Dear Mr. Cerjan,
Thanks for your kindly and detailed reply. I feel that I have understood
what you said.
However I am not sure I treated coupling strength sigma correctly. For
example, there are parameters for four-level gain atoms adopted from the
reference Phys. Rev. Lett. 2000, 85, 70 as follows.
Transition rates:
freq_21=6e14 Hz (omega_21=2*pi*6e14)
rate_32=1e13 Hz
rate_21=1e9 Hz (tao_21=1e-9 s)
rate_10=1e11 Hz
gamma_21=1/tao_21+2/tao_2=9e13 Hz (tao_2=2.18e-14 s)
Pumping rate
Rp=1e7
Density of gain atom
N0=5.5*6.02e23 (per cubic meter)
coupling strength sigma_21
gamma_r=1/tao_21
gamma_c=(e**2/m)*omega_21**2/(6*pi*epsilon0*c**3)
sigma_21=(gamma_r/gamma_c)*e**2/m=6*pi*epsilon0*c**3/(omega_21**2*tao_21)=1e-7
here,
e = magnitude of elementary charge
m = mass of electron
epsilon0 - dielectric constant of vacuum
c = speed of light in vacuum
In meep, I set length unit a=1 um. Then the above parameters are normalized as
follows
freq_21=6e14/(c/a)=6e14/(3e8/1e-6)=2
rate_32=1e13/(c/a)=0.033
rate_21=1e9/(c/a)=3.33e-6
rate_10=1e11/(c/a)=3.33e-4
gamma_21=9x13/(c/a)=0.3
Rp=1e7/(c/a)=3.33e-8
N0=5.5*6.02e23*(1e-9)**3=3.31e-3 (because resolution=1000, the volume
of each pixel is (1e-9)**3 cubic meter)
As for the coupling strength, I did not normalize it and I used it as its value
in SI unit(sigma_21=1e-7). I am not quite sure whether it is correct. And
perhaps you may find other problems in the normalization for other parameters
above.
Anyway, your have helped me a lot. Thank you very much!
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