<title>Amplitude matching concept for design of wave-transforming systems</title>

Abstract

Most optical systems may be understood as wave-transforming systems. One input wave is transformed into a corresponding output wave. The quality of the system is evaluated by merit functions applied to the output wave. In monofunctional or multifunctional design methods free parameters of the optical system are optimized with respect to one or more pairs of input waves and merit functions, respectively. Laser beam shaping may be understood as the transformation of waves originated by laser sources. In this paper we present a strategy for the systematic design of systems to realize monofunctional wave transformations. By this method we obtain not only a suitable phase-only transmission, which must be realized by a suitable element or module, but also their position, the number of transmissions/elements necessary to maximize the conversion efficiency of the system, and the upper limit of the conversion efficiency for a specific number of introduced transmissions/elements. We call this strategy amplitude matching. It is based on an inverse design approach. The input field is propagated forward and a desired output field is propagated backward. The system is designed with the goal to find a plane in which the magnitudes of both fields match perfectly. If required more than one element are introduced in the optical system by synthesis of phase-only transmission functions.