Angular shift of a Gaussian beam reflected near the Brewster angle

Area of Science:

• Optics and Photonics
• Electromagnetism

Background:

• Gaussian beams are fundamental in laser optics.
• Partial reflection at dielectric interfaces causes beam shifts.
• Understanding these shifts is crucial for optical system design.

Purpose of the Study:

• To derive a general and accurate expression for the angular shift of a Gaussian beam upon partial reflection.
• To analyze the behavior of this shift across all incidence angles, especially near the Brewster angle.
• To illustrate the associated beam distortion effects.

Main Methods:

• Analytical derivation of the reflected Gaussian beam's angular shift.
• Mathematical analysis for arbitrary incidence angles.
• Numerical simulation and visualization of reflected beam profiles.

Main Results:

• A general, explicit formula for the Gaussian beam angular shift was obtained.
• The formula accurately describes shifts for all incidence angles, including Brewster incidence.
• Beam distortion effects near the Brewster angle were clearly demonstrated.

Conclusions:

• The derived expression provides a comprehensive understanding of Gaussian beam angular shifts.
• This work refines existing models, particularly around the Brewster angle.
• The findings are relevant for precise optical measurements and device engineering.