Research On Mode Characteristics Of Magneto-optical Micro-ring Resonator Under Voigt Configuration

Owing to the small mode volume and high quality factor,optical whisperinggallery-mode micro-resonators have gained various research in modern photonics such as cavity quantum electrodynamics(QED),lasers,sensors as well as nonlinear optics.With the development of the optical integration in recent years,whispering-gallerymode resonators gradually show potential advantages in on-chip photonic devices because of small footprints and good flexibility.Meanwhile,the magneto-optic effect,as a method of optical modulation,is widely used in the research of silicon integrated optical devices.Especially,the first-order magneto-optic effect such as Faraday effect or nonreciprocal phase shift(NRPS)is the physical basis of many nonreciprocal optical devices.In recent years,the interdisciplinary research of combing microcavity with magneto-optic effect has gradually emerged both in theoretical research and practical research.The theoretical researches are mostly about the physical mechanism of the magneto-optical coupling and the practical researches mainly focus on the applications of silicon-based magneto-optical micro-ring resonator nonreciprocal devices.However,there are no further research and analysis on the mode characteristics of the micro-ring resonator under the Voigt magnetic field configuration.This paper innovatively proposes a magneto-optical micro-ring resonator model under Voigt configuration and the finite element method is used to research the mode characteristics in this proposed resonator.Firstly,according to the dielectric constant tensor theory,we derive the weak form finite element equation from the Maxwell equation which can describe the whispering gallery modes under the external magnetic field.Then,we can solve the weak form equation using the weak solution partial differential equation module in the COMSOL Multiphysics software respectively under radial and vertical magnetic field.According to the results of the dispersion curves,mode polarization states and energy distribution,we can find the eigenmodes in the resonator will experience a polarization mode coupling when the coupling condition is satisfied.The coupling phenomenon is obviously nonreciprocal because it only exists in one light propagation direction and depends on the direction of light propagation and magnetic field.This coupling brings the changes of the linearly polarized light's orientation and the energy exchange between resonant modes.Finally,we apply the theoretical analysis results of the micro-ring resonator under the Voigt configuration into the design of practical optical devices.Based on the polarization mode conversion caused by the mode coupling in the resonator model under the radial magnetic field,a silicon-based polarization modulator has been shown.This modulator can control the polarization angle of output light by adjusting the intensity of the external magnetic field.On the other hand,on the platform of the microring resonator with specific geometry under the vertical magnetic field,an optical isolator is designed based on the phenomenon that during the coupling region,the resonant modes in the forward and backward light propagation directions have the same resonant frequency but mutually perpendicular polarization directions.This paper analyzes the mode characteristics of the magneto-optical micro-ring resonator under Voigt configuration.It not only enriches the mode coupling theory of magneto-optical micro resonators,but also provides new ideas for the design and application of integrated optical devices.