Optical amplifier
Keywords
optical, unidirectional
Ports
Name | Type |
---|---|
input | Optical Signal |
output | Optical Signal |
Properties
General Properties
Name | Default value | Default unit | Range |
---|---|---|---|
name Defines the name of the element. |
Optical Amplifier | - | - |
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). |
Optical Amplifier | - | - |
description A brief description of the elements functionality. |
Optical amplifier | - | - |
prefix Defines the element name prefix. |
AMP | - | - |
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 |
---|---|---|---|
gain Defines the gain the amplifier. |
20 | dB | [0, +∞) |
noise figure Defines the noise figure of the amplifier. |
4 | dB | [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 | - | - |
Numerical Properties
Name | Default value | Default unit | Range |
---|---|---|---|
enable noise Defines whether or not to add ASE noise to the output signal. |
true | - | [true, false] |
noise center frequency The center frequency of the generated noise spectrum. |
193.1 | THz* *std. unit is Hz |
(0, +∞) |
noise bandwidth The ASE noise spectral range. |
5 | THz* *std. unit is Hz |
[0, +∞) |
generate noise bins Defines whether to generate noise bins or not. |
false | - | [true, false] |
noise bin width Defines the noise bins frequency spacing. |
100 | GHz* *std. unit is Hz |
(0, +∞) |
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, +∞) |
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 Optical Amplifier element amplifies a signal and optionally adds noise. The "gain" of the amplifier can be set in dB or as a ratio. If "enable noise" is set to true, amplified spontaneous emission (ASE) noise can be added as well. The amount of noise added is determined by the "noise figure", which can also be specified in dB or as a ratio (in which case it is the noise factor).
Please see the example file [[amplifier_example.icp]] for more information on its implementation. The following figure is the system in the example file:
The figures below show the amplification effect of the optical amplifier in time and frequency domain. The noise added by this element can also be clearly observed in these figures.
The "noise bandwidth" property is used to determine the total noise bandwidth in a transient block mode simulation with noise bins enabled. In this case, the noise and signal are treated separately and the noise bandwidth can be different than the signal bandwidth. Here is an example of the output spectrum of the AMP element in a transient block mode simulation with "generate noise bins" set to true, a "noise bandwidth" of 1 THz and a "noise bin width" of 0.1 THz:
When sample mode is used, the noise and signal are combined. It is assumed that the noise bandwidth matches the signal bandwidth, and the "noise bandwidth" property is ignored. The noise power is determined by the "noise figure" property.
Noise Figure Definition
The noise factor \(F\) of an amplifier is defined as the ratio of the signal-to-noise ratio (SNR) of the input and output:
$$F=\frac{SNR_{in}}{SNR_{out}} \tag{1}$$
The noise figure \(NF\) is the noise factor expressed in dB. The standard convention for optical amplifiers is that the noise figure is measured for the shot noise limited input. This is the definition used in INTERCONNECT. The noise figure value set in the amplifier element should be the value measured for the shot noise limited input.
In this section we focus on the amplifier and use the following notation for the amplifier: “in” means input of the amplifier and “out” means output of the amplifier. Then the amplifier noise factor is given by:
$$F_{amp}=\frac{SNR_{in,sn}}{SNR_{out}}=\frac{N_{out}}{N_{in,sn}}\frac{S_{in}}{S_{out}}=\frac{N_{out}}{G N_{in,sn}} \tag{2}$$
where \(N\) is noise power, \(S\) is signal power, \(G\) is the amplifier gain, and the subscript “sn” means “shot noise limited”. From this, the amplifier can calculate how much its excess noise \(N_{amp}\) should be:
$$N_{amp}=N_{out}−G N_{in,sn}=(F_{amp}−1) GN_{in,sn} \tag{3}$$
Now, we can calculate the expected noise factor \(F_{exp}\) in equation (1) if there is excess noise in the input above the shot noise limit:
$$F_{exp}=\frac{SNR_{in}}{SNR_{out}}=\frac{N_{out}}{N_{in}}\frac{S_{in}}{S_{out}}=\frac{N_{out}}{GN_{in}}=\frac{N_{amp}+GN_{in}}{GN_{in}}=\frac{(F_{amp}−1)N_{in,sn}}{N_{in}}+1 \tag{4}$$
From this we can see that when there is a large excess noise in the input signal
$$N_{in} ≫ N_{in,sn} \tag{5} $$
then
$$F_{exp}≅1 \tag{6}$$
which means the expected \(NF\) is then approximately zero :
$$NF_{exp}=SNR_{in}−SNR_{out}≅0 \tag{7}$$
This can be confirmed in the simulation if the CW laser source noise is much above the shot noise limit (e.g. RIN = -100 dB/Hz for 1 mW RIN reference power in the CW source). Physically, this is expected and it means that the input excess noise dominates the amplifier noise, so that the amplifier has negligible effect on the output SNR and output SNR is approximately equal to the input SNR.
We have
$$F_{exp}=F_{amp} \tag{8}$$
only when the input is shot noise limited:
$$N_{in}=N_{in,sn} \tag{9}$$
To test this one can set RIN in the CW laser source to correspond to the shot noise limit:
$$RIN_{sn}=10\log_{10}{\left( \frac{2hf}{P_{ref}} \right)} \tag{10}$$
in units of dB/Hz, where \(P_{ref}\) is the RIN reference power and \(f\) is the CW laser source frequency. In the electrical domain (CW laser + photodetector) this shot noise limit can also be created by disabling the RIN in the laser and enabling shot noise in the photodetector.
Actual equation for the amplifier noise factor in INTERCONNECT
Starting from equation (2) the noise factor of the amplifier can be derived as [2]:
\[ F_{amp}=\frac{(N_{out}−N_{in}G)}{h f\Delta f G}+\frac{1}{G} \tag{11}\]
where
\(N_{out}\) – output noise power of the amplifier (W)
\(N_{in}\) – input noise power of the amplifier (W)
\(G\) – amplifier power gain (output to input power ratio)
\(\Delta f\) - channel bandwidth (in Hz)
\(f\) - channel frequency (in Hz)
\(h\) – Planck’s constant
The noise figure is given by
$$NF=10\log_{10}(F) \tag{12}$$
The equation for the noise factor calculation for the OCN element is also given by equation (11). Equation (11) is derived under the following assumptions:
- The photodetector is considered ideal and does not introduce any additional noise.
- The input signal in the optical amplifier is considered shot noise limited.
- The output noise includes the amplified signal shot noise and the signal-spontaneous beat noise. The beat noise is due to the mixing of the amplified signal and spontaneous emission from the amplifier in the photodetector. The spontaneous emission shot noise is neglected because the amplified spontaneous power is usually much smaller than the amplified signal power. The spontaneous-spontaneous beat noise (due to mixing different frequencies of spontaneous emission) is neglected because it can be minimized by a narrow optical bandpass filter before the photodetector.
Noise Figure Example
In the circuit in the attached file [[amplifier_NF_example.icp]] the input and output signal of an optical amplifier element are measured by an OCN analyzer:
In the "RIN_sweep" parameter sweep in this file, the RIN of the CW laser source is swept and the SNR of the input and output signals of the optical amplifier element are measured. Running the script file [[amplifier_NF_example.lsf]] with this simulation file will calculate the NF using equation (1) with the measured SNRs. As the SNRs are measured in dB, the NF is equal to the difference in the input and output SNR. The script then plots the measured NF as a function of the source RIN, along with the amplifier NF setting and the shot noise limit RIN calculated using equation (10):
We can see from this plot that the measured NF (from equation (1)) is equal to the amplifier NF (from equation (11)) when the noise of the input is shot noise limited. We can also see that the measured NF approaches zero for large input RIN, as expected from equation (7).
References
- D. M. Baney, P. Gallion, and R. S. Tucker, “Theory and Measurement Techniques for the Noise Figure of Optical Amplifiers”, Optical Fiber Technology, vol. 6, pp.122-154, April 2000.
- G. Kweon, “Noise Figure of Optical Amplifiers”, Journal of the Korean Physical Society, vol. 41, pp. 617-628, November 2002.