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Fabrication And Characterization Of Photonic Crystal Slow Light Waveguides And Cavities

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Published on: November 30, 2012

Exact ray paths in bent waveguides.

A Ghatak, E Sharma, J Kompella

|June 10, 2010

Summary

We developed a Lagrangian approach to precisely map light ray paths in cylindrically symmetric optical media. This method accurately calculates ray trajectories in bent slabs and separable profile bent fibers.

Area of Science:

Optics and Photonics
Mathematical Physics

Background:

Studying light propagation in optical media is crucial for designing advanced optical devices.
Existing methods for analyzing ray paths in complex geometries can be computationally intensive.
Cylindrically symmetric media present unique challenges for ray tracing.

Purpose of the Study:

To introduce a novel Lagrangian formalism for analyzing ray paths.
To apply this formalism to derive exact ray paths in specific optical configurations.
To provide a robust analytical tool for optical media with cylindrical symmetry.

Main Methods:

Development of the Lagrangian formalism tailored for cylindrically symmetric media.
Application of the derived formalism to bent slab geometries.

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Application of the derived formalism to bent fibers with separable refractive index profiles.

Main Results:

The Lagrangian formalism provides an exact analytical solution for ray paths.
Demonstrated the successful application to bent slabs, yielding precise trajectory calculations.
Achieved exact ray path determination in bent fibers featuring separable profiles.

Conclusions:

The presented Lagrangian formalism offers an efficient and exact method for ray path analysis.
This approach is particularly effective for cylindrically symmetric optical systems.
The findings facilitate the design and optimization of optical components like bent fibers and slabs.