Analytical frequency-doubled HG modes in astigmatic mode converters for composite vortex beam generation

Area of Science:

• Quantum Optics
• Structured Light Generation
• Beam Propagation Physics

Background:

• Hermite-Gaussian (HG) modes are fundamental in optics but controlling their complex propagation and conversion is challenging.
• Astigmatic mode conversion (AMC) plays a crucial role in transforming optical beam properties.
• Deterministic generation of complex light structures like composite vortex beams (CVBs) is vital for advanced applications.

Purpose of the Study:

• To present a comprehensive analytical framework for characterizing the propagation and AMC of frequency-doubled HG modes.
• To enable the deterministic generation of CVBs using this framework.
• To provide a theoretical basis for controlling complex structured light.

Main Methods:

• Rigorous modal decomposition of frequency-doubled HG modes into HG basis modes.
• Analytical derivation of modal coefficients and phase accumulation during propagation.
• Modeling AMC as a unitary transformation between HG and Laguerre-Gaussian (LG) bases.

Main Results:

• The framework accurately describes the propagation of frequency-doubled HG modes as superpositions of constituent HG modes.
• AMC is shown to be a transformation mapping HG modes to LG modes.
• The resulting CVBs are expressed as superpositions of LG modes with inherited coefficients.

Conclusions:

• The developed analytical framework provides full characterization of frequency-doubled HG mode propagation and AMC.
• This enables the on-demand generation and precise control of CVBs.
• The findings offer significant advancements for optical manipulation, quantum communication, and high-dimensional information processing.