Series Solution Methods and Special Functions

Chapter 3 Series Solution Methods and Special Functions finally obtain the first solution... 

The weak-guidance approximation, described in Chapter 13, greatly simplifies the determination of the modal fields of optical waveguides, because it depends on solutions of the scalar wave equation, rather than on vector solutions of Maxwell s equations. For circular fibers, with an arbitrary profile, the scalar wave equation must normally be solved by purely numerical methods. We discussed the few profiles that have analytical solutions in Chapter 14. These solutions, including those for profiles of practical interest such as the step and clad power-law profiles, are given in terms of special functions or by series expansions, which usually necessitate tables or numerical evaluation to reveal the physical attributes of the modes. 

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