Frozen mode in coupled single-mode waveguides with gratings

Abstract

We present a systematic methodology for designing slow-light photonic integrated circuits with a frozen mode based on a special kind of exceptional point of degeneracy (EPD) of order three named stationary inflection points (SIPs). This is realized through three-way coupled waveguides with lateral gratings operating at telecommunication wavelengths. We provide two designs and analyze sensitivity to geometric perturbations. We have fabricated a periodic waveguide with integrated taper loads and demonstrate reasonable agreement with full-wave simulations. These findings confirm the feasibility of integrating SIP-based delay functionalities in standard silicon photonic platforms.

Figures (8)

• Figure 1: (a) Modal dispersion diagram of the SIP-supporting mode of the TWG2RA (in blue) and the closest RBE mode (in orange); and (b) group velocity $v_g$ against Bloch wavenumber around the SIP.
• Figure 2: Schematic representations: (a) TWG1 waveguide with a central grating side-coupled to two straight waveguides; (b) TWG2 waveguide made of a central straight waveguide side-coupled to two grating waveguides; (c) top view of the two TWG1 and TWG2 waveguides showing the unit cells.
• Figure 3: Design steps for creating a stationary inflection point (SIP)-based frozen mode photonic integrated circuit (PIC) using the TWG1 configuration. (a) Dispersion diagram of a grating coupled to a straight waveguide, with parameters selected to open a bandgap near the target point $(k_S, f_S)$. (b) Dispersion diagram of an isolated straight waveguide showing a mode near the same target region. (c) Dispersion diagram of the TWG1 configuration, formed by adding the additional waveguide from (b) to the grating–straight waveguide pair in (a). The resulting structure produces the blue dispersion curve with a local maximum and minimum near the target point $(k_S, f_S)$. (d) Optimized TWG1 dispersion diagram after adjusting waveguide gap sizes, where a stationary inflection point (SIP) emerges at the target $(k_S, f_S)$ location (blue curve).
• Figure 4: Dispersion diagram of the SIP-TWG2A waveguide with a rectangular and a trapezoidal cross section. The trapezoidal geometry alters the mode profile. This slightly disrupts the SIP condition, which must be restored through fine tuning of the waveguide parameters.
• Figure 5: Dispersion diagram of the TWG2RB design showing the nominal case (black), and variations with waveguide widths increased (blue) and decreased (red) by $\Delta = 10$ nm. The SIP condition is sensitive to these changes, highlighting the importance of designing for robustness to perturbations.