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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 crosssection 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
20030324