Re: Unit problem with Mpb software

On Jul 14, 2009, at 11:08 AM, Alexandre Besnier wrote:

> Good morning,
>
> I'm a student and I work currently on your software Mpb, I try to  
> make a rectangular lattice of 0.204µm x 0.561µm size, and I would  
> like to understand units give by band diagram.
>
> On your wiki pages you say that frequency is given in c/a unit, but  
> I don't understand several things :
>     - In band diagram, if I obtain frequency = 1, that say a=c, ie  
> a=3.10^8 meters ?

No, it means that frequency = 1 (c/a).  Since frequency = c / lambda,  
this means that

	c/lambda = 1 (c/a)

and thus

	lambda = a

Put another way, the frequency in MPB's units is exactly the same as a/ 
lambda  (where lambda = vacuum wavelength).

>     - Normally, "a" is the lattice period, but with rectangular  
> lattice, I have two periods, so what is "a" compared with my two  
> periods ?

"a" is whatever unit of distance you want; it doesn't have to have  
anything to do with the lattice constant(s).

You are perfectly free to use a=1um, for example, and then specify the  
size of your computation cell as 0.204 x 0.561, and give all distance  
units in microns.  In this case the frequencies returned by MPB are  
equivalent to 1/(lambda in microns).

>
>     - In the page "Mpb User Tutorial/A few words on units", you say  
> at the last paragraph : "Thus, the corresponding vacuum wavelength  
> is a over the frequency eigenvalue." It is not "Thus, the  
> corresponding vacuum wavelength is c over the frequency  
> eigenvalue." ? Because frequency * lambda = c ?

See above.  This is a consequence of using c/a units of frequency.

| Finally,  if I would like to have frequency in Hz, what I have to do  
to convert it ?

Multiply Meep's units by c/a in SI units.

Steven

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