Re: Precision of calculated frequencies

On Thu, 25 Oct 2007, wuqi wrote:
>   I have a similar question.
>   I am calculating a PC waveguide mode and the group v by taking dw/dk.
>  As I decrease the k point step dk, the changing of dw is very small for 
> the slow light region.
>
>   How can I increase the # of significant point of the calculated 
> frequencies?
>
>  I am using a control .ctl file and (run-te) command.

To calculate the group velocity, you should use the 
display-group-velocities command in MPB, which calculates it using an 
analytical formula rather than by finite differences.

(And if you do want to differentiate something by finite differences, you 
should use the "deriv" function in libctl, which uses Richardson 
extrapolation as described in e.g. Numerical Recipes.)

Steven