Re: Problem with integration of fields

On 21/09/2007, Steven G. Johnson <[email protected]> wrote:
> By the way, I should just make one general comment about this formula: it
> is only strictly valid in the limit of low index contrast, although many
> people blindly plug it in even for high-contrast fibers.
>
> A typical use for the effective area is as a figure of merit for the
> strength of nonlinearities in the fiber.  The above formula is derived in
> the low-contrast scalar limit, but the correct generalization to
> high-contrast fibers is different and was derived in:
>         Tzolov et al, Optics Letters, vol. 20 (no. 5), p. 456 (1995).

Yes, I was aware of this fact, I was using the formulation given in
JOSA B, vol. 20 (10) p. 2037 (2003), which appears to be similar.

> You most definitely should be wary of these scalar-based formulas for
> micron-scale silica strands surrounded by air!  In such a high-contrast
> case, the scalar-based formulas give at best only qualitative information.

Well only, if you are using a scalar approximation. The silica strand
in air can be solved analytically without approximation right? I have
been following the solution in Snyder and Love, Optical Waveguide
Theory. They do not make a low-index contrast approximation for
cylindrically symmetric step-index fibers. Although the formula I gave
does not give a useful value of effective index for nonlinearity it
ought to agree with the value calculated for the analytic fields.
Happily it does to within the numerical tolerances I used.

Anyway, thanks for responding, and for the excellent software.
Best regards,
John Travers