# [Getdp] Eigenmodes of a dielectric structure

**Pablo Bianucci**
bianucci at ualberta.ca

*Thu Sep 25 02:19:48 CEST 2008*

Hi Sebastien!
On Tue, Sep 23, 2008 at 09:38:59AM +0100, Guenneau, Sebastien wrote:
>* Please note that it's neither a scalar nor a vector Helmholtz
*>* equation that you'll have to implement in Getdp, but the vector Maxwell
*>* system involving modified curl operators: you should replace
*>* all z derivatives by a multiplication by i*beta*z, where i*i=-1,
*>* beta is a conical parameter and z is the variable along the axis
*>* of your fibres. So, it requires a bit of thinking (details of the
*>* derivation can be found in Zolla et al, Foundation of PCFs, ICP 2005).
*
I'm interested in cavity modes (bound, or at most quasi-bound), no propagating
modes. For that case, the Helmoltz equation should work fine (as in the case
for Mie theory; I want to compute modes similar to the Mie modes, but with
perturbations that make the theory quite annoying).
In fact, looking at my notes I could go for solving a vector Helmholtz equation
(to get the fields) or a scalar one (where I would get a "potential" and get
the fields by taking the curl of it). Could anybody comment on that?
Bye & Good Luck!
Pablo B.