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The boundary condition for the eigenfunction of the
th higher mode
defined in equation (2.31) is:
 |
(2.63) |
 |
(2.64) |
The solution is most conveniently expressed by separating it into the
dependent and
dependent parts:
 |
(2.65) |
where
 |
(2.66) |
 |
(2.67) |
Performing the differentiation from equation (2.31)
gives the corresponding eigenvalues as
 |
(2.68) |
As with circular cross-section it is possible to use a lossy boundary
condition to give lossy versions of
and
but the
effect of losses will be noticeable in the
direction only and
will therefore be represented entirely by the choice of
direction
wavenumber,
.
 |
(2.69) |
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Jonathan Kemp
2003-03-24