Analytical description of interference between two misaligned and mismatched complete Gaussian beams

Area of Science:

• Optics and Photonics
• Metrology
• Laser Physics

Background:

• Laser interferometers are crucial for precision length measurements, relying on interferometric phase shifts.
• Predicting these phase shifts typically requires complex numerical solutions of overlap integrals.
• Existing methods often struggle with arbitrary beam misalignments and mismatches.

Purpose of the Study:

• To derive analytical representations for interferometric phase and contrast (fringe visibility).
• To provide a simplified theoretical framework for two-beam interferometers (homodyne and heterodyne).
• To address the challenge of arbitrary Gaussian beam misalignment and mismatch.

Main Methods:

• Derivation of analytical formulas for interferometric phase and contrast.
• Analysis of two-beam interferometers, including homodyne and heterodyne configurations.
• Consideration of fundamental Gaussian beams with arbitrary misalignment and mismatch.

Main Results:

• Successful derivation of analytical expressions for phase and contrast.
• The analytical results are valid for arbitrarily misaligned and mismatched Gaussian beams.
• A key experimental requirement is complete detection of both beams using a large photodetector.

Conclusions:

• Analytical solutions offer a more direct approach to calculating interferometric phase shifts.
• This work simplifies the theoretical understanding and prediction of interferometer performance.
• The findings facilitate more accessible precision measurements in optical metrology.