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 η0. |
0.4 | - | (0, 1] |
|
active volume Defines the active volume Va. |
0.15e-015 | 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. |
30e-006 | - | (0, +∞) |
|
photon lifetime Defines the photon lifetime τp. |
3e-012 | 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 τn. |
1e-009 | 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. |
10e-024 | m^3 | (0, +∞) |
|
gain coefficient Defines the gain coefficient a0. |
25e-021 | m^2 | (0, +∞) |
|
carrier density at transparency Defines the carrier density at transparency n0. |
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 (top-most) element. |
%sample rate% | Hz | [0, +∞) |
====================================
Implementation Details
The Directly Modulated Laser (DML) model is based on reference [1] and it is basically a Fabry-Perot 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 out-coupling through the mirrors.
The laser is directly modulated by electrical current. Parameters listed in the following table follows equation (1) to (6) [1].
|
η0 |
total quantum efficiency |
vg |
group velocity |
|---|---|---|---|
|
β |
spontaneous emission coupling factor |
α |
linewidth enhancement factor |
|
τn |
carrier lifetime |
Γ |
mode confinement factor |
|
ε |
gain compression factor |
τp |
photon lifetime |
|
n0 |
carrier density at transparency |
Va |
active volume |
|
a0 |
gain coefficient |
|
$$ \frac{d p}{d t}=\Gamma G\left(n-n_{0}\right) p-\frac{p}{\tau_{p}}+\frac{\beta \Gamma n}{\tau_{n}} $$ |
(1) |
|
$$ \frac{d n}{d t}=\frac{I(t)}{q V_{a}}-G\left(n-n_{0}\right) p-\frac{n}{\tau_{n}} $$ |
(2) |
|
$$ \frac{d \phi}{d t}=\frac{1}{2} \alpha\left\{\Gamma v_{g} a_{0}\left(n-n_{0}\right)-\frac{1}{\tau_{p}}\right\} $$ |
(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 (Fp), electron (Fn) and phase (Fϕ) 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.
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|
|
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, 568-573 (1989)
[2] G .P. Agrawal, N.K. Dutta, Semiconductor Laser, Van Nostrad Reinhold, New York, 1993.