An overview of the recent developments in the field of cylindrical vector beams is
provided. As one class of spatially variant polarization, cylindrical vector beams
are the axially symmetric beam solution to the full vector electromagnetic wave
equation. These beams can be generated via different active and passive methods.
Techniques for manipulating these beams while maintaining the polarization symmetry
have also been developed. Their special polarization symmetry gives rise to unique
high-numerical-aperture focusing properties that find important applications in
nanoscale optical imaging and manipulation. The prospects for cylindrical vector
beams and their applications in other fields are also briefly discussed.

Cylindrical vector beams: from mathematical concepts to applications

A higher-order Poincare sphere and Stokes parameter representation of the higher-order states of polarization of vector vortex beams that includes radial and azimuthal polarized cylindrical vector beams is presented. The higher-order Poincare sphere is constructed by naturally extending the Jones vector basis of plane wave polarization in terms of optical spin angular momentum to the total optical angular momentum that includes higher dimensional orbital angular momentum. The salient properties of this representation are illustrated by its ability to describe the higher-order modes of optical fiber waveguides, more exotic vector beams, and a higher-order Pancharatnam-Berry geometric phase.

Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light

Modal decomposition of light has been known for a long time, applied mostly to pattern recognition. With the commercialization of liquid-crystal devices, digital holography as an enabling tool has become accessible to all, and with it all-digital tools for the decomposition of light have finally come of age. We review recent advances in unravelling the properties of light, from the modal structure of laser beams to decoding the information stored in orbital angular momentum (OAM)-carrying fields. We show application of these tools to fiber lasers, solid-state lasers, and structured light created in the laboratory by holographic laser beam shaping. We show by experimental implementation how digital holograms may be used to infer the intensity, phase, wavefront, Poynting vector, polarization, and OAM density of some unknown optical field. In particular, we outline how virtually all the previous ISO-standard beam diagnostic techniques may be readily replaced with all-digital equivalents, thus paving the way for unravelling of light in real time. Such tools are highly relevant to the in situ analysis of laser systems, to mode division multiplexing as an emerging tool in optical communication, and for quantum information processing with entangled photons.

Creation and detection of optical modes with spatial light modulators

We describe the polarization topology of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge q at its center (q-plate). The polarization topological structures for different q-plates and different input polarization states have been studied experimentally by measuring the Stokes parameters point-by-point in the beam transverse plane. Furthermore, we used a tuned q=1/2-plate to generate cylindrical vector beams with radial or azimuthal polarizations, with the possibility of switching dynamically between these two cases by simply changing the linear polarization of the input beam.

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Polarization pattern of vector vortex beams generated by q-plates with different topological charges

Vector beams, and in particular vector vortex beams, have found many applications in recent times, both as classical fields and as quantum states. While much attention has focused on the creation and detection of scalar optical fields, it is only recently that vector beams have found their place in the modern laboratory. In this review, we outline the fundamental concepts of vector beams, summarise the various approaches to control them in the laboratory, and give a concise overview of the many applications they have spurned.

https://iopscience.iop.org/article/10.1088/2040-8986/aaeb7d/pdf

A review of complex vector light fields and their applications

We describe a convenient approach for generating arbitrary vector beams in a 4-f system with a spatial light modulator (SLM) and a common path interferometric arrangement. A computer-generated hologram is introduced onto SLM for performing the beam conversion. Optical realization of a variety of polarization configurations confirms the reliability and flexibility of our method.

Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement

In this paper, a modified low-bandwidth sub-Nyquist sampling receiving scheme enabled by optical shaping is investigated in an intensity modulation/direct detection (IM/DD) orthogonal frequency-division multiplexing (OFDM) system, which can reduce the sampling rate and analog bandwidth of an analog-to-digital converter (ADC) at the receiving end. By changing the phase matrix of preprocessing, the modified scheme can distinguish different groups of data only by controlling the delay of the shaping module. In addition, the proposed RF sharing architecture can further reduce the cost and increase the feasibility of the scheme. Based on arcsine digital pre-distortion (DPD) technology, a DPD optical pulse shaping scheme is proposed to achieve better spectrum aliasing in the optical domain. With the help of the DPD shaping, we successfully experimentally demonstrate the 12.5-GHz/44.45-Gbit/s IM/DD OFDM system with low-bandwidth (3.125 GHz) and sub-Nyquist sampling rate (6.25 GSa/s) ADC. The experiment results show that the proposed scheme can not only effectively achieve low-bandwidth reception, but also achieve about 0.4 dB receiver sensitivity improvement compared with the traditional high-bandwidth scheme at BER of 3.8×10-3 after 10.2 km standard single mode fiber transmission, which indicates that the proposed scheme is a promising low-cost candidate to provide large transmission capacity for the next-generation network.

Modified low-bandwidth sub-Nyquist sampling receiving scheme in an IM/DD OFDM system enabled by improved optical shaping.

Maximum likelihood sequence estimation (MLSE) is an optimal solution to realize sequence detection in the digital signal processing (DSP) of short reach O-band intensity modulation/direct detection (IM/DD) systems with bandwidth limitation. However, traditional MLSE requires relatively high computational complexity for short reach optical interconnect. Although the computational complexity of single-symbol sequence detection is quite low, the capability of combating with the inter symbol interference (ISI) is inadequate. To combine the low computational complexity of single-symbol sequence detection with the high reliability of multi-symbol sequence detection in MLSE, decision region partition aided MLSE (DRP-MLSE) is proposed and verified with 60-Gbaud and 65-Gbaud PAM-4 IM/DD systems over 40-km single-mode fiber (SMF) transmission. The experimental results show that the DRP-MLSE can realize similar performance of conventional MLSE with negligible penalty and significantly lower computational complexity.

Decision region partition aided MLSE for O-band 65-Gbaud PAM-4 system over 40-km transmission with a severe bandwidth constraint.

In this paper, a joint application of simplified Tomlinson-Harashima precoding (THP) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -log-maximum a posteriori probability ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -log-MAP) decoder at transceivers is proposed for low complexity faster than Nyquist (FTN) 4-ary pulse amplitude modulation (PAM4) signaling. A THP with only two taps is applied at the transmitter for FTN-induced inter-symbol interference elimination and equalization-induced noise amplification issue mitigation, which effectively relieves the burden of the receiver. At the receiver, a low complexity M-log-MAP decoder is equipped for residual impairments cancellation, thus a feedback channel is not required to accurately obtain the channel state information for the transmitter. Taking advantage of this collaborative approach, the proposed scheme performs much better than applying the two schemes separately. We experimentally demonstrate the proposed scheme in 70, 75, and 80GBaud PAM4 systems with a 32-GHz brick-wall filter, corresponding to 0.914, 0.853, and 0.8 FTN compression factor, respectively. The results show that the 80GBaud PAM4 signal is successfully transmitted over 2-km single mode fiber with the bit-error-rate (BER) under the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> . It is also observed that the proposed scheme shows about 0.7dB receiver sensitivity improvement compared to the error propagation-free decision feedback equalizer, namely the performance upper bound of the THP, at BER of 7% HD-FEC threshold in a 75GBaud FTN PAM4 system. According to the experimental results, the proposed scheme is a promising solution for bandwidth-starved low-cost intra-datacenter interconnect. 

Simplified THP and M-log-MAP Decoder Based Faster than Nyquist Signaling for Intra-datacenter Interconnect

Real-valued neural network nonlinear equalization for complex-valued signals combined with single sideband (SSB) modulation is proposed to be a promising scheme for long-reach passive optical networks (LR-PONs). With the assist of neural network equalizer (NNE), fiber nonlinearity induced by large launch power can be mitigated. We experimentally demonstrate a transmission of 120 Gbps 16-QAM SSB signal in C-band over an 80-km single mode fiber (SMF) without optical inline amplifier and pre-amplifier.

Wei-Jiang Ni

Papers

Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement

Modified low-bandwidth sub-Nyquist sampling receiving scheme in an IM/DD OFDM system enabled by improved optical shaping.

Decision region partition aided MLSE for O-band 65-Gbaud PAM-4 system over 40-km transmission with a severe bandwidth constraint.

Simplified THP and M-log-MAP Decoder Based Faster than Nyquist Signaling for Intra-datacenter Interconnect

Real-Valued Neural Network Nonlinear Equalization for Long-Reach PONs Based on SSB Modulation