Propagation of vector vortex beams through a turbulent atmosphere

Laguerre-Gaussian laser filamentation for the control of electric discharges in air

We study the use of Laguerre-Gaussian (LG) femtosecond laser filament with multi GW peak power to guide electric sparks in the atmosphere. We demonstrate that an LG beam with a vortex phase or with 6 azimuthal phase steps generates a filamentation regime, where a longer and more uniform energy deposition is produced compared to a normal beam with a flat phase. Such filaments can guide electric discharges over much longer distances. This technique could significantly extend the guiding range of laser filaments for lightning control and other long-range atmospheric experiments involving filamentation.

Full-Dimensional Geometric-Phase Spatial Light Metamodulation

Full-dimensional spatial light modulation requires simultaneous, arbitrary, and independent manipulation of the spatial phase, amplitude, and polarization. This is crucial for leveraging the complete physical dimension resources of light. However, full-dimensional metamodulation can be challenging due to the need for multiple independent control factors. To address this challenge, here we propose parallel-tasking metasurfaces to enable full-dimensional spatial light metamodulation based fully on the geometric-phase concept. Indeed, the meta-atoms are divided into several subphases, each of which serves as an independent control factor to manipulate light phase, amplitude, and polarization through geometric phase, interference, and orthogonal polarization superposition, respectively. Therefore, the macroscopic group of meta-atoms leads to metasurfaces that can achieve broadband full-dimensional spatial light metamodulation, as demonstrated by various types of structured light generation. This approach paves the way to future wide applications of light manipulation enabled by full-dimensional spatial light metamodulation.

Resonance of vector vortex beams in a triangular optical cavity

We experimentally demonstrate resonance of first-order vector vortex beams (VVB) with a triangular optical cavity. We also show that, due to their symmetry properties, the VVBs commonly known as radial and azimuthal beams do not resonate at the same cavity length, which could be explored to use the triangular resonator as a mode sorter. In addition, an intracavity Pancharatnam phase shifter (PPS) is implemented in order to compensate for any birefringent phase that the cavity mirrors may introduce.

Optical Force Effects of Rayleigh Particles by Cylindrical Vector Beams

High-order cylindrical vector beams possess flexible spatial polarization and exhibit new effects and phenomena that can expand the functionality and enhance the capability of optical systems. However, building a general analytical model for highly focused beams with different polarization orders remains a challenge. Here, we elaborately develop the vector theory of high-order cylindrical vector beams in a high numerical aperture focusing system and achieve the vectorial diffraction integrals for describing the tight focusing field with the space-variant distribution of polarization orders within the framework of Richards-Wolf diffraction theory. The analytical formulae include the exact three Cartesian components of electric and magnetic distributions in the tightly focused region. Additionally, utilizing the analytical formulae, we can achieve the gradient force, scattering force, and curl-spin force exerted on Rayleigh particles trapped by high-order cylindrical vector beams. These results are crucial for improving the design and engineering of the tightly focused field by modulating the polarization orders of high-order cylindrical vector beams, particularly for applications such as optical tweezers and optical manipulation. This theoretical analysis also extends to the calculation of complicated optical vortex vector fields and the design of diffractive optical elements with high diffraction efficiency and resolution.

Propagation properties of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam through anisotropic atmospheric turbulence

Using the extended Huygens-Fresnel principle and the Rytov approximation, the analytical formula for the propagation of a partially coherent electromagnetic hyperbolic-sine-Gaussian vortex beam (PCEShVB) in anisotropic atmospheric turbulence has been theoretically derived. Detailed studies have been conducted on the evolution characteristics of the average intensity, the degree of coherence (DOC), and the degree of polarization (DOP) of the beam in turbulence. The results show that during propagation, the intensity distribution of the beam will exhibit a spiral structure, and the overall distribution of the light spots will rotate in a direction related to the sign of the topological charge. The DOC distribution of PCEShVB will display a pattern reminiscent of beam interference fringes with an increase in propagation distance, with the number of "interference fringes" greatly impacted by the hyperbolic sine parameter. Furthermore, PCEShVB with a large initial coherent length and hyperbolic sine parameter will increase the degree of separation of the spots and yield a large DOP. Finally, for the validation of the theoretical findings, the random phase screen method was employed to simulate the propagation of PCEShVB through anisotropic atmospheric turbulence. The studies revealed a consistent alignment between the simulation results and the theoretical predictions.

Underwater entanglement propagation of auto-focusing Airy beams

In underwater wireless optical communication, orbital angular momentum (OAM) states suffer from turbulence distortions. This study aims to investigate the effectiveness of auto-focusing and OAM entanglement of the beams in reducing the turbulence effects. We implement the single-phase approximation and the extended Huygens-Fresnel principle to derive the detection probability of the entangled Airy beams under unstable oceanic turbulence. The results show that auto-focusing can protect the signal OAM mode and suppress modal crosstalks, while entangled OAM states can further enhance the resistance against oceanic turbulence around the focus position. The numerical analysis demonstrates that after the auto-focusing position, the beams evolve in completely opposite directions, indicating that the focal length should be modulated according to the length of a practical link to enhance received signals. These findings suggest that entangled auto-focusing vortex beams may be a desirable light source in underwater communication systems.

Generation of vector vortex wave modes in cylindrical waveguides

In this paper, we propose a method to generate Vector Vortex Modes (VVM) inside a metallic cylindrical waveguide at microwave frequencies and demonstrate the experimental validation of the concept. Vector vortex modes of EM waves can carry both spin and orbital angular momentum as they propagate within a tubular medium. The existence of such waves in tubular media can be beneficial to wireless communication in such structures. These waves can carry different orbital angular momentum and spin angular momentum, and therefore, they feature the ability to carry multiple orthogonal modes at the same frequency due to spatial structure of the phase and polarization. In essence, high data rate channels can be developed using such waves. In free space, Orbital Angular Momentum carrying vortex waves have beam divergence issues and a central field-minima, which makes these waves unfavorable for free space communication. But vector vortex mode waves in guided structures do not suffer from these drawbacks. This prospect of enhancement of communication spectrum in waveguides provides the background for the study of vortex wave in circular waveguides. In this work, new feed structures and a radial array of monopoles are designed to generate the VVM carrying waves inside the waveguide. The experimental findings on the distribution of the amplitude and phase of the electromagnetic fields inside the waveguide are presented and the relationship between the waveguide fundamental modes and VVMs are discussed for the first time. The paper also presents methods for varying the cutoff frequency of the VVMs by introducing dielectric materials in the waveguide.

Turbulence-resilient detection of the rotational Doppler effect with cylindrical vector beams

Recent years have witnessed a growing research interest in the rotational Doppler effect associated with orbital angular momentum of light, emerging as a powerful tool to detect rotating bodies in remote sensing. However, this method, when exposed to the turbulence in a realistic environment, has some severe limitations, leading to the unrecognizable rotational Doppler signals overwhelmed in background noise. Here we put forward a concise yet efficient method that enables the turbulence-resilient detection of the rotational Doppler effect with cylindrical vector beams. Specifically, by adopting the polarization-encoded dual-channel detection system, the low-frequency noises caused by turbulence can be individually extracted and subtracted, and thus mitigate the effect of turbulence. We demonstrate our scheme by conducting proof-of-principle experiments, whose results manifest the feasibility of a practical sensor to detect the rotating bodies in non-laboratory conditions.

On-chip generation of Bessel-Gaussian beam via concentrically distributed grating arrays for long-range sensing

Bessel beam featured with self-healing is essential to the optical sensing applications in the obstacle scattering environment. Integrated on-chip generation of the Bessel beam outperforms the conventional structure by small size, robustness, and alignment-free scheme. However, the maximum propagation distance (Z_max) provided by the existing approaches cannot support long-range sensing, and thus, it restricts its potential applications. In this work, we propose an integrated silicon photonic chip with unique structures featured with concentrically distributed grating arrays to generate the Bessel-Gaussian beam with a long propagation distance. The spot with the Bessel function profile is measured at 10.24 m without optical lenses, and the photonic chip's operation wavelength can be continuously performed from 1500 to 1630 nm. To demonstrate the functionality of the generated Bessel-Gaussian beam, we also experimentally measure the rotation speeds of a spinning object via the rotational Doppler Effect and the distance through the phase laser ranging principle. The maximum error of the rotation speed in this experiment is measured to be 0.05%, indicating the minimum error in the current reports. By the compact size, low cost, and mass production potential of the integrated process, our approach is promising to readily enable the Bessel-Gaussian beam in widespread optical communication and micro-manipulation applications.

Influences of salinity and temperature on propagation of radially polarized rotationally-symmetric power-exponent-phase vortex beams in oceanic turbulence

In this paper, the propagation properties of radially polarized rotationally-symmetric power-exponent-phase vortex beams (RP-RSPEPVBs) in oceanic turbulence were theoretically and experimentally studied. Based on the extended Huygens-Fresnel diffraction integral and vector beams theories, the theoretical propagation model of RP-RSPEPVBs in the oceanic turbulence was established. Then, the numerical simulations were carried out to study the influences of the propagation distance z, the rate of dissipation of turbulence kinetic energy per unit mass of fluid ε, the temperature-salinity contribution ratio ω, and the dissipation rate of the mean-squared temperature χT on the optical intensity, spectral degree of polarization (DOP) and spectral degree of coherence (DOC) of RP-RSPEPVBs. Further, an experiment setup was demonstrated to confirm the influences of salinity and temperature on propagation of RP-RSPEPVBs in oceanic turbulence. The results showed that increasing salinity, propagation distance, and turbulence intensity, will result in beam diffusion and intensity reduction of the RP-RSPEPVBs, as well as depolarization and decoherence. Contrarily, high temperature mitigated the intensity loss of the RP-RSPEPVBs and the spectral DOP and spectral DOC increased when the turbulence tends to be dominated by temperature. As a vector beam, the RP-RSPEPVB shows well anti-turbulence interference characteristics, which provides a new choice for optical underwater communication and imaging.

Femtosecond filamentation of optical vortices for the generation of optical air waveguides

We study the filamentation in air of multi-millijoule optical vortices and compare them with the classical filamentation regime. The femtosecond vortex beam generates multiple plasma filaments organized in a cylindrical geometry. This plasma configuration evolves into a meter-scale tubular neutral gas column that can be used as a waveguide for nanosecond laser pulses at 532 nm. It appears that optical vortices produce a more uniform heating along the propagation axis, when compared with Gaussian or super-Gaussian beams, and that the resulting low-density channel is poorly sensitive to the laser input power thanks to the combination of filamentation intensity clamping and phase vorticity.

Super cosh-Gauss nonuniformly correlated radially polarized beam and its propagation characteristics

In this paper, a new kind of partially coherent vector beam termed as super cosh-Gauss nonuniformly correlated radially polarized (SCNRP) beam is introduced. Such beam source exhibits almost perfect coherence between two points that are within the beam center region or located on a ring concentric with the beam center. However, the coherence drops or even vanishes when the two points leave the central region and are located on the concentric rings with different radii. The second-order statistical properties, such as the spectral density, the state of polarization (SOP), and the degree of polarization (DOP) of such beam upon free-space propagation are studied through numerical examples. Our results reveal that the beam displays a self-focusing property during propagation. The focusing ability can be enhanced with increasing the beam index and decreasing the beam's spatial coherence width, whereas the DOP and SOP remain unchanged on propagation. Meanwhile, we establish an experimental system with the use of a radial polarization converter and a digital micro-mirror device to synthesize the SCNRP beam with controllable beam index and spatial coherence width. The spectral density and polarization properties of the synthesized beam during propagation are measured and analyzed in the experiment. The experimental results agree well with our theoretical predictions.

Multiple quasi-perfect vector vortex beams with arbitrary 3D position on focus

We show a method for creating multiple independent quasi-perfect vector vortex beams with real-time programmable radii, topological charges, polarization orders, and position in three dimensions using a device based on a phase-only liquid-crystal-on-silicon display. We achieved the simultaneous generation of up to seven independent beams, with topological charges from -3 to 3, and found great agreement between the simulated and the measured phases and polarization structures. Additionally, we used the same scheme for enhancing the depth of focus of a single beam, resulting in a "tube" beam that preserves its properties during propagation.

Self-focusing propagation characteristics of a radially-polarized beam in nonlinear media

In this study, an analytical formula for the self-focusing length of a radially polarized beam (RPB) is first derived, which has a similar behavior to the semi-empirical Marburger formula of a Gaussian beam, and is beneficial to quantitatively and qualitatively analyze practical experimental scenarios. However, the relation of the self-focusing length with the states of polarization (SoPs) was evaluated, and it was found that RPB with spatially inhomogeneous SoP at the field cross-section can retain a further self-focusing length compared to a beam with a spatially homogeneous one. The influence of the topological charge on the self-focusing length is explored, which shows that RPB with a low topological charge can achieve a high-power density at a relatively further receiver plane. Therefore, it is demonstrated that the RPB as a laser source not only extends the self-focusing length, but also improves the power density of the target. With the help of RPB, it is possible to realize a controllable self-focusing length and a high target optical power density, which may have potential applications in fine optical manipulation, optical communication, high-power long-range laser atmospheric propagation, and related areas.

Unscrambling OAM mode using digital phase-shifting in the Stokes fluctuations correlation

In this Letter, we propose and experimentally demonstrate a new, to the best of our knowledge, non-interferometric and highly stable technique to unscramble the incident orbital angular momentum (OAM) state and quantitatively measure the phase structure from the non-imaged random light. A new theoretical basis is developed and also verified by numerical simulation and experimental demonstration. We also quantitatively investigate the OAM modes of the incident light using orthogonal projection.

Cylindrical vector beam multiplexer/demultiplexer using off-axis polarization control

The emergence of cylindrical vector beam (CVB) multiplexing has opened new avenues for high-capacity optical communication. Although several configurations have been developed to couple/separate CVBs, the CVB multiplexer/demultiplexer remains elusive due to lack of effective off-axis polarization control technologies. Here we report a straightforward approach to realize off-axis polarization control for CVB multiplexing/demultiplexing based on a metal-dielectric-metal metasurface. We show that the left- and right-handed circularly polarized (LHCP/RHCP) components of CVBs are independently modulated via spin-to-orbit interactions by the properly designed metasurface, and then simultaneously multiplexed and demultiplexed due to the reversibility of light path and the conservation of vector mode. We also show that the proposed multiplexers/demultiplexers are broadband (from 1310 to 1625 nm) and compatible with wavelength-division-multiplexing. As a proof of concept, we successfully demonstrate a four-channel CVB multiplexing communication, combining wavelength-division-multiplexing and polarization-division-multiplexing with a transmission rate of 1.56 Tbit/s and a bit-error-rate of 10-6 at the receive power of -21.6 dBm. This study paves the way for CVB multiplexing/demultiplexing and may benefit high-capacity CVB communication.

Weak turbulence effects on different beams carrying orbital angular momentum

The study of beams carrying orbital angular momentum (OAM) has been of interest for its use in free-space optical communications (FSOC), directed energy applications, and remote sensing (RS). For FSOC and RS, it is necessary to measure the wavefront of the beam to recover transmitted or environmental information, respectively. In this computational study, common OAM beams such as the Laguerre-Gaussian (LG), Bessel-Gaussian (BG), and Bessel beams are propagated through atmospheric turbulence and compared to their Gaussian beam counterpart. The turbulence is simulated using multiple phase screens within the framework of a split-step method. Beam metrics used to quantify beam propagation will include the spatial coherence radius, OAM spectrum, on-axis intensity, spot size, divergence, and on-axis scintillation. Atmospheric turbulence along the path is limited to the weak scintillation limit, where beam parameters can be predicted analytically using the Rytov approximation. The results show that BG beams and multiplexed BG beams retain more OAM information than their LG and Bessel beam counterparts. The LG beam on-axis intensity and on-axis scintillation are seen to be independent of OAM mode. The scintillation of the LG beam is less than a BG, Bessel, and Gaussian beam across low- and high-order OAM modes. Insight into these results is discussed through studying the beam divergence, while the initial spot sizes of the Gaussian, LG, and BG beams are limited to the same spatial extent.

Polarization-spatial Gaussian entanglement in partially coherent light fields

The problem of bipartite entanglement in partially coherent paraxial vector light fields is addressed. A generalized uncertainty principle suited for the polarization-spatial degrees of freedom is introduced. Partial transpose is implemented through the obtained generalized uncertainty principle. Partial transpose is shown to be necessary and sufficient in detecting entanglement for a class of partially coherent vector light fields which have a spatial part to be Gaussian. An experimental realization of the studied entangled states using classical optical interferometry is outlined.

Intra-symbol frequency-domain averaging for turbulence mitigation in optical orbital angular momentum multiplexing

Optical vortex beams (VBs) possessing helical phase-front have attracted considerable attention in multiplexing communication for their orthogonal orbital angular momentum (OAM) modes. However, the mode-crosstalk and signal jitter caused by turbulence fluctuation are two main challenges in OAM multiplexing communication. Here, we introduce an intra-symbol frequency-domain averaging technology (ISFA) for turbulence mitigation. By equalizing the distorted multiplexing signals, ISFA mitigates the amplitude and phase jitter of received signals without adding system complexity and information redundancy. The experimental results show that VBs are successfully demultiplexed, and the transmission rate reaches 48 Gbit/s. After ISFA, the bit-error-rate of QPSK-OFDM signals is reduced from 1.10 × 10^-3 to 6.31 × 10^-4, and the error-vector-magnitude (EVM) is reduced from 31.69% to 26.29% under the turbulence strength of Cn2 = 1×10^-13m^-2/3 and equivalent transmission distance of 200 m. By combining ISFA with MIMO diversity gain, the EVM can be further reduced from 46.70% to 26.70%. These indicate that ISFA is available for turbulence mitigation and compatible with MIMO technology, which may have perspective potential in improving the performance of OAM multiplexing communication.

Direct axial plane imaging of particle manipulation with nondiffracting Bessel beams

Optical manipulation with nondiffracting beams has been attracting great interest and finding widespread applications in many fields such as chemistry, physics, and biomedicine. Generally, optical manipulation is conducted in an optical microscopy system, which, in general, only allows for imaging motions of particles in the transverse plane, rendering the observation of dynamics processes occurring in the axial plane impractical. We propose and demonstrate an optical manipulation system that incorporates an axial plane imaging module. With this system, the trapping behavior in the transverse plane and the transportation process in the axial plane of a particle immersed in a Bessel beam were acquired simultaneously in real time.

Compensation-free high-dimensional free-space optical communication using turbulence-resilient vector beams

Free-space optical communication is a promising means to establish versatile, secure and high-bandwidth communication between mobile nodes for many critical applications. While the spatial modes of light offer a degree of freedom to increase the information capacity of an optical link, atmospheric turbulence can introduce severe distortion to the spatial modes and lead to data degradation. Here, we demonstrate experimentally a vector-beam-based, turbulence-resilient communication protocol, namely spatial polarization differential phase shift keying (SPDPSK), that can reliably transmit high-dimensional information through a turbulent channel without the need of any adaptive optics for beam compensation. In a proof-of-principle experiment with a controllable turbulence cell, we measure a channel capacity of 4.84 bits per pulse using 34 vector modes through a turbulent channel with a scintillation index of 1.09, and 4.02 bits per pulse using 18 vector modes through even stronger turbulence corresponding to a scintillation index of 1.54.

Resistance to turbulence is an ongoing challenge for point-to-point freespace communications. Here the authors present a protocol for encoding a large amount of information in vector beams that are transmittable through a moderately strong turbulent channel without adaptive beam compensation.

Cylindrical vector beam multiplexing for radio-over-fiber communication with dielectric metasurfaces

Radio-over-fiber (ROF) technology, loading microwave signal on light beams, has attracted considerable attention in wireless access network for its superiority in processing high-frequency microwave signals. Multiplexing for achieving high-capacity density, however, remains elusive in ROF communication because the optical microwave occupies large bandwidth. Here, we introduce a cylindrical vector beam (CVB) multiplexing for ROF communication with dielectric Pancharatnam-Berry phase-based metasurfaces (PBMs). CVBs, a structured light beam possessing spatially nonuniform polarization distribution and carrying vector mode, provide an additional multiplexing dimension for optical communication with the advantages of weak scintillation in free-space and low mode injure in few-mode-fiber. Exploiting the spin-orbit interaction of the PB phase, we construct PBMs to manipulate CVBs, which show broadband working wavelengths ranging from C- to L-band. After 3 m free-space propagation, two multiplexed CVBs carrying 100 GHz microwave are successfully demultiplexed, and the 100 GHz ROF communication with 12 Gbit/s QPSK-OFDM signals is realized. The crosstalk of the multiplexed CVBs is less than -15.13 dB, and the bit-error-rates (BERs) are below 3.26 × 10^-5. With 5 km few-mode-fiber transmission, the CVBs are also demultiplexed with the BERs of 6.51 × 10^-5. These results indicate that CVB is not only capable of free-space transmission but also available for few-mode-fiber transmission, which might pave new avenues for the multiplexing of ROF communications.

Few-mode random fiber laser with a switchable oscillating spatial mode

Random fiber lasers are of tremendous interest to diverse applications for optical fiber sensing, speckle-free imaging. To date, random fiber lasers with fundamental mode oscillation have been well developed. However, controllable oscillating spatial mode in random fiber lasers have not been reported yet. Here, we propose and demonstrate a few-mode random fiber laser with a switchable oscillating spatial mode based on mode injection locking. An external signal light is injected to realize the locking of transverse mode in this random fiber laser and the direct oscillations of the fundamental mode, hybrid mode, and high order mode can be realized, respectively. This random fiber laser operates in the high-order LP₁₁ mode stably with a threshold of as low as 88 mW. High efficiency and high purity cylindrical vector beams can be obtained by removing the degeneracy of the LP₁₁ mode. This work may pave a path towards random fiber lasers with controllable spatial modes for specific applications in mode division multiplexing, imaging, and laser material processing.

Orbital angular momentum mode detection of the combined vortex beam generated by coherent combining technology

Coherent beam combining (CBC) technology has distinct advantages in generating high power vortex beam. In this paper, a circularly arranged coherent beam array (CBA) with discrete vortex phases is constructed to generate vortex beams. We demonstrated that the combined vortex beam (CVB) generated by the CBA is a multiplexing vortices optical field, which sidelobe is the coaxial interference pattern of these spiral harmonic components. Using the designed Dammam vortex grating (DVG), the orbital angular momentum (OAM) spectrum of the CVB is detected. Moreover, taking the target OAM mode purity of the CVB as the evaluation function of active phase control system, we realized the closed-loop phase control of the CBA and obtained the phase-locked output of the CVB.

Propagation of structured light through tissue-mimicking phantoms

Optical interrogation of tissues is broadly considered in biomedical applications. Nevertheless, light scattering by tissue limits the resolution and accuracy achieved when investigating sub-surface tissue features. Light carrying optical angular momentum or complex polarization profiles, offers different propagation characteristics through scattering media compared to light with unstructured beam profiles. Here we discuss the behaviour of structured light scattered by tissue-mimicking phantoms. We study the spatial and the polarization profile of the scattered modes as a function of a range of optical parameters of the phantoms, with varying scattering and absorption coefficients and of different lengths. These results show the non-trivial trade-off between the advantages of structured light profiles and mode broadening, stimulating further investigations in this direction.

Filament-induced breakdown spectroscopy with structured beams

Filament-induced ablation represents an attractive scheme for long-range material identification via optical spectroscopy. However, the delivery of laser energy to the target can be severely hindered by the stochastic nature of multiple-filamentation, ionization of ambient gas, and atmospheric turbulence. In order to mitigate some of these adverse effects, we examine the utility of beam shaping for femtosecond filament-induced breakdown spectroscopy with Gaussian and structured (Laguerre-Gaussian, Airy, and Bessel-Gaussian) beams in the nonlinear regime. Interaction of filaments with copper, zinc, and brass targets was studied by recording axially-resolved broadband emission from the filament-induced plasma. The laser-solid coupling efficacy was assessed by inferring thermodynamic parameters such as excitation temperature and electron density. While under our experimental conditions the ablation rate with Gaussian- and Laguerre-Gaussian beams is found to be similar, the Airy and Bessel-Gaussian beams offer the advantage of longitudinally extended working zones. These results provide insights into potential benefits of structuring ultrafast laser beams for standoff sensing applications.

Direct generation of 1108 nm and 1173 nm Laguerre-Gaussian modes from a self-Raman Nd:GdVO4 laser

We demonstrate a continuous-wave self-Raman Nd:GdVO₄ Laguerre-Gaussian (LG) mode laser based on different Raman shifts of 382 cm^-1 and 882 cm^-1 by shaping the pumping beam with the use of an axicon lens and a focusing lens. Selective generation of LG mode beams at 1108 nm or 1173 nm, or simultaneously 1108 nm and 1173 nm, was achieved by carefully adjusting the alignment of the laser cavity. The maximum Raman LG mode output powers at the wavelengths of 1108 nm (the first-Stokes emission of the 382 cm^-1 Raman shift) and 1173 nm (the first-Stokes emission of the 882 cm^-1 Raman shift) were measured to be 49.8 mW and 133.4 mW at the absorbed pump power of 5.69 W, respectively. The generated LG modes, formed via the incoherent superposition of two LG mode beams with positive and negative topological charges, carry zero orbital angular momentum. Such LG mode laser sources have the potential to fill in the wavelength gap of lasers in the visible and infrared regions.

Turbulence aberration correction for vector vortex beams using deep neural networks on experimental data

The vector vortex beams (VVB) possessing non-separable states of light, in which polarization and orbital angular momentum (OAM) are coupled, have attracted more and more attentions in science and technology, due to the unique nature of the light field. However, atmospheric transmission distortion is a recurring challenge hampering the practical application, such as communication and imaging. In this work, we built a deep learning based adaptive optics system to compensate the turbulence aberrations of the vector vortex mode in terms of phase distribution and mode purity. A turbulence aberration correction convolutional neural network (TACCNN) model, which can learn the mapping relationship of intensity profile of the distorted vector vortex modes and the turbulence phase generated by first 20 Zernike modes, is well designed. After supervised learning plentiful experimental samples, the TACCNN model compensates turbulence aberration for VVB quickly and accurately. For the first time, experimental results show that through correction, the mode purity of the distorted VVB improves from 19% to 70% under the turbulence strength of D/r0 = 5.28 with correction time 100 ms. Furthermore, both spatial modes and the light intensity distribution can be well compensated in different atmospheric turbulence.

Scintillation properties of a partially coherent vector beam with vortex phase in turbulent atmosphere

We undertake a computational and experimental study of an advanced class of structured beams, partially coherent radially polarized vortex (PCRPV) beams, on propagation through atmospheric turbulence. A computational propagation model is established to simulate this class of beams, and it is used to calculate the average intensity and on-axis scintillation index of PCRPV beams. On comparison with other classes of structured beams, such as partially coherent vortex beams and partially coherent radially polarized beams, it is found that the PCRPV beams, which structure phase, coherence and polarization simultaneously, show marked improvements in atmospheric propagation. The simulation results agree reasonably well with the experimental results. These beams will be useful in free-space optical communications and remote sensing.

Helicity conservation in V-point diffraction

In singular beams, topological charge is conserved during diffraction. Like scalar field diffraction, in vector field diffraction also, there are conserved quantities. A diffracting V-point disintegrates into a number of C-points of the same polarity in which the polarization singularity index is conserved. In this Letter, we show for the first time, to the best of our knowledge, that apart from the index, the helicity (handedness) is also conserved in V-point diffraction. Since V-point is devoid of any handedness, the helicity conservation entails that there is an equal number of opposite handed C-points in the diffracted field, which are interestingly also found to be orthogonal pairs. Further, coexistence of C-points of opposite handedness in the diffraction demands the presence of L-line, which is also shown. We experimentally demonstrate these by studying the diffraction phenomenon through two different types of apertures.

Propagation of converging polarization singular beams through atmospheric turbulence

We report investigations on propagation of converging vector beams containing C-point and V-point polarization singularities through atmospheric turbulence. The C-point singularity is generated by superposition of the l=0 and l=1 orbital angular momentum (OAM) states, whereas the V-point singularity is generated by a superposition of the l=-1 and l=1 OAM states in orthogonal polarizations. The propagation of these beams through extended atmosphere is modeled by placing random phase screens along a 2 km propagation path. The random phase screens were generated using the FFT method with von Karman spectrum and Cn2=10^-14  m^-2/3. The quality of intensity profile of the focused vector beams after propagation through turbulence is assessed using the instantaneous signal-to-noise ratio and the on-axis scintillation index measurements. Our simulation results show that although both the C-point and V-point beams perform better than their scalar OAM components, C-point beams are seen to maintain much better beam intensity profile compared to the V-point beams. This observation is explained in terms of the OAM diversity of the individual polarization states and the correlation of their associated speckle patterns. The results presented here are important for engineering laser beams that can maintain a robust intensity profile on propagation through long-range atmospheric turbulence.

Propagation of Cylindrical Vector Laser Beams in Turbid Tissue-Like Scattering Media

We explore the propagation of the cylindrical vector beams (CVB) in turbid tissue-like scattering medium in comparison with the conventional Gaussian laser beam. The study of propagation of CVB and Gaussian laser beams in the medium is performed utilizing the unified electric field Monte Carlo model. The implemented Monte Carlo model is a part of a generalized on-line computational tool and utilizes parallel computing, executed on the NVIDIA Graphics Processing Units (GPUs) supporting Compute Unified Device Architecture (CUDA). Using extensive computational studies, we demonstrate that after propagation through the turbid tissue-like scattering medium, the degree of fringe contrast for CVB becomes at least twice higher in comparison to the conventional linearly polarized Gaussian beam. The results of simulations agree with the results of experimental studies. Both experimental and theoretical results suggest that there is a high potential of the application of CVB in the diagnosis of biological tissues.

Nonparaxial propagation of vector vortex beams diffracted by a circular aperture

In terms of the vectorial Rayleigh-Sommerfeld diffraction integral, the analytical expressions of the arbitrary vector vortex Laguerre-Gaussian beams on the higher-order Poincaré sphere diffracted by a circular aperture propagating in the nonparaxial and paraxial regimes are presented. The cylindrical vector beam, circularly polarized vortex beam, and elliptically polarized vortex beam are viewed as the special cases of our general result. The analyses show that the nonparaxial evolution properties of the apertured vector vortex beams are determined by the waist width, the truncation parameter, the topological charge, and the ellipticity angle.

Sculpting complex polarization singularity networks

Polarization singularities in vectorial light fields have become an important tool for different cutting-edge applications such as information processing with integer information units. However, even though vectorial singularities naturally form configurations of multiple singular points, up to now only rather simple, mostly cylindrical vector beams including single central singularities, have been considered. Here we demonstrate the customization of extended singularity networks embedded in a class of complex polarization structures based on general Ince-Gaussian modes, namely, Ince-Gaussian vector modes. Contributing to fundamental singular optics, our investigations evince the conservation of tailored singularity arrangements upon 3D propagation, whereby respective modes enlarge the range of stable vectorial fields, paving the way to information technologies with a significantly enhanced number of degrees of freedom.

Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

Demonstration of a vectorial optical field generator with adaptive close loop control

We experimentally demonstrate a vectorial optical field generator (VOF-Gen) with an adaptive close loop control. The close loop control capability is illustrated with the calibration of polarization modulation of the system. To calibrate the polarization ratio modulation, we generate 45° linearly polarized beam and make it propagate through a linear analyzer whose transmission axis is orthogonal to the incident beam. For the retardation calibration, circularly polarized beam is employed and a circular polarization analyzer with the opposite chirality is placed in front of the CCD as the detector. In both cases, the close loop control automatically changes the value of the corresponding calibration parameters in the pre-set ranges to generate the phase patterns applied to the spatial light modulators and records the intensity distribution of the output beam by the CCD camera. The optimized calibration parameters are determined corresponding to the minimum total intensity in each case. Several typical kinds of vectorial optical beams are created with and without the obtained calibration parameters, and the full Stokes parameter measurements are carried out to quantitatively analyze the polarization distribution of the generated beams. The comparisons among these results clearly show that the obtained calibration parameters could remarkably improve the accuracy of the polarization modulation of the VOF-Gen, especially for generating elliptically polarized beam with large ellipticity, indicating the significance of the presented close loop in enhancing the performance of the VOF-Gen.

Generation of perfect polarization vortices using combined gratings in a single spatial light modulator

Perfect polarization vortices (PPVs) are a type of vector beam with a diameter independent of the polarization order. In this paper, an experimental method is proposed to generate PPVs with an anisotropic polarization distribution. First, a specially designed hologram is generated on a liquid-crystal spatial light modulator (SLM) to obtain Bessel-Gaussian (BG) beams. Second, the BG beams are transformed into PPVs in the Bessel region by an interferometer, which includes a polarized beam splitter, two reflectors, and several lenses. In our experiment, PPVs with adjustable polarization orders and diameters are obtained by generating various combined holograms on the SLM.

Robust laser beam engineering using polarization and angular momentum diversity

We describe a laser beam engineered to carry l = 0 and l = 1 orbital angular momentum (OAM) states in orthogonal polarizations. It is observed that on collinear transmission through a random phase screen, the far field diffraction intensity patterns for the individual polarization states are complementary with significant negative correlation. As a result the combined intensity profile for the beam remains robust against time varying phase fluctuations. In our simulation and experiment the SNR for the central lobe of the combined far-field diffraction pattern defined as mean divided by the standard deviation of intensity values shows significant improvement over that for individual polarizations. The concept of polarization and OAM diversity as demonstrated here can be considered valuable for robust laser beam engineering without the requirement of any active real-time correction methods.

Precise transverse alignment of spatial light modulator sections for complex optical field generation

Based on the properties of the dove prism and the Fourier optics approach, the coordinate relationships among four spatial light modulator (SLM) sections in a vectorial optical field generator are derived and experimentally verified. Taking the coordinate system of the first SLM section as a reference, the coordinate displacements between the first section and subsequent sections are determined via employing specially designed four-quadrant patterns, which enable the visualization of the degree of freedom controlled by each SLM section. A complex optical field could be accurately generated through combining the derived coordinate relationships and pre-compensation of the measured coordinate displacements. Several typical complex optical fields are experimentally generated to demonstrate the validity of the proposed transverse alignment method.

Circularly symmetric cusped random beams in free space and atmospheric turbulence

A class of random stationary, scalar sources producing cusped average intensity profiles (i.e. profiles with concave curvature) in the far field is introduced by modeling the source degree of coherence as a Fractional Multi-Gaussian-correlated Schell-Model (FMGSM) function with rotational symmetry. The average intensity (spectral density) generated by such sources is investigated on propagation in free space and isotropic and homogeneous atmospheric turbulence. It is found that the FMGSM beam can retain the cusped shape on propagation at least in weak or moderate turbulence regimes; however, strong turbulence completely suppresses the cusped intensity profile. Under the same atmospheric conditions the spectral density of the FMGSM beam at the receiver is found to be much higher than that of the conventional Gaussian Schell-model (GSM) beam within the narrow central area, implying that for relatively small collecting apertures the power-in-bucket of the FMGSM beam is higher than that of the GSM beam. Our results are of importance to energy delivery, Free-Space Optical communications and imaging in the atmosphere.

Topological features of vector vortex beams perturbed with uniformly polarized light

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell’s equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams.

Decoherence of orbital angular momentum tangled photons in non-Kolmogorov turbulence

Orbital angular momentum (OAM) entangled photons propagating through non-Kolmogorov turbulence are studied by numerical simulations. Here, the paper uses the multiphase screen model, especially focusing on the influences of the azimuthal mode and the turbulence parameters (i.e., the generalized exponent, the outer scale of turbulence, and the inner scale of turbulence) on entanglement evolution in the weak scintillation regime. The results indicate that the azimuthal mode, the generalized exponent, and the outer scale of turbulence have obvious influences on OAM entanglement. However, the influence of the turbulence inner scale on OAM entanglement can be ignored.

Square array of optical vortices generated by multiregion spiral square zone plate

Herein, we present a so-called multiregion spiral square zone plate (MRSSZP), in which a spiral square zone plate is divided into a few regions, so that every region is composed of Fresnel zones, and the first zone of a given region is the same as the last zone of the previous region from a transmission point of view. We show that an MRSSZP can generate unique features of an array of an optical vortex with topological charge ±1, so that the number of vortices is directly related to the number of regions. We also demonstrate that, for an MRSSZP with topological charge 2, an array of dark cores is formed, which have phase structures similar to that of the interference of optical vortices with opposite topological charges. Besides, the focused vortex array follows a modulo-4 transmutation rule. In addition, when the topological charge becomes multiples of 4, an array of focal bright spots surrounded by a dark ring is generated. Numerical and experimental results verify the superior features of an MRSSZP.

Generating perfect polarization vortices through encoding liquid-crystal display devices

Perfect polarization vortices (PPVs) are a new kind of vector beams with identical diameters. In this paper, we propose an approach that uses encoded liquid-crystal display devices to generate PPVs and is based on the Fourier transformation of high-order Bessel-Gaussian (BG) beams. The liquid-crystal display device used here is a phase-only liquid-crystal spatial light modulator (SLM). In the experiment, a hologram consists of a holographic axicon, and a spiral phase plate is encoded on a SLM to generate high-order BG beams. Then, another SLM and a convex lens can realize the transformation from BG beams into PPVs. We analyze the diameter of the PPV obtained by our approach, and find it is impacted by the focal length of the lens as well as the period of the holographic axicon, but is little influenced by polarization order.

On the resilience of scalar and vector vortex modes in turbulence

Free-space optical communication with spatial modes of light has become topical due to the possibility of dramatically increasing communication bandwidth via Mode Division Multiplexing (MDM). While both scalar and vector vortex modes have been used as transmission bases, it has been suggested that the latter is more robust in turbulence. Using orbital angular momentum as an example, we demonstrate theoretically and experimentally that the crosstalk due to turbulence is the same in the scalar and vector basis sets of such modes. This work brings new insights about the behaviour of vector and scalar modes in turbulence, but more importantly it demonstrates that when considering optimal modes for MDM, the choice should not necessarily be based on their vectorial nature.

Bessel beams with spatial oscillating polarization

Bessel beams are widely used in optical metrology mainly because of their large Rayleigh range (focal length). Radial/azimuthal polarization of such beams is of interest in the fields of material processing, plasma absorption or communication. In this paper an experimental set-up is presented, which generates a Bessel-type vector beam with a spatial polarization, oscillating along the optical axis, when propagating in free space. A first holographic axicon (HA) HA1 produces a normal, linearly polarized Bessel beam, which by a second HA2 is converted into the spatial oscillating polarized beam. The theory is briefly discussed, the set-up and the experimental results are presented in detail.

High-dimensional encoding based on classical nonseparability

Based on the formal analogy between classical nonseparability and quantum entanglement, we present a multi-ary encoding protocol exploiting the nonseparability of orbital angular momentum (OAM) and polarization for a hybrid vector beam. Such an encoding can be realized in high-dimensional state space by transforming OAM of the vector beam under the assistance of polarization, which is called "high-dimensional" encoding. It is shown that N-ary encoding using N-dimensional non-separable basis can be obtained by manipulating N/2 different OAM modes, which is equivalent to encoding log2N bits of information. It is also shown that the decoding of vector beams can be realized with very low cross talk. Compared with the encoding protocol transforming OAM modes of scalar beams, our encoding scheme, based on classical nonseparability of vector beams, can encode much more information. This is of great benefit to the optical communication.

Experimental verification of significant reduction of turbulence-induced scintillation in a full Poincaré beam

It is theoretically predicted in [Opt. Lett.37, 1553 (2012)] that a full Poincaré (FP) beam can significantly reduce turbulence-induced scintillation. In this paper, we propose a method for synthesizing a FP beam for different beam orders and report experimental generation of the first-, second- and third-order FP beams. Furthermore, we carry out experimental measurement of the scintillation index of a FP beam passing through thermally induced turbulence. It is demonstrated that the FP beam indeed can significantly reduce the scintillation index compared to a Gaussian beam under certain conditions. Our results will be useful in long-distance free-space optical communications.

Splitting and combining properties of an elegant Hermite-Gaussian correlated Schell-model beam in Kolmogorov and non-Kolmogorov turbulence

Elegant Hermite-Gaussian correlated Schell-model (EHGCSM) beam was introduced in theory and generated in experiment just recently [Phys. Rev. A 91, 013823 (2015)]. In this paper, we study the propagation properties of an EHGCSM beam in turbulent atmosphere with the help of the extended Huygens-Fresnel integral. Analytical expressions for the cross-spectral density and the propagation factors of an EHGCSM beam propagating in turbulent atmosphere are derived. The statistical properties, such as the spectral intensity, the spectral degree of coherence and the propagation factors, of an EHGCSM beam in Kolmogorov and non-Kolmogorov turbulence are illustrated numerically. It is found that an EHGCSM beam exhibits splitting and combing properties in turbulent atmosphere, and an EHGCSM beam with large mode orders is less affected by turbulence than an EHGCSM beam with small mode orders or a Gaussian Schell-model beam or a Gaussian beam, which will be useful in free-space optical communications.

Correlation singularities in a partially coherent electromagnetic beam with initially radial polarization

We have investigated the correlation singularities, coherence vortices of two-point correlation function in a partially coherent vector beam with initially radial polarization, i.e., partially coherent radially polarized (PCRP) beam. It is found that these singularities generally occur during free space propagation. Analytical formulae for characterizing the dynamics of the correlation singularities on propagation are derived. The influence of the spatial coherence length of the beam on the evolution properties of the correlation singularities and the conditions for creation and annihilation of the correlation singularities during propagation have been studied in detail based on the derived formulae. Some interesting results are illustrated. These correlation singularities have implication for interference experiments with a PCRP beam.