# Re: [MPB-discuss] Unit problem with Mpb software

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

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

and thus

lambda = a

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Put another way, the frequency in MPB's units is exactly the same as a/ lambda (where lambda = vacuum wavelength).
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- Normally, "a" is the lattice period, but with rectangular lattice, I have two periods, so what is "a" compared with my two periods ?
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"a" is whatever unit of distance you want; it doesn't have to have anything to do with the lattice constant(s).
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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).
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- 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 ?
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See above.  This is a consequence of using c/a units of frequency.

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| Finally, if I would like to have frequency in Hz, what I have to do to convert it ?
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Multiply Meep's units by c/a in SI units.

Steven

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• Re: [MPB-discuss] Unit problem with Mpb software Steven G. Johnson