Aberrations in lenslike antiguides for semiconductor lasers

A lenslike diverging medium is potentially useful in semiconductor lasers (1-6). A laser of this type was previously fabricated and tested(1). The performance was substantially better than a comparable laser without a lenslike region, although refinements of the design were needed to obtain an output beam that was essentially diffraction limited. For this type of laser, the structure of the wafer is designed so that the effective refractive index depends on x, the lateral distance from the center of the wafer. The shape of the wavefronts of the mode depends on the functional form of the index of refraction. In principle, the index can be tailored so that the wavefronts will be cylindrical. In practice, this profile will not be achieved perfectly, and it is important to be able to calculate the aberrations that are introduced. It is also useful to calculate the index profile that would result in ideal cylindrical wavefronts. Equations are derived for the mode wavefronts given the index profile and for the index profile that will result in a given wavefront, and examples are discussed.