Regulation Method of Fano Resonance Effect Based on Deep Learning in Micro-ring Resonators
To precisely control the transmission spectra of micro-ring resonators,a design incorporating arrays of etched air holes was introduced into the micro-ring resonator and coupled waveguide system.Modeling was completed using deep learning algorithms and inverse design techniques to predict the forward transmission spectra and optimize the performance of Fano resonance spectrum through inverse design.Based on the inverse design results,the slope of the transmission spectra was nearly doubled after 12 iterations of enhancement.For the preparation of the dataset,a system consisting of a single micro-ring resonator coupled with a straight waveguide was investigated.Six rows by six columns of air holes,each with a diameter of 100 nm,were introduced at both ends.Light enters the micro-ring resonator from the left design area and passes through to the right design area.The etched air hole arrays in these areas affect the propagation of light.Based on this micro-ring waveguide system,5 000 samples were obtained using Finite-Difference Time-Domain(FDTD)simulations.These samples included the distribution of air hole arrays at both ends of the coupled waveguide and the corresponding micro-ring transmission spectra data.Utilizing the deep learning multi-layer perceptron algorithm,modeling was performed with the structure of the air hole arrays as input and the transmission spectra as output.This successfully enabled the prediction of micro-ring transmission output spectra within 24 ms for different air hole etchings.The cosine similarity values between the predicted spectra and traditional simulation spectra were close to 1.0.Next,an asymmetry index was defined and combined with the number of resonance peaks to distinguish between Fano and non-Fano line shapes in the dataset.To establish an inverse design model,the slope was defined as a performance indicator for the Fano resonance line shape in micro-ring resonators,representing the degree of tilt of the Fano line shape.This indicator was then used to control the Fano line shape.By employing a convolutional neural network,the transmission spectra and performance indicators were used as inputs,with the corresponding air hole etching arrays as outputs.This approach enabled the prediction of air hole etching structures that produce Fano line shapes.The etching probabilities of the air holes were displayed in the form of 6×6 grayscale images.Here,a value close to zero indicates that the air holes are not etched,while a value of 1 indicates that they are etched.The predicted structures were validated using FDTD simulations,and the results were very similar.Starting with structures predicted by inverse design,traditional optimization algorithms were integrated to enhance the slope.As the consistency between the design areas on the left and right sides increased,this change results a significant enhancement in the slope.Specifically,the slope of the Fano line shape increased from 0.08 in the first iteration to 0.14 in the twelfth iteration.Finally,with the slope of the Fano line shape serving as an indicator,the impact of the air hole distribution in the design areas on both sides of the coupled waveguide was discussed.The correlation between the slope and the x coordinates of the centroids on both sides was not significant,indicating that horizontal movement of the centroids has little effect on the slope.However,a negative correlation was observed between the slope and the y coordinates of the centroids on both sides.As the centroids moved upward,the slope is increased.In summary,based on deep learning predictions controlling the air hole etching arrays in designated areas,this approach provides a new perspective and method for analyzing the coupling mechanisms of micro-cavities with waveguides and for controlling Fano resonance.
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