Ince-Gaussian beams in a quadratic-index medium

Area of Science:

• Optics and Photonics
• Wave Propagation

Background:

• Ince-Gaussian beams are a class of optical beams with applications in various fields.
• Understanding beam propagation in non-uniform media is crucial for optical system design.

Purpose of the Study:

• To analyze the propagation characteristics of Ince-Gaussian beams in quadratic index media.
• To derive explicit expressions for key beam parameters and phase shifts.
• To investigate conditions for maintaining constant beam width.

Main Methods:

• Theoretical analysis of beam propagation using derived mathematical expressions.
• Derivation of complex beam parameter and longitudinal phase shift.
• Examination of Ince-Gaussian eigenmodes in quadratic and complex lenslike media.

Main Results:

• Explicit expressions for the complex beam parameter and longitudinal phase shift were obtained.
• A specific relation between beam width and quadratic-medium coefficient allows for constant beam width.
• The study accounts for propagation in complex lenslike media with refractive index and gain/loss variations.

Conclusions:

• The derived expressions provide a comprehensive understanding of Ince-Gaussian beam propagation in quadratic media.
• Conditions for stable beam propagation (constant width) were identified.
• The framework is applicable to complex optical systems including those with gain or loss.