Modal methods for the scalar wave equation
In Chapter 11 we presented the fundamental properties of modes of optical waveguides. These properties were derived from Maxwell’s equations in Chapters 30 and 31. Then, for the weakly guiding waveguides discussed in Chapter 13, we presented simplified expressions for these properties in Chapter 32, as summarized in Table 13-2. The corresponding simplification for radiation-mode properties was given in Chapter 25. There are two ways in which these simplified expressions can be obtained. One way is to take the limit Δ → 0 of the exact expressions holding V constant. Alternatively, we can recognize from the outset that the transverse electric field e t of a mode of the weakly guiding waveguide satisfies the scalar wave equation, and thus derive the modal properties by studying properties of the solutions of the scalar wave equation. In this chapter we follow the second and more direct approach. We emphasize that the polarization effects due to the waveguide structure, discussed in Chapter 13, are neglected here.
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