Accurate Modeling Of Micro-ring Resonator

Due to their superior selectivity, compactness, and possibility of dense integration, micro-ring resonators are attractive add-drop filter elements for applications in photonic chips related to optical networks and all-optical signal processing. Rigirous and accurate modelling of micro-ring resonator is of utmost important for the optimum design of the device.Generally, micro-ring resonator is analyzed by model which is characterized by some parameters (such as coupling coefficients of bend-straight coupler, bending loss of bend waveguide etc.). The objective of this work is to present a systematic approach to compute these free parameters for given resonator configurations. The eignmodes of bend and straight waveguide are modelled by full vectorial mode matching method, and the scattering matrices of bend-straight waveguide are computed by coupled mode theory, and finally the spectrum of micro-ring resonator is computed. The main contents are as follows:(1) The operation principle of micro-ring resonator as well as the comparison to FP filter is presented. The "standard model" of micro-ring resonator is discussed in a qualitative way. The device is functionally represented in terms of two bent-straight waveguide couplers with appropriate connections using bent and straight waveguides.(2) The fundamental theory of full vectorial mode matching method is presented, and the eigenmodes of bent rib waveguide, bent strip waveguide, straight strip waveguide and straight step waveguide are computed. Comparison of the strip waveguide with radius of 12μm and 50μm indicate that the phenomena of TE-TM coupling occurring on the side wall will become significantly strong when the bending radius is decreased, and this is the reason why the modes in the bend waveguide with small radius are hybrid mode instead of TE mode or TM mode in traditional sense.(3) A model of bent-straight waveguide couplers using a frequency domain spatial coupled mode formalism, derived by means of Lorentz reciprocity theorem. The resulting scattering matrices describe the transfer characteristics of bend-straight waveguide coupler. Simulation results for the scattering matrices for different horizontal separation distances and different wavelengths are presented. (4) The "standard model" of micro-ring resonator is formulated, and the spectral responses of the device are computed using fast spectrum evaluation method.(5) The response of micro-ring resonator is strongly polarization dependent and the resonance wavelengths are different for TE mode and TM mode. Such property allows for the design of wavelength-sensitive integrated polarization splitter. The influence of geometrical parameters and wavelengths on splitting ratio is investigated.