Stochastic ray tracing for Fresnel diffraction.

Area of Science:

• Optics and Photonics
• Quantum Mechanics
• Computational Physics

Background:

• Understanding laser beam propagation is crucial in optics.
• The duality between wave and ray optics presents a theoretical challenge.
• Fresnel diffraction effects are essential for accurate beam modeling.

Purpose of the Study:

• To propose a novel stochastic ray tracing method for laser beam propagation.
• To explore the duality between wave and ray representations in optical phenomena.
• To naturally incorporate Fresnel diffraction effects into a ray tracing framework.

Main Methods:

• Transformation of Maxwell's equations to the Schrödinger equation for a monochromatic laser beam.
• Interpretation of the Schrödinger equation as a stochastic process, analogous to Nelson's stochastic mechanics.
• Development and numerical testing of the stochastic ray tracing method for a Gaussian laser beam.

Main Results:

• The stochastic ray tracing method successfully illustrates stochastic paths and the wavefront of optical beams.
• Fresnel diffraction effects are inherently included in the proposed method.
• Numerical tests demonstrate that stochasticity effectively shapes the beam waist around the Rayleigh range.

Conclusions:

• Stochastic ray tracing provides a unified framework for understanding laser beam propagation, bridging wave and ray optics.
• The method offers a new perspective on incorporating diffraction phenomena in optical simulations.
• This approach has potential applications in designing and analyzing optical systems with complex beam dynamics.