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Ray tracing in concentric gradient-index media: optical Binet equation.
Summary
The optical Binet equation (OBE) extends a mechanics formula for ray tracing in gradient-index (GRIN) media. This tool determines ray paths and propagation times in optical systems like lenses and deflectors.
Area of Science:
- Optics
- Mathematical Physics
Background:
- The Binet equation models particle orbits in central force fields.
- Ray tracing in gradient-index (GRIN) media requires specialized optical formulations.
Purpose of the Study:
- To generalize the Binet equation for optical applications.
- To introduce the optical Binet equation (OBE) for ray tracing in GRIN media.
- To demonstrate OBE's utility in determining ray paths and propagation times.
Main Methods:
- Inferred OBE from Fermat's principle.
- Applied OBE to analyze ray tracing in various GRIN optical systems.
- Validated results through simulations.
Main Results:
- OBE effectively models ray trajectories in concentric GRIN fields.
- OBE allows calculation of ray paths and propagation times.
- Demonstrated applicability to Maxwell fish-eye, Luneburg, Eaton lenses, concentrators, and hyperbolic deflectors.
Conclusions:
- The optical Binet equation is a versatile tool for analyzing concentric GRIN optical systems.
- OBE simplifies the determination of ray traces and propagation times.
- Results align with simulations, confirming OBE's effectiveness.
