Compact representation of the spatial modes of a phase-sensitive image amplifier

Area of Science:

• Nonlinear Optics
• Quantum Optics
• Laser Physics

Background:

• Optical parametric amplifiers (OPAs) are crucial for generating entangled photons and manipulating light properties.
• Understanding the spatial eigenmodes of OPAs is essential for optimizing their performance in various applications.
• Previous studies often involved complex numerical methods for eigenmode computation.

Purpose of the Study:

• To develop a simplified representation for the spatial eigenmodes of a spatially-broadband optical parametric amplifier.
• To identify the optimal basis modes for compact representation of amplified eigenmodes.
• To facilitate improved experimental techniques in image amplification and vacuum squeezing.

Main Methods:

• Numerical computation of eigenmodes for an OPA with an elliptical Gaussian pump.
• Analysis of the spatial characteristics of the amplified eigenmodes.
• Comparison with Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) modes for basis representation.

Main Results:

• Well-amplified eigenmodes can be compactly represented by a low-dimensional subspace of LG or HG modes.
• The first few eigenmodes closely match single LG or HG modes.
• An optimal basis waist size is found near the geometric average of the pump waist and crystal inverse bandwidth for large pump waists.

Conclusions:

• A compact representation of OPA eigenmodes using LG/HG modes significantly simplifies numerical computations.
• This simplification can enhance experimental capabilities in traveling-wave image amplification.
• The findings contribute to advancements in spatially-broadband vacuum squeezing techniques.