• Opto-Electronic Engineering
  • Vol. 44, Issue 7, 747 (2017)
Xiaoting Wang1, Ruiqiang Chen1, Shundi Hu1, Peng Zhao1, Luhong Wen1, and Xiang Wu2
Author Affiliations
  • 1The Research Institute of Advanced Technologies, Ningbo University, Ningbo 315211, China
  • 2Center Key Lab for Micro and Nanophotonic Structures (Ministry of Education), Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China
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    DOI: Cite this Article
    Xiaoting Wang, Ruiqiang Chen, Shundi Hu, Peng Zhao, Luhong Wen, Xiang Wu. Optical microcavity transmission spectrum fitting algorithm based on the implicit function model[J]. Opto-Electronic Engineering, 2017, 44(7): 747 Copy Citation Text show less

    Abstract

    Due to its high quality factor and high sensitivity, the optical microcavity has well promising applications in opti-cal sensing, biomedical, nonlinear optics, environmental monitoring and quantum physics. The principle is that when analyses enter the optical microcavity, the effective refractive index of the solution will change, and the res-onant wavelength will be shifted. Therefore, it is very important to find out the variation of resonant wavelength to improve the sensing accuracy of the optical microcavity. A traditional method to do this is using the Lorentz algo-rithm to fit the transmission spectrum of the optical microcavity. However, the Lorentz fitting algorithm cannot well fit the spectrum when it is an asymmetric waveform or there is a splitting mode waveform within the optical microcavity. In order to deal with the problem, the implicit function model algorithm is proposed in this study. The process of our method can be described as follows. The template waveform was selected and established first, followed by the panning and zooming operations. Then, a traditional method was used to set the initial value of the parameter of objective function, and the parameter values were optimized by the Levenberg-Marquardt (LM) algorithm, which could achieve data fitting results of symmetrical waveform, asymmetric waveform and splitting mode waveform. Note that there was no definite mathematical expression according to the implicit function model algorithm, so different methods were used to obtain the partial derivative of the factor in the Jacobian matrix by means of the template data. In this study, experimental platform, including the optical microcavity, tunable laser source and controller, data acquisition and control system, was established. Different concentrations of solutions of dimethyl sulfoxide, glucose and glycerol were tested as the analyte, and the Gauss, the Lorentz and the implicit function model algorithm were used to fit the experimental data of different transmission spectrums. The results show that MSE of the implicit function model algorithm is one order of magnitude lower than other two algorithms, and the coefficient of determination (R2) is 0.99. The resonant frequency error of implicit function model algo-rithm is the smallest, the resonant frequency of implicit function model algorithm is the largest, and the sensitivi-ty of implicit function model algorithm is the highest. Therefore, the fitting effect of the implicit function model algorithm is better and it can efficiently improve the sensitivity of the optical microcavity and has a reliable basis on the follow-up to find the spectral resonance center to detect the biological components. The digital implicit function model algorithm will have a wide application prospect in any shape waveform data fitting.
    Xiaoting Wang, Ruiqiang Chen, Shundi Hu, Peng Zhao, Luhong Wen, Xiang Wu. Optical microcavity transmission spectrum fitting algorithm based on the implicit function model[J]. Opto-Electronic Engineering, 2017, 44(7): 747
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