Re: [Meep-discuss] question about dispersive complex epsilon for gain
as best i can tell, you've set the dimension of your structure to 3, but the size in the x and y directions to be a single pixel. This is, depending on what you're trying to do, a somewhat odd situation, because you have no absorbing boundary condition in the x-y plane, only for waves which are propagating in the + or - z direction. As such, there will always be "infinite-Q" modes in your system, which correspond to waves propagating below the light line in the x-y plane. Even if the slab is the same dielectric as the surrounding vacuum, the pml in the z-direction won't absorb waves travelling entirely in the x or y directions. So, these states will see the gain, and grow exponentially, as there is nothing to absorb them. So yes, if I understand what you've set up correctly, any gain > 0 will yield divergent behavior. how to fix this? depends on what you want to do. If you're not trying to simulate a 3D system, you should change the dimensionality of your system. If you are trying to simulate a 3D system, which has bound modes below the light line, then you're always going to see lasing for any gain > 0, because that is what is physically expected. On Sat, Jul 25, 2020 at 11:40 PM 裴延波 wrote: > > Dear Cerjan, thank you for your kind help. > Now let me summarize my tests. Firstly, I decreased sigma to 1e-100. > However the electric field still grows fast to infinity. My test results > show that sigma=1e-120 made the calculation converge. But why sigma is > required so small. It does not make sense. > Secondly, the interface reflections were removed. In my structure under > calculation, uniform gain medium was sandwiched between air and the light > was propagating along z direction. The reflections from the gain medium-air > interfaces provided optical feedback for this Fabry-Perot like lasing. For > test, the instantaneous dielectric constant of the gain medium was set the > same as the air. But the field did not converge in this case also. > Thirdly, gamma was set to positive and sigma was set to negative. In this > case, the electric field converged finally. And I check the results, and > found the spectrum was likely correct. I wonder if those are the correct > parameters in using complex epsilon to calculate the lasing. > That's all for my tests. After those tests, I am confused with modelling > gain medium by complex dielectric function. Can you give me any clue to > solve this problem? > > Bests, > Pei > > > > At 2020-07-26 04:47:29, "Alexander Cerjan" wrote: > - 隐藏引用文字 - > > This is likely the physically expected behavior. If your gain is coupling > to a mode of your system whose loss rate is less than that of the rate of > stimulated emission, your system will begin to lase, i.e. the field will > begin to grow exponentially. In real, physical systems, this is then > compensated by gain saturation, which prohibits the fields from growing > exponentially forever. However, as the Lorentzian susceptibility model does > not contain this physics, nothing prohibits the fields from continuing > their exponential growth. > > On Sat, Jul 25, 2020 at 2:02 PM 裴延波 wrote: > >> I am trying to use dispersive complex epsilon to describe gain in my >> calculation. The parameters for the epsilon is defined as follows. >> freq_32 = 2# emission frequency (units of 2\pi c/a) >> gamma_32 = 0.306# FWHM emission linewidth in sec^-1 (units of 2\pi >> c/a) >> sigma_32 = 1e-4 >> susceptibilities = [mp.LorentzianSusceptibility(frequency=freq_32, >> gamma=-gamma_32, sigma=sigma_32)] >> geometry = [mp.Block(center=mp.Vector3(z=0), >> size=mp.Vector3(mp.inf,mp.inf,dcell), >> >> material=mp.Medium(epsilon=2.25,E_susceptibilities=susceptibilities))] >> >> Here gamma is negative indicating the material has gain, just as that in >> the tutorial. However, when running the field increase to infinity even >> though sigma is very very small. I try to set gamma positive and sigma >> negative. In this case there is a result which looks normal. I don't know >> why and what is the problem in my code. Can anyone explain this. Thanks in >> advance. >> >> The following is my full python code. >> >> import meep as mp >> import math >> resolution = 100 >> dimensions = 3 >> ns = 1.0 >> nlead = ns >> dlead = 2.0 >> npad = ns >> dpad = 2.0 >> dpml = 2.0 >> Ncell = 20 >> dcell = 96 >> sz = dcell + dlead + dpad + 2*dpml >> cell_size = mp.Vector3(0,0,sz) >> pml_layers = [mp.PML(dpml)] >> freq_32 = 2# emission frequency (units of 2\pi c/a) >> gamma_32 = 0.306# FWHM emission linewidth in sec^-1 (units of 2\pi >> c/a) >> df1 = gamma_32/2/math.pi >> sigma_32 = 1e-4 # dipole coupling strength (hbar = 1) >> default_material = mp.Medium(index=ns) >> sources = [mp.Source(mp.GaussianSource(freq_32, fwidth=df1), >> component=mp.Ex, center=mp.Vector3(-dcell/2-dpad/2))] >> >> sim = mp.Simulation(cell_size=cell_size, >> sources=sources, >>
Re: [Meep-discuss] question about dispersive complex epsilon for gain
Dear Cerjan, thank you for your kind help. Now let me summarize my tests. Firstly, I decreased sigma to 1e-100. However the electric field still grows fast to infinity. My test results show that sigma=1e-120 made the calculation converge. But why sigma is required so small. It does not make sense. Secondly, the interface reflections were removed. In my structure under calculation, uniform gain medium was sandwiched between air and the light was propagating along z direction. The reflections from the gain medium-air interfaces provided optical feedback for this Fabry-Perot like lasing. For test, the instantaneous dielectric constant of the gain medium was set the same as the air. But the field did not converge in this case also. Thirdly, gamma was set to positive and sigma was set to negative. In this case, the electric field converged finally. And I check the results, and found the spectrum was likely correct. I wonder if those are the correct parameters in using complex epsilon to calculate the lasing. That's all for my tests. After those tests, I am confused with modelling gain medium by complex dielectric function. Can you give me any clue to solve this problem? Bests, Pei At 2020-07-26 04:47:29, "Alexander Cerjan" wrote: - 隐藏引用文字 - This is likely the physically expected behavior. If your gain is coupling to a mode of your system whose loss rate is less than that of the rate of stimulated emission, your system will begin to lase, i.e. the field will begin to grow exponentially. In real, physical systems, this is then compensated by gain saturation, which prohibits the fields from growing exponentially forever. However, as the Lorentzian susceptibility model does not contain this physics, nothing prohibits the fields from continuing their exponential growth. On Sat, Jul 25, 2020 at 2:02 PM 裴延波 wrote: I am trying to use dispersive complex epsilon to describe gain in my calculation. The parameters for the epsilon is defined as follows. freq_32 = 2# emission frequency (units of 2\pi c/a) gamma_32 = 0.306# FWHM emission linewidth in sec^-1 (units of 2\pi c/a) sigma_32 = 1e-4 susceptibilities = [mp.LorentzianSusceptibility(frequency=freq_32, gamma=-gamma_32, sigma=sigma_32)] geometry = [mp.Block(center=mp.Vector3(z=0), size=mp.Vector3(mp.inf,mp.inf,dcell), material=mp.Medium(epsilon=2.25,E_susceptibilities=susceptibilities))] Here gamma is negative indicating the material has gain, just as that in the tutorial. However, when running the field increase to infinity even though sigma is very very small. I try to set gamma positive and sigma negative. In this case there is a result which looks normal. I don't know why and what is the problem in my code. Can anyone explain this. Thanks in advance. The following is my full python code. import meep as mp import math resolution = 100 dimensions = 3 ns = 1.0 nlead = ns dlead = 2.0 npad = ns dpad = 2.0 dpml = 2.0 Ncell = 20 dcell = 96 sz = dcell + dlead + dpad + 2*dpml cell_size = mp.Vector3(0,0,sz) pml_layers = [mp.PML(dpml)] freq_32 = 2# emission frequency (units of 2\pi c/a) gamma_32 = 0.306# FWHM emission linewidth in sec^-1 (units of 2\pi c/a) df1 = gamma_32/2/math.pi sigma_32 = 1e-4 # dipole coupling strength (hbar = 1) default_material = mp.Medium(index=ns) sources = [mp.Source(mp.GaussianSource(freq_32, fwidth=df1), component=mp.Ex, center=mp.Vector3(-dcell/2-dpad/2))] sim = mp.Simulation(cell_size=cell_size, sources=sources, resolution=resolution, boundary_layers=pml_layers, dimensions = dimensions, default_material=default_material) nfreq = 50 #number of frequencies at which to compute flux pt = mp.Vector3(0,0,dcell/2+dpad/2) flux_detection_point = mp.FluxRegion(center=pt) incidence = sim.add_flux(freq_32,df1,nfreq,flux_detection_point) sim.run(until_after_sources=mp.stop_when_fields_decayed(50,mp.Ex,pt,1e-3)) incident_flux = mp.get_fluxes(incidence) sim.reset_meep() susceptibilities = [mp.LorentzianSusceptibility(frequency=freq_32, gamma=-gamma_32, sigma=sigma_32)] geometry = [mp.Block(center=mp.Vector3(z=0), size=mp.Vector3(mp.inf,mp.inf,dcell), material=mp.Medium(epsilon=2.25,E_susceptibilities=susceptibilities))] geometry.append(mp.Block(center=mp.Vector3(z=-sz/2+(dpml+dlead)/2), size=mp.Vector3(mp.inf,mp.inf,dpml+dlead), material=mp.Medium(index=nlead))) geometry.append(mp.Block(center=mp.Vector3(z=sz/2-(dpml+dpad)/2), size=mp.Vector3(mp.inf,mp.inf,dpml+dpad), material=mp.Medium(index=npad))) sim = mp.Simulation(cell_size=cell_size, sources=sources, resolution=resolution, boundary_layers=pml_layers,
Re: [Meep-discuss] question about dispersive complex epsilon for gain
Thank you for your kind help.
Actually, I have tried the strength parameter sigma as small as 1e-20. But the
field rises to infinity rapidly. sigma can be used to tune the gain, can't it?
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在 2020-07-26 04:47:29，"Alexander Cerjan" 写道：
This is likely the physically expected behavior. If your gain is coupling to a
mode of your system whose loss rate is less than that of the rate of stimulated
emission, your system will begin to lase, i.e. the field will begin to grow
exponentially. In real, physical systems, this is then compensated by gain
saturation, which prohibits the fields from growing exponentially forever.
However, as the Lorentzian susceptibility model does not contain this physics,
nothing prohibits the fields from continuing their exponential growth.
On Sat, Jul 25, 2020 at 2:02 PM 裴延波 wrote:
I am trying to use dispersive complex epsilon to describe gain in my
calculation. The parameters for the epsilon is defined as follows.
freq_32 = 2# emission frequency (units of 2\pi c/a)
gamma_32 = 0.306# FWHM emission linewidth in sec^-1 (units of 2\pi c/a)
sigma_32 = 1e-4
susceptibilities = [mp.LorentzianSusceptibility(frequency=freq_32,
gamma=-gamma_32, sigma=sigma_32)]
geometry = [mp.Block(center=mp.Vector3(z=0),
size=mp.Vector3(mp.inf,mp.inf,dcell),
material=mp.Medium(epsilon=2.25,E_susceptibilities=susceptibilities))]
Here gamma is negative indicating the material has gain, just as that in the
tutorial. However, when running the field increase to infinity even though
sigma is very very small. I try to set gamma positive and sigma negative. In
this case there is a result which looks normal. I don't know why and what is
the problem in my code. Can anyone explain this. Thanks in advance.
The following is my full python code.
import meep as mp
import math
resolution = 100
dimensions = 3
ns = 1.0
nlead = ns
dlead = 2.0
npad = ns
dpad = 2.0
dpml = 2.0
Ncell = 20
dcell = 96
sz = dcell + dlead + dpad + 2*dpml
cell_size = mp.Vector3(0,0,sz)
pml_layers = [mp.PML(dpml)]
freq_32 = 2# emission frequency (units of 2\pi c/a)
gamma_32 = 0.306# FWHM emission linewidth in sec^-1 (units of 2\pi c/a)
df1 = gamma_32/2/math.pi
sigma_32 = 1e-4 # dipole coupling strength (hbar = 1)
default_material = mp.Medium(index=ns)
sources = [mp.Source(mp.GaussianSource(freq_32, fwidth=df1), component=mp.Ex,
center=mp.Vector3(-dcell/2-dpad/2))]
sim = mp.Simulation(cell_size=cell_size,
sources=sources,
resolution=resolution,
boundary_layers=pml_layers,
dimensions = dimensions,
default_material=default_material)
nfreq = 50 #number of frequencies at which to compute flux
pt = mp.Vector3(0,0,dcell/2+dpad/2)
flux_detection_point = mp.FluxRegion(center=pt)
incidence = sim.add_flux(freq_32,df1,nfreq,flux_detection_point)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50,mp.Ex,pt,1e-3))
incident_flux = mp.get_fluxes(incidence)
sim.reset_meep()
susceptibilities = [mp.LorentzianSusceptibility(frequency=freq_32,
gamma=-gamma_32, sigma=sigma_32)]
geometry = [mp.Block(center=mp.Vector3(z=0),
size=mp.Vector3(mp.inf,mp.inf,dcell),
material=mp.Medium(epsilon=2.25,E_susceptibilities=susceptibilities))]
geometry.append(mp.Block(center=mp.Vector3(z=-sz/2+(dpml+dlead)/2),
size=mp.Vector3(mp.inf,mp.inf,dpml+dlead),
material=mp.Medium(index=nlead)))
geometry.append(mp.Block(center=mp.Vector3(z=sz/2-(dpml+dpad)/2),
size=mp.Vector3(mp.inf,mp.inf,dpml+dpad),
material=mp.Medium(index=npad)))
sim = mp.Simulation(cell_size=cell_size,
sources=sources,
resolution=resolution,
boundary_layers=pml_layers,
geometry=geometry,
dimensions = dimensions,
default_material=default_material)
transmission = sim.add_flux(freq_32,df1,nfreq,flux_detection_point)
sim.run(until_after_sources=mp.stop_when_fields_decayed(50,mp.Ex,pt,1e-3))
transmitted_flux = mp.get_fluxes(transmission)
flux_freqs = mp.get_flux_freqs(transmission)
data1 = open("lasing.dat",'w')
for ii in range(0,nfreq):
data1.write("%f %f %f%f\n"
%(flux_freqs[ii],incident_flux[ii],transmitted_flux[ii],transmitted_flux[ii]/incident_flux[ii]))
data1.close()
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Re: [Meep-discuss] question about dispersive complex epsilon for gain
This is likely the physically expected behavior. If your gain is coupling
to a mode of your system whose loss rate is less than that of the rate of
stimulated emission, your system will begin to lase, i.e. the field will
begin to grow exponentially. In real, physical systems, this is then
compensated by gain saturation, which prohibits the fields from growing
exponentially forever. However, as the Lorentzian susceptibility model does
not contain this physics, nothing prohibits the fields from continuing
their exponential growth.
On Sat, Jul 25, 2020 at 2:02 PM 裴延波 wrote:
> I am trying to use dispersive complex epsilon to describe gain in my
> calculation. The parameters for the epsilon is defined as follows.
> freq_32 = 2# emission frequency (units of 2\pi c/a)
> gamma_32 = 0.306# FWHM emission linewidth in sec^-1 (units of 2\pi c/a)
> sigma_32 = 1e-4
> susceptibilities = [mp.LorentzianSusceptibility(frequency=freq_32,
> gamma=-gamma_32, sigma=sigma_32)]
> geometry = [mp.Block(center=mp.Vector3(z=0),
> size=mp.Vector3(mp.inf,mp.inf,dcell),
>
> material=mp.Medium(epsilon=2.25,E_susceptibilities=susceptibilities))]
>
> Here gamma is negative indicating the material has gain, just as that in
> the tutorial. However, when running the field increase to infinity even
> though sigma is very very small. I try to set gamma positive and sigma
> negative. In this case there is a result which looks normal. I don't know
> why and what is the problem in my code. Can anyone explain this. Thanks in
> advance.
>
> The following is my full python code.
>
> import meep as mp
> import math
> resolution = 100
> dimensions = 3
> ns = 1.0
> nlead = ns
> dlead = 2.0
> npad = ns
> dpad = 2.0
> dpml = 2.0
> Ncell = 20
> dcell = 96
> sz = dcell + dlead + dpad + 2*dpml
> cell_size = mp.Vector3(0,0,sz)
> pml_layers = [mp.PML(dpml)]
> freq_32 = 2# emission frequency (units of 2\pi c/a)
> gamma_32 = 0.306# FWHM emission linewidth in sec^-1 (units of 2\pi c/a)
> df1 = gamma_32/2/math.pi
> sigma_32 = 1e-4 # dipole coupling strength (hbar = 1)
> default_material = mp.Medium(index=ns)
> sources = [mp.Source(mp.GaussianSource(freq_32, fwidth=df1),
> component=mp.Ex, center=mp.Vector3(-dcell/2-dpad/2))]
>
> sim = mp.Simulation(cell_size=cell_size,
> sources=sources,
> resolution=resolution,
> boundary_layers=pml_layers,
> dimensions = dimensions,
> default_material=default_material)
>
> nfreq = 50 #number of frequencies at which to compute flux
> pt = mp.Vector3(0,0,dcell/2+dpad/2)
> flux_detection_point = mp.FluxRegion(center=pt)
> incidence = sim.add_flux(freq_32,df1,nfreq,flux_detection_point)
> sim.run(until_after_sources=mp.stop_when_fields_decayed(50,mp.Ex,pt,1e-3))
> incident_flux = mp.get_fluxes(incidence)
> sim.reset_meep()
> susceptibilities = [mp.LorentzianSusceptibility(frequency=freq_32,
> gamma=-gamma_32, sigma=sigma_32)]
> geometry = [mp.Block(center=mp.Vector3(z=0),
> size=mp.Vector3(mp.inf,mp.inf,dcell),
>
> material=mp.Medium(epsilon=2.25,E_susceptibilities=susceptibilities))]
> geometry.append(mp.Block(center=mp.Vector3(z=-sz/2+(dpml+dlead)/2),
> size=mp.Vector3(mp.inf,mp.inf,dpml+dlead),
> material=mp.Medium(index=nlead)))
> geometry.append(mp.Block(center=mp.Vector3(z=sz/2-(dpml+dpad)/2),
> size=mp.Vector3(mp.inf,mp.inf,dpml+dpad),
> material=mp.Medium(index=npad)))
> sim = mp.Simulation(cell_size=cell_size,
> sources=sources,
> resolution=resolution,
> boundary_layers=pml_layers,
> geometry=geometry,
> dimensions = dimensions,
> default_material=default_material)
>
> transmission = sim.add_flux(freq_32,df1,nfreq,flux_detection_point)
> sim.run(until_after_sources=mp.stop_when_fields_decayed(50,mp.Ex,pt,1e-3))
> transmitted_flux = mp.get_fluxes(transmission)
> flux_freqs = mp.get_flux_freqs(transmission)
> data1 = open("lasing.dat",'w')
> for ii in range(0,nfreq):
> data1.write("%f %f %f%f\n"
> %(flux_freqs[ii],incident_flux[ii],transmitted_flux[ii],transmitted_flux[ii]/incident_flux[ii]))
> data1.close()
>
>
>
>
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