Theoretical Study Of Temporal Bloch Oscillation In Coupled Microring Resonator Array

The microring resonator has many characteristics such as spectral selectivity,enhanced resonant optical power,and enhanced light-substance interaction.Compared with a single microring resonator,the array system composed of multiple microring cavities enriches applications in the frequency and time domains,and its design flexibility is greatly improved.It has been applied to optical filtering,modulation,and wavelength division,multiplexing and demultiplexing.In recent years,there have been studies on the realization of dynamic control of the microring resonator system through small refractive index modulation,but there are few cases about geometric modulation to realize the control of the microring resonator system.This paper mainly uses time-domain coupledmode equations and quantum mechanics methods to study the dynamic behavior of light waves in a microring resonator system with linear change of geometric height(gradient potential).First,starting from the single band model,the dispersion relation and group velocity of the microring resonator array are derived without applying gradient potential,and then the time domain coupling equation is used to study the influence on the light evolution when the geometric height of the microring resonator changes linearly.The study found that a height of linear change will produce a constant frequency difference between adjacent resonators,localize the eigenmodes of the system,and produce Bloch oscillations.When the initial excitation conditions are different,the oscillation modes are different,and when the resonator-to-resonator coupling parameters change,the amplitude of the Bloch oscillation will be modulated.Then we extended the single-band model to the dual-band model.We designed two microring resonator systems,one is the AB compound microring resonator array structure,and the other is the periodic coupling type microring resonator array structure.The dispersion relationship of these two systems is deduced without applying the gradient potential,and then the evolution properties of light waves with linear changes in geometric height are studied by quantum mechanics method.The study found that in this dual-band model,Bloch-Zener Oscillations(Bloch-Zener Oscillations)can be obtained due to the interaction of Bloch oscillations and Zener tunneling.By controlling the frequencies of the two microring cavities Difference and coupling parameters can realize the conversion of light waves between two energy bands.Finally,the Parity-Time-symmetry(PT symmetry)optical potential is introduced into the microring resonator array,and the dispersion relationship of the PT symmetry microring resonator array when the gradient potential is not applied is deduced.Then,the dynamic behavior of the geometrical height linear change optical wave is studied by the quantum mechanics method.The study found that the gain-loss parameter will have a certain influence on Bloch oscillation.