modulates an optical signal depending on electrical signal
Keywords
electrical, optical, bidirectional
Ports
| Name | Type |
|---|---|
| port 1 | Optical Signal |
| modulation | Electrical Signal |
| port 2 | Optical Signal |
Properties
General Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
name Defines the name of the element. |
Traveling Wave Optical Modulator Measured | - | - |
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). |
Traveling Wave Optical Modulator Measured | - | - |
description A brief description of the elements functionality. |
modulates an optical signal depending on electrical signal | - | - |
prefix Defines the element name prefix. |
TWOMM | - | - |
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 |
|---|---|---|---|
configuration Defines the bidirectional or unidirectional element configuration. |
bidirectional | - | [bidirectional, unidirectional |
frequency Central frequency of operation. |
193.1 | THz* *std. unit is Hz |
(0, +∞) |
length The interaction length of the modulator. |
1 | m | [0, +∞) |
input parameter Defines whether the input parameter is a table with voltage dependent values or coefficients of a polynomial function. |
table | - | [table, coefficients |
Standard/Table Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
load from file Defines whether or not to load measurements from an input file or to use the currently stored values. |
false | - | [true, false] |
measurement filename The file containing the measurement data. Refer to the Implementation Details section for the format expected. |
- | - | - |
measurement type Defines the type of measurement data. |
effective index | - | [absorption & phase, effective index |
measurement A matrix editor for users to read the element current modulation data values. |
<11,3> [-5, -4.5, -4,...] | - | - |
Standard/Coefficients Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
absorption coefficient a The polynomial coefficient for the absorption function. |
-0.0617 | dB/V^3/m | (-∞, +∞) |
absorption coefficient b The polynomial coefficient for the absorption function. |
-0.2804 | dB/V^2/m | (-∞, +∞) |
absorption coefficient c The polynomial coefficient for the absorption function. |
-0.6635 | dB/V/m | (-∞, +∞) |
absorption coefficient d The polynomial coefficient for the absorption function. |
-0.0719 | dB/m | (-∞, +∞) |
phase coefficient a The polynomial coefficient for the phase function. |
-0.0038 | rad/V^3/m | (-∞, +∞) |
phase coefficient b The polynomial coefficient for the phase function. |
0.1132 | rad/V^2/m | (-∞, +∞) |
phase coefficient c The polynomial coefficient for the phase function. |
-0.4825 | rad/V/m | (-∞, +∞) |
phase coefficient d The polynomial coefficient for the phase function. |
-0.0107 | rad/m | (-∞, +∞) |
Waveguide Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
modes List of optical mode labels supported by the element. |
TE,TM | - | - |
Enhanced Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
microwave frequency Central frequency of operation. |
10 | GHz* *std. unit is Hz |
(0, +∞) |
microwave loss Defines the microwave loss. |
0 | dB/m | [0, +∞) |
microwave index Defines the the microwave group index. |
3 | - | [0, +∞) |
optical index Defines the waveguide effective index. |
3 | - | [0, +∞) |
source resistance Defines the source resistance. |
50 | Ohms | [0, +∞) |
source reactance Defines the source reactance. |
0 | Ohms | (-∞, +∞) |
characteristic resistance Defines the characteristic resistance. |
50 | Ohms | (0, +∞) |
characteristic reactance Defines the characteristic reactance. |
0 | Ohms | (-∞, +∞) |
terminating resistance Defines the terminating resistance. |
50 | Ohms | [0, +∞) |
terminating reactance Defines the terminating reactance. |
0 | Ohms | (-∞, +∞) |
Numerical Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
stability factor Determines the size of the spatial grid spacing used during the microwave transmission line simulation, defined as a fraction of the Courant numerical stability limit (must be less than 1 for numerical stability). |
1 | - | (0, 1] |
Diagnostic Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
run diagnostic Enables the gain and spontaneous emission spectrum response to be generated as results. |
true | - | [true, false] |
record junction capacitance fit Enables junction capacitance fitting coefficients. |
false | - | [true, false] |
record characteristic impedance spectrum profile Enables unloaded characteristic impedance profile as a function of frequency. |
false | - | [true, false] |
record load voltage waveform Enables output of the time-varying voltage at the load. |
true | - | [true, false] |
Enhanced/Junction Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
junction resistance Defines the junction resistance. |
0 | ohm.m | [0, +∞) |
junction capacitance type Defines if the junction capacitance is constant or voltage dependent. |
constant | - | [constant, table |
constant junction capacitance Defines the junction capacitance. |
0 | F/m | [0, +∞) |
load junction capacitance from file Defines whether or not to load measurements from an input file or to use the currently stored values. |
false | - | [true, false] |
junction capacitance filename The file containing the measurement data. Refer to the Implementation Details section for the format expected. |
- | - | - |
junction capacitance table A matrix editor for users to read the element current data values. |
<30,2> [-3, -2.896551724, -2.793103448,...] | - | - |
fit polynomial order The order of the polynomial used to fit the tabulated junction capacitance vs voltage data. |
2 | - | (2, 10] |
====================================
Implementation Details
The Traveling Wave Optical Modulator Measured (TWOMM) element induces a phase shift through electro-optic (free-carrier interaction) effect. The electrodes are modeled as distributed transmission lines where the signal amplitude can vary in space and time. The TWOMM model is a time-domain model and is based on solving the transmission line differential equations:
$$ \begin{aligned} \frac{d V(x, t)}{d x} &=-R I(x, t)-L \frac{d I(x, t)}{d t} \\ \frac{d I(x, t)}{d x} &=-G V(x, t)-C \frac{d V(x, t)}{d t} \end{aligned} $$
The equivalent circuit of a section of a transmission line is shown in the figure below. Here \(v(x, t)\) and \(i(x, t)\) represent the instantaneous voltage and current at position \(x\) and time \(t\). The \(R\), \(L\), \(G\), and \(C\) represent the resistance, inductance, conductance, and capacitance per unit length, respectively. The reverse bias PN junction is modeled as a series distributed \(R_{j}\) and \(C_j\) elements in parallel with \(TL\).
The complex characteristic impedance, \(Z_0\) requires as an input to the model is for the de-embedded electrode only. This means it represents only the RGLC components excluding the diode branch.
The model extracts the RGLC component from the user provided complex \(Z_0\) and complex microwave refractive index (microwave loss and microwave index), according to [1]:
$$ \begin{gathered} Z_{0}=\sqrt{\frac{R+j 2 \pi f L}{G+j 2 \pi f C}} \\ \gamma=\sqrt{(R+j 2 \pi f L)(G+j 2 \pi f C)} \end{gathered} $$
where \(f\), is the input microwave frequency. If the combination of \(Z_0\) and \(\gamma\) is non-physical resulting in a negative value of any of the RLGC components, an error occurs, and simulation is aborted.
Different than the Optical Modulator Measured (OMM) element, the TWOMM can model the effect of the PN junction as a series of distributed resistances and junction capacitances. The junction capacitance can be a constant value or a function of voltage. If a table/file is used then the data is fit a polynomial of order that is specified by the user. The default value is 2 and the range is any integer from 2 to 10.
Example
In the following example, we test the implementation of a non-linear junction capacitance. In order to show how the TL voltage varies with non-linear junction capacitance, we add two tests with constant junction capacitance representing the upper and lower bound of the non-linear junction capacitance. Therefore, the three cases for the transmission line:
- \(Cj = C_{min}\)
- \(Cj = C_{max}\)
- Nonlinear \(Cj = [C_{min}, C_{max}]\)
The load voltage of test 3 is bounded by the first two test cases. The test circuit is shown below:
The script file [[TWOMM_LossyTL_nonlinearCj.lsf]] loads different junction capacitance for the three test cases to the TWOMM model, run the simulation and generates the optical output signal for comparison of the 3 cases:
Frequency response for matched terminating impedance
The frequency response of the TWOMM is represented by the S21 parameter. To linearize the transmission line response at a specific operating point, a small-signal analysis is performed and hence the S21 parameter is extracted. A test bench is created to sweep the frequency then calculates the S21 parameter. The parameters of the modulators are selected from the literature [2]. The frequency response is shown below, and the 3dB optical bandwidth is approximately 7 GHz which agrees with the analytical expression:
$$f_{3 d B}=\frac{1.9 c}{\pi l\left(n_{e}-n_{g}\right)}$$
where \(l\) is the length, \(n_e\) is the microwave index, \(n_g\) is the optical group index, and \(c\) is the speed of light.
Related Publications
[1] David M. Pozar, “Microwave engineering”, 3rd Ed., Wiley (2005)
[2] Lin, S. H., and Shih-Yuan Wang. "High-throughput GaAs PIN electrooptic modulator with a 3-dB bandwidth of 9.6 GHz at 1.3 µm." Applied Optics 26.9 (1987).