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Updated: Jun 11, 2026
12:14
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Robust and fast computation for the polynomials of optics
1QED Technologies Inc., Rochester, NY 14627, USA. forbes@qedmrf.com
Optics Express
|July 1, 2010
Summary
New mathematical methods using orthogonal polynomials enable higher-order optical applications. Simple algorithms derived from recurrence relations overcome common limitations, enhancing optical design and analysis.
Area of Science:
- Optics and Photonics
- Applied Mathematics
Background:
- Orthogonal polynomials are widely used in physics and optics.
- Challenges arise when employing orthogonal polynomials to higher orders in optical systems.
Purpose of the Study:
- To adapt lesser-known mathematical methods for optics.
- To demonstrate robust algorithms for higher-order optical applications.
Main Methods:
- Utilizing well-known recurrence relations to derive simple and robust algorithms.
- Applying these methods to standard optical applications requiring higher orders.
Main Results:
- Successfully enabled arbitrarily high-order applications of orthogonal polynomials.
- Demonstrated the significance of adapted mathematical methods in optics.
Conclusions:
- The developed algorithms offer a powerful solution for high-order optical problems.
- These methods are crucial for advancing optical design trends towards higher orders.
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