On Jun 10, 2010, at 12:32 PM, Mischa Megens wrote:
Because Steven is smart and he defined the fourier transform the way
engineers and mathematicians do, i.e.
f(x)=int dk F(k) exp(2 pi i k x)
F(k)=int dx f(x) exp(2 pi i k x)
This connects more closely to the discrete fourier transform.
Physicists tend to write shorthand
f(x)=int dk F(k) exp(i k x)
but this is a bad idea, the 2 pi bites back:
F(k)=(1/(2pi)) int dx f(x) exp(i k x)
Actually, it's because I like using natural units. The natural units
of k in a periodic system are 2*pi/a, where a is the period. Because
I usually choose the units of distance so that the period is 1, this
means that the natural units of k are 2*pi. Then the Brillouin zone
is from -0.5 to 0.5.
Also, it's useful to define k in these units because Meep uses
frequency, not angular frequency (or equivalently Meep uses natural
units of 2*pi*c/a for angular frequency omega). Because k and
frequency are related in dispersion relations, for specifying
planewaves, etcetera, it is useful to either include or omit the 2*pi
factor in the units for both so that the dispersion relations don't
have extra 2*pi factors floating around.
Steven
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