Although fruitful studies have been conducted on carrier frequency offset (CFO) estimations in linear coherent optical fiber communication systems, there are few studies on CFO estimations and recoveries in the systems based on the nonlinear Fourier transform (NFT). Although the CFO is originated from the linear frequency domain, it definitely has effects on nonlinear spectra, including the shift of the nonlinear frequency and the phase rotations of the scattering data, which are similar to its effects on linear spectra. This work indicates that it is feasible to estimate frequency offset (FO) by capturing symbol variations in the nonlinear frequency domain (NFD) rather than in the linear frequency domain; the latter was usually exploited in the literature. Based on a thorough investigation of the FO induced behavior that appears in a nonlinear frequency division multiplexing (NFDM) system, we proposed a nonlinear frequency domain estimation method aided by training symbols (TS) using an angle search algorithm after NFT operations at the receiver. The discussions in this paper prove that the proposed method is generally applicable to the NFDM systems regardless of whether using single or multiple eigenvalues. A performance comparison between the NFD method and the conventional method in the linear frequency domain is performed with different modulation formats for both single and multiple eigenvalue NFDM transmission systems. The analysis results show that the proposed method holds the better stability and estimation accuracy in contrast with the linear domain estimation method. The TS overhead can also be deduced dramatically, which implies better transmission efficiency. Therefore, the NFD method is more powerful for eigenvalue NFDM transmission systems, especially for the scenarios where high order modulation formats and multiple eigenvalues are utilized.

A joint scheme introducing probabilistic shaping (PS) at the transmitter and utilizing a neural network (NN) equalizer at the receiver is proposed to improve the performance of the b -modulated nonlinear frequency division multiplexing (NFDM) system. Through a numerical simulation, we demonstrate that PS plays a leading role for low launch power case, which improves the performance of the system effectively, while the NN equalizer’s superiority appears in a high launch power region, whose main role is to weaken the correlation among subcarriers for improving system performance. The proposed scheme would enlighten the optimum modulation and detection schemes of the NFDM system.

A novel all-fiber broadband mode multiplexer based on an elliptical ring core fiber structure mode selective coupler (MSC) is proposed and analyzed numerically. The MSC is composed of a core-doped single-mode fiber and a polarization-maintaining elliptical ring-shaped core few-mode fiber (FMF). The mode multiplexing can be implemented by a single ${\mathrm{LP}}_{01}$ mode excitation that does not introduce insertion loss, which can simplify and promote the multiplexer. The high refractive index difference between the elliptical annular region and the cladding of the FMF, as well as the ellipticity of the ring-shaped core of the FMF could not only decompose the degenerate modes, but also reduce the mode coupling of the adjacent spatial modes to eliminate the multiple-input-multiple-output digital-signal processing in the receiver of the mode division multiplexing system. Finally, a seven-mode multiplexer is modeled and optimized for operation covering the C+L band. Furthermore, the multiplexer provides a high coupling efficiency ($>64\%$ for the worst case) for the seven spatial modes, ${\mathrm{LP}}_{01}$, ${\mathrm{LP}}_{11a}$, ${\mathrm{LP}}_{11b}$, ${\mathrm{LP}}_{21a}$, ${\mathrm{LP}}_{21b}$, ${\mathrm{LP}}_{31a}$, and ${\mathrm{LP}}_{31b}$, and relatively high mode extinction ratios of more than 15 dB in the C-band.

Orbital angular momentum (OAM) mode-division multiplexing (MDM) has recently been under intense investigations as a new way to increase the capacity of fiber communication. In this paper, a two-layer Erbium-doped fiber amplifier (EDFA) for an OAM multiplexing system is proposed. The amplifier is based on the circular photonic crystal fiber (C-PCF), which can maintain a stable transmission for 14 OAM modes by a large index difference between the fiber core and the cladding. Further, the two-layer doped region can balance the amplification performance of different modes. The relationship between the performance and the parameters of the amplifier is analyzed numerically to optimize the amplifier design. The optimized amplifier can amplify 18 modes (14 OAM modes) simultaneously over the C-band with a differential mode gain (DMG) lower than 0.1 dB while keeping the modal gain over 23 dB and noise figure below 4 dB. Finally, the fabrication tolerance and feasibility are discussed. The result shows a relatively large fabrication tolerance in the OAM EDFA parameters.

Nonlinear Fourier transform (NFT)-based nonlinear frequency division multiplexing (NFDM) system has the potential to overcome the limit of fiber nonlinearity. In the NFDM system, the symbol information is modulated onto the nonlinear spectra, which consist of continuous and discrete spectrum. In theory, the dual-polarization (DP) NFDM system with the continuous and discrete spectrum (full spectrum, FS) modulation has the potential to achieve higher spectral efficiency. However, due to the complexity of the NFT and inverse NFT (INFT) numerical algorithms, the DP-FS modulated NFDM system is rarely reported. For the FS-NFDM system, the existing INFT algorithms either only support q-modulation and present poor performance, or have large discrete spectral error as the continuous spectrum energy increases. In this paper, we propose an INFT algorithm design theory. Based the theory, an accurate DP-INFT algorithm is proposed. The algorithm supports not only q-modulation, but also b-modulation with better performance. Employing the proposed INFT algorithm, we demonstrate, for the first time, a 174.5 Gbit/s FS modulated NFDM transmission system with 1440 km.

A micro-fiber Mach–Zehnder interferometer (MZI), with a thousands-µm-long ring-core fiber (RCF), is demonstrated, and its performance investigation is also implemented. In this paper, the proposed MZI is manufactured by ends-splicing the short RCF segment with single-mode fiber (SMF-28), respectively. The scheme of the MZI is a typically core-mismatch structure, which has the advantages of miniaturization and simplification. Due to the core mismatch between RCF and SMF, the light from the SMF can be well separated into ring core (RC) and silica center (SC) of the RCF at the first splicing point. After transmitting through the RC and SC, the two separated light beams encounter each other and interfere at the second splicing point. Different from conventional micro-fiber MZIs using SMFs or few-mode fibers, the RCF has a higher numerical aperture, which can generate a larger optical path-length difference with a short length fiber, accumulates a higher extinction ratio and suppresses the crosstalk between the core and cladding modes. Therefore, our proposed MZI is more stable and the best extinction ratios can reach up to 18.2 dB. Meanwhile, owing to the core structure of RCF (where SC is surrounded by high-index ring core), the power propagating through low-index area of RCF is mostly confined into SC (termed the silica-center modes). These characteristics would lead to the lower sensitivity to external disturbances.