication. In this paper, we present a photonic device with highly programmable nonlinear functionality: an optical slab waveguide with an arbitrarily reconfigurable two-dimensional distribution of $χ^{(2)}$ nonlinearity. The nonlinearity is realized using electric-field-induced $χ^{(2)}$ in a $χ^{(3)}$ material. The programmability is engineered by massively parallel control of the electric-field distribution within the device using a photoconductive layer and optical programming with a spatial light pattern. To showcase the versatility of our device, we demonstrated spectral, spatial, and spatio-spectral engineering of second-harmonic generation by tailoring arbitrary quasi-phase-matching (QPM) grating structures in two dimensions. Second-harmonic light was generated with programmable spectra, enabled by real-time in situ inverse design of QPM gratings. Flexible spatial control was also achieved, including the generation of complex waveforms such as Airy beams and the simultaneous engineering of spectral and spatial features. This allowed us to create distinct spatial light profiles across multiple wavelengths. The programmability also allowed us to demonstrate in situ, real-time compensation of fluctuations in pump laser wavelength. Our work shows that we can transcend the conventional one-device--one-function paradigm, expanding the potential applications of nonlinear optics in situations where fast device reconfigurability is not merely practically convenient but essential -- such as in programmable optical quantum gates and quantum light sources, all-optical signal processing, optical computation, and structured light for sensing.

Figures (41)

• Figure 1: Illustration of the working principle and capabilities of a programmable nonlinear waveguide. (a) Structured light projected onto the surface of a planar waveguide plays the role of a programming illumination $I(x,z)$, inducing the same pattern of $\chi^{(2)}$ nonlinearity, $\chi^{(2)}(x,z)$, which allows versatile control of broadband SHG via quasi-phase-matching. Here, $x$ and $z$ are the transverse and longitudinal positions on the waveguide. (b) The structure and physical working mechanism of a programmable waveguide. The device is composed of a SiN waveguide ($2.05µ m$ thick SiN core and $1µ m$ thick SiO$_2$ cladding at the top and bottom), photoconductor layer ($7.5µ m$ thick silicon-rich silicon nitride), and transparent electrode ($20nm$ thick indium tin oxide). The photoconductor, when illuminated by green ($532nm$) laser light, becomes locally conductive, letting the external bias electric field through to the waveguide core. The resulting spatially shaped $E_\text{bias}(x,z)$ induces a spatially programmable $\chi^{(2)}$ nonlinearity according to $\chi^{(2)}(x,z) = 3\chi^{(3)}E_\text{bias}(x,z)$. See Appendix \ref{['appendix:device-fabrication']} and \ref{['appendix:electric-properties']} for details on the device fabrication and electrical characterization of the device, respectively. (c) Varying the longitudinal and transverse structure of quasi-phase-matching gratings enables spectral and spatial control of NLO, respectively. By programming the full two-dimensional structure of $\chi^{(2)}(x,z)$, we can simultaneously engineer the spectral and spatial structure of the generated output light.
• Figure 2: Real-time programmable periodic poling with a programmable nonlinear waveguide. (a) Experimental setup. We pumped a prototype programmable nonlinear waveguide using a CW laser with a tunable wavelength $\lambda$. A grating pattern with period $\Lambda$ was projected onto the waveguide, realizing QPM for an SHG process. The output second-harmonic (SH) power was measured by a photodetector, and the measurements could be used to update $\Lambda$. (b) Nonlinear-optical characterization of the device. (b–i) For various choices of $\Lambda$, we scanned $\lambda$ and measured the SHG conversion efficiency, which we report as an efficiency normalized by input power. (b–ii) The optimal pump wavelength $\lambda$ for each poling period $\Lambda$. The quadratic fit gives the group-velocity mismatch (GVM) between the fundamental and second harmonic at $1560nm$. The colors of the markers serve as legends for $\Lambda$, corresponding to those in (b–i). (c) Real-time feedback control of $\Lambda$ to compensate for a random walk of the pump wavelength shown in (c–i). To compensate for these fluctuations, we dithered $\Lambda$ and used the measured SHG signal to update $\Lambda$ in a way that optimizes the SHG efficiency. The evolution of $\Lambda$ is shown as a solid green line in (c–ii). In (c–iii), the SHG efficiency with and without such real-time feedback control are shown as blue solid and gray dashed lines, respectively. See Appendix \ref{['appendix:cw-pumped-SHG']} for experimental details.
• Figure 3: Spectral engineering of second-harmonic generation (SHG). (a) Output second-harmonic (SH) spectrum of broadband SHG pumped by ultrashort pump pulses for various illumination patterns. (a–i) Periodic grating with a period $\Lambda=16.64µ m$, (a–ii) superposition of four monotonic grating patterns with different periods, and (a–iii) an adiabatically chirped grating pattern. Due to the rapid spatial oscillations of these quasi-phase-matching (QPM) gratings, displaying the raw illumination patterns is not visually informative. Instead, in the green patterns shown above the results plots, we present the projected QPM grating patterns downsampled to a spatial period of $17µ m$ in the longitudinal direction. The same applies to the patterns shown in (b). See Appendix \ref{['appendix:spectral']} for the original (un-downsampled) illumination patterns. (b) By constructing a feedback loop based on the measured SH spectrum, we optimized the illumination pattern to obtain various target SH output spectra. Dashed lines represent the target spectrum. (c) The illumination pattern was updated in real-time to output a sequence of SH spectra, using pre-recorded illumination patterns. We show the results for drawing "CORNELL" in the SH spectrum, with time as the horizontal axis of the image. See Appendix \ref{['appendix:spectral']} for experimental details.
• Figure 4: Spatial engineering of second-harmonic generation (SHG). (a) Experimental setup. The waveguide was pumped with a pulsed pump laser with fixed Gaussian spatial profile, and the spatial distribution of the generated SH on a camera was measured. (b) A part of the programming illumination pattern (left column), simulated SHG dynamics within the waveguide (middle column), and a comparison between the experimentally measured and simulated SH spatial profiles. (b–i) Monotonic grating pattern. (b–ii) Quadratically chirped grating pattern. (b–iii) Superposition of nine quadratically chirped grating patterns with transverse offsets. (b–iv) Cubically chirped grating pattern. See Appendix \ref{['appendix:spatial']} for experimental details.
• Figure 5: Spatio-spectral engineering of second-harmonic generation (SHG). (a) Experimental setup. We combined a reflective grating with a 4$f$ imaging setup to record spectrally-resolved one-dimensional spatial profiles of the output second-harmonic (SH) light. The waveguide was pumped by pulses with a fixed Gaussian spatial profile. (b) Results for an illumination pattern designed to generate various numbers of spatial peaks at five different wavelengths. (c) Results for an illumination pattern designed to generate oppositely chirped Airy beams at two different wavelengths. In each of (b) and (c), the left inset shows a part of the projected grating pattern. The bottom-right inset shows the spatial distribution of the SH light at various wavelengths, marked with dashed lines in the top-right inset. See Appendix \ref{['appendix:spatio-spectral']} for experimental details.