Highly nonparaxial propagation and optical power exchange in uniaxial crystals: Analytical and numerical study

We present an analytical solution to the nonparaxial propagation of a Gaussian beam, which is based on the asymptotic expansion of a highly oscillatory integral. The advantage of this method is its application to a highly nonparaxial beam and large transverse radius regime, which are hard to reach by previous approximations. The validity of this analytical expansion is fully investigated, by benchmarking it against the accurate numerical solutions. We extend this method to deduce the analytical expression for a nonparaxial optical field in uniaxial crystals, from which we reveal the vortex generation in each component of the optical field and discuss their evolution dynamics. Moreover, we study the optical power exchange between two circular components of a nonparaxial field. We find that the powers carried by both components undergo a saturation and become equal as the propagating distance increases