[Getdp] Eigenmodes of a dielectric structure

Guenneau, Sebastien guenneau at liverpool.ac.uk
Tue Sep 23 10:38:59 CEST 2008

Dear Pablo,

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).

Best wishes,


-----Original Message-----
From: getdp-bounces at geuz.org on behalf of Pablo Bianucci
Sent: Fri 9/19/2008 2:57 AM
To: Andre Nicolet
Cc: getdp at geuz.org
Subject: Re: [Getdp] Eigenmodes of a dielectric structure
Hi Andre!

On Thu, Sep 18, 2008 at 02:57:02PM +0200, Andre Nicolet wrote:

> GetDP is probably able to compute your resonances if you write your  
> problem in the form of a clean (mathematically speaking) eigenvalue 
> problem.

That should not be a problem, as it would be a Helmoltz equation in 2D or 3D
(probably 2D, if I can take advantage of the cylindrical symmetry).

> About the continuity of field components, there should be no problem if  
> you use the correct function spaces. Have you heard about edge elements,  
> Whitney elements and all that?

Of course not, I'm a poor experimentalist! :-) I'm going to start reading to
see if I can understand a bit more (I was initially looking for something more
"black-boxy", but it seems worth to delve deeper into GetDP).


Bye & Good Luck!

Pablo B.

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