Experimental Measurement of Enhanced Group Delay Silicon Photonic Waveguides Indicative of the Frozen Mode Regime Around the Stationary Inflection Point

TL;DR

This work targets the observation of SIP-associated frozen-mode regime slow light in a silicon photonic waveguide by designing a three-path (3PD) periodic structure whose Floquet-Bloch dispersion supports two SIPs inside the Brillouin zone. The authors combine high-resolution, chip-to-chip measurements with transfer-matrix modeling of finite-length units and boundary terminations to extract transfer functions and group delays, observing enhanced delay near SIP resonances. They introduce a reverse-modeling approach that perturbs unit-cell widths to better match measured spectra and delays, demonstrating improved agreement and indicating fabrication disorder shifts SIP positioning. Across multiple AIM Photonics MPW chips and device lengths, the results provide robust evidence that the devices operate in or near the SIP/FMR, with implications for delayed/slow-light applications and for designing disorder-tolerant SIP-based photonic components. The study also clarifies the role of boundary conditions and disorder in SIP observations and situates its findings within the broader EPD literature, offering a path toward more reliable SIP-based silicon photonics devices.

Abstract

The dispersion engineering of periodic silicon photonic waveguides presents opportunities for significant group delay enhancement compared to uniform waveguides of comparable length. We describe the spectral response characteristics for measured devices and compare their properties to modeled data. These waveguides support the frozen mode regime (FMR) around near infrared wavelengths and are expected to show enhanced group delays around the FMR resonances. Measurements of fabricated devices provide evidence for enhanced delays and spectral properties associated with the FMR. We study how perturbations to the waveguide model impact agreement with measurements and its meaning for these devices operating in the FMR.

Figures (12)

• Figure 1: Finite-length geometry of the 3PD waveguide for $N=10$ unit cells with unit cell geometry enlarged and marked with parameters given in Table \ref{['tab:ParameterValues-3PD']}. The DBR in the 3PD unit cell has $M = 12 + 8$ segments where $12$ are fully perturbed and four on each side have gradually decreasing inner waveguide widths (apodized grating). The 3PD has an additional termination geometry at each end working to separate the coupled waveguides and reduce the reflection at the waveguide boundaries. The continuous straight paths on the top waveguide represent the input and output waveguides.
• Figure 2: The Floquet-Bloch dispersion diagram for the 3PD waveguide's modes where the SIP wavelength is marked with a horizontal dashed line. Propagating modes are shown in black and evanescent modes are shown in red. At each of the two SIPs, symmetric with respect to the $kd = \pi$ point, all three of the coalescing wavenumbers are real.
• Figure 3: Reflectivity of the termination tapers across a subset of the design space when varying the taper length, angle, and minimum width. The length is defined as the projection of the taper on the $z$-axis, the angle is defined from the $z$-axis, and the minimum width is defined as the width of the waveguide at the end of the taper ($100$ or $200\;\mathrm{nm}$). The geometric parameters of the tapers were chosen to minimize the reflection coefficient. In the rest of the paper, we choose the taper to have a length of $4\;\mathrm{\upmu m}$ set at an angle of $40\degree$ and an end width of $200\;\mathrm{nm}$. Reflectivities are given at $\lambda_{\mathrm{SIP}}$.
• Figure 4: Finite-length waveguide transfer function and group delay for the 3PD waveguide for various numbers of unit cells $N$. A reflection coefficient of $\Gamma = 0$ is shown in (a) and $\Gamma = 1$ is shown in (b). By reducing the reflection coefficient at the waveguide boundaries we can more clearly distinguish the SIP associated resonance and group delay.
• Figure 5: Example measurement setup with a photonic chip on the left and V-groove fiber array on the right. Light is edge-coupled into the chip from the fiber array connecting to the measurement system.