Kerr optical frequency combs based on whispering-gallery mode (WGM) microresonators have great potential for applications in various fields, such as precision measurement, spectral analysis, optical communication, and quantum technology. The interaction between dispersion and nonlinearity is crucial for determining the stability and bandwidth performance of optical frequency combs. In particular, the Kerr bright soliton optical frequency comb requires a suitable anomalous group velocity dispersion (GVD) to maintain the dissipative system. Therefore, designing the dispersion of the WGM microresonator is essential for generating the Kerr optical frequency comb. However, WGM microresonators typically have normal and fixed material dispersion, and their dispersion design is mainly based on modulating the mode field distribution by changing the microresonator structure to achieve anomalous dispersion, which limits their flexibility. In this paper, we introduce a radially distributed gradient refractive index n(r) into WGM microresonators and propose to use the refractive index profile for controlling the dispersion of gradient-index (GRIN) microresonators. Numerical simulations and finite element analysis demonstrate that the refractive index gradient constrains the mode field and pushes it away from the cavity edge, resulting in near-zero geometric dispersion in the GRIN microresonator. Two dispersion modulation methods are explored: modifying the microresonator’s geometric shape and constructing a dual potential well. The effects of microresonator radius, wedge angle, ion diffusion sequence, and potential well width and spacing on dispersion are systematically investigated. Simulation results show that both methods can achieve a wide range of anomalous dispersion within the communication band. In the first method, mode field leakage in the bilateral wedge-shaped GRIN microresonator produces anomalous dispersion, while no leakage results in normal dispersion. When the mode field is pushed away from the edge, near-zero dispersion is achieved. In the second method, energy coupling between the inner mode and the outer mode in the dual potential well structure leads to anomalous dispersion in the inner mode and normal dispersion in the outer mode. Our findings highlight the flexibility of GRIN microresonator dispersion control and indicate great potential for nonlinear optical applications.
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