Generation of hollow Gaussian beams by spatial filtering

TLDR

The scheme is implemented with a 4f optical system or a Michelson interferometer, enabling generation of hollow and other polynomial Gaussian beams. Hollow Gaussian beams are produced by Fourier‑transforming Gaussian beam differentials and spatial filtering with binomial Hermite‑polynomial filters, and numerical simulations confirm the method’s validity and potential for nanophotonic applications.

Abstract

We demonstrate that hollow Gaussian beams can be obtained from Fourier transform of the differentials of a Gaussian beam, and thus they can be generated by spatial filtering in the Fourier domain with spatial filters that consist of binomial combinations of even-order Hermite polynomials. A typical 4f optical system and a Michelson interferometer type system are proposed to implement the proposed scheme. Numerical results have proved the validity and effectiveness of this method. Furthermore, other polynomial Gaussian beams can also be generated by using this scheme. This approach is simple and may find significant applications in generating the dark hollow beams for nanophotonic technology.