Diffraction of a finite-cross-section light beam by the grating: Theoretical analysis and experimental verification

We propose a method for analyzing the diffraction of beams with finite cross-section by a waveguide grating. In this method a beam is expanded into a series of plane waves utilizing the Fourier transform. For each plane wave the amplitude reflectance and transmittance coefficients were determined by RCWA. The field distribution of the reflected and transmitted beams was found through the inverse discrete Fourier transform. The numerical studies of the diffraction of the beams described by one-dimensional Gaussian and rect(x) functions were performed. It is established that at waveguide resonance the widths of the reflected and transmitted beams are much larger than the width of the incident beam. It is also shown that, in the case of diffraction of finite-cross-section beams, the bandwidth s of spectral and angular resonance curves exceed the values obtained in the case of an incident plane wave. The measurements of the reflected beam characteristics for a specialy fabricated resonant waveguide grating were performed in order to verify the method applicability.