Friedmann–Robertson–Walker transformational technique in paraxial wave optics

We introduce in optics a transformational technique inspired by the Friedmann–Robertson–Walker (FRW) cosmology. We found that the extended covariant scaling transformation used in the FRW theory can be applied to light wave phenomena under scalar paraxial approximation. Our method provides new ways to propagate light beams as well as novel guidelines for advanced optical structure design, as discussed in some application examples. In the first example we study Talbot imaging in different configurations comprising illumination with spherical beams or with Gaussian beams and propagation in homogeneous or inhomogeneous gradient-index media. In the second example we derive an exact analytical solution for the propagation of self-accelerating parabolic beams in parabolic gradient-index media. Finally, in the third example we show how the new insightful transformational method can be exploited to design lossless nonadiabatic waveguide tapers and adapters.