Morteza Kamalian

Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives

The nonlinear Fourier transform is a transmission and signal processing technique that makes positive use of the Kerr nonlinearity in optical fibre channels. I will overview recent advances and some of challenges in this field.

Periodic nonlinear Fourier transform for fiber-optic communications, Part I: theory and numerical methods.

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Modified nonlinear inverse synthesis for optical links with distributed Raman amplification

We propose a modification of the nonlinear digital signal processing technique based on the nonlinear inverse synthesis for the systems with distributed Raman amplification. The proposed path-average approach offers 3 dB performance gain, regardless of the signal power profile.

Experimentally characterized nonlinear fourier transform of a mode-locked fibre laser

Fibre lasers are known to provide a rich tapestry of operational regimes, which can be attributed to the nonlinear nature of light dynamics in optical fibre at high powers, and the multidimensional system parameter space. Given their inherent complexity, identifying and discerning the underlying physical processes that gives rise to them still remains a formidable challenge. Here, for the first time in experiment, we show how the Nonlinear Fourier Transform (NFT) (see e.g. [1-3] and references therein) can be used as an effective tool for the identification and classification of lasing regimes. The NFT provides a framework for identification of coherent structures (nonlinear multi-soliton modes) embedded into dispersive radiation [2, 3].

Energy based transmission optimisation in nonlinear Fourier domain

The systems employing nonlinear Fourier transform (NFT) as a method of nonlinearity mitigation have recently become the subject of intensive study (see e.g. [1-4] and references therein). In particular the so-called nonlinear inverse synthesis (NIS) method was proposed in [2]. Within this method the data is modulated using the continuous part of the NFT spectrum. Then the time domain waveform is generated using the inverse NFT (INFT) before being launched into the fiber. At the receiver NFT operation is performed to retrieve the continuous NFT spectrum (Fig. 1a, see [4]). We consider here the model channel when signal evolution is described by the lossless nonlinear Schrodinger equation (NLSE) with AWGN term arising due to ideal distributed amplification [5]. The signal-noise interaction inside the NFT domain was studied in [3] including the noise statistics.