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By Albert Budden
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995–1043. 20 COUPLED LINE EQUATIONS 2. Huang Hung-chia, Coupled Mode Theory, VNU Science Press, Utrecht, The Netherlands, 1984. 3. , Robert E. Krieger, Malabar, FL, 1989. 4. , Academic Press, New York, 1991. 5. S. E. Miller, “Coupled Wave Theory and Waveguide Applications,” Bell System Technical Journal, Vol. 33, May 1954, pp. 661–719. 6. H. E. Rowe and W. D. Warters, “Transmission in Multimode Waveguide with Random Imperfections,” Bell System Technical Journal, Vol. 41, May 1962, pp. 1031–1170.
Take the limit as z → 0. 60). 4. Treatment of general frequency-dependent Cij , αi , and βi is straightforward by the present methods [3]. Both co- and cross-variances of the transfer functions are obtained by this analysis. We do not assume that different transfer functions are uncorrelated [2, 4]. 2). 7. 6 for transfer-function statistics was carried out in the frequency domain. 2, with frequency-independent attenuation α1 and α2 , coupling coefficient C0 , and group velocities v1 and v2 . 103) The expected value and covariance of the transfer function are independent of the frequency f .
For more than two modes, there are too many parameters for a general treatment. We therefore consider a particular 4-mode guide described in Appendix F, and use MAPLE to obtain the average mode powers. Finally, the nondegenerate case, in which all modes have distinct propagation constants, yields much simpler approximate results. These approximate results are readily modified to include degenerate modes, while retaining substantial simplification from the general exact results if most modes are nondegenerate.