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Non-orthogonal basis transformations in structured light via ellipticity-dependent Ince-Gaussian modes
Optics Letters
|June 1, 2026
Summary
Researchers developed a new analytical method to transform between Ince-Gaussian light modes with varying ellipticity. This breakthrough enables precise control and manipulation of structured light for advanced optical information processing.
Area of Science:
- Optics and Photonics
- Wave Physics
Background:
- Ince-Gaussian (IG) modes are solutions to the paraxial wave equation.
- They offer a continuous transition between Laguerre- and Hermite-Gaussian modes via an ellipticity parameter (ε).
- Existing IG bases for fixed ellipticities are orthogonal, but modes across different ellipticities are not mutually orthogonal.
Purpose of the Study:
- To derive an explicit analytical transformation between Ince-Gaussian bases of arbitrary ellipticity.
- To enable direct and experimentally accessible mapping between non-orthogonal structured-light representations.
- To introduce ellipticity as a controllable degree of freedom in structured light engineering.
Main Methods:
- Derivation of a finite analytical expression for transformation between IG bases.
- Experimental implementation using spatial light modulators (SLMs).
- Demonstration of ellipticity-resolved modal decomposition.
Main Results:
- The first explicit finite analytical expression for transforming between arbitrary ellipticity IG bases was derived.
- An experimental method using SLMs was successfully demonstrated for modal decomposition.
- Ellipticity was established as a controllable parameter for structured light.
Conclusions:
- The derived transformation provides a framework for mapping between non-orthogonal structured-light representations.
- This work enables new strategies for mode conversion, optical encoding, and high-dimensional information processing.
- The introduced framework enhances control over structured light for advanced optical applications.
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