Optical single bus ring resonator

## Keywords

optical, bidirectional

## Ports

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

port 1 | Optical Signal |

port 2 | Optical Signal |

## Properties

### General Properties

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

Defines the name of the element. |
Single Bus Ring Resonator | - | - |

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). |
Single Bus Ring Resonator | - | - |

A brief description of the elements functionality. |
Optical single bus ring resonator | - | - |

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

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. |
- | - | - |

### Standard Properties

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

Defines the bidirectional or unidirectional element configuration. |
bidirectional | - | [bidirectional, unidirectional |

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, +∞) |

The length of the waveguide. |
10e-006 | m | [0, +∞) |

### Waveguide/Mode 1 Properties

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

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, +∞) |

The label corresponding to the first orthogonal identifier. |
TE | - | - |

The loss corresponding to the first orthogonal identifier. |
0 | dB/m | [0, +∞) |

The effective index corresponding to the first orthogonal identifier. |
1 | - | (-∞, +∞) |

The group index coefficient corresponding to the first orthogonal identifier. |
1 | - | [0, +∞) |

The dispersion coefficient corresponding to the first orthogonal identifier. |
0 | s/m/m | (-∞, +∞) |

Defines the dispersion slope corresponding to the first orthogonal identifier. |
0 | s/m^2/m | (-∞, +∞) |

The power coupling coefficient corresponding to the first orthogonal identifier. |
0.5 | - | [0, 1] |

### Waveguide/Mode 2 Properties

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

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, +∞) |

The label corresponding to the second orthogonal identifier. |
TM | - | - |

The loss corresponding to the second orthogonal identifier. |
0 | dB/m | [0, +∞) |

The effective index corresponding to the second orthogonal identifier. |
1 | - | (-∞, +∞) |

The group index coefficient corresponding to the second orthogonal identifier. |
1 | - | [0, +∞) |

The dispersion coefficient corresponding to the second orthogonal identifier. |
0 | s/m/m | (-∞, +∞) |

Defines the dispersion slope corresponding to the second orthogonal identifier. |
0 | s/m^2/m | (-∞, +∞) |

The power coupling coefficient corresponding to the second orthogonal identifier. |
0.5 | - | [0, 1] |

### Waveguide/Mode 1/Thermal Properties

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

Defines the ratio between effective index variation and temperature. |
0 | /K | (-∞, +∞) |

Defines the ratio between loss variation and temperature. |
0 | /K | [0, +∞) |

### Waveguide/Mode 2/Thermal Properties

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

Defines the ratio between effective index variation and temperature. |
0 | /K | (-∞, +∞) |

Defines the ratio between loss variation and temperature. |
0 | /K | [0, +∞) |

### Thermal Properties

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

Defines whether or not to enable thermal effects. |
false | - | [true, false] |

Defines the temperature. |
%temperature% | K | (-∞, +∞) |

Defines the nominal temperature where temperature sensitivity values are measured. |
300 | K | (-∞, +∞) |

The waveguide length ratio affected by the thermal effects. |
1 | - | [0, 1] |

### Numerical/Digital Filter Properties

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

Defines whether or not to use a single tap digital filter to represent the element transfer function in time domain. |
false | - | [true, false] |

Defines the method used to estimate the number of taps of the digital filter. |
fit tolerance | - | [disabled, fit tolerance, group delay |

Defines the mean square error for the fitting function. |
0.001 | - | (0, 1) |

Defines the window type for the digital filter. |
rectangular | - | [rectangular, hamming, hanning |

Defines the number of coefficients for digital filter. |
256 | - | [1, +∞) |

Defines the number of coefficients for digital filter. |
4096 | - | [1, +∞) |

Defines the time delay equivalent to a number of coefficients for digital filter. |
0 | s | [0, +∞) |

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 |
---|---|---|---|

Enables the frequency response of the designed filter implementation and the ideal frequency response to be generated as results. |
false | - | [true, false] |

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

An optical ring resonator consists of a waveguide which looped back on itself, and the resonance occurs when the circumference of the ring is exactly a multiple number of wavelengths. Hence a ring resonator supports multiple resonances, and the free spectral range (FSR) depends on the resonator's circumference.

Commonly there is an adjacent waveguide bus beside the ring resonator to couple the light out. For a single bus ring resonator, the transmission spectrum shows dips around the resonance wavelengths, hence it behaves like a spectral filter. In this way, the single bus ring resonator can be used in optical communication systems, especially in wavelength division multiplexing (WDM) systems. Please see the WDM application example for more information.

Given the propagation constant β and the circumference L of the ring, the working principle of the single bus ring resonator can be deducted by the following equations:

$$ \varphi = \beta \cdot L $$

$$ \frac{E_{pass}}{E_{input}} = e^{j(\pi+\varphi)} \frac{a-t e^{-i \varphi}}{1-t a e^{i \varphi}} $$

$$ \frac{T_{pass}}{T_{input}}=\frac{a^{2}-2 a t \cdot \cos \varphi+t^{2}}{1-2 a t \cdot \cos \varphi+(a t)^{2}} $$

where t is the self-coupling coefficient and theoretically, t^{2} + k^{2} = 1; a is the amplitude transmission for single pass, which consists of propagation loss in the ring and coupling loss.

The figures below show the sweep results of the phase delay and gain/loss for the system in the example file single_bus_ring_resonator.icp. The gain/loss are measured for 0.1 coupling coefficient and the phase delays are measured for the coupling coefficients sweep through the values indicated in the plot.

## References

[1] Bogaerts, Wim, et al. "Silicon microring resonators." Laser & Photonics Reviews 6.1 (2012): 47-73.