Fig. 1. Schematic diagram of a Reuleaux-triangle resonator with the corner-cut (a) 3D model; (b) plane view of the 2D model. The solid arc indicates the geometry boundary of the microcavity and the corner-cut, and the blue strip indicates the attached waveguide.

Fig. 2. The TE polarized modes of the compared results in a complex dimensionless frequency plane. (a) Traditional circular resonator. (b)–(d) Corresponding to the RTR with p = 0.98, 0.97, and 0.94, respectively. High Q factor optical modes in RTRs are shown as red dots. ΔKR is the spacing between two adjacent resonance wavelengths. The intensity pattern |H_z|² of (e) base mode in the circular resonator. (f)–(h) Resonator modes in b = 120 µm with p = 0.97 and p = 0.94.

Fig. 3. (a) The phase space in PSOS of the RTR with b = 120 µm and p = 0.97. The horizontal pink line at sin χ = 1/n₁ (n₁ = 1.575) is the criteria for TIR. (b) and (c) Real-space representation of the period-3 orbit and chaotic trajectory in the green and blue lines, respectively. (d) A magnification on the top of the PSOS in (a). (e) The schematic diagram of the light ray orbit (red line) in the period-9 stable islands shown in (d).

Fig. 4. (a) Husimi map H1inc(em) of the resonance mode in Fig. 2(f). The period-9 island for TE polarization distributes both in the phase space of sin χ > 0 (CCW) and sin χ < 0 (CW). KR = 252.71 + 0.008i. (b) Husimi map H0(em) of the resonance mode in Fig. 2(f).

Fig. 5. (a) The wave function TE polarized |ψ|² with a coupling waveguide. The white arrow represents the rotation angle ϕ of the coupling position. (b) Typical transmission spectrum of the coupling system. The FSR is about 4.12 nm. (c) The transmission varies with rotation angle ϕ. Inset: Field distributions of two secondary maximum transmissions. (d) The relationship between the transmission and coupling gap g specified in Fig. 1.

Fig. 6. (a) Definition of the x–y rectangular coordinate direction in RTR. (b)–(d) The x–y plane wave vectors defined on the three corner-cuts of the RTR, and α is the incident angle. (e) The contrast results of simulation and theoretical FSR. Inset: The box-plot of the error rate with FSRs.

Fig. 7. (a) Fabrication process of the RTR using the UV lithography system and FR4 substrates. (b) The SEM top view of the fabricated device. (c) Amplified SEM images of sidewall of the corner-cuts. (d) Coupling region of RTR.

Fig. 8. (a) Experimental setup for the transmission spectra and coupling efficiency characterization of the RTR. Inset: The coupling end face of the lensed fiber and waveguide. TSL, tunable semiconductor laser; OSC, oscilloscope; PC, polarization controller; PD, photodetector. (b) and (c) Cross-section distributions of TM₀ and TE₀ modes in EpoCore waveguides.

Fig. 9. (a) Experimentally measured normalized transmission spectra. Different numbers of angular modes under TE polarization are calculated through Eq. (3). (b) The magnified view of the resonant mode TE_1,331 with the Lorentz fitting gives a Q factor of about 1.1 × 10⁴. (c) Experimental dependence of the coupling efficiency and Q factor as the functions of the designed coupling gap.