Star coupler
Keywords
optical, bidirectional
Ports
Name  Type 

port 1  Optical Signal 
port 2  Optical Signal 
port 3  Optical Signal 
port 4  Optical Signal 
Properties
General Properties
Name  Default value  Default unit  Range 

name Defines the name of the element. 
Star Coupler     
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). 
Star Coupler     
description A brief description of the elements functionality. 
Star coupler     
prefix Defines the element name prefix. 
STAR     
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 
number of ports Defines the number of input and output ports for the element. 
2    [1, +∞) 
radius The radius of the star coupler. 
10e006  m  [0, +∞) 
angle Separation angle between adjacent input and output ports. 
0.01  rad  (∞, +∞) 
frequency Central frequency of the waveguide. A Taylor expansion around this frequency is performed to estimate the propagation transfer function of the waveguide. 
193.1  THz* *std. unit is Hz 
(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. 
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    (∞, +∞) 
group index 1 The group index coefficient corresponding to the first orthogonal identifier. 
1    [0, +∞) 
dispersion 1 The dispersion coefficient corresponding to the first orthogonal identifier. 
0  s/m/m  (∞, +∞) 
dispersion slope 1 Defines the dispersion slope corresponding to the first orthogonal identifier. 
0  s/m^2/m  (∞, +∞) 
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    (∞, +∞) 
group index 2 The group index coefficient corresponding to the second orthogonal identifier. 
1    [0, +∞) 
dispersion 2 The dispersion coefficient corresponding to the second orthogonal identifier. 
0  s/m/m  (∞, +∞) 
dispersion slope 2 Defines the dispersion slope corresponding to the second orthogonal identifier. 
0  s/m^2/m  (∞, +∞) 
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, +∞) 
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 

remove disconnected ports Defines whether or not to remove disconnected ports from the internal sparameters. 
false    [true, false] 
Numerical/Digital Filter Properties
Name  Default value  Default unit  Range 

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] 
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. 
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Implementation Details
The above figure [1] shows the geometry structure of the radiation region of the star coupler without the input and output waveguides. The two surfaces, each with radius R are separated by distance R. The angle between adjacent points is α. Then the distance between the random two points P and Q is calculated as:
$$ P Q^{2}=R^{2}\left\{\left(\sin \theta_{1}\sin \theta_{2}\right)^{2}+\left[1\left(1\cos \theta_{1}\right)\left(1\cos \theta_{2}\right)\right]^{2}\right\} $$ 
(1) 
Using the small angle approximation we can get the simplified equation for the distance as:
$$ PQ \approx R \left(1  \theta_{1}\theta_{2} \right) $$ 
(2) 
Assume that P and Q are chosen from a set of N equally separated and symmetrically allocated points from the surfaces, the p th and q th points, respectively. Then equation (2) can be written as equation (3):
$$ \theta_{1} \approx \alpha q $$ 

$$ \theta_{2} \approx \alpha p $$ 

$$ PQ \approx R \left( 1  \alpha^2 pq \right) $$ 
(3) 
Assume a signal with amplitude \( A_{p} \) presented at the input surface point P, the output signal amplitude at point Q at the output surface can be calculated based on the propagation equation as:
$$ A_{q}=\frac{A_{p}}{\sqrt{N}} \exp \left\{j \beta R\left(1\alpha^{2} p q\right)\right\} $$ 
(4) 
Reference
[1] Syms, R. R. A. "Silicaon silicon integrated optics." Advances in Integrated Optics. Springer US, 1994. 121150.