Re: propagation constant in MPB

On Jul 11, 2008, at 10:41 AM, Yiling Qi wrote:
>  I am now simulating a 2D (square lattice) photonic crystal. I set k- 
> points to be Gamma-X-M. instead of the relationship between  
> frequency and parallel k-vectors, I am more concerned about the  
> propagation constant(generally named as beta, actually is z  
> component of wave vector in this situation I think). So how could I  
> convert frequency into kz? Could it be deduced by the formula shown  
> as follows:
> beta^2=(2pi*f*n)^2-(2pi*kx)^2-(2pi*ky)^2
> ( suppose a=1 and f, kx, ky are all got from MPB)
>

No, that formula is just for plane waves in a homogeneous medium.  In  
general, there is no analytical formula relating frequency and  
propagation constant -- solving for this relationship (the dispersion  
relation) is the whole point of MPB.

The propagation constant is just one component of the k vector.  So,  
in MPB you are actually specifying the propagation constant and  
computing the corresponding frequency; to specify the frequency and  
compute the propagation constant, see this section of the manual:

http://ab-initio.mit.edu/wiki/index.php/MPB_User_Reference#The_inverse_problem 
:_k_as_a_function_of_frequency

Steven