String method for efficient design of metasurface-based optical systems

We present an efficient method for calculating the phase profiles of imaging and nonimaging optical systems composed of one or more cascaded metasurfaces, such as metalenses and concentrating metasurfaces. This method is a generalization of the string method from nonimaging optics, where strings of equal length represent optical paths, and metasurfaces contribute with phase shifts along these paths. We demonstrate the method by deriving phase profiles for various metasurface-based optical configurations, specifically metaconcentrators and metalens systems. The deduced phase profiles are validated through ray-tracing simulations. These analytical phase profiles provide an excellent starting point for further optimization and the realization of robust final designs.