Multimode Single-Ring Photonic Molecule

Abstract

Photonic molecules can mimic interactions of atomic energy levels, offering new ways to manipulate cavity eigenstates. Current methods using evanescent coupling of multiple cavities face challenges in scalability, flexibility, and coupling control, especially for complex systems. Here we introduce a new method that uses a single multimode optical ring resonator to create photonic molecules. Our design uses multiple waveguide transverse modes in one resonator, providing flexibility to engineer complex interactions without typical coupling constraints. We demonstrate arbitrary inter-mode coupling through transmissive mode converters, allowing precise tuning of resonance splitting and intrinsic losses. This approach enables selective bright-dark mode pair generation and the exploration of novel photonic phenomena such as exceptional points. This multimode photonic molecule overcomes traditional limitations and offers new possibilities for integrated photonic circuits, optical processing, and studies in non-Hermitian and nonlinear photonics.

Figures (5)

• Figure 1: Conventional and multimode photonic molecules. (a) A conventional photonic molecule (PM) formed by two evanescently coupled rings. (b) A multimode single-ring photonic molecule that exploits multiple waveguide transverse modes and transmissive mode converters (TMCs). The schematic illustrates the coupling dynamics between the $\mathrm{TE_0}$ and $\mathrm{TE_1}$ modes within the multimode architecture.
• Figure 2: Properties of a multimode single-ring photonic molecule. (a) Artistic rendering of a corrugated multimode ring resonator, overlaid with a simulated supermode intensity profile (bus waveguide not shown). (b) Simulated power conversion efficiency $\eta$ versus wavelength and the grating period number $N_1$ of the $\mathrm{TE_0}$-$\mathrm{TE_1}$ TMC. Inset: schematic of an asymmetric-grating TMC segment. Device parameters: Ring waveguide width $W$ = 1100 nm, radius 80 $\mu$m, thickness 220 nm, corrugation depth $h_1$ = 20 nm, period $\Lambda$ = 6300 nm. (c) Measured normalized transmission (NT) spectrum of a multimode single-ring photonic molecule (yellow curve: fit using Eq. 2). The free spectral range is $\Delta \omega_\text{FSR} = 2\pi\times147.7$ GHz. Two hybridized modes are split by $2\text{Re}(\sigma) = 2\pi\times21.8$ GHz, with linewidths $\gamma_0 = 2\pi\times1.5$ GHz and $\gamma_1 = 2\pi\times2.3$ GHz, corresponding to loaded optical quality factors of $Q_0 = 6.5\times10^4$ and $Q_1 = 4.3\times10^4$. (d) Symmetric (S) and antisymmetric (AS) optical modes profiles, represented by $\mathrm{Re(H_z)}$. Arrows indicate propagation direction.
• Figure 3: Theoretical analysis of resonance frequency splitting behavior in a multimode single-ring photonic molecule. Calculated real part of the eigenvalue splitting (normalized to the free spectral range), $\pm\mathrm{Re}(\sigma)/ \Delta\omega_\text{FSR}$, as a function of various system parameters using the coupled-mode theory. (a) $\gamma_\text{diff}$ = 0. (b) $\omega_\text{diff}$ = 0. (c) $\eta$ = 0.5. (d) $\gamma_\text{diff}$ = 0 and $\eta$ = 0.05 (blue curve), 0.5 (purple curve), and 1 (red curve). (e) $\omega_\text{diff}$ = 0 and $\gamma_\text{diff}/\Delta\omega_\text{FSR}$ = 0 (red curve), 0.1 (blue curve), and 0.15 (purple curve). DP: diabolic point, AC: anti-crossing, EP: exceptional point. (f, g) Analytically calculated transmission spectra of the single-ring photonic molecule system obtained using the transfer matrix method. (f) $\eta$ = 0.1 and $\gamma_\text{diff}$ = 0. (g) $\gamma_\text{diff}/\Delta\omega_\text{FSR}$ = 0.1 and $\omega_\text{diff}$ = 0. The white dashed lines indicate fits derived from coupled-mode theory.
• Figure 4: Experimental demonstration of a multimode single-ring photonic molecule. (a) Optical microscope image of a fabricated single-ring multimode resonator. Insets show tilted scanning electron microscope images for the waveguide coupler (WC) and TMC. The device parameters are the same as in Fig. 2. (b,c) Simulated and experimentally measured normalized transmission spectrum at the bus waveguide output of a single-ring photonic molecule when varying $N_1$. The yellow circles highlight the positions of anti-crossing (AC) and diabolic point (DP). (d) Experimentally measured resonance frequency splitting normalized to the free spectral range ($\mathrm{2Re(\sigma)/\Delta\omega_\text{FSR}}$) as a function of the resonance frequency when varying $N_1$. (e,f) Measured real (blue dots) and imaginary (red dots) components of the eigenvalue splitting (e) and the corresponding intrinsic quality factors (f) of the single-ring photonic molecule system when $N_1$ = 9, as a function of the resonance frequency.
• Figure 5: Single-ring photonic trimer. (a) Schematic illustration of a single-ring photonic trimer and its mode coupling dynamics (insert), consisting of a ring resonator integrated with two TMCs for $\mathrm{TE_0}$-$\mathrm{TE_1}$ and $\mathrm{TE_0}$-$\mathrm{TE_2}$ mode interactions. (b) Simulated power conversion efficiency $\eta_{02}$ as a function of operating wavelength and the grating period number $N_2$ of the $\mathrm{TE_0}$-$\mathrm{TE_2}$ TMC. Inset: schematic of a segment of the $\mathrm{TE}_0$–$\mathrm{TE}_2$ TMC featuring symmetric gratings ($h_2$ = 15 nm, $\Lambda$ = 2250 nm). (c) Simulated transmission spectrum at the bus waveguide output, along with the intracavity power spectra of $\mathrm{TE}_0$, $\mathrm{TE}_1$, and $\mathrm{TE}_2$ modes when varying $N$, with the grating period numbers of the $\mathrm{TE_0}$–$\mathrm{TE_1}$ TMC and $\mathrm{TE_0}$–$\mathrm{TE_2}$ TMC set as $N_1 = N$ and $N_2 = 2N$, respectively.