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Applied Optics

Applied Optics


  • Vol. 25, Iss. 13 — Jul. 1, 1986
  • pp: 2184–2187

The ABCD matrix in arbitrarily tapered quadratic-index waveguides

J. N. McMullin  »View Author Affiliations

Applied Optics, Vol. 25, Issue 13, pp. 2184-2187 (1986)

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The general form for the ABCD matrix in an arbitrarily tapered quadratic-index waveguide is given in terms of the two independent solutions of the second-order differential ray-tracing equation. A procedure for finding taper functions which admit analytical solutions in terms of known functions is presented with several examples.

© 1986 Optical Society of America

Original Manuscript: September 13, 1985
Published: July 1, 1986

J. N. McMullin, "The ABCD matrix in arbitrarily tapered quadratic-index waveguides," Appl. Opt. 25, 2184-2187 (1986)

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  1. A. Yariv, Optical Electronics (Holt, Rinehart, & Winston, New York, 1985), Chap. 2.
  2. L. W. Casperson, J. L. Kirkwood, “Beam Propagation in Tapered Quadratic Index Waveguides: Numerical Solutions,” IEEE/OSA J. Lightwave Technol. LT-3, 256 (1985). [CrossRef]
  3. L. W. Casperson, “Beam Propagation in Tapered Quadratic-Index Waveguides: Analytical Solutions,” IEEE/OSA J. Lightwave Technol. LT-3, 264 (1985). [CrossRef]
  4. S. Yamamoto, T. Makimoto, “On the Ray Transfer Matrix of a Tapered Lenslike Medium,” Proc. IEEE 34, 1254 (1971). [CrossRef]
  5. S. Yamamoto, T. Makimoto, “Equivalence Relations in a Class of Distributed Optical Systems—Lenslike Media,” Appl. Opt. 10, 1160 (1971). [CrossRef] [PubMed]
  6. J. Matthews, R. L. Walker, Mathematical Methods of Physics (Benjamin, New York, 1965), Chap. 7.
  7. R. Courant, D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1970), p. 329.
  8. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (NBS, Washington, DC, 1964), Chap. 8.

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