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We assume that there is no material
dispersion (n1 and n2 are frequency independent). At zero
frequency we have b = kn2. When the optical frequency increases, V
increases proportionally and u tends toward an asymptotic value of p/2 (b tends toward kn1).
In many case the waveguide is illuminated by a small bandwidth light centered
at w0. In this case, the propagation
constant can be developed at the second order
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(A-7) |
where b0 = b(w), b0' = db/dw and b0'' = d2b/dw2 evaluated at w0. The term b0' represents the group time delay per unit length and the term -b0'' the chromatic dispersion due to the waveguide.
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