jacksontom
Newbie level 4
I tried to build a simple QCL(quantum cascade laser) model based on 2-level rate equations in Pspice. The codes are as follows, but I can't get the right probe output. May someone give me some advice, please. your help will be very appreciated !
The codes:
QCL MODEL
Id 0 1 1A AC 0.5A
Itr 0 1 pulse(0 3A 0.05ns 0.05ns 0.05ns 5ns 10ns)
Xlaser 1 0 2 QCL
rout 2 0 1e9
.SUBCKT QCL N3 N0 OUT
***************************************************************
** Name: qcl.cir
**
** Purpose: simple qcl model based on 2-level rate equations in pspice
**
** References:
**
**
**
**
** Date: September 23, 2012
**
** Author: Xia Xiaojun
**
***************************************************************
** constants **************************************************
.PARAM pi = 3.1415926535898
.PARAM q = 1.60217733e-19 ; electronic charge..........[A s]
.PARAM kb = 1.380658e-23 ; boltzmann constant.........[J/K]
.PARAM c0 = 2.99792458e8 ; vacuum speed of light......[m/s]
.PARAM h = 6.6260755e-34 ; planck constant............[J s]
***************************************************************
** parameter **************************************************
**general physics parameter
.PARAM Rr = 0.27 ; right facet reflectivity
.PARAM Rl = 0.27 ; left facet reflectivty
.PARAM alpha_w = 13.3 ; waveguide losses [cm^(-1)]
.PARAM tau_3 = 1.3e-12 ; carrier lifetime on energy level 3
.PARAM tau_32 = 2.1e-12 ; transition between level 3 and level 2
.PARAM tau_21 = 4e-13 ; transition between level 2 and level 1
**gain parameter
.PARAM sigma_32 = 1.796e-14 ; differential gain cross section [cm^2]
.PARAM ng = 3.29 ; group refraction index
.PARAM gamma = 0.53 ; optical confinment factor [single gain stage]
**geometrical parameters
.PARAM L = 0.3 ; cavity length [cm]
.PARAM W = 1.17e-3 ; cavity width [cm]
.PARAM Lp = 4.53e-6 ; single gain stage thickness [cm]
.PARAM Ns = 25 ; #gain stages
*thermal parameters
.PARAM lambda = 5000 ; emission wavelength @300K [nm]
**calculated parameters
.PARAM vg = {100*c0/ng} ; group velocity [cm/s]
.PARAM alpha_m = {1/L*LOG(1/SQRT(Rr*Rl))} ; mirror losses
.PARAM tau_p = {1/(vg*(alpha_w + alpha_m))} ; photon lifetime for each mode
.PARAM Vcav = {Ns*L*W*Lp} ; active volume [cm^3]
.PARAM eta_opt = {alpha_m/(alpha_w + alpha_m)*(1-Rr)/
+ (1-Rr+(1-Rl)*SQRT(Rr/Rl))} ; optical power output coupling efficiency
.PARAM hvl = {h*c0/1e-9} ; photon energy [J*nm]
** arbitrary constants
.PARAM zn = 1e3
*.PARAM k = 1.5e-19
.PARAM del = 4.0e3
** for power calculations
.PARAM k_power = {hvl/lambda*eta_opt/tau_p}
***************************************************************
** netlist ****************************************************
** carrier numbers
RN3 N3 N0 {tau_3/(q*zn)}
CN3 N3 N0 {q*zn}
GN32 N3 N2 value={q*zn*vg*sigma_32*gamma*V(N3,N2)*(V(P)+del)*(V(P)+del)/(k_power*Vcav)}
RN2 N2 N0 {tau_21/(q*zn)}
CN2 N2 N0 {q*zn}
GN2 N0 N2 value={q*zn*V(N3)/tau_32}
** phonton numbers
GNP 0 P value={zn*tau_p*Ns*gamma*vg*sigma_32*V(N3,N2)*(V(P)+del)/Vcav-del}
RNP P 0 1
CNP P 0 {2*tau_p}
** output power
Eout OUT 0 value={(V(P)+del)*(V(P)+del)}
***************************************************************
.ENDS
.option list expand node opts
.op
.dc Id 0 5A 0.05A
.tran 0.05ns 20ns 0 0.01ns
.ac dec 100 0.1G 10G
.probe
.end
the images are electric model of QCL based on 2-level rate equations.
And the 2-level rate equations are as follows :
Also I have do some transform to the number of electrons and photons as follows:
Thanks !
gashyazh@126.com
The codes:
QCL MODEL
Id 0 1 1A AC 0.5A
Itr 0 1 pulse(0 3A 0.05ns 0.05ns 0.05ns 5ns 10ns)
Xlaser 1 0 2 QCL
rout 2 0 1e9
.SUBCKT QCL N3 N0 OUT
***************************************************************
** Name: qcl.cir
**
** Purpose: simple qcl model based on 2-level rate equations in pspice
**
** References:
**
**
**
**
** Date: September 23, 2012
**
** Author: Xia Xiaojun
**
***************************************************************
** constants **************************************************
.PARAM pi = 3.1415926535898
.PARAM q = 1.60217733e-19 ; electronic charge..........[A s]
.PARAM kb = 1.380658e-23 ; boltzmann constant.........[J/K]
.PARAM c0 = 2.99792458e8 ; vacuum speed of light......[m/s]
.PARAM h = 6.6260755e-34 ; planck constant............[J s]
***************************************************************
** parameter **************************************************
**general physics parameter
.PARAM Rr = 0.27 ; right facet reflectivity
.PARAM Rl = 0.27 ; left facet reflectivty
.PARAM alpha_w = 13.3 ; waveguide losses [cm^(-1)]
.PARAM tau_3 = 1.3e-12 ; carrier lifetime on energy level 3
.PARAM tau_32 = 2.1e-12 ; transition between level 3 and level 2
.PARAM tau_21 = 4e-13 ; transition between level 2 and level 1
**gain parameter
.PARAM sigma_32 = 1.796e-14 ; differential gain cross section [cm^2]
.PARAM ng = 3.29 ; group refraction index
.PARAM gamma = 0.53 ; optical confinment factor [single gain stage]
**geometrical parameters
.PARAM L = 0.3 ; cavity length [cm]
.PARAM W = 1.17e-3 ; cavity width [cm]
.PARAM Lp = 4.53e-6 ; single gain stage thickness [cm]
.PARAM Ns = 25 ; #gain stages
*thermal parameters
.PARAM lambda = 5000 ; emission wavelength @300K [nm]
**calculated parameters
.PARAM vg = {100*c0/ng} ; group velocity [cm/s]
.PARAM alpha_m = {1/L*LOG(1/SQRT(Rr*Rl))} ; mirror losses
.PARAM tau_p = {1/(vg*(alpha_w + alpha_m))} ; photon lifetime for each mode
.PARAM Vcav = {Ns*L*W*Lp} ; active volume [cm^3]
.PARAM eta_opt = {alpha_m/(alpha_w + alpha_m)*(1-Rr)/
+ (1-Rr+(1-Rl)*SQRT(Rr/Rl))} ; optical power output coupling efficiency
.PARAM hvl = {h*c0/1e-9} ; photon energy [J*nm]
** arbitrary constants
.PARAM zn = 1e3
*.PARAM k = 1.5e-19
.PARAM del = 4.0e3
** for power calculations
.PARAM k_power = {hvl/lambda*eta_opt/tau_p}
***************************************************************
** netlist ****************************************************
** carrier numbers
RN3 N3 N0 {tau_3/(q*zn)}
CN3 N3 N0 {q*zn}
GN32 N3 N2 value={q*zn*vg*sigma_32*gamma*V(N3,N2)*(V(P)+del)*(V(P)+del)/(k_power*Vcav)}
RN2 N2 N0 {tau_21/(q*zn)}
CN2 N2 N0 {q*zn}
GN2 N0 N2 value={q*zn*V(N3)/tau_32}
** phonton numbers
GNP 0 P value={zn*tau_p*Ns*gamma*vg*sigma_32*V(N3,N2)*(V(P)+del)/Vcav-del}
RNP P 0 1
CNP P 0 {2*tau_p}
** output power
Eout OUT 0 value={(V(P)+del)*(V(P)+del)}
***************************************************************
.ENDS
.option list expand node opts
.op
.dc Id 0 5A 0.05A
.tran 0.05ns 20ns 0 0.01ns
.ac dec 100 0.1G 10G
.probe
.end
the images are electric model of QCL based on 2-level rate equations.
And the 2-level rate equations are as follows :
Also I have do some transform to the number of electrons and photons as follows:
Thanks !
gashyazh@126.com
Last edited: