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Zero-order bows in radially inhomogeneous spheres: direct and inverse problems
1Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia 23508, USA. jadam@odu.edu
Applied Optics
|October 22, 2011
Summary
Negative refractive index gradients in spheres can create zero-order bows, enabling rainbow refractometry and optical fiber studies. This ray theory analysis offers insights into scattering and lensing phenomena.
Area of Science:
- Optics and Photonics
- Wave Scattering Theory
Background:
- Ray paths in inhomogeneous media are complex.
- Rainbow phenomena typically involve higher-order rays.
Purpose of the Study:
- To investigate the existence and characteristics of zero-order bows in radially inhomogeneous spheres.
- To explore the relationship between refractive index profiles and bow formation.
- To connect ray-theoretic findings to broader physics concepts.
Main Methods:
- Analysis of zero-order ray paths in spheres with differentiable refractive index profiles.
- Application of Abel inversion to reconstruct refractive index profiles from observed bow phenomena.
Main Results:
- Demonstrated the possibility of zero-order and twin zero-order bows under specific negative refractive index gradients.
- Showcased the ability to recover refractive index profiles using Abel inversion.
- Established a link between specific bow types and their inducing refractive index profiles.
Conclusions:
- Zero-order bows are feasible in certain inhomogeneous spheres, expanding the understanding of optical phenomena.
- The methodology allows for the prediction and design of optical systems exhibiting specific bow characteristics.
- The study highlights parallels with orbiting, gravitational lensing, and wave scattering, suggesting unified principles across different scientific domains.
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