#### 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: