Abstract

Nonlinear beam shaping refers to spatial reconfiguration of a light beam at a new frequency, which can be achieved by using nonlinear photonic crystals (NPCs). Direct nonlinear beam shaping has been achieved to convert second-harmonic waves into focusing spots, vortex beams, and diffraction-free beams. However, previous nonlinear beam shaping configurations in one-dimensional and two-dimensional (2D) NPCs generally suffer from low efficiency because of unfulfilled phase-matching condition. Here, we present efficient generations of second-harmonic vortex and Hermite-Gaussian beams in the recently-developed three-dimensional (3D) lithium niobate NPCs fabricated by using a femtosecond-laser-engineering technique. Since 3D χ(2) modulations can be designed to simultaneously fulfill the requirements of nonlinear wave-front shaping and quasi-phase-matching, the conversion efficiency is enhanced up to two orders of magnitude in a tens-of-microns-long 3D NPC in comparison to the 2D case. Efficient nonlinear beam shaping paves a way for its applications in optical communication, super-resolution imaging, high-dimensional entangled source, etc.

Highlights

  • Nonlinear beam shaping refers to spatial reconfiguration of a light beam at a new frequency, which can be achieved by using nonlinear photonic crystals (NPCs)

  • We have experimentally demonstrated efficient SH beam shaping in 3D NPCs fabricated by using a femtosecond laser to selectively erase χ(2) inside a LiNbO3 crystal

  • Considering the binary-amplitude modulated χ(2), the 3D NPC structure is theoretically designed according to the computer-generatedhologram method

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Summary

Introduction

Nonlinear beam shaping refers to spatial reconfiguration of a light beam at a new frequency, which can be achieved by using nonlinear photonic crystals (NPCs). The general scheme is to input a fundamental light beam along the z-axis of a LiNbO3 NPC and utilize the 2D binary phase modulation of a second-harmonic (SH) wavefront in the x–y plane (Fig. 1a) This configuration has been applied to generate SH vortex beam, nonlinear superfocusing spot, SH non-diffracting beam, etc[27,28,29,32,33,34]. The recent breakthrough in three-dimensional (3D) NPC fabrication techniques[35,36,37] provides an excellent new platform for achieving efficient nonlinear beam shaping Such 3D NPCs with full 3D modulations of χ(2) are capable to simultaneously shape nonlinear beam profiles and fulfill the needed QPM condition at the same time. The conversion efficiency of nonlinear beam shaping in a tens-of-microns-long 3D

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