Re: [Meep-discuss] the unit of N0 and Rp in the multiLevel susceptibility
Dear Mr. Cerjan, I will do it along this way. Thank you very much. Yanbo At 2019-07-09 23:38:12, "Alexander Cerjan" 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 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" 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 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 ___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
Re: [Meep-discuss] the unit of N0 and Rp in the multiLevel susceptibility
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 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" 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 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 > > > > > ___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
Re: [Meep-discuss] the unit of N0 and Rp in the multiLevel susceptibility
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" 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 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___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
Re: [Meep-discuss] the unit of N0 and Rp in the multiLevel susceptibility
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
Re: [Meep-discuss] the unit of N0 and Rp in the multiLevel susceptibility
Dear Yanbo Pei, In this essentially classical treatment of the interactions between a saturable gain/absorbing medium and the electromagnetic fields, there are three different variables that can all be tuned to control the effective gain/loss that the field sees -- the two that you mentioned, N0 and the various decay and pumping rates (including Rp), as well as the coupling element sigma (or theta, depending on which set of conventions you are using). If you wish to use physical units for N0 and the pumping/decay rates, you'll also need to be careful to pick the coupling element to also use these units (it should be quite small in this case). Note. that N0 should be interpreted as a density, number of atoms per unit pixel of your system. In the tutorial, the values chosen do not correspond to any particular physical system, they're just a convenient set of values to confirm the stable multimode lasing regime of meep. This choice was made for two reasons: (1) because it is a bit difficult to find physical values for sigma/theta for realistic systems in the literature alongside pumping / decay rates. (at least, at the time when I was focused on these problems, ~6 years ago, maybe that's changed.) and (2) only the combination of these parameters discussed in the tutorial, D0, actually matters for calculating the lasing behavior. (i.e., you have 3 knobs to turn to choose a single parameter.) If you cared about the noise of the system, this is no longer true, and all 3 parameters play independent roles, but the quantum noise of a laser is beyond the scope of what meep currently calculates. alex On Thu, Jul 4, 2019 at 9:59 AM 裴延波 wrote: > Dear Meep users and developers > I am using multilevel-Atomic Susceptibility of MEEP to do some > simulation. I wonder what is the unit of N0 - total number of gain atoms in > the system and Rp - pumping rate. > In the code of the tutorial documents(Multilevel_atomic Susceptibility), > N0 is equal to 37 and Rp is equal to 0.0051. However the reference [Opt. > Express 2011, 20,474] says that N0 is in in the order of magnitude of 1e23 > /m3 and Rp is in the order of magnitude of 1e8 /s. According to above data, > N0 seems to be normalized. But I cannot find the document that explains how > to normalize. As for Rp, if we normalize Rp with (c/a=3e8/1e-6=3e14), the > result is about 1e-6 which deviates a lot from the value in the tutorial > document 0.0051. > Thanks a lot in advance for any help and also meep developers for this > excellent tool > > > > Yanbo Pei > > > > > > > ___ > meep-discuss mailing list > meep-discuss@ab-initio.mit.edu > http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss ___ meep-discuss mailing list meep-discuss@ab-initio.mit.edu http://ab-initio.mit.edu/cgi-bin/mailman/listinfo/meep-discuss
