One- and two-dimensional ring array formed by birefringence in tandem with conical refraction: theoretical analysis

This study proposes a method to create a ring array using birefringence (BR) and conical refraction (CR), where a circularly polarized beam is first divided into 2^m sub-beams in m BR crystals and then transformed into 2^m CR rings in a CR crystal. To validate the method, the propagation of a circularly polarized Gaussian beam in a sequence of two BR YVO₄ crystals and a CR KGW crystal is simulated. The results show a parallelogram spatial structure formed by four sub-beams behind the BR crystals and four CR rings behind the CR crystal. By adjusting the relative orientation of two BR crystals and rotating a half-wave plate between them, either a linear or rectangular CR ring array can be formed. This method is applicable for particle trapping, space communication, and annular pumped solid-state lasers.