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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 28 — Oct. 1, 2011
  • pp: F50–F59

Zero-order bows in radially inhomogeneous spheres: direct and inverse problems

John A. Adam  »View Author Affiliations


Applied Optics, Vol. 50, Issue 28, pp. F50-F59 (2011)
http://dx.doi.org/10.1364/AO.50.000F50


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Abstract

Zero-order ray paths are examined in radially inhomogeneous spheres with differentiable refractive index profiles. It is demonstrated that zero-order and sometimes twin zero-order bows can exist when the gradient of refractive index is sufficiently negative. Abel inversion is used to “recover” the refractive index profiles; it is therefore possible in principle to specify the nature and type of bows and determine the refractive index profile that induces them. This may be of interest in the field of rainbow refractometry and optical fiber studies. This ray-theoretic analysis has direct similarities with the phenomenon of “orbiting” and other phenomena in scattering theory and also in seismological, surface gravity wave, and gravitational “lensing” studies. For completeness these topics are briefly discussed in the appendixes; they may also be of pedagogic interest.

© 2011 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.3870) General : Mathematics
(080.2720) Geometric optics : Mathematical methods (general)
(080.5692) Geometric optics : Ray trajectories in inhomogeneous media
(110.3200) Imaging systems : Inverse scattering
(260.2710) Physical optics : Inhomogeneous optical media

History
Original Manuscript: April 7, 2011
Revised Manuscript: July 25, 2011
Manuscript Accepted: July 26, 2011
Published: September 6, 2011

Citation
John A. Adam, "Zero-order bows in radially inhomogeneous spheres: direct and inverse problems," Appl. Opt. 50, F50-F59 (2011)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-28-F50

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