Generation of second-harmonic Ince-Gaussian beams

Abstract

As a continuous transition between the Hermite-Gaussian and Laguerre-Gaussian beams, the Ince-Gaussian beams form a family of exact orthogonal solutions of the free-space paraxial wave equation in elliptic coordinates. Ince-Gaussian beams have multiple transverse mode patterns, which make them unique in terms of application in the fields of bioengineering, particle manipulation, and quantum entanglement. Here, based on binary nonlinear computer-generated holograms with a domain structure (realized via electric field poling at room temperature), we generate a second-harmonic Ince-Gaussian beam pumped with a fundamental Gaussian beam. In this process, the transverse part of the phase-matching condition is satisfied, which is called the Raman–Nath-type nonlinear diffraction. Both frequency conversion and beam shaping can be realized simultaneously, thereby offering the advantage of integration of both functions into a single device.