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By Waddington, George

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31) In general, the total field propagating along a waveguide is given in terms of an expansion over the complete set of forwardand backward-propagating bound and radiation modes of a longitudinally invariant waveguide, each of the form given in Eq. 32) where, as well as the discrete set of bound modes, the summation implicitly includes an integration over the continuum of radiation modes [3 (Chap. 25)]. 33) A 8 where the modal subscript j is implicit and Aco is the core cross section. This page intentionally left blank CHAPTER 3 Circular Isotropic Longitudinally Invariant Fibers Even this seemingly innocent building block, the circular isotropic fiber, reveals a rich and instructive set of phenomena.

4, we provide quantitative evaluation of polarization eigenvalue level splitting. 1 SUMMARY OF MODAL REPRESENTATIONS For azimuthally invariant index n = n(r), we consider the transverse dependence for the field solutions of the wave equations of 35 CHAPTER 3 36 Secs. 7. In particular, our major concern is with the scalar field ψ(r) and, to zeroth order in ∆, the transverse component of the vector field et (r). 1, we give the two sets of scalar mode field solutions of the scalar wave equation (SWE), Eq.

10-3)] that eti have indeed been chosen as the linear combination of VWE(0) solutions which form the ∆ → 0 limit of the exact fields. ) Given e(tj1) one may continue the expansion of Eq. 21) to obtain the second-order eigenvalue correction U (j 2 ) etc. 3 Simplifications due to Symmetry As will be discussed in Sec. 4, symmetry can be exploited qualitatively to determine particular modal degeneracies without the necessity to explicitly evaluate the eigenvalue corrections, and quantitatively to simplify the evaluation of the diagonal terms Hjj = < etj , Hp1etj > in the first-order eigenvalue corrections.

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