Generation of arbitrary spatially variant polarization beams with a trapezoid Sagnac interferometer

Generation of cylindrical vector modes via astigmatic mode conversion

In this work, we propose and demonstrate experimentally a compact technique for generating cylindrical vector beams based on a Michelson interferometer and a π-astigmatic mode converter. The latter is required to invert the topological charge of higher-order Laguerre-Gauss (LG) beams. Our proposed technique generalizes the use of astigmatic mode conversion, commonly associated only with scalar beams, to vector beams with a non-homogeneous polarization distribution. We anticipate that many applications based on Michelson interferometers will benefit from the unique properties of vector beams.

Optically polarized selective transmission of a fractional vector vortex beam by the polarized atoms with external magnetic fields

We investigate the role of external magnetic fields and linearly polarized pump light, especially when their directions are parallel or vertical, on the propagation of the fractional vector vortex beams (FVVBs) through a polarized atomic system. Herein, the different configurations of external magnetic fields lead to various optically polarized selective transmissions of FVVBs with different fractional topological charge α caused by the polarized atoms, which is theoretically demonstrated by the atomic density matrix visualization analysis and experimentally explored by Cesium atom vapor. Meanwhile, we find that the FVVBs-atom interaction is a vectorial process due to the different optical vector polarized states. In this interaction process, the atomic optically polarized selection property provides potential for the realization of the magnetic compass based on warm atoms. For the FVVBs, due to the rotational asymmetry of the intensity distribution, we can observe some transmitted light spots with unequal energy. Compared with the integer vector vortex beam, it is possible to obtain a more precise magnetic field direction by fitting the different "petal" spots of the FVVBs.

Non-orthogonal polarization encoding/decoding assisted by structured optical pattern recognition

The complex vector beams yield up an abundance of polarization information that has not yet been well utilized in information encoding. In this paper, we propose a polarization encoding scheme with the non-orthogonal polarization states using a stationary vector beam. Recognizing those non-orthogonal polarization states is assisted by the structured patterns of the single vector beams under different polarization projections. We show that one can achieve different capacities of encoding bits by changing the step of the polarization angle with the single vector beam. We also demonstrate the non-orthogonal polarization encoding scheme can be well decoded with the machine learning classification algorithm. A 64×64 gray image is successfully transmitted by using 4 bits/symbol encoding-decoding scheme with 99.94 % transmission accuracy. Besides, by extending the encoding-decoding scheme to 8 bits/symbol based on the same single vector beam, we achieve a higher transmission rate with 65.58% transmission accuracy. Our work holds promise for small-angle non-orthogonal polarization encoding for free-space optical communications.

Refractive Bi-Conic Axicon (Volcone) for Polarization Conversion of Monochromatic Radiation

A new element is proposed for producing an azimuthally polarized beam with a vortex phase dependence. The element is formed by two conical surfaces in such a way that the optical element resembles a mountain with a crater on top, like a volcano (volcanic cone is volcone). The element in the form of a refractive bi-conic axicon is fabricated by diamond turning, in which an internal conical cavity is made. Polarization conversion in this optical element occurs on the inner surface due to the refraction of beams at the Brewster angle. The outer surface is used to collimate the converted beam, which significantly distinguishes the proposed element from previously proposed approaches. The paper describes a method for calculating the path of beams through a refractive bi-conic axicon, taking into account phase and polarization conversions. In the case of incident circularly polarized radiation, azimuthally polarized ring-shape beam radiation is generated at the output. The proposed element is experimentally made of polymethyl methacrylate on a CNC milling machine. The experiment demonstrates the effectiveness of the proposed element.

Optimization-free customization of optical tightly focused fields: uniform needles and hotspot chains

An optimization-free method based on an inverse problem of nonlinear equations is employed to design the binary phase diffraction optical element (BPDOE) that could modulate the incident light of a high-numerical-aperture (NA) objective lens so that the axisymmetric focal fields can be customized on demand. For example, a 43λ-long optical longitudinally polarized needle with its lateral size beyond diffraction limit is reported by using a 27-belt BPDOE, where the cost evaluated by the ratio of the belt number of BPDOE to the length of needle is record small compared with other optimization algorithms. Moreover, another longitudinal field with multiple hotspots along the propagation direction of light is also achieved with a 10-belt BPDOE. These achieved focal fields are verified doubly by using a finite-difference time-domain (FDTD) method, indicating the validity of Richards-Wolf vector diffraction theory. This optimization-free approach makes the design of BPDOEs with numerous belts viable to generate the expected focal fields, which might benefit various applications such as optical trapping, super-resolution imaging, and lithography.

Compact optical module to generate arbitrary vector vortex beams

We demonstrated a compact optical module that is capable of efficiently generating vector vortex beams (VVB). With this device, a linearly polarized input beam can be converted into a vector beam with arbitrary spatial polarization and phase distributions, accompanied by an energy utilization up to 61%. Equally important, the area utilization of the spatial light modulator, a key component in the device, is as high as 65.5%. With the designed vector-vortex-beam-generation module, several types of VVBs with different vortex topological charges and spatial polarization distributions were created experimentally. This device may find applications in optical tweezers, laser machining, and so on.

Theoretical analysis based on mirror symmetry for tightly focused vector optical fields

A theoretical analysis based on mirror symmetry is proposed to analyze and predict the symmetry in intensity, phase and polarization distributions of the tightly focused vector optical field (VOF). We extend the analysis to more cases including more complicated polarization states and weak focusing cases. We further show the symmetric tightly focused fields of the eccentric cylindrical VOF and the redesigned VOF with a radially variant polarization state, which are achieved by redesigning the polarization state of the incident VOF based on the symmetry analysis. We also take the laser fabrication as an example to further show how to apply this symmetry analysis in a specific application area. Such a theoretical analysis can improve the calculation efficiency, provide new insights into the tight focusing process and offer a convenient way to engineer the field distributions in the focal plane, which may have potential applications in areas needing flexibly controllable tightly focused fields, such as laser fabrication, optical trapping, and optical storage.

Multicolor concentric annular ultrafast vector beams

Novel multicolor concentric annular ultrafast vector beams (MUCAU-VB) are firstly generated simply by using cascaded four-wave mixing (CFWM) in a glass plate pumped by two intense vector femtosecond pulses. A proof-of-principle experiment shows that up to 10 frequency up-conversion concentric annular radially polarized sidebands are obtained simultaneously based on CFWM process, where the spectra range of the first 7 order sidebands extending from 545 nm to 725 nm. The results prove the polarization transfer property from the pump beam to the signal beams even in the CFWM, a third-order optical parametric process. The pulse duration of the first order sideband is measured to be 74 fs which is according with those of two input beams. These novel MUCAU-VB, which are manipulated in temporal, spectral, spatial domain and polarization state simultaneously, are expected to apply in wide fields, such as manipulating particles and multicolor pump-probe experiments.

Production of azimuthally polarized beam with helical phase by use of the axicons and annular glass cylinder

In this paper, we proposed a method for producing the azimuthally polarized vector beam experimentally. The experimental setup includes two of the same axicons and one annular glass cylinder. The top angles of the two axicons were placed facing each other and the annular cylinder was set among the two axicons. One circular polarized beam was passed through the first axicon, the annular cylinder, and the second axicon in turn. When the beam incident on the inner surface of the annular cylindrical satisfied the Brewster angle, we obtained the azimuthally polarized beam for the reflected light from the annular cylindrical that only contains the $s$s-polarization component. We have derived that the azimuthally polarized vector beam has the helical phase factor with the helical phase factor of ${\exp}( - {\rm i}\varphi )$exp(-iφ) for the left circularly polarized beam incident and ${\exp}({\rm i}\varphi )$exp(iφ) for the right circularly polarized beam incident.

Shaping vector fields in three dimensions by random Fourier phase-only encoding

Simultaneously controlling the spatial distribution of multiple parameters of a light field in a three-dimensional (3D) space is highly desirable because of its prominent applications in the areas of optical imaging, microscopy, and manipulation. Phase-only encoding techniques that use a phase-only computer-generated hologram (CGH) to reshape and efficiently reconstruct target fields have fostered substantial interests. In this paper, we propose a convenient encoding method to construct vector fields with spatially structured multiple parameters in a 3D space by integrating the Fourier phase-only encoding technique into a modified Sagnac polarization conversion system. Without spatial filtering, various vector fields are constructed instantly at the image plane. Furthermore, utilizing a macro-pixel encoding approach, we demonstrate the possibility of a simultaneous and an independent construction of multiple vector fields in a 3D space. This method can also benefit the design of a metasurface to implement a polarization hologram.

Single ultra-high-definition spatial light modulator enabling highly efficient generation of fully structured vector beams

Ultra-high-definition (UHD) spatial light modulators (SLMs) enhance the degree of freedom in the versatile engineering of optical field. Among efforts to explore the capability of SLMs, enhancing the efficiency of light utilization is an everlasting quest to find SLM-based applications. We propose a new method to efficiently generate arbitrary vector beams with a phase-only UHD-SLM. By enabling the UHD-SLM with a rectangle window to work in an in-line and split-screen manner with the help of a polarizing beam splitter, the total conversion efficiency as high as 49% of light beams is realized. Several complex beams, including cylindrical vector beams and higher-order Poincaré sphere beams, are experimentally demonstrated. Our method can facilitate application of SLM in optical field manipulation.

Redistributing the energy flow of a tightly focused radially polarized optical field by designing phase masks

Redistributing the transverse energy flow in the focal plane of a tightly focused radially polarized optical field is described. We develop from theory a generalized analytical model for calculating the distributions of the electromagnetic field and the Poynting vector for a tightly focused radially polarized laser beam superposed with an optical vortex. We further explore the redistribution of the energy flow by designing phase masks, including traditional and annular vortex phase masks. Flexible control of the transverse energy flow rings is obtained with these phase masks. They provide a simple solution to transport absorptive particles along certain paths and therefore might be help in optical tweezer manipulations.

Creation of independently controllable multiple focal spots from segmented Pancharatnam-Berry phases

Recently, based on space-variant Pancharatnam-Berry (PB) phases, various flat devices allowing abrupt changes of beam parameters have been predicted and demonstrated to implement intriguing manipulation on spin states in three dimensions, including the efficient generation of vector beams, spin Hall effect of light and light-guiding confinement, and so on. Here, we report on the construction of independently controllable multiple focal spots with different inhomogeneous polarization states by utilizing segmented PB phases. Combining the phase shift approach with PB phases, we engineer fan-shaped segmented PB phases and encode them onto two spin components that compose a hybrid polarized vector beam in a modified common-path interferometer system. Experimental results demonstrate that the fan-shaped segmented PB phase enables the flexible manipulation of focal number, array structure and polarization state of each focal spot. Furthermore, we demonstrate that this fan-shaped approach enables to flexibly tailor the polarization state and the spin angular momentum distribution of a tightly focused field, which have potential applications in optical manipulation, tailored optical response and imaging etc.

Focusing properties of arbitrary optical fields combining spiral phase and cylindrically symmetric state of polarization

The tight focusing properties of optical fields combining a spiral phase and cylindrically symmetric state of polarization are presented. First, we theoretically analyze the mathematical characterization, Stokes parameters, and Poincaré sphere representations of arbitrary cylindrical vector (CV) vortex beams. Then, based on the vector diffraction theory, we derive and build an integrated analytical model to calculate the electromagnetic field and Poynting vector distributions of the input CV vortex beams. The calculations reveal that a generalized CV vortex beam can generate a sharper focal spot than that of a radially polarized (RP) plane beam in the focal plane. Besides, the focal size decrease accompanies its elongation along the optical axis. Hence, it seems that there is a trade-off between the transverse and axial resolutions. In addition, under the precondition that the absolute values between polarization order and topological charge are equal, a higher-order CV vortex can also achieve a smaller focal size than an RP plane beam. Further, the intensity for the sidelobe admits a significant suppression. To give a deep understanding of the peculiar focusing properties, the magnetic field and Poynting vector distributions are also demonstrated in detail. These properties may be helpful in applications such as optical trapping and manipulation of particles and superresolution microscopy imaging.

Investigation of propagation dynamics of truncated vector vortex beams

In this Letter, we experimentally investigate the propagation dynamics of truncated vector vortex beams generated using a Sagnac interferometer. Upon focusing, the truncated vector vortex beam is found to regain its original intensity structure within the Rayleigh range. In order to explain such behavior, the propagation dynamics of a truncated vector vortex beam is simulated by decomposing it into the sum of integral charge beams with associated complex weights. We also show that the polarization of the truncated composite vector vortex beam is preserved all along the propagation axis. The experimental observations are consistent with theoretical predictions based on previous literature and are in good agreement with our simulation results. The results hold importance as vector vortex modes are eigenmodes of the optical fiber.

Focus shaping by tailoring arbitrary hybrid polarization states that have a combination of orthogonal linear polarization bases

We report a focus shaping method by tailoring hybrid states of polarization of arbitrary polarized beams that have a combination of orthogonal linear polarization bases. Such hybridly polarized beams comprising linear, elliptical, and circular polarizations in the beam cross section, have completely different optical properties compared to the scalar and locally linear-polarized vector beams. We demonstrate that, apart from the orientation of the local polarization state, another two degrees of freedom including the local ellipticity and the handedness in the beam cross section can be used in focus shaping. Square-shaped patterns, multiple foci, three-dimensional optical cages, optical needles, and channels can be obtained due to the increased control without any additional phase or amplitude modulations.

All-fiber radially/azimuthally polarized lasers based on mode coupling of tapered fibers

We demonstrate a mode converter with an insertion loss of 0.36 dB based on mode coupling of tapered single-mode and two-mode fibers, and realize all-fiber flexible cylindrical vector lasers at 1550 nm. Attributing to the continuous distribution of a tangential electric field at taper boundaries, the laser is switchable between the radially and azimuthally polarized states by adjusting the input polarization. In the temporal domain, the operation is controllable among continuous-wave, Q-switched, and mode-locked statuses by changing the saturable absorber or pump strength. The duration of Q-switched radially/azimuthally polarized laser spans from 10.4/10.8 to 6/6.4 μs at the pump range of 38 to 58 mW, while that of the mode-locked pulse varies from 39.2/31.9 to 5.6/5.2 ps by controlling the laser bandwidth. The proposed laser combines the features of a cylindrical vector beam, a fiber laser, and an ultrafast pulse, providing a special and cost-effective source for practical applications.

Enhanced second harmonic generation from a plasmonic Fano structure subjected to an azimuthally polarized light beam

We show that an azimuthally polarized beam (APB) excitation of a plasmonic Fano structure made by coupling a split-ring resonator (SRR) to a nanoarc can enhance second harmonic generation (SHG). Strikingly, an almost 30 times enhancement in SHG peak intensity can be achieved when the excitation is switched from a linearly polarized beam (LPB) to an APB. We attribute this significant enhancement of SHG to the corresponding increase in the local field intensity at the fundamental frequency of SHG, resulting from the improved conversion efficiency between the APB excitation and the plasmonic modes of the Fano structure. We also show that unlike LPB, APB excitation creates a symmetric SHG radiation pattern. This effect can be understood by considering an interference model in which the APB can change the total SHG far-field radiation by modifying the amplitudes and phases of two waves originating from the individual SRR and nanoarc of the Fano structure.

Simultaneous generation of multiple vector beams on a single SLM

Complex vector light fields, classically entangled in polarization and phase, have become ubiquitous in a wide variety of research fields. This has triggered the demonstration of a wide variety of generation techniques. Of particular relevance are those based on computer-controlled devices due to their great flexibility. In particular, spatial light modulators have demonstrated their high capabilities to generate any vector beam, with various spatial profiles and polarization distributions. Here, we put forward a novel technique that exploits the superposition principle in optics to enable the simultaneous generation of many vector beams using a single digital hologram. As proof-of-principle, we demonstrated the simultaneous generation of sixteen vector vortex beams with various polarization distributions and spatial shapes on a single SLM, each with their own spatial shape and polarization distribution.

Focus engineering based on analytical formulae for tightly focused polarized beams with arbitrary geometric configurations of linear polarization

Highly confined electromagnetic fields with controllable intensity profiles and polarization orientations are greatly desired in many fields. In this paper, we report on the generation of highly confined fields through tightly focused locally linearly polarized beams. Using the Richards-Wolf vectorial diffraction method, we derive and build integrated analytical formulae for calculating the tightly focused field of polarized beams with arbitrary geometric configurations of linear polarization. Based on the analytical model, the focusing properties of four types of polarized light beams, i.e., linearly, azimuthally, radially, and spatially variant polarized beams, with locally linear states of polarization are investigated numerically and discussed in detail. By manipulating the radial and azimuthal indices and initial phases, we obtain a tunable three-dimensional optical cage, multifoci, optical needles, and channels in the focal volume of a high-numerical-aperture objective lens. These peculiar properties may find applications in fields such as optical trapping and manipulation of nanoparticles and super-resolution microscopy imaging.

High-efficiency and flexible generation of vector vortex optical fields by a reflective phase-only spatial light modulator

The scheme for generating vector optical fields should have not only high efficiency but also flexibility for satisfying the requirements of various applications. However, in general, high efficiency and flexibility are not compatible. Here we present and experimentally demonstrate a solution to directly, flexibly, and efficiently generate vector vortex optical fields (VVOFs) with a reflective phase-only liquid crystal spatial light modulator (LC-SLM) based on optical birefringence of liquid crystal molecules. To generate the VVOFs, this approach needs in principle only a half-wave plate, an LC-SLM, and a quarter-wave plate. This approach has some advantages, including a simple experimental setup, good flexibility, and high efficiency, making the approach very promising in some applications when higher power is need. This approach has a generation efficiency of 44.0%, which is much higher than the 1.1% of the common path interferometric approach.

Lateral shearing common-path digital holographic microscopy based on a slightly trapezoid Sagnac interferometer

We propose a compact and easy-to-align lateral shearing common-path digital holographic microscopy, which is based on a slightly trapezoid Sagnac interferometer to create two laterally sheared beams and form off-axis geometry. In this interferometer, the two beams pass through a set of identical optical elements in opposite directions and have nearly the same optical path difference. Without any vibration isolation, the temporal stability of the setup is found to be around 0.011 rad. Compared with highly simple lateral shearing interferometer, the off-axis angle of the setup can be easily adjusted and quantitatively controlled, meanwhile the image quality is not degraded. The experiments for measuring the static and dynamic specimens are performed to demonstrate the capability and applicability.

Efficient generation of vector beams by calibrating the phase response of a spatial light modulator

The spatial light modulator (SLM) is considered as an effective device to create beams with inhomogeneous phases and polarizations, such as vortex beams and vector beams. However, the nonlinear responses of SLM severely reduce the generation efficiency of these beams. In this paper, by calibrating the SLM to present a linear phase response in the scope of 0-2π, we propose a convenient and efficient method of creating vector beams with arbitrary polarizations based on phase encoding. Compared with the common methods of generating vector beams, our approach can distinctly enhance the generation efficiency.

Ultrashort vortex from a Gaussian pulse - An achromatic-interferometric approach

The more than a century old Sagnac interferometer is put to first of its kind use to generate an achromatic single-charge vortex equivalent to a Laguerre-Gaussian beam possessing orbital angular momentum (OAM). The interference of counter-propagating polychromatic Gaussian beams of beam waist ω_λ with correlated linear phase (ϕ₀ ≥ 0.025 λ) and lateral shear (y₀ ≥ 0.05 ω_λ) in orthogonal directions is shown to create a vortex phase distribution around the null interference. Using a wavelength-tunable continuous-wave laser the entire range of visible wavelengths is shown to satisfy the condition for vortex generation to achieve a highly stable white-light vortex with excellent propagation integrity. The application capablitiy of the proposed scheme is demonstrated by generating ultrashort optical vortex pulses, its nonlinear frequency conversion and transforming them to vector pulses. We believe that our scheme for generating robust achromatic vortex (implemented with only mirrors and a beam-splitter) pulses in the femtosecond regime, with no conceivable spectral-temporal range and peak-power limitations, can have significant advantages for a variety of applications.

High efficiency mode-locked, cylindrical vector beam fiber laser based on a mode selective coupler

We propose and demonstrate an all-fiber passively mode-locked laser with a figure-8 cavity, which generates pulsed cylindrical vector beam output based on a mode selective coupler (MSC). The MSC made of a two mode fiber and a standard single mode fiber is used as both the intracavity transverse mode converter and mode splitter with a low insertion loss of about 0.65 dB. The slope efficiency of the fiber laser is > 3%. Through adjusting the polarization state in the laser cavity, both radially and azimuthally polarized beams have been obtained with high mode purity which are measured to be > 94%. The laser operates at 1556.3 nm with a spectral bandwidth of 3.2 nm. The mode-locked pulses have duration of 17 ns and a repetition rate of 0.66 MHz.

Fano resonance with high local field enhancement under azimuthally polarized excitation

Being an enabling technology for applications such as ultrasensitive biosensing and surface enhanced spectroscopy, enormous research interests have been focused on further boosting the local field enhancement at Fano resonance. Here, we demonstrate a plasmonic Fano resonance resulting from the interference between a narrow magnetic dipole mode and a broad electric dipole mode in a split-ring resonator (SRR) coupled to a nanoarc structure. Strikingly, when subjected to an azimuthally polarized beam (APB) excitation, the intensity enhancement becomes more than 60 times larger than that for a linearly polarized beam (LPB). We attribute this intensity enhancement to the improved conversion efficiency between the excitation and magnetic dipole mode along with improved near-field coupling. The APB excited Fano structure is further used as a nanoruler and beam misalignment sensor, due to the high sensitivity of intensity enhancement and scattering spectra to structure irregularities and excitation beam misalignment. Interestingly, we find that, regardless of the presence of structural translations, the proposed structure still maintains over 60 times better intensity enhancement under APB excitation compared to LPB excitation. Moreover, even if the APB excitation is somewhat misaligned, our Fano structure still manages to give a larger intensity enhancement than its counterpart excited by LPB.

Generation and self-healing of vector Bessel-Gauss beams with variant state of polarizations upon propagation

We propose a generalized model for the creation of vector Bessel-Gauss (BG) beams having state of polarization (SoP) varying along the propagation direction. By engineering longitudinally varying Pancharatnam-Berry (PB) phases of two constituent components with orthogonal polarizations, we create zeroth- and higher-order vector BG beams having (i) uniform polarizations in the transverse plane that change along z following either the equator or meridian of the Poincaré sphere and (ii) inhomogeneous polarizations in the transverse plane that rotate during propagation along z. Moreover, we evaluate the self-healing capability of these vector BG beams after two disparate obstacles. The self-healing capability of spatial SoP information may enrich the application of BG beams in light-matter interaction, polarization metrology and microscopy.

Quasi-Bessel beams with longitudinally varying polarization state generated by employing spectrum engineering

We report on the generation and control of quasi-Bessel beams having not only a uniform axial intensity but also a longitudinally varying polarization state. Based on the optimization routine of the spatial spectrum of the so-called Durnin ring, we generate quasi-Bessel beams possessing longitudinally variant axial intensity with linear or sinusoidal envelopes. By utilizing a Sagnac interferometer, we create and coaxially composite two orthogonally polarized beams with complementary axial intensities to form quasi-Bessel beams with uniform axial intensity but a longitudinally varying polarization state. Furthermore, we demonstrate the possibility and flexibility of manipulating the trajectory, speed, and period of polarization state transformation upon propagation. Our results may enable Bessel beams to be used in other applications including optical communications, material processing, and polarimetry.

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.

Polarization-based control of spin-orbit vector modes of light in biphoton interference

We report the experimental generation of a class of spin-orbit vector modes of light via an asymmetric Mach-Zehnder interferometer, obtained from an input beam prepared in a product state of its spin and orbital degrees of freedom. These modes contain a spatially varying polarization structure which may be controllably propagated about the beam axis by varying the retardance between the vertical and horizontal polarization components of the light. Additionally, their transverse spatial intensity distributions may be continuously manipulated by tuning the input polarization parameters. In the case of an analogous biphoton input, we predict that this device will exhibit biphoton (Hong-Ou-Mandel) interference in conjunction with the aforementioned tunable mode transformations.

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.

Cylindrical vector beam generation in fiber with mode selectivity and wavelength tunability over broadband by acoustic flexural wave

Theoretical analysis and experimental demonstration are presented for the generation of cylindrical vector beams (CVBs) via mode conversion in fiber from HE₁₁ mode to TM₀₁ and TE₀₁ modes, which have radial and azimuthal polarizations, respectively. Intermodal coupling is caused by an acoustic flexural wave applied on the fiber, whereas polarization control is necessary for the mode conversion, i.e. HE11x→TM₀₁ and HE11y→TE₀₁ for acoustic vibration along the x-axis. The frequency of the RF driving signal for actuating the acoustic wave is determined by the phase matching condition that the period of acoustic wave equals the beatlength of two coupled modes. With phase matching condition tunability, this approach can be used to generate different types of CVBs at the same wavelength over a broadband. Experimental demonstration was done in the visible and communication bands.

Generation of perfect vectorial vortex beams

We propose the concept of perfect vectorial vortex beams (VVBs), which not merely have intensity profile independent of the polarization order and the topological charge of spiral phase, but also have stable intensity profile and state of polarization (SoP) upon propagation. Utilizing a Sagnac interferometer, we approximately generate perfect VVBs with locally linear and elliptical polarizations, and demonstrate that such beams can keep their intensity profile and SoP at a certain propagation distance. These proposed VVBs can be expanded to encode information and quantum cryptography, as well as to enrich the conversion of spin and orbital angular momenta.

Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors

We present an arbitrary vector field with hybrid polarization based on the combination of a pair of orthogonal elliptically polarized base vectors on the Poincaré sphere. It is shown that the created vector field is only dependent on the latitude angle 2χ but is independent on the longitude angle 2ψ on the Poincaré sphere. By adjusting the latitude angle 2χ, which is related to two identical waveplates in a common path interferometric arrangement, one could obtain arbitrary type of vector fields. Experimentally, we demonstrate the generation of such kind of vector fields and confirm the distribution of state of polarization by the measurement of Stokes parameters. Besides, we investigate the tight focusing properties of these vector fields. It is found that the additional degree of freedom 2χ provided by arbitrary vector field with hybrid polarization allows one to control the spatial structure of polarization and to engineer the focusing field.

Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift

Spin Hall effect of light, which is normally explored as a transverse spin-dependent separation of a light beam, has attracted enormous research interests. However, it seems there is no indication for the existence of the longitudinal spin separation of light. In this paper, we propose and experimentally realize the spin separation along the propagation direction by modulating the Pancharatnam-Berry (PB) phase. Due to the spin-dependent divergence and convergence determined by the PB phase, a focused Gaussian beam could split into two opposite spin states, and focuses at different distances, representing the longitudinal spin separation. By combining this longitudinal spin separation with the transverse one, we experimentally achieve the controllable spin-dependent focal shift in three dimensional space. This work provides new insight on steering the spin photons, and is expected to explore novel applications of optical trapping, manipulating, and micromachining with higher degree of freedom.

Hyperbolic-symmetry vector fields

We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.

Simple method for generation of vector beams using a small-angle birefringent beam splitter

A simple and practical system for generation of vector beams with arbitrary polarization and complex-amplitude distributions is proposed. The system mainly consists of a scalar computer-generated hologram (CGH), a small-angle birefringent beam splitter (BBS), and a Fourier lens with a filtering aperture (FA). The CGH is placed in front of the Fourier lens. The BBS is inserted between the CGH and the Fourier lens. When the CGH specially designed according to the method described in this Letter is illuminated by a plane beam or a Gaussian beam, a desired vector beam can be obtained through the FA placed at the back focal plane of the Fourier lens. Because no coupling element and half-wave plate are to be placed between the CGH and the BBS, the extinction ratios of both the two orthogonal polarization components for the vector beam can be better than 10(-5) and so high-quality vector beams can be generated.

Unveiling the photonic spin Hall effect of freely propagating fan-shaped cylindrical vector vortex beams

An intriguing photonic spin Hall effect (SHE) for a freely propagating fan-shaped cylindrical vector (CV) vortex beam in a paraxial situation is theoretically and experimentally studied. A developed model to describe this kind of photonic SHE is proposed based on angular spectrum diffraction theory. With this model, the close dependences of spin-dependent splitting on the azimuthal order of polarization, the topological charge of the spiral phase, and the propagation distance are accurately revealed. Furthermore, it is demonstrated that the asymmetric spin-dependent splitting of a fan-shaped CV beam can be consciously managed, even with a constant azimuthal order of polarization. Such a controllable photonic SHE is experimentally verified by measuring the Stokes parameters.

Generating polarization vortices by using helical beams and a Twyman Green interferometer

A stable interferometric arrangement consisting of a polarizing beam splitter, a reflector, and a right-angle prism is designed to transform helical beams into polarization vortices. The computer-generated holograms are loaded on the liquid crystal spatial light modulator (LC-SLM) in order to generate different helical beams. Then the helical beams are transformed into polarization vortices with different kinds of intensity distribution successfully.

Modulation mechanism of multi-azimuthal masks on the redistributions of focused azimuthally polarized beams

We propose a theoretical model to semi-quantitatively describe the modulation mechanism of multi-azimuthal masks on the focal fields of azimuthally polarized (AP) beam. With this model, we cannot only explain the redistributions of the polarization and intensity at the focal plane, but also consciously manage the focal fields by designing the mask structure parameters, such as the symmetry, area, and phase retardation of the sector photic regions. Our results may supply a guideline to realize the manipulation on the polarizations, angular momenta, and the distribution of focused fields.

Encoding high-order cylindrically polarized light beams

In this work we present a setup for the experimental production of cylindrically polarized beams, as well as other variations of polarized light beams. The optical system uses a single transmissive phase-only spatial light modulator, which is used to apply different spatial phase modulation to two output collinear R and L circularly polarized components. Different cylindrically polarized light beams can be obtained by applying different phase shifts to these two circularly polarized components. The system is very efficient since modulation is directly applied to the light beam (as opposed to other common methods operating in the first order of encoded diffraction gratings). Different variations to the cylindrically polarized light beams are also reported, obtained by adding linear or quadratic relative phase shifts between the two circular polarization components of the light beam. Experimental results are provided in all cases.

Generation of vector beams in planar photonic crystal cavities with multiple missing-hole defects

We propose a novel method to generate vector beams in planar photonic crystal cavities with multiple missing-hole defects. Simulating the resonant modes in the cavities, we observe that the optical fields in each defect have different phase and polarization state distributions, which promise the compositions of vector beams by the scattered light from the defects. The far-field radiation patterns of the cavity modes calculated via the Sommerfeld diffraction theory present vector beams possessing hollow intensity profiles and polarization singularities. In addition, the extraction efficiencies of the vector beams from the cavities could be improved by modifying the air-holes surrounding the defects. This planar photonic crystal cavity-based vector beam generator may provide useful insights for the on-chip controlling of vector beams in their propagations and interactions with matter.

Manipulation of radial-variant polarization for creating tunable bifocusing spots

We propose and generate a new radial-variant vector field (RV-VF) with a distribution of states of polarization described by the square of the radius and exploit its focusing property. Theoretically, we present the analytical expressions for the three-dimensional electric field of the vector field focused by a thin lens under the nonparaxial and paraxial approximations based on the vectorial Rayleigh-Sommerfeld formulas. Numerical simulations indicate that this focused field exhibits bifocusing spots along the optical axis. The underlying mechanism for generating the bifocusing property is analyzed in detail. We give the analytical formula for the interval between two foci. Experimentally, we generate the RV-VFs with alterable topological charge and demonstrate that the interval between two foci is controllable by tuning the radial topological charge. This particular focal field has specific applications for biparticle trapping, manipulating, alignment, transportation, and accelerating along the optical axis.

Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators

A flexible approach is presented to generate vector beams with arbitrary polarization and complex amplitude by means of two cascaded transmissive liquid crystal spatial light modulators (LCSLMs). The configuration of the cascaded LCSLM system and its modulation characteristic are introduced. Theoretical analysis and experimental demonstration prove that the system in combination with a double-pass computer-generated hologram and a black-and-white pattern can generate vector beams with arbitrary polarization and complex amplitude by respectively controlling the complex amplitudes of two orthogonal polarization components of the beams. Using this system, we successfully generate radially polarized vector beams with helical phase distributions and vector Bessel beams with inhomogeneous amplitude distributions in experiments.

Double-channel vector spatial light modulator for generation of arbitrary complex vector beams

We propose an approach for implementation of an arbitrary vector beam based on a vector spatial light modulator (VSLM), which is simply composed by a phase-only spatial light modulator (SLM) and a composed half-wave plate with checkerboard structure. In combination with a four-phase encoding algorithm, the VSLM can transform a linear polarized Gaussian beam or a plane wave into a vector beam with both arbitrary spatial polarization and complex amplitude distributions in two dimensions. It is demonstrated that the VSLM can directly transform pure phase values into two orthogonal polarized complex values with high-diffraction efficiency. Compared with the existing methods for generation of vector beams with SLMs, our approach is on-axis and common-path with simple structure and only involves the zero-order diffraction. The proposed structure is also easier to make an integration and design portable device since it abstains from using optical elements such as special gratings, prisms, and reflectors.

Effect of polarization purity of cylindrical vector beam on tightly focused spot

The tightly focused spots of cylindrical vectors (CVs) are dependent on polarization composition. We experimentally demonstrate the effect of polarization purity (PP) of the CV beam on the tightly focused spot quantitatively, which should be strictly controlled for the effective applications of the CV beam. The focal spots measured by a knife-edge scanning method showed that the azimuthally polarized (AP) component increases the transverse field and the size of the focal spots, while the radially polarized component results in a nonzero intensity distribution at the center of the focus even in a high PP AP beam.

Vector optical fields with bipolar symmetry of linear polarization

We focus on a new kind of vector optical field with bipolar symmetry of linear polarization instead of cylindrical and elliptical symmetries, enriching members of family of vector optical fields. We design theoretically and generate experimentally the demanded vector optical fields and then explore some novel tightly focusing properties. The geometric configurations of states of polarization provide additional degrees of freedom assisting in engineering the field distribution at the focus to the specific applications such as lithography, optical trapping, and material processing.

Abrupt polarization transition of vector autofocusing Airy beams

We experimentally and theoretically study the abrupt polarization transitions of vector autofocusing Airy beams associated with the spin-orbit interactions. It is shown that when the topological charges of the polarization and the attached spiral phase are equal in number, the local polarizations undergo an abrupt transition from linear to circular polarizations at the focal point, and the associated orbital angular momentum partially converts into the spin of photons. The experimental results are theoretically explained from the far-field properties of the beams in terms of Hankel transformations.

Vector optical fields with polarization distributions similar to electric and magnetic field lines

We present, design and generate a new kind of vector optical fields with linear polarization distributions modeling to electric and magnetic field lines. The geometric configurations of "electric charges" and "magnetic charges" can engineer the spatial structure and symmetry of polarizations of vector optical field, providing additional degrees of freedom assisting in controlling the field symmetry at the focus and allowing engineering of the field distribution at the focus to the specific applications.

Reconfigurable beams with arbitrary polarization and shape distributions at a given plane

Methods for generating beams with arbitrary polarization based on the use of liquid crystal displays have recently attracted interest from a wide range of sources. In this paper we present a technique for generating beams with arbitrary polarization and shape distributions at a given plane using a Mach-Zehnder setup. The transverse components of the incident beam are processed independently by means of spatial light modulators placed in each path of the interferometer. The modulators display computer generated holograms designed to dynamically encode any amplitude value and polarization state for each point of the wavefront in a given plane. The steps required to design such beams are described in detail. Several beams performing different polarization and intensity landscapes have been experimentally implemented. The results obtained demonstrate the capability of the proposed technique to tailor the amplitude and polarization of the beam simultaneously.