Discussion Forum

Hello,

I am struggling to understand what Mode analysis is actually calculating in the case of axial symmetry - such as in the Application Library example for optical fiber bend.

In particular, according to the description, the solution is sought in the form:

where lambda is the eigenvalue.

Also, according to the Wave Optics documentation, the effective index is defined as:

where k0 is the wave vector in vacuum. I am assuming this is also the case for the axisymmetrical example like the bent fiber.

Now, here is one thing which confuses me.

For the symmetry reasons, I expect any eigenvalue lambda to satisfy:

(in other words, I expect Im(lambda) to be an integer number).

In terms of n_eff, this should be:

However, this is not what I observe. Using global evaluation, if I calculate

it gives me something which is definitely not 1.

On the other hand, as an interesting observation, if I evaluate

it gives me 1 to a very high accuracy.

In other words, it looks like the stated value of n_eff is actually the imaginary part of lambda, and not lambda/k0?

On the other hand, when divided by the radius, it actually gives something very close to the effective index of the straight fiber mode. This is very confusing...

Am I missing something?