Calculates the power spectral density of frequency noise from time-domain signal

## Keywords

analyzer, optical

## Ports

Name | Type |
---|---|

input | Optical Signal |

## Properties

### General Properties

Name | Default value | Default unit | Range |
---|---|---|---|

Defines the name of the element. |
Optical Frequency Noise Spectrum Analyzer | - | - |

Defines whether or not to display annotations on the schematic editor. |
true | - | [true, false] |

Defines whether or not the element is enabled. |
true | - | [true, false] |

Defines the element unique type (read only). |
Optical Frequency Noise Spectrum Analyzer | - | - |

A brief description of the elements functionality. |
Calculates the power spectral density of frequency noise from time-domain signal | - | - |

Defines the element name prefix. |
OFNSA | - | - |

Defines the element model name. |
- | - | - |

Defines the element location or source in the library (custom or design kit). |
- | - | - |

Defines the local path or working folder $LOCAL for the element. |
- | - | - |

An optional URL address pointing to the element online help. |
- | - | - |

Defines the icon or element symbol view option. |
small | - | [small, medium |

### Standard Properties

Name | Default value | Default unit | Range |
---|---|---|---|

Enables setting the time range( start/stop) of the analysis. |
false | - | [true, false] |

Time instant to start the signal analysis. |
0 | s | [0, +∞) |

Time instant to stop the signal analysis. |
1 | s | [0, +∞) |

Defines the linewidth shape. The formula used to estimate the linewidth depends on the linewidth shape either Lorentzian or Gaussian |
Lorentzian | - | [Lorentzian, Gaussian |

Defines the number of segments for partitioning the input signal for the purpose of statistical averaging of the frequency noise power spectral density. |
10 | - | [1, +∞) |

The power spectral density is smoothed on a log scale. The smoothing window parameter defines the frequency range with the minimum frequency equal to the minimum frequency in the frequency noise power spectral density plot over which to smooth the plot to estimate the linewidth. |
10 | GHz* *std. unit is Hz |
(0, +∞) |

### Simulation Properties

Name | Default value | Default unit | Range |
---|---|---|---|

Input signal selection option. |
last | - | [last, index |

The signal index to analyzed. |
1 | - | [1, +∞) |

Defines whether inserted delays should be included as part of the signal or not. |
false | - | [true, false] |

### Display Properties

Name | Default value | Default unit | Range |
---|---|---|---|

Defines whether or not to update display and annotations during the simulation. |
true | - | [true, false] |

Defines how ofter to update the element. This is the minimum number of new data values available at the element input port that will trigger the element update. |
1024 | - | [0, +∞) |

Defines whether or not to limit the number of values displayed in the element display. |
false | - | [true, false] |

This is the number of data values used to update the display and annotations during the simulation. |
2048 | - | [2, +∞) |

## Results

Name | Description |
---|---|

mode #/linewidth | The calculated linewidth of the signal spectrum. |

mode #/power spectral density | The single-sided frequency noise power spectral density. |

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## Implementation Details

The optical frequency noise spectrum analyzer (OFNSA) estimates the linewidth of a laser signal by calculating the frequency noise spectral density. Theoretical derivation establishes the relation between the frequency noise spectral density and the linewidth [1]. For a Lorentzian line shape, the full width at half maximum (FWHM) is given by:

$$ \begin{gathered} FWHM_{Lorentzian}={\pi\ h_0} \end{gathered} $$ |
(1) |

where \(h_0(Hz^2/Hz)\) is the constant level of the spectral density below a cutoff frequency \(f_{c}\). The cutoff frequency is defined as the frequency where the spectral density falls to zero. For a Gaussian line shape, the FWHM is given by:

$$ \begin{gathered} FWHM_{Gaussian}=\sqrt{8 ln (2)h_0 f_c} \end{gathered} $$ |
(2) |

The key parameters of the OFNSA are the *linewidth shape*, *number of segments* and *psd smoothing window*. The *linewidth shape* is either Lorentzian or Gaussian. The user must select the expected line shape as the linewidth is calculated according to eq (1) or eq (2) above. The default linewidth shape is Lorentzian.

The *number of segments* defines the number of partitions the input time signal is divided into for the purpose of statistical averaging of the frequency noise spectral density. The default value is 10 which means the input time-domain signal is divided into 10 segments, then an average is taken after calculating the single-sided psd of each segment. Another important parameter is the *psd smoothing window* which defines the frequency range over which the signal will be smoothed with the minimum frequency equal to the minimum frequency in the frequency noise power spectral density plot. The power spectral density is smoothed on a log scale. The user should be careful when selecting this window as it should extend only to the constant (flat) region of the frequency noise spectral density curve.

Another key parameter is the *refresh* in Display settings. If this parameter is set to true, then annotations and displays will be updated during simulation. By default, the linewidth calculated value is annotated and therefore it will be updated during simulation. In addition, enabling the *limit display memory* allows an update of the frequency noise and the smoothed frequency noise spectra as the simulation is running. Before the simulation starts, the user should right click on the OFNSA and select *Display results. *Note that this option might slow down the simulation and therefore should be used carefully. The feature is disabled by default.

To view the results, the user can right click on the *power spectral density* in the Result view, then select Visualize **->** New visualizer, or just double click on the results. To view the spectral density properly, the user will need to change the linear scale to loglog scale, as shown below. From the figure, one can decide the range for the smoothing window. For example, the window chosen in the figure below is 40 GHz, which represents the constant region of the spectrum. No need to re-run the simulation, only change the parameters then right-click on the analyzer and select *Validate analyzer*.

To achieve an accurate estimation of the linewidth, the user should be careful when selecting the number of segments. The phase noise is a random process and therefore a *statistical* *averaging* is required by selecting many segments. While increasing the number of segments improves statistical averaging, it decreases the segment time window and therefore increases the minimum frequency of the frequency noise spectrum causing the constant level of the spectral density curve to be smaller. In this case, the user can increase the simulation time window, or decrease the number of segments if the simulation time window is already too large.

NOTE: The linewidth estimation is based on the fact there is only one peak in the spectrum. Therefore, if there is more than one peak, the user should use optical bandpass filters to separate the different peaks then use the OFNSA to estimate the linewidth of each peak independently. |

**References**

[1] Gianni Di Domenico, Stéphane Schilt, and Pierre Thomann, "Simple approach to the relation between laser frequency noise and laser line shape," Appl. Opt. 49, 4801-4807 (2010).