An analytical approximation is derived which provides a transcendental relationship for the spherically symmetric inhomogeneous index distribution which perfectly focuses infinite objects. Using this expression, the index profiles (called generalized Luneburg lenses) were calculated for lenses having <i>f</i> numbers down to <i>f</i>/1. It is shown through a ray-tracing example that these profiles have sufficient accuracy to provide diffraction-limited performance in the optical wavelength region. It is also shown how these lenses may be utilized in a two-dimensional integrated optics waveguide. Utilizing the focusing property achieved by variations in planar waveguide thickness, circularly symmetric waveguide thickness profiles are derived which have the perfect focusing properties of the generalized Luneburg lenses.
© 1977 Optical Society of America
W. H. Southwell, "Index profiles for generalized Luneburg lenses and their use in planar optical waveguides," J. Opt. Soc. Am. 67, 1010-1014 (1977)