Recently there is an increasing interest in tailored optical fields with complex amplitude, phase and polarization spatial distributions, as well as specifically designed temporal waveforms. Scalar optical vortices carrying orbital angular momentum and vectorial vortices such as radially and azimuthally polarized beams are among the most intensively studied examples. Comprehensive summaries of earlier developments can be found in several recent articles and edited books, e.g., by Zhan (Adv. Opt. Photon.1, 1, 20091943-8206), Padgett (Adv. Opt. Photon.3, 161, 20111943-8206 ), Forbes (Adv. Opt. Photon.8, 200, 20161943-8206), Zhan (Vectorial Optical Fields, World Scientific Publishing, 2013), and Forbes (Laser Beam Propagation, CRC Press, 2014), while applications of these complex optical fields in promising areas continue to emerge. To capture the latest developments in this important emerging field of optics, it is our pleasure to introduce the Chinese Optics Letters Special Issue on the Complex Optical Fields with contributions from scientists around the world who are active in this field.

It is known that one can determine the mode orders (i.e., the azimuthal order and radial order) of a partially coherent LGpl beam (i.e., a partially coherent vortex beam) based on the measurement of the cross-correlation function (CCF) and the double correlation function (DCF) together. The technique for measuring the CCF is known. In this Letter, we propose a method for measuring the DCF. Based on the proposed method, the determination of the mode orders of a partially coherent LGpl beam is demonstrated experimentally.

We investigate the linear momentum density of light, which can be decomposed into spin and orbital parts, in the complex three-dimensional field distributions of tightly focused vortex segmented beams. The chosen angular spectrum exhibits two spatially separated vortices of opposite charge and orthogonal circular polarization to generate phase vortices in a meridional plane of observation. In the vicinity of those vortices, regions of negative orbital linear momentum occur. Besides these phase vortices, the occurrence of transverse orbital angular momentum manifests in a vortex charge-dependent relative shift of the energy density and linear momentum density.

In this Letter, a refractive index measurement of a dielectric sample using highly focused radially polarized light is reported. Through imaging analysis of the optical field at the pupil plane of a high numerical aperture (NA) objective lens reflected by the sample under study, the Brewster angle is found. Employing a high NA objective lens allows the measurement of multiple angles of incidence from 0° to 64° in a single shot. The refractive index of the sample is estimated using the measured Brewster angle. The experimental results are compared with the theoretical images computed with the Fresnel theory, and a good agreement is obtained.

Tailored complex optical fields, may find applications in optical manipulation, imaging, microscopy, quantum information processing, and optical communications. Here, we focus on data information transfer for optical communications using complex optical fields. We review recent research progress in complex optical field modulation, multiplexing, and multicasting for data information transfer on different platforms of waveguides, free space, and fiber. Challenges and perspectives are also discussed.

We investigate the stimulated Brillouin scattering (SBS) properties of light beams carrying orbit angular momentum (OAM). The phase conjugation of light beams carrying OAM is experimentally achieved in an SBS mirror with a random phase plate. The spectrum and the pulse width compression of SBS light are measured. It is shown that the phenomena of pulse compression is observed and OAM conservation is confirmed in the SBS process. The OAM transfer from photons to phonons may find potential applications in photon-phonon conversion-based signal-processing schemes by using OAM multiplexing.

Femtosecond (fs) cylindrical vector beams (CVBs) have found use in many applications in recent years. However, the existing rigid generation methods seriously limit its development. Here, we propose a flexible method for generating fs-CVBs with arbitrary polarization order by employing half wave plates and vortex retarders. The polarization state, autocorrelation width, pulse width, and spectrum features of the input and generated CVB pulses are measured and compared. The results verify that the generated CVBs remain in the fs regime with no appreciable temporal distortion, and the energy conversion efficiency can reach as high as 96.5%, even for a third-order beam. As a flexible way to generate fs-CVBs, this method will have great significance for many applications.

In this Letter, an effective method using a mode selective coupler (MSC), which is composed of a three-core fiber is presented to generate optical vortices (OVs). The conversions of OVs with different topological charges, 0→±1 and 0→±3, are simulated in detail. We also prove that a higher-order topological charge can be obtained simply by changing the parameters of the fiber to increase the number of modes in the fiber. The polarization of OVs can be controlled as well.

We generate and measure the versatile vortex linear light bullet, which combines a high-order Bessel beam and an Airy pulse. This three-dimensional optical wave packet propagates without distortion in any medium, while carrying an orbital angular momentum. Its non-varying feature in linear propagation is verified by a three-dimensional measurement. Such a novel versatile linear light bullet can be useful in various applications such as micromachining.

We design and demonstrate new types of optical tweezers with lateral pulling forces that allow full control of biological samples with complex geometric shapes. With appropriate beam shaping, the dual tug-of-war tweezers effectively hold and stretch elongated biological objects of different sizes, and the triangular tug-of-war tweezers with threefold rotational symmetry steadily hold asymmetric objects in the plane of observation and exert stretching forces along three directions. We successfully apply these tweezers to manipulate microparticles and bacterial cells in aqueous media.

Light fields with extraordinary propagation behaviors, such as nondiffracting and self-bending, are useful in the optical delivery of energy, information, and even objects. A kind of helical beam is constructed here based on the caustic method. With the appropriate design, the main lobe of these helical beams can be both well-confined and almost nondiffracting, while moving along a helix with its radius, period, number of rotations, and main lobes highly adjustable. In addition, the peak intensity of the main lobe fluctuates below 15% during propagation. These promising characteristics may enable a variety of potential applications based on these beams.

Remotely sensing an object with light is essential for burgeoning technologies, such as autonomous vehicles. Here, an object’s rotational orientation is remotely sensed using light’s orbital angular momentum. An object is illuminated by and partially obstructs a Gaussian light beam. Using an SLM, the phase differences between the partially obstructed Gaussian light beam’s constituent OAM modes are measured analogous to Stokes polarimetry. It is shown that the phase differences are directly proportional to the object’s rotational orientation. Comparison to the use of a pixelated camera and implementation in the millimeter wave regime are discussed.

We show the power of spirally polarized doughnut beams as a tool for tuning the field distribution in the focus of a high numerical aperture (NA) lens. Different and relevant states of polarization as well as field distributions can be created by the simple turning of a λ/2 retardation wave plate placed in the excitation path of a microscope. The realization of such a versatile excitation source can provide an essential tool for nanotechnology investigations and biomedical experiments.

We present the investigation on deformation of orbital angular momentum (OAM) modes in bending ring-core fibers (RCFs) with different structure sizes through numerical and experimental studies. The effective refractive index differences of even and odd fiber eigenmodes, which constitute OAM±1,1 modes, induced by RCF bending and their impacts on the OAM±1,1 mode intensity distributions are analyzed. Bending experiments are also carried out on three different RCFs, and the results match well with simulation values. It is found that RCFs with smaller inner and outer radii show preferable tolerance to the fiber bending.

An optical sensor is designed to support the Fano effect based on a compound resonant waveguide grating (CRWG). The transmission spectra of the CRWG are investigated by utilizing a theoretical method that combines the temporal coupled mode theory with the eigenmode information of the grating structure. The theoretical results, which are observed to agree closely with those acquired by rigorous coupled-wave analysis, show that the linewidth of the transmission spectrum decreases upon increasing the distance between the grating strips, and the central resonance frequency decreases as the refractive index of the analyte increases. Here, the proposed CRWG structures will find potential uses in optical sensing.

The common and traditional method for optical dispersion compensation is concatenating the transmitting optical fiber by a compensating optical fiber having a high-negative dispersion coefficient. In this Letter, we take the opposite direction and show how an optical fiber with a high-positive dispersion coefficient is used for dispersion compensation. Our optical dispersion compensating structure is the optical implementation of an iterative algorithm in signal processing. The proposed dispersion compensating system is constructed by cascading a number of compensating sub-systems, and its compensation capability is improved by increasing the number of embedded sub-systems. We also show that the compensation capability is a trade-off between the transmission length and bandwidth. We use the simulation results to validate the performance of the introduced dispersion compensating module. Photonic crystal fibers with high-positive dispersion coefficients can be used for constructing the proposed optical dispersion compensating module.

In this Letter, we propose a novel constellation-shaping carrier-less amplitude and phase (CAP) modulation scheme to alleviate the systematic nonlinearity in visible light communication (VLC) systems. A simple geometric transformation shaping method is employed to convert the normal square lattice constellation into multiple circular constellations. The feasibility and performance are investigated and experimentally demonstrated by a 1.25 Gb/s CAP-modulated VLC system. The results indicate that the circular constellation has better resistance to systematic nonlinearity compared with a rectangular constellation. The dynamic range of input signal peak-to-peak values promotes 20% at a low bias voltage nonlinear area and 50% at a high bias voltage nonlinear area. To the best of our knowledge, this is the first time constellation-shaping CAP has ever been reported in indoor high data rate VLC systems.

We present compact silicon-arrayed waveguide grating routers (AWGRs) with three different channel spacings of 20, 6.4, and 3.2 nm for optical interconnect systems. The AWGR with the 20 nm channel spacing shows a low loss of 2.5 dB and a low crosstalk of 20 dB and has a footprint of only 0.27 mm×0.19 mm. The AWGR with the channel spacing of 6.4 nm has loss ranging from 3 to 8 dB, and the crosstalk is 18 dB. As for the 3.2 nm channel spacing, the loss is about 4 dB, and the crosstalk is 12 dB.

The influence of the nonlinear propagation effect on three 400 Gb/s/ch (400G) optical fiber communication systems with typical modulation formats, dual-carrier 16-quadrature amplitude modulation (16QAM), single-carrier 16QAM (single-16QAM), and four-carrier quadrature phase-shift keying, are investigated. The received optical signal-to-noise ratio (OSNR), affected by the nonlinear interference noise together with the amplified spontaneous emission noise, are compared with three 400G systems and a standard 100 Gb/s/ch system by numerical simulations. Both single channel and multichannel cases are considered. Single-16QAM is found to have the best OSNR among those modulation formats.

A dual optical time domain reflectometry (OTDR) system, which employs two different continuous waves at the optical line terminal and a pair of fiber Bragg gratings at the end of each optical network unit, is proposed in a time-division multiplexing passive optical network (PON). The proposed scheme accomplishes the fiber fault monitoring by comparing the different wavelength’s testing curves. Complete complementary code is utilized to measure multiple wavelength signals simultaneously with only one receiver and to improve the dynamic range of this system. The PON system consisting of 20 km feeding fiber and a 1:16 splitter is investigated by the experiments. The experimental results show that the faulty branch can be successfully identified by using our scheme. What is more, we also demonstrate that our scheme can be applied to the multi-stage PON.

A frequency-stabilized laser system at 1572 nm for space-borne carbon dioxide (CO2) detection LIDAR to realize the precise measurement of the global atmospheric CO2 concentration is presented in this Letter. A distributed-feedback laser diode serves as the master laser (ML) and is wavelength locked to the CO2 line center at 1572.0179 nm using the external frequency modulation technique. The root mean square frequency drift is suppressed to about 50 kHz at an average time of 0.1 s over 8 h. Based on optical phase-locked loops, an online seeder and an offline seeder are offset locked to the reference laser at 1572.024 and 1572.081 nm, respectively, retaining virtually the same frequency stability as the ML.

We demonstrate a single-longitudinal-mode Ho3+:YVO4 unidirectional ring laser based on the acousto-optic effect, utilizing the features of the acousto-optical Q switch and half-wave plate to achieve unidirectional operation. The maximum power achieved in the single-longitudinal-mode at 2053.9 nm is 941 mW when the absorbed power is set as 4.4 W, yielding a nearly 50% slope efficiency. The M2 factor is 1.1. The results show that such a technique offers a potentially promising new method for achieving a high power and narrow linewidth 2 μm single-longitudinal-mode laser.

We report a waveguide crossing based on a multimode-interference (MMI) structure for metal-insulator-metal (MIM) waveguides. The MMI-based crossing comprises two orthogonal intersecting MMI waveguides that are connected to the single-mode input/output waveguide symmetrically. Single self-images are formed at the crossing center and output plane of the MMI waveguide, thereby mitigating the crosstalk and improving the throughput. The characteristics of the proposed MMI-based crossing are investigated with the finite element method of Comsol Multiphysics. The results show that the throughput reaches 1.8 dB and the crosstalk is less than 46 dB at the wavelength of 1550 nm.

We present a simple method to measure the spatial coherence of hard x-ray beams. Based on the convolution of Gaussian functions, we analyze the diffraction patterns of a grating irradiated by partially coherent hard x rays with a constrained beam diameter. The spatial coherence properties of an x-ray beam are obtained from the width of the diffraction peaks with high accuracy. The results of experiments conducted by combining a pinhole with a grating show a good agreement with our calculation using the Gaussian–Schell model.