Inverse problem of laser light scattering in an integrated optical waveguide: 2D solution with accurate input data

A linear inverse problem of light scattering in an integrated optical waveguide with 2D statistical irregularities is analyzed with the use of accurate input data (at a high signal-to-noise ratio). Using the natural physical and mathematical limitations imposed on the measured scattering pattern, a correct solution to the inverse problem of waveguide scattering is derived. The uniqueness of the solution to the inverse problem is based on the properties of analytic functions. The stability of the solution to small variations in the input data is related to the narrowing of the possible class of solutions by a certain compact set. The estimates of the solution to the inverse problem in the class of integer functions are inferred: the estimate of the minimum error achievable in the approximation of the original infinitely extended spectral density function using finitely extended functions, the estimate of accuracy for the case of inaccurate data setting in the scattering pattern (only the first N coefficients of the Taylor series are known for the spectral density function of irregularities), the estimate of the effect of inaccuracy in the measurement (setting) of the scattering pattern on the error in the solution to the inverse problem, and the estimate of the maximum allowed rms deviation of irregularities from the mean value (in particular, the rms height of irregularities of the waveguide interfaces relative to a plane). A model of irregularities inferred from the solution to the inverse problem in the class of integer functions is described.