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" <alexcer...@gmail.com> 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 <peiya...@163.com> 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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