# Ultra-Wideband WDM Optical Network Optimization

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## Abstract

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## 1. Introduction

## 2. Problem Formulation

- $\mathcal{N}$
- set of all nodes
- $\mathcal{T}$
- set of transponders
- $\mathcal{S}$
- set of frequency slices
- $\mathcal{E}$
- set of edges
- ${\mathcal{P}}_{(n,{n}^{\prime})}$
- set of paths between nodes $n,{n}^{\prime}\in \mathcal{N}$; $p\subseteq \mathcal{E}$
- $\mathcal{B}$
- set of bands
- ${\mathcal{S}}_{b}$
- set of frequency slices used by band $b\in \mathcal{B}$; ${\mathcal{S}}_{b}\subseteq \mathcal{S}$; $\bigcup _{b\in \mathcal{B}}}{\mathcal{S}}_{b}=\mathcal{S$
- ${\mathcal{S}}_{t}$
- set of frequency slices that can be used as starting slices for transponder $t\in \mathcal{T}$; ${\mathcal{S}}_{t}\subseteq \mathcal{S}$

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of a two-dimensional colourless, directionless, contentionless, flexible grid (CDC-F) ROADM used in C + L WDM systems; WSS—Wavelength Selective Switch, IFA—Ingress Fiber Amplifier, EFA—Egress Fiber Amplifier.

**Figure 2.**Schematic diagram of Wavelength Selective Switch (WSS) array used in CDC-F ROADM from Figure 2.

**Figure 6.**The dependence of network cost on the number of paths for Polish, American and German networks.

Network | # Nodes | # Link | # Demand |
---|---|---|---|

Polish | 12 | 18 | 66 |

USA | 12 | 15 | 66 |

German | 17 | 26 | 136 |

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 |

2 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | |

3 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | ||

4 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | |||

5 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | ||||

6 | 50 | 50 | 50 | 50 | 50 | 50 | |||||

7 | 50 | 50 | 50 | 50 | 50 | ||||||

8 | 50 | 50 | 50 | 50 | |||||||

9 | 50 | 50 | 50 | ||||||||

10 | 50 | 50 | |||||||||

11 | 50 |

Set | Set Settings |
---|---|

$\mathcal{N}$ | in Table 1 |

$\mathcal{E}$ | in Table 1 |

$\mathcal{S}$ | 768 slots |

$\mathcal{B}$ | 2 bands |

$\mathcal{T}$ | 3 transponders |

${\mathcal{S}}_{b}$ | ${\mathcal{S}}_{1}=\{1\dots 384\}$, ${\mathcal{S}}_{2}=\{385\dots 768\}$ |

${\mathcal{S}}_{t}$ | ${\mathcal{S}}_{1}=\{1\cdots 380\}\cup \{385\cdots 764\}$ ${\mathcal{S}}_{2}=\{1\cdots 378\}\cup \{385\cdots 762\}$ ${\mathcal{S}}_{3}=\{1\cdots 376\}\cup \{385\cdots 760\}$ |

Constant | Constant Settings |
---|---|

bitrate [Gbps] | $v\left(1\right)=100$, $v\left(2\right)=200$, $v\left(3\right)=400$ |

OSNR [dB] | $c\left(1\right)=$ 12, $c\left(2\right)=$ 15, $c\left(3\right)=$ 22 |

d(n,n’) [Gbps] | an example in Table 2 |

$\xi \left(b\right)$ | $\xi \left(1\right)=1$, $\xi \left(2\right)=2$ |

$\xi (t,b)$ | $\xi (1,1)=5$, $\xi (2,1)=7$, $\xi (3,1)=9$ $\xi (1,2)=6$, $\xi (2,2)=8.4$, $\xi (3,2)=11.8$ |

$\Delta \left(t\right)$ [GHz] | $\Delta \left(1\right)=$ 25, $\Delta \left(2\right)=50$, $\Delta \left(3\right)=75$, |

$\nu \left(b\right)$ [THz] | $\nu \left(1\right)=193.8$, $\nu \left(2\right)=188.5$ |

$\mu \left(s\right)$ [dB/km] | $\mu \left(s\right)=0.046$ for $b=1$ and $\mu \left(s\right)=0.055$ for $b=2$ |

W [dB] | 15 |

V [dB] | 15 |

${P}_{0}$ [W] | ${10}^{-3}$ |

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**MDPI and ACS Style**

Kozdrowski, S.; Żotkiewicz, M.; Sujecki, S.
Ultra-Wideband WDM Optical Network Optimization. *Photonics* **2020**, *7*, 16.
https://doi.org/10.3390/photonics7010016

**AMA Style**

Kozdrowski S, Żotkiewicz M, Sujecki S.
Ultra-Wideband WDM Optical Network Optimization. *Photonics*. 2020; 7(1):16.
https://doi.org/10.3390/photonics7010016

**Chicago/Turabian Style**

Kozdrowski, Stanisław, Mateusz Żotkiewicz, and Sławomir Sujecki.
2020. "Ultra-Wideband WDM Optical Network Optimization" *Photonics* 7, no. 1: 16.
https://doi.org/10.3390/photonics7010016