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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 11 — Nov. 1, 2001
  • pp: 2806–2818

Polarization eccentricity of the transverse field for modes in chiral core planar waveguides

Warren N. Herman  »View Author Affiliations

JOSA A, Vol. 18, Issue 11, pp. 2806-2818 (2001)

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The general solution for modes in an asymmetric planar waveguide with a homogeneous and isotropic chiral core is given in terms of a pair of parameters related to the eccentricity of the polarization ellipse for the transverse electric field. This formulation provides insight into the transition, with increasing chirality of the core, from TE/TM modes to right-handed and left-handed circular polarization modes. Mode polarization as a function of waveguide thickness and of frequency is discussed in detail. Beyond a mode-dependent maximum thickness (or frequency), the left-handed elliptical modes consist of a slow-wave component whose cutoff properties are examined. The limiting case of a symmetric waveguide is also discussed.

© 2001 Optical Society of America

OCIS Codes
(230.7390) Optical devices : Waveguides, planar
(250.5460) Optoelectronics : Polymer waveguides
(310.2790) Thin films : Guided waves

Original Manuscript: November 9, 2000
Revised Manuscript: March 21, 2001
Manuscript Accepted: April 23, 2001
Published: November 1, 2001

Warren N. Herman, "Polarization eccentricity of the transverse field for modes in chiral core planar waveguides," J. Opt. Soc. Am. A 18, 2806-2818 (2001)

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  25. Here we adopt the convention for circularly polarized light used in most optics texts: For RHC (LHC) polarization, the electric field at a fixed position rotates clockwise (counterclockwise) when viewed from the direction toward which the wave is traveling. The opposite designation is used in much of the engineering literature, including Refs. 12-14 cited here. For a discussion, see B. E. A. Salah, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Sec. 6.1.
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  28. Solutions for all examples in this paper were obtained by using built-in routines in Mathcad 2000 Professional (MathSoft, Inc., Cambridge, Mass.).
  29. The TE- and TM-mode equations are normally written by using arctangent rather than arccotangent. However, the arguments of the arctangent are positive definite, and arctan x=arccot(1/x) for x>0,as is true for the achiral case. There is an advantage to using arccotangent in the chiral case because singularities of the argument cause π discontinuities of arccotangent at only the endpoints of the range |g|<1,while if arctangent is used, there are π discontinuities at g=±r0 inside this range.
  30. This merging of effective index curves was first noted in Ref. 12 without discussion of the polarization effects.

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