Rigorous solutions without paraxial approximation for Gaussian beams in planar optical waveguides

Abstract Rigorous and analytical solutions without paraxial approximation for Gaussian beams in planar optical waveguides have been derived by the combined imaginary-shifted-wave method, based on the cylindrical wave solutions in optical waveguides. The two-dimensional Gaussian beam solutions including higher-order modes were obtained. Analytical solutions are useful for understanding the beam characteristics.