# Polynomial Closed Form Model for Ultra-Wideband Transmission Systems

## TL;DR

This paper introduces a polynomial closed-form model for ultra-wideband optical transmission systems that offers improved accuracy and generality, validated against numerical models in complex scenarios, and accompanied by reconfigurable software.

## Contribution

The paper presents a novel Polynomial Closed-Form Model (PCFM) that analytically computes the GN/EGN model for ultra-wideband systems using polynomial spatial power profiles, enhancing reliability and applicability.

## Key findings

- High accuracy in multiband scenarios including Raman effects
- Effective in systems with multiple lumped losses
- Broad applicability demonstrated through validation

## Abstract

Ultrafast and accurate physical layer models are essential for designing, optimizing and managing ultra-wideband optical transmission systems. We present a closed-form GN/EGN model, named Polynomial Closed-Form Model (PCFM), improving reliability, accuracy, and generality. The key to deriving PCFM is expressing the spatial power profile of each channel along a span as a polynomial. Then, under reasonable approximations, the integral calculation can be carried out analytically, for any chosen degree of the polynomial. We present a full detailed derivation of the model. We then validate it vs. the numerically integrated GN-model in a challenging multiband (C+L+S) scenario, including Raman amplification and inter-channel Raman scattering. We then show that the approach works well also in the special case of the presence of multiple lumped loss along the fiber. Overall, the approach shows very good accuracy and broad applicability. A software implementing the model, fully reconfigurable to any type of system layout, is available for download under the Creative Commons 4.0 License.