Fig. 1. Schematic of the on-chip bidirectional multi-dimensional (de)multiplexer employing PBMRA. Illustrations depict the operation principles of (a) the bidirectional micro-ring resonator array and (b) the single-level mode conversion facilitated by the photonic crystal.

Fig. 2. Scanning electron microscopy (SEM) images showcasing the fabricated multi-dimensional (de)multiplexer utilizing the PBMRAs. (a) Top view of the bidirectional micro-ring resonator (BMRR). (b) Top view of the inverse photonic-like crystal (IPC). (In the “l th” and “rth,” “l” denotes light waves received from the left drop port and “r” indicates transmission from the right drop port.)

Fig. 3. (a) Simulated intensity maps showing wavelengths of 1545.5 nm, 1550.0 nm, and 1554.5 nm decoupled from the left and right output ports of the BMRA, respectively. (b) Intensity distributions illustrating the mode conversion for TE0, TE1, and TE2 in the IPC TE mode (de)multiplexer.

Fig. 4. (a) Experiment transmittance measurements of wavelengths 1545.5 nm, 1550.0 nm, and 1554.5 nm decoupled from the left and right drop ports of the BMRA, respectively. (b) Experiment transmittance measurements of TE0, TE1, and TE2 modes in the IPC TE mode (de)multiplexer.

Fig. 5. Experiment measurements of the coupling efficiency within the PBMRA. (l/r: input or output the light from the left/right drop port of the bidirectional micro-ring resonator.)

Fig. 6. (a) BER curves of the signal transmitted across nine multi-dimensional channels from the left end to the right end. (b) BER curves of the signal transmitted across nine multi-dimensional channels from the right end to the left end. (λ1,1545.5  nm; λ2,1550.0  nm; λ3,1554.5  nm). (c) Constellation of the signal transmitted across the multi-dimensional channels. (L/R: input or output the light from the left/right drop port of the bidirectional micro-ring resonator.)

Fig. 7. (a) Schematic of the simplex mode and wavelength channel (de)multiplexing communication system. (b) BER curves of the signal transmitted for 18 multi-dimensional channels supporting (b1) TE0, (b2) TE1, and (b3) TE2 modes, respectively. (λ1,1545.5  nm; λ2,1550.0  nm; λ3,1554.5  nm; L/R, decouple the signal from the left/right ports.)

Fig. 8. Direct binary search (DBS) algorithm for the inverse-designed photonic crystal. (a) Pixelated representation of the photonic crystal region. (b) Optimization flow chart for the inverse-designed photonic crystal.

Fig. 9. Effective refractive index of three distinct TE modes (TE0 to TE2) across the wavelength range of 1540 nm to 1570 nm, corresponding to various waveguide widths.

Fig. 10. Flow chart for the fabrication of the silicon-based waveguide device.

Fig. 11. Illustration of the crossing waveguide. (a) Simulated intensity maps representing the horizontal and vertical transmission directions. (b) Scanning electron microscopy (SEM) image displaying the fabricated crossing waveguide.

Fig. 12. SEM images and simulated intensity maps of bent waveguides with radii of (a) 1.4 μm and (b) 2.9 μm.

Fig. 13. (a) Simulated transmittance spectra of wavelengths 1545.5 nm, 1550.0 nm, and 1554.5 nm decoupled from the left and right drop ports of the BMRA, respectively. (b) Simulated transmittance spectra of TE0, TE1, and TE2 modes in the IPC TE mode (de)multiplexer.

Fig. 14. Structural parameter deviation of the IPC TE mode multiplexer. (a) Demonstration of the mode multiplexer with varying diameters. (b) Transmission spectra of the mode multiplexers with varying diameters. (c) Demonstration of the mode multiplexer with air pillar distortion. (d) Transmission spectra of the mode multiplexer with different aberration degrees.

Fig. 15. Communication experimental system based on PBMRA. WDM, (de)wavelength division multiplexer; PC, polarization controller; AWG, arbitrary waveform generator; IM, intensity modulator; EDFA, erbium-doped fiber amplifier; BS, beam splitter; VFCA, vertical fiber coupling array; VOA, variable optical attenuator; PD, photo-detector; Osc., oscilloscope; DSP, digital signal processor.