Analysis of the accuracy of the inverse problem solution for a differential heterodyne microscope as applied to rectangular plasmonic waveguides

The existence, uniqueness, and stability of the inverse problem solution for a scanning differential heterodyne microscope as applied to rectangular plasmonic waveguides have been analyzed. The consideration is based on an algorithm using a trial-and-error method that we proposed previously to characterize plasmonic waveguides with a triangular profile. The error of the inverse problem (IP) solution is calculated as dependent on the initial data and with allowance for their errors. Instability domains are found for the IP solution, where the solution error sharply increases. It is shown that the instability domains can be eliminated and the accuracy of the IP solution can be significantly improved in the entire range of initial data by taking initial data in the form of two phase responses of the microscope at different wavelengths.