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! >> >> >> >> >> _______________________________________________ >> meep-discuss mailing list >> meep-discuss@ab-initio.mit.edu >> http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss > > > > >
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