Dual-Bus Resonator for Multi-Port Spectral Engineering

TL;DR

The paper tackles the rigidity of single-bus microresonator coupling, where critical coupling, a transmission zero, and maximum intra-cavity power are linked. It introduces a dual-bus racetrack resonator built from an asymmetric three-waveguide coupler, enabling channel-specific coupling, broadband Lorentzian-to-Fano lineshapes, and decoupled control of transmission zeros, intra-cavity power, and coupling regimes. The authors develop a three-waveguide coupled-mode theory with pole-zero analysis, demonstrating that zeros traverse the unit circle to create UC/OC-phase and TZ regimes, while a common pole governs the loaded resonance; this yields complementary spectra across four ports and tunable Fano features. Experimental validation on SOI (and Si$_3$N$_4$) platforms confirms the model: measured spectra show complementary coupling, robust TZs, and tunable Fano behavior, with extracted $Q_L$ in agreement with theory and a near-constant round-trip loss $\alpha \approx 0.95$. Collectively, the work establishes multi-port spectral engineering as a general framework for reconfigurable filters, modulators, sensors, and nonlinear photonics across broad wavelengths.

Abstract

Microresonators are essential in integrated photonics, enabling optical filters, modulators, sensors, and frequency converters. Their spectral response is governed by bus-to-resonator coupling, typically classified as under-, critical-, or over-coupling. Conventional single-bus designs inevitably link the conditions for critical coupling, a transmission zero, and maximum intra-cavity power, preventing independent control of these phenomena and restricting the ability to engineer coupling regimes and resonance lineshapes. Here we propose and experimentally demonstrate a dual-bus racetrack resonator that breaks this constraint. Our design demonstrates complementary channel-specific coupling regimes and enables wavelength-dependent Lorentzian-to-Fano lineshaping. We model the device using three-waveguide coupled-mode theory and pole-zero analysis, which reveals that transmission zeros are decoupled from cavity-defined critical coupling and maximum intra-cavity power. Furthermore, the dual-bus scheme operates broadband, spanning visible to mid-infrared across all four transmission channels, highlighting its spectral richness and platform independence. These results establish a general framework for multi-port spectral engineering in integrated photonics, with broad implications for tunable filters, modulators, sensors, and nonlinear optical systems.

Figures (12)

• Figure 1: Bus-to-resonator coupling configurations.a, Point coupling (straight coupling). b, Pulley coupling. c, Directional coupling. d, Dual-bus coupling (this work). While a–c exhibit single bus–resonator interactions, the proposed scheme in d introduces dual-bus interactions with the resonator.
• Figure 2: Schematic of the dual-bus racetrack resonator and its transmission spectra.a, Schematic of the proposed device. b, Top view of the coupling region, consisting of a three-waveguide directional coupler; waveguide $B$ is bent, varying gaps $g_1$ and $g_2$, and thus coupling coefficients $\kappa_{AB}$ and $\kappa_{BC}$ along $z$. c-f, Simulated transmission spectra for four input-output configurations: c, $T_{AA}$, d, $T_{BB}$, e, $T_{AB}$, and f, $T_{BA}$. The loss coefficient is set to $\alpha=0.95$ (black lines). Coupling regimes are determined by the relative magnitude between $\alpha$ and the transmission coefficient ratios $t_{11}/t_{22}$ ($T_{AA}$, red), $t_{22}/t_{11}$ ($T_{BB}$, blue), $t_{21}/t_{12}$ ($T_{AB}$, green), and $t_{12}/t_{21}$ ($T_{BA}$, yellow). The yellow and blue shaded regions represent channel-defined under- and over-coupling-phase regimes, respectively.
• Figure 3: Pole–zero analysis.a, Pole–zero map of all four transfer functions over the wavelength range of 1490–1640 nm. b, Zoomed-in trajectories of the pole and zeros near the unit circle; arrows indicate the direction of evolution with increasing wavelength. c, Pole and zero locations at a resonance near 1608 nm. d-g, Representative transmission spectra and phase responses: d, $T_{AB}(\lambda)$: Near Lorentzian dip with high extinction and sharp phase transition (transmission zero). e, $T_{AA}(\lambda)$: Lorentzian dip with full $2\pi$ phase shift (OC phase regime). f, $T_{BA}(\lambda)$: Fano-like lineshape due to angular separation between the pole and zero, with minimal phase variation (UC phase regime). g, $T_{BB}(\lambda)$: Fano-like lineshape with low extinction and limited phase change. The Fano lineshapes in f and g are mirror-symmetric, corresponding to a sign reversal of the Fano asymmetry parameter $q$.
• Figure 4: Experimental characterization of the dual-bus resonator.a, Optical microscope image of the fabricated device. b--e, Measured transmission spectra b$T_{AA}$, c$T_{BB}$, d$T_{AB}$, and e$T_{BA}$. f, Extracted loaded ($Q_L$, black dots), intrinsic ($Q_i$, blue dots), and coupling ($Q_c$, green dots) quality factors; solid lines denote theoretical values. g--r, Representative resonance spectra (blue lines) in UC-phase, TZ, and OC-phase regimes: g--i$T_{AA}$, j--l$T_{BB}$, m--o$T_{AB}$, and p--r$T_{BA}$. Blue and yellow shaded regions represent OC- and UC-phase regimes, respectively. Each resonance is fitted to the generalized Fano model in Eq. (\ref{['eq:Fanofunction']}) (red dashed lines), quantifying the Fano asymmetry parameter $q'=\sqrt{q^2+r^2}$ (annotated in each plot).
• Figure 5: Intra-cavity power and transmission zeros.a, b Simulated intra-cavity powers $P_{\text{cavity},A}$ and $P_{\text{cavity},B}$ for waveguide excitations $A$ and $B$, respectively. c, d, Simulated absorbed powers $P_{\text{abs},A}$ and $P_{\text{abs},B}$. e, f, Corresponding experimental results of absorbed power. Red circles mark the wavelengths of maximum power. Vertical colored lines indicate the transmission-zero wavelengths for $T_{AA}$ (red), $T_{BB}$ (blue), $T_{AB}$ (green), and $T_{BA}$ (yellow).