Angle-to-retardance converter and a universal polarization-state synthesizer

Area of Science:

• Optical Engineering
• Photonics
• Polarimetry

Background:

• Designing tunable optical retarders and polarization-state generators is crucial for advanced polarimetric instrumentation.
• Existing geometric and numerical methods have limitations in design and calibration.

Purpose of the Study:

• To develop a compact analytical framework for designing tunable retarders and universal polarization-state generators.
• To derive closed-form expressions for polarimetrically equivalent systems of linear retarder cascades.

Main Methods:

• Derivation of closed-form expressions for pairs of linear retarders.
• Analysis of symmetric three-plate retarder cascades.
• Investigation of a specific configuration with a central half-wave plate and two quarter-wave plates.

Main Results:

• Closed-form expressions for two-retarder systems, including a pure rotator case.
• Explicit expressions for the effective parameters of symmetric three-plate retarder cascades.
• A configuration yielding a fixed-axis retarder (retardance Δ=4θ) acting as an angle-to-retardance converter.

Conclusions:

• The analytical framework facilitates the design, calibration, and implementation of polarization devices.
• The proposed configuration, combined with a polarizer, acts as a universal polarization-state synthesizer.
• This work complements existing approaches and enhances polarimetric instrumentation capabilities.