The Angular Spectrum Representation of Electromagnetic Fields in Crystals. I. Uniaxial Crystals

The electromagnetic field in a linear, nonmagnetic nonabsorbing biaxial crystal which fills the entire half‐space z ≥ 0 and which has one of its principal dielectric axes perpendicular to the plane z = 0 is represented as an angular spectrum of plane waves. The angular spectrum representation consists of a superposition of plane waves expressed as the sum of two integrals. Each integral contains in general both homogeneous and evanescent plane waves. Each plane wave of the angular spectrum (whether homogeneous or evanescent) satisfies the identical equations which are obeyed by the entire field. The spectral amplitudes of the field are explicitly expressed in terms of the Fourier transform of the field in the plane z = 0. The special case of a uniaxial crystal whose optic axis is parallel to the plane z = 0 is treated in some detail. The far zone structure of the field in such a crystal is determined using the method of stationary phase. The field in the far zone is expressed explicitly in terms of the Fourier transform of the field in the plane z = 0.