Dear Mr. Cerjan,
I will do it along this way. Thank you very much.
Yanbo
At 2019-07-09 23:38:12, "Alexander Cerjan" <alexcer...@gmail.com> wrote:
1 million increments of MEEP's internal dt is not a very long time necessarily.
if i recall correctly, the tutorial example runs for 3.5 or 7 million time
steps.
Near the first lasing threshold (or subsequent thresholds) it can take quite a
bit of runtime for the system to reach the steady state, as the system
undergoes relaxation oscillations.
if you are looking specifically for the first lasing threshold, it may be
easier to look further above threshold, as you are doing, and then linearly
interpolate based on the observed intensities back to where the first lasing
threshold should be.
On Mon, Jul 8, 2019 at 6:21 PM 裴延波 <peiya...@163.com> wrote:
Yes. The problem of using the above parameters is that no lasing takes place
after 1000 000 MEEP's time step. At that time I wondered whether I used correct
units for those parameters and therefore I raised question about the units of
N0 and Rp.
I increased N0, Rp, or sigma and I saw the emergence of lasing in my system.
But I want to reproduce some results in published work so that the transform of
the values of parameters from the published work to MEEP's units is required.
Actually, I feel I know MEEP's units of time, frequency, length, and maybe N0
(you just told me) well, however I am so confused with others, for example,
electric field strength E, coupling strength sigma and so on.
I will read more and try more.
Thank you very much!
Yanbo
At 2019-07-08 23:57:02, "Alexander Cerjan" <alexcer...@gmail.com> wrote:
I'm not sure what problem you're having, maybe that you're not seeing lasing.
One of the potential problems with using real units is that the rates you're
entering might be quite long compared with MEEP's time step, so long simulation
times may be required to see lasing as the gain medium is initialized with all
of the atoms in the lower energy state, which are then slowly pumped to the
upper energy state.
On Sat, Jul 6, 2019 at 10:59 AM 裴延波 <peiya...@163.com> wrote:
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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