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Optical waveguiding in graded‐index layers
1.H. F. Taylor, W. E. Martin, D. B. Hall, and V. N. Smiley, Appl. Phys. Lett. 21, 95 (1972).
2.I. P. Kaminow and J. R. Carruthers, Appl. Phys. Lett. 22, 326 (1973).
3.E. Garmire, Appl. Phys. Lett. 23, 403 (1973).
4.E. M. Conwell, Appl. Phys. Lett. 23, 328 (1973).
5.H. H. Woodbury and R. B. Hall, Phys. Rev. 157, 641 (1967).
6.L. Y. Wei, J. Phys. Chem. Solids 18, 162 (1961).
7.W. M. Caton, W. E. Martin, D. B. Hall, and H. F. Taylor, Topical Conference on Integrated Optics, New Orleans, 1974 (unpublished).
8.The WKB method has been applied to the calculation of modes of a graded‐index guide by D. Marcuse, IEEE J. Quantum Electron. QE‐9, 1000 (1973). Marcuse has approximated the varying dielectric constant ε by three straight lines of different slope, which should be good for very small, very slowly varying ε such as found in the guides of Ref. 2. He has used this to evaluate the WKB integrals and obtain an approximate expression for the number of TE modes that can be supported.
9.E. M. Conwell, Solid State Commun. (to be published).
10.L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960).
11.D. Bohm, Quantum Theory (Prentice‐Hall, Englewood Cliffs, N. J., 1951), p. 274.
12.Most of the results of this paragraph could be obtained fairly directly from Eqs. (4) and (5) and thus have more general validity than the WKB approximation. It is convenient, however, to deduce them through the use of WKB solutions, and, of course, the solutions can be used to obtain approximate values of the
13.D. H. Smithgall and F. W. Dabby, IEEE J. Quantum Electron. QE‐9, 1023 (1973).
14.E. Garmire, H. Stoll, A. Yariv, and R. S. Hunsperger, Appl. Phys. Lett. 21, 87 (1972). Note, however, that their result contains an extra factor of
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