Waveguide Bragg grating
Keywords
optical, bidirectional
Ports
| Name | Type |
|---|---|
| port 1 | Optical Signal |
| port 2 | Optical Signal |
Properties
General Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
|
name Defines the name of the element. |
Bragg Grating | - | - |
|
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). |
Bragg Grating | - | - |
|
description A brief description of the elements functionality. |
Waveguide Bragg grating | - | - |
|
prefix Defines the element name prefix. |
WBG | - | - |
|
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 |
|
length The length of the waveguide. |
0.005 | m | [0, +∞) |
|
input parameter Defines whether to provide the grating period or the Bragg frequency. |
Bragg frequency | - | [grating period, Bragg frequency |
|
period The grating period. |
0.53e-006 | m | [0, +∞) |
|
frequency Central frequency of operation. |
1550 |
nm* *std. unit is Hz |
(2.99792e-83, +∞) |
|
coupling parameter Defines whether to provide the grating coupling coefficient or the effective index change. |
effective index change | - | [effective index change, coupling coefficient |
|
effective index change ac The effective index change over the grating length. |
0.0004 | - | [0, +∞) |
|
effective index change dc The background effective index change over the grating length. |
0 | - | [0, +∞) |
|
grating coupling coefficient Defines the grating coupling coefficient. |
800 | 1/m | (-∞, +∞) |
|
phase shift The phase shift for a phase shifted grating. |
0 | rad | (-∞, +∞) |
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. |
TE | - | - |
|
loss 1 The loss corresponding to the first orthogonal identifier. |
0 | dB/m | [0, +∞) |
|
effective index 1 The effective index corresponding to the first orthogonal identifier. |
1.447 | - | (-∞, +∞) |
|
group index 1 The group index coefficient corresponding to the first orthogonal identifier. |
1.447 | - | [0, +∞) |
|
facet reflectivity left 1 Defines the facet reflectivity left. |
0 | - | [0, 1] |
|
facet phase left 1 Defines the facet phase left. |
0 | rad | (-∞, +∞) |
|
facet reflectivity right 1 Defines the facet reflectivity right. |
0 | - | [0, 1] |
|
facet phase right 1 Defines the facet phase right. |
0 | rad | (-∞, +∞) |
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. |
TM | - | - |
|
loss 2 The loss corresponding to the second orthogonal identifier. |
0 | dB/m | [0, +∞) |
|
effective index 2 The effective index corresponding to the second orthogonal identifier. |
1.447 | - | (-∞, +∞) |
|
group index 2 The group index coefficient corresponding to the second orthogonal identifier. |
1.447 | - | [0, +∞) |
|
facet reflectivity left 2 Defines the facet reflectivity left. |
0 | - | [0, 1] |
|
facet phase left 2 Defines the facet phase left. |
0 | rad | (-∞, +∞) |
|
facet reflectivity right 2 Defines the facet reflectivity right. |
0 | - | [0, 1] |
|
facet phase right 2 Defines the facet phase right. |
0 | rad | (-∞, +∞) |
Waveguide/Mode 1/Thermal Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
|
effective index temperature sensitivity 1 Defines the ratio between effective index variation and temperature. |
0 | /K | (-∞, +∞) |
|
excess loss temperature sensitivity 1 Defines the ratio between loss variation and temperature. |
0 | /K | [0, +∞) |
Waveguide/Mode 2/Thermal Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
|
effective index temperature sensitivity 2 Defines the ratio between effective index variation and temperature. |
0 | /K | (-∞, +∞) |
|
excess loss temperature sensitivity 2 Defines the ratio between loss variation and temperature. |
0 | /K | [0, +∞) |
Waveguide/Apodization Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
|
apodization function Defines the grating apodization type. |
uniform | - | [uniform, user defined, Gaussian, raised cosine, hyperbolic tangent, sinc |
|
apodization parameter The grating apodization parameter. |
0.5 | - | (-∞, +∞) |
|
apodization table Table containing normalized length versus apodization parameters. |
<2,2> [0, 1, 1,...] | - | - |
|
load apodization from file Defines whether or not to load apodization parameters from an input file or to use the currently stored values. |
false | - | [true, false] |
|
apodization filename The file containing the normalized length versus apodization parameter values. Refer to the Implementation Details section for the format expected. |
apodization.dat | - | - |
Waveguide/Chirp Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
|
chirp function Defines the grating chirp type. |
none | - | [none, user defined, linear chirp parameter, linear chirp coefficient |
|
chirp parameter The chirp parameter for a linear chirped grating. |
0 | - | (-∞, +∞) |
|
chirp coefficient The chirp coefficient (dλ/dz) for a linear chirped grating. |
0 | - | (-∞, +∞) |
|
chirp table Table containing normalized length versus chirp coefficients. |
<2,2> [0, 1, 0,...] | - | - |
|
load chirp from file Defines whether or not to load chirp coefficients from an input file or to use the currently stored values. |
false | - | [true, false] |
|
chirp filename The file containing the normalized length versus chirp coefficient values. Refer to the Implementation Details section for the format expected. |
chirp.dat | - | - |
Thermal Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
|
thermal effects Defines whether or not to enable thermal effects. |
false | - | [true, false] |
|
temperature Defines the temperature. |
%temperature% | K | (-∞, +∞) |
|
nominal temperature Defines the nominal temperature where temperature sensitivity values are measured. |
300 | K | (-∞, +∞) |
|
thermal fill factor The waveguide length ratio affected by the thermal effects. |
1 | - | [0, 1] |
Numerical Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
|
number of steps The number of discretization steps for a chirped or apodized grating. |
50 | - | [1, +∞) |
Numerical/Digital Filter Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
|
digital filter Defines whether or not to use a digital filter to represent the element transfer function in time domain. |
false | - | [true, false] |
|
single tap filter Defines whether or not to use a single tap digital filter to represent the element transfer function in time domain. |
false | - | [true, false] |
|
number of taps estimation Defines the method used to estimate the number of taps of the digital filter. |
fit tolerance | - | [disabled, fit tolerance, group delay |
|
filter fit tolerance Defines the mean square error for the fitting function. |
0.001 | - | (0, 1) |
|
window function Defines the window type for the digital filter. |
rectangular | - | [rectangular, hamming, hanning |
|
number of fir taps Defines the number of coefficients for digital filter. |
256 | - | [1, +∞) |
|
maximum number of fir taps Defines the number of coefficients for digital filter. |
4096 | - | [1, +∞) |
|
filter delay Defines the time delay equivalent to a number of coefficients for digital filter. |
0 | s | [0, +∞) |
|
initialize filter taps Defines whether to use the initial input signal to initialize filter state values or to set them to zero values. |
false | - | [true, false] |
|
delay compensation The number of delays to compensate for latency. |
0 | - | [0, +∞) |
Diagnostic Properties
| Name | Default value | Default unit | Range |
|---|---|---|---|
|
run diagnostic Enables the frequency response of the designed filter implementation and the ideal frequency response to be generated as results. |
false | - | [true, false] |
|
diagnostic size The number of frequency points used when calculating the filter frequency response. |
1024 | - | [2, +∞) |
Results
| Name | Description |
|---|---|
| diagnostic/response #/transmission | The complex transmission vs. frequency corresponding to the ideal and designed filter. |
| diagnostic/response #/gain | The gain vs. frequency corresponding to the ideal and designed filter. |
| diagnostic/response #/error | Mean square error comparing the frequency response of the designed filter implementation with the ideal frequency response. |
====================================
Implementation Details
This element represents a Waveguide Bragg Grating (WGB), which can be used to create optical filters that reflect light at some wavelengths and transmits at others.
WBGs are commonly formed by periodic varied refractive index in a segment of waveguide. The working principle of the WBG is based on Fresnel reflection and refraction theory, when different segments in the WBG has different refractive indices, the light both reflects and refracts at the interfaces.
Some advance features such as apodization & chirp are available in this model.
Determining model settings
Coupling coefficient
One of the important features to define the WBG property is the coupling coefficient (kappa). The coupling coefficient can be interpreted as the amount of reflections of the WBG per unit length. Based on the configuration of the WBG, we provide the two most common Ways to define the coupling coefficient:
Use the coupling coefficient coupling parameter
When the “coupling parameter” is set to “coupling coefficient”, the “grating coupling coefficient” parameter will be enabled and used to set the coupling coefficient kappa. In this case, the WBG has a step-wise index change as indicated in the figure below:
The relationship between the parameters are:
$$
\begin{gathered}
\lambda_{B}=2 n_{e f f} \Lambda \\
\Delta n=n_{e f f}-n_{e f f} 1
\end{gathered}
$$
And kappa is calculated as:
$$
\kappa=\frac{2 \Delta n}{\lambda_{B}}
$$
Use the effective index change coupling parameter
When the “coupling parameter” is set to “effective index change”, the “effective index change dc” and the “effective index change ac” parameters will be enabled and used to define the coupling coefficient. In this case, the WGB model has a sinusoidal index perturbation as shown in the figure below:
The relationship between the parameters are:
$$
\begin{aligned}
\lambda_{B} &=2 n_{e f f} \Lambda \\
\beta_{0} &=\frac{2 \pi}{\lambda_{B}} n_{e f f} \\
\Delta n &=n_{e f f_{-} A C} \\
n(z)=n_{e f f} &+\Delta n / 2 \cdot \cos \left(2 \beta_{0} z\right)
\end{aligned}
$$
And kappa is calculated as:
$$
\kappa=\frac{\pi \Delta n}{2 \lambda_{B}}
$$
Phases
There are two phase terms that can be defined in this model. The “phase shift” term under “Standard” category defines the phase shift due to designated defection in the WBG center; and the “facet phase” terms under the “Mode” categories define the phase caused by the facet at the end of the WBG.
“phase shift” due to defection in the WBG center
A phase-shifted WBG opens a narrowband transmission window inside the stopband of the WBG. The amount of phase shift changes the transmission peak wavelength. The phase shift is usually achieved by a designated defection in the center of the WBG, as shown in the figure below.
In the example file “WGB_phase_shift.icp”, we included a pi/2 phase shift in the center of a WGB. The WGB without the phase shift has a stopband at 1550 nm with a bandwidth around 1 nm. Then with the pi/2 phase shift in the center, the WBG opens a very narrow passband at 1550 nm in the original stopband.
“facet phase” at the ends of the WBG
The facet phase is the phase shift caused by the facet at the end of the WBG, when light enters a high index material from a low index material or vice versa. Since this WBG model doesn’t specify the index perturbation orders (the WBG starts with a high index or a low index), users can use the facet phase parameters at each end of the WBG to represent all combinations of the index perturbation orders.
The following table shows the combinations of the index perturbation orders and the facet phase on the right and left side of the WBG to achieve them.
Chirp
An advanced feature of the waveguide Bragg Grating is the chirp in the grating period. User can define the linear chirp
Apodization
Another advanced feature of the waveguide Bragg Grating is the apodization. User can either specify the apodization by directly defining its function and parameter or loading in a file that contains the normalized length versus apodization parameter information. The apodization parameter \(a_{eff}\) is the parameter that measure the strength of the apodization profile, and consequently the reduction of the effective length. It is defined as
$$
a_{e f f}=\frac{\int_{0}^{L_{g}}|z| T(z) d z}{\int_{0}^{L_{g}}|z| d z}
$$
where \(L_g\) is the grating length and \(T(z)\) is the apodization profile. The normalized grating length is defined as \(\kappa*L_g\).