A hybrid analysis method for planar lens-like structures

Planar lens structures such a Rotman lens, micro-lens and star coupler are currently used or have been proposed for various signal splitting applications in microwave/millimeter waves and guided-wave opto-electronics. The general topology of a planar lens junction is shown. The transmission characteristics of the structure can be analyzed by asymptotic techniques. The hybrid approach presented is based upon a combination of a numerical propagator like the beam propagation method (BPM) for determining the fields over the input surface, due to incoming waves from the left and physical optics for wave transmission through the lens medium. The modal amplitudes in the output waveguides are then determined by an overlap integral based on reciprocity. The method is accurate and very efficient, and therefore is particularly suitable for the design and optimization of large planar junctions. Although it can be applied to a general 3D structure, to simplify the presentation, the analytical development and numerical results for a 2D case are discussed.