Multi-timescale frequency-phase matching for high-yield nonlinear photonics

Abstract

Integrated nonlinear photonic technologies, even with state-of-the-art fabrication with only a few nanometer geometry variations, face significant challenges in achieving wafer-scale yield of functional devices. A core limitation lies in the fundamental constraints of energy and momentum conservation laws. Imposed by these laws, nonlinear processes are subject to stringent frequency and phase matching (FPM) conditions that cannot be satisfied across a full wafer without requiring a combination of precise device design and active tuning. Motivated by recent theoretical and experimental advances in integrated multi-timescale nonlinear systems, we revisit this long-standing limitation and introduce a fundamentally relaxed and passive framework: nested frequency-phase matching. As a prototypical implementation, we investigate on-chip multi-harmonic generation in a two-timescale lattice of commercially available silicon nitride (SiN) coupled ring resonators, which we directly compare with conventional single-timescale counterparts. We observe distinct and striking spatial and spectral signatures of nesting-enabled relaxation of FPM. Specifically, for the first time, we observe simultaneous fundamental, second, third, and fourth harmonic generation, remarkable 100 percent multi-functional device yield across the wafer, and ultra-broad harmonic bandwidths. Crucially, these advances are achieved without constrained geometries or active tuning, establishing a scalable foundation for nonlinear optics with broad implications for integrated frequency conversion and synchronization, self-referencing, metrology, squeezed light, and nonlinear optical computing.

Figures (17)

• Figure 1: (a) Schematic of nested harmonic generation in a simplified 2D array of coupled SiN resonators (see Figure S1 for actual device). A tunable telecom pump is coupled into the lattice at the input port and circulates along the edge of the 2D AQH SiN lattice (clockwise mode shown). Generated harmonics are analyzed via optical spectrum analyzers (OSAs), revealing the two characteristic timescales: $\tau_{\rm{F}}$ of the individual rings and $\tau_{\rm{S}}$ of the super-ring. Harmonics are also imaged with infrared and visible cameras (not shown). (b) Schematic of the nonlinear processes and wavelength regimes for each harmonic band (see Figure S1 for details of all the other possible nonlinear pathways). Phase-matching illustration for SHG in (c) a single-timescale ring vs. (d) two-timescale lattice (right). Insets: simulated fundamental and higher order TE mode profiles of an 800 nm × 1200 nm SiN waveguide at fundamental and SH wavelengths (see SI section S2 for detailed FDTD mode simulations). In the nested case (right), discrete single-ring phase-matching points are replaced with a two-timescale grid set by $\tau_{\rm{S}}$ (note that the two timescales are not to scale). Circle size reflects the mode linewidth inversely proportional to its quality factor Q.
• Figure 1: (a) Detailed schematic of the measurement setup. A tunable pulsed laser operating at telecommunication wavelengths passes through a variable attenuator and a polarization controller before being fiber-coupled into the SiN device. The harmonics are collected via fiber, optionally passed through a second variable attenuator and a notch filter for pump suppression, and then routed to the grating-based and heterodyne-based OSAs, and ESA for analysis. Simultaneously, the harmonics are imaged from above using a 10$\times$ objective followed by a 50:50 beam splitter (BS), with one optical path directed to a visible camera and the other reaching an IR-sensitive camera (both are filtered by harmonic-selective filters prior to the camera). A high-quality optical image of the sample is also shown at the top left. (b) The available pure harmonic as well as sum-frequency processes inside the device for the generation of light in each harmonic band.
• Figure 2: (a) From right to left: Measured pump-power-dependent spectra of the fundamental, second, and third harmonic (FH, SH, and TH, respectively) bands from the drop port of the 10 × 10 SiN lattice, when pumping the center of the edge band. The inset in the SH panel shows a zoom-in of the pump-power dependence of the SH signal near 776.3 nm, with the 100 pm bandwidth indicated by the white arrows. An optical image of the device, indicating the input and drop ports, as well as an FDTD simulation of part of a typical edge profile, is shown in the inset of the FH panel (the color bar indicates the normalized electric field intensity). Insets in the TH panel show visible green emission from the device edges in both clockwise (CW) and counter-clockwise (CCW) directions. (b) Examples of the corresponding FH, SH, and TH spectra at different pump powers. (c) Bottom row: unfiltered real-color pump-power-dependent spatial imaging of the harmonics, when pumping the edge at 1548.60 nm. Top row, from right to left: simulated linear intensity profile of a typical edge mode, followed by real-color spectrally filtered FH, SH, TH, and the fourth harmonics, respectively.
• Figure 2: (a-c) FDTD simulation of electric field intensity profiles of the SiN waveguide modes (for our SiN waveguide's cross-sectional dimension of 1200 nm in width and 800 nm in thickness) as a function of wavelength and effective group index. The field profiles are shown at the pump and SH wavelengths. (d) Corresponding higher-order modes of the waveguide. Transverse-electric (TE) and transverse-magnetic (TM) modes are indexed by even and odd numbers, respectively.
• Figure 3: (a) From right to left: Broadband optical spectrum analysis of the nested fundamental, second, and third harmonics (FH, SH, and TH) as a function of pump wavelength, at approximately 185 mW average pump power. The bulk and edge regions of the spectrum are highlighted in gray and green, respectively. (b) Spectral analysis and bandwidth comparison of a representative FH (right), two adjacent SH modes (middle), and a typical TH fast-timescale resonance (left). The observed bandwidths—approximately 400 pm and 100 pm for FH and SH, respectively—indicate full occupation of the edge band at each longitudinal mode. The dashed circle in the SH panel highlights the nested substructure of the harmonics, limited by the 20 pm resolution of the grating-based OSAs (see the SI section S9 for the high-resolution heterodyne-based spectral analysis of the nested FH).