The model of a laser directly modulated by the electrical current
Keywords
electrical, optical, unidirectional
Ports
Name  Type 

modulation  Electrical Signal 
output  Optical Signal 
Properties
General Properties
Name  Default value  Default unit  Range 

name Defines the name of the element. 
DM Laser     
annotate Defines whether or not to display annotations on the schematic editor. 
true    [true, false] 
enabled Defines whether or not the element is enabled. 
true    [true, false] 
type Defines the element unique type (read only). 
DM Laser     
description A brief description of the elements functionality. 
The model of a laser directly modulated by the electrical current     
prefix Defines the element name prefix. 
DML     
model Defines the element model name. 
     
library Defines the element location or source in the library (custom or design kit). 
     
local path Defines the local path or working folder $LOCAL for the element. 
     
url An optional URL address pointing to the element online help. 
     
Standard Properties
Name  Default value  Default unit  Range 

frequency Central frequency of operation. 
193.1  THz* *std. unit is Hz 
(0, +∞) 
total quantum efficiency Defines the total quantum efficiency η_{0}. 
0.4    (0, 1] 
active volume Defines the active volume V_{a}. 
0.15e015  m^3  (0, +∞) 
Polarization Properties
Name  Default value  Default unit  Range 

azimuth The azimuth angle (polarization ellipse) of the signal output. 
0  rad  [1.5708, 1.5708] 
ellipticity The ellipticity angle (polarization ellipse) of the signal output. 
0  rad  [0.785398, 0.785398] 
Waveguide Properties
Name  Default value  Default unit  Range 

mode confinement factor Defines the mode confinement factor Γ. 
0.4    (0, 1] 
spontaneous emission factor Defines the spontaneous emission coupling factor β. 
30e006    (0, +∞) 
photon lifetime Defines the photon lifetime τ_{p}. 
3e012  s  (0, +∞) 
group index Defines the waveguide group index. 
3.526970094    [0, +∞) 
Waveguide/Mode 1 Properties
Name  Default value  Default unit  Range 

orthogonal identifier 1 The first identifier used to track an orthogonal mode of an optical waveguide. For most waveguide, two orthogonal identifiers '1' and '2' are available (with the default labels 'TE' and 'TM' respectively). 
1    [1, +∞) 
label 1 The label corresponding to the first orthogonal identifier. 
X     
Waveguide/Mode 2 Properties
Name  Default value  Default unit  Range 

orthogonal identifier 2 The second identifier used to track an orthogonal mode of an optical waveguide. For most waveguide, two orthogonal identifiers '1' and '2' are available (with the default labels 'TE' and 'TM' respectively). 
2    [1, +∞) 
label 2 The label corresponding to the second orthogonal identifier. 
Y     
Waveguide/Recombination Properties
Name  Default value  Default unit  Range 

carrier lifetime Defines the carrier lifetime τ_{n}. 
1e009  s  (0, +∞) 
Waveguide/Gain Properties
Name  Default value  Default unit  Range 

gain compression factor Defines the gain compression factor ϵ. The meaning of this value depends on the chosen gain compression factor type. For more information check the description of the gain compression factor type option. 
10e024  m^3  (0, +∞) 
gain coefficient Defines the gain coefficient a_{0}. 
25e021  m^2  (0, +∞) 
carrier density at transparency Defines the carrier density at transparency n_{0}. 
1e+024  m^3  (0, +∞) 
Waveguide/Spontaneous Emission Properties
Name  Default value  Default unit  Range 

linewidth enhancement factor Defines the linewidth enhancement factor α. 
5    (0, +∞) 
Numerical Properties
Name  Default value  Default unit  Range 

calculate noise Defines whether or not to include noise in the rate equation model. It 'true', laser RIN and linewidth will be enabled. 
false    [true, false] 
number of steps The number of steps the ODE solver will take for each time step. 
2    [2, +∞) 
automatic seed Defines whether or not to automatically create an unique seed value for each instance of this element. The seed will be the same for each simulation run. 
true    [true, false] 
seed The value of the seed for the random number generator. A value zero recreates an unique seed for each simulation run. 
1    [0, +∞) 
Simulation Properties
Name  Default value  Default unit  Range 

output signal mode The output signal mode. 
%output signal mode%    [sample, block 
sample rate The sample rate of the generated signal. This is typically set by the global properties in the root (topmost) element. 
%sample rate%  Hz  [0, +∞) 
====================================
Implementation Details
The Directly Modulated Laser (DML) model is based on reference [1] and it is basically a FabryPerot model. The model assumes equivalent facet reflectivity on both ends and the output power is from one end of the laser, which is half of the total output power from the model on both ends. The actual facet reflectivity may be controlled by the photon lifetime parameter, which also includes any internal optical losses and not just outcoupling through the mirrors.
The laser is directly modulated by electrical current. Parameters listed in the following table follows equation (1) to (6) [1].
η_{0} 
total quantum efficiency 
v_{g} 
group velocity 

β 
spontaneous emission coupling factor 
α 
linewidth enhancement factor 
τ_{n} 
carrier lifetime 
Γ 
mode confinement factor 
ε 
gain compression factor 
τ_{p} 
photon lifetime 
n_{0} 
carrier density at transparency 
V_{a} 
active volume 
a_{0} 
gain coefficient 
$$ \frac{d p}{d t}=\Gamma G\left(nn_{0}\right) p\frac{p}{\tau_{p}}+\frac{\beta \Gamma n}{\tau_{n}} $$ 
(1) 
$$ \frac{d n}{d t}=\frac{I(t)}{q V_{a}}G\left(nn_{0}\right) p\frac{n}{\tau_{n}} $$ 
(2) 
$$ \frac{d \phi}{d t}=\frac{1}{2} \alpha\left\{\Gamma v_{g} a_{0}\left(nn_{0}\right)\frac{1}{\tau_{p}}\right\} $$ 
(3) 
$$ G=v_{\varepsilon} a_{0} /(1+\varepsilon p) $$ 
(4) 
$$ m(t)=0.5 p(t) V_{a} \eta_{0} h v /\left(\Gamma \tau_{p}\right) $$ 
(5) 
$$ \Delta v(t)=\frac{1}{2 \pi} \frac{d \phi}{d t} $$ 
(6) 
where n and p are the electron and photon densities in the laser active region, Φ and G are the optical phase and gain, and m and Δv defines for the optical power time variations and laser chirp, respectively.
The Relative Intensity Noise (RIN) for this model is defined based on the Langevin formulation, and please refer to Reference [2] for the detailed implementation of the photon (F_{p}), electron (F_{n}) and phase (F_{ϕ}) noises.
The state of polarization (SOP) of the DM Laser model is defined by using the polarization ellipse as shown in Fig. 1, where ω is the ellipticity angle and α is the azimuth angle, a and b are the major and minor axis of the ellipse, respectively. Then the unified Stokes Parameters are defined by Equation. 7.


Please see the example file DM_Laser.icp for more information on this element. The following figure shows the system in the example file:
The following figure plots the waveforms monitored by the oscilloscope and the optical oscilloscope.
References
[1] J.C. Cartledge and G.S. Burley, "The Effect of Laser Chirping on Lightwave System Performance," JLT Vol 7, No. 3, 568573 (1989)
[2] G .P. Agrawal, N.K. Dutta, Semiconductor Laser, Van Nostrad Reinhold, New York, 1993.