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Approximate Solutions for the Coupled Line Equations

1962; Institute of Electrical and Electronics Engineers; Volume: 41; Issue: 3 Linguagem: Inglês

10.1002/j.1538-7305.1962.tb00486.x

2376-7154

Harrison E. Rowe,

Advanced Fiber Optic Sensors

The coupled line equations for only two modes, representing the TE 01 signal mode and a single spurious mode in circular waveguide, are solved in series form by the method of successive approximations. Bounds are found on the magnitudes of the terms in the series solution. These bounds decrease rapidly only for “short” waveguides; for long guides many terms of the series must be included in the solution. The coupled line equations are transformed to a new form, in which one of the unknowns Λ is given by Λ = −ln G 0 , where G 0 is the (complex) TE 01 transfer function of the original coupled line equations. Thus Re Λ = −ln | G 0 |, the TE 01 loss in nepers, Im Λ = −∠ G 0 , the TE 01 phase in radians. These transformed equations are again solved by successive approximations; the first term is the commonly used solution that has been obtained by physical arguments. Bounds are determined for the magnitudes of the terms in these series solutions; for a suitable restriction on the coupling coefficient that includes many cases of practical interest, these bounds decrease rapidly for long guides. In present calculations of the TE 01 loss statistics in random guides, only the first term of the series expansion for Λ is considered. Unfortunately this approximation has not so far been justified.