Research On Mechanism Of Spherical Optical Waveguide Coupling Based On Barrier Model

A variety of waveguide couplers,in the past few decades,have received significant attention for applications in various areas with the development of photonic circuits,optical communication,and optical fiber sensors.In order to futhur improve the calculation efficiency,the non linear effect in photonic circuits need to be enhanced.In optical fiber communication,there is a need that the central wavelength of the filter which is used to isolate the upload and download signal is tunable.In fiber sensors,a coupling structure is needed to convert the environmental variables to the light signal.The application of spherical couplers meets the demands mentioned above.A micro sphere optically induced transparency,generating different whispering gallery modes,is used to realize the tunning of the transmission spectrum using four waves mixing.A micro sphere resonator is used to realize the add/drop filting due to its high quality factor.A number of fiber sensors use spherical coupler as probe tip to convert the the environmental variables to the light signal.However,the coupling efficiency of a common incomplete spherical coupler is still quite low.It is hard to use it to translate a stable light signal in the applications mentioned above.A quite low coupling efficiency results an inaccurate tunning of the transmission sperctrum of the optically induced transparency,and an inaccurate tunning of the working wavelength of the add/drop filter,and a low signal to noise ratio of the fiber sensor.Therefore,there is a need improving the coupling efficiency of the spherical coupler effectively.To realize an accurate calculation of the coupling efficiency,and to improve the coupling efficiency,studies analyzing the light propagation inside the spherical coupler have been done.The main purposes and methods used in this study are summarized as followed.Mathematic models analyzing the light propagation in the spherical coupler are proposed to achieve an accurate calculation of the coupling efficiency.The input light is depicted as linear superposition of momentum eigenstates.To investigate the light propagation inside the spherical coupler,the most probability route model is proposed.The eigen-arclength and eigen-angle are proposed to calculate the pathway of the incident light.A barrier model is proposed to analyze the refraction and reflection of the input light at the boundary of the spherical coupler.With the proposed mathematic models mentioned above,for those spherical couplers with an arbitrary sphere diameter and an arbitrary interval between the sphere-center and the principal axis of the input fiber,a rather precise calculation of the coupling efficiency can be achieved.Based on the analyzation of the most probability route,a method optimizing the spherical coupler is proposed to reduce the light energy loss.The relation between the variables in the proposed mathematic models and the parameters of the coupler is analyzed.And then,the main reasons of the low coupling efficiency of common spherical couplers are studied.For common spherical couplers,a large proportion of the input light arrive the entrance port earlier than the output and returns back.Light has a rather high probability of refracting and then escaping at the boundary and that light reflects too many times inside the coupler.Optimizations modifying the sphere diameter and the interval between sphere center and the principal axis of input fiber are proposed.A polished sphere coupler with microstructures of micro-steps at the boundary of the coupler is proposed to increase the reflectance of the light.The effectiveness of the proposed mathematic modes and opimazations are verified through experiments.A Matlab GUI program is proposed to calculate the coupling efficiency of the spherical couplers.Calculation results are compared with the results from FDTD method to verify the effectiveness of the proposed mathematic modes.A micro-sphere polishing system is designed and assembled to fabricate the microstructures at the boundary of the sphere.Experiment results indicate the proposed mathematic model is effective predicting the coupling efficiency of the spherical coupler.Compared to the calculation results from FDTD method,results from the proposed mathematic models in this paper are closer to the experiment results.Experiment results indicate that,the coupling efficiency of the sample in experiments is effectively improved from 0.6% to 8.2% by optimizing sphere diameter.By optimizing the sphere-axis interval,the coupling efficiency of the sample in experiments is improved from 2.2% to 5.8%.When the radius of the spherical coupler is 127.2 ?m,the micro-structure on the boundary of the coupler improves the coupling efficiency from 8.2% to 45.6%.When the radius of the spherical coupler is 199.8 ?m,the micro-structure on the boundary of the coupler improves the coupling efficiency from 0.6% to 39.8%.