Effects of anisotropy in a nonlinear crystal for squeezed vacuum generation

TL;DR

This paper investigates how optical anisotropy affects squeezed vacuum generation in nonlinear crystals and proposes a method using multiple crystals to compensate for anisotropy, resulting in symmetric two-photon amplitudes.

Contribution

The study introduces a novel approach of using consecutive crystals to reduce anisotropy-induced distortions in squeezed vacuum generation.

Findings

Transverse walk-off significantly influences the spatial spectrum of generated radiation.

Using multiple crystals can effectively compensate anisotropy effects.

Compensation leads to symmetric two-photon amplitudes suitable for Schmidt expansion.

Abstract

Squeezed vacuum (SV) can be obtained by an optical parametric amplifier (OPA) with the quantum vacuum state at the input. We are interested in a degenerate type-I OPA based on parametric down-conversion (PDC) where due to phase matching requirements, an extraordinary polarized pump must impinge onto a birefringent crystal with a large \chi(2) nonlinearity. As a consequence of the optical anisotropy of the medium, the direction of propagation of the pump wavevector does not coincide with the direction of propagation of its energy, an effect known as transverse walk-off. For certain pump sizes and crystal lengths, the transverse walk-off has a strong influence on the spatial spectrum of the generated radiation, which in turn affects the outcome of any experiment in which this radiation is employed. In this work we propose a method that reduces the distortions of the two-photon amplitude (TPA) of the states considered, by using at least two consecutive crystals instead of one. We show that after anisotropy compensation the TPA becomes symmetric, allowing for a simple Schmidt expansion, a procedure that in practice requires states that come from experimental systems free of anisotropy effects.