Controllable conversion between Hermite Gaussian and Laguerre Gaussian modes due to cross phase

Area of Science:

• Optical physics
• Quantum optics
• Laser physics

Background:

• Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) modes are fundamental solutions in paraxial optics.
• Understanding mode inter-conversion is crucial for advanced optical beam shaping and manipulation.
• Controlling the spatial structure of light beams is a key challenge in optical sciences.

Purpose of the Study:

• To investigate the inter-conversion mechanism between HG and LG optical modes.
• To analyze the dynamics of intensity rotation during mode transformation.
• To demonstrate a controllable method for generating optical modes by engineering phase structures.

Main Methods:

• Theoretical analysis of the transformation between HG and LG modes.
• Incorporation of cross-phase modulation in the theoretical framework.
• Mathematical modeling of the intensity rotation, angular velocity, and acceleration of optical beams.

Main Results:

• HG modes with cross phase can transform into LG modes, and vice versa.
• The conversion process involves radially dependent intensity rotations with varying angular velocities and accelerations.
• Initial opposite rotations of outer peaks and inner hollows evolve into same-direction rotations at different speeds.
• Controllable generation of diverse optical patterns by adjusting cross-phase coefficients.

Conclusions:

• The study provides a theoretical foundation for the controllable inter-conversion of HG and LG modes.
• Engineering the phase structure offers a precise method for generating desired optical modes.
• The findings have implications for advanced optical beam generation and manipulation techniques.