A design of waveguide collimating lenses in the presence of anisotropic aberrations

Anisotropic aberration correction is discussed on the basis of the extraordinary-ray ray-tracing method. Two closed analytical forms of anisotropic-aberration-free profiles are derived. The two profiles are referred to as pseudoelliptic and pseudohyperbolic, and a comparison is made between the two surfaces. The latter profiles are aberration-free in an isotropic medium. A design limit in the aperture angle is investigated. The relationship between the aperture and the energy reflection coefficient is investigated using the Fresnel formula. The pseudo-hyperbolic surface has a lower energy reflection coefficient in focusing and the pseudo-elliptic surface has a lower energy reflection coefficient in collimating