Complete shaping of optical vector beams

Absolutely interferometric calibration of phase liquid crystal spatial light modulators using honeycomb gratings composited with Billet-split Fresnel zone plates

The traditional interferometric calibration of phase spatial light modulators (SLM) based on interference fringes shift is easily disturbed due to environmental vibration. Here a kind of absolutely interferometric calibration of phase SLM is investigated to eliminate the disturbance using dual honeycomb gratings composited with Billet-split Fresnel zone plates (BsFZP), in which honeycomb gratings split an incident beam into three beams and the first two beams are interfered by BsFZP while the last beam is chosen as the absolute reference point. The experiments on both 532 and 632.8 nm incident wavelengths were separately carried out, and the measuring accuracy was proved by a SID4 wavefront sensor. The proposed high-accuracy calibration provided the basis for SLM application scenarios with high precision.

Metasurface Enabled On-Chip Generation and Manipulation of Vector Beams from Vertical Cavity Surface-Emitting Lasers

Metasurface polarization optics that consist of 2D array of birefringent nano-antennas have proven remarkable capabilities to generate and manipulate vectorial fields with subwavelength resolution and high efficiency. Integrating this new type of metasurface with the standard vertical cavity surface-emitting laser (VCSEL) platform enables an ultracompact and powerful solution to control both phase and polarization properties of the laser on a chip, which allows to structure a VCSEL into vector beams with on-demand wavefronts. Here, this concept is demonstrated by directly generating versatile vector beams from commercially available VCSELs through on-chip integration of high-index dielectric metasurfaces. Experimentally, the versatility of the approach for the development of vectorial VCSELs are validated by implementing a variety of functionalities, including directional emission of multibeam with specified polarizations, vectorial holographic display, and vector vortex beams generations. Notably, the proposed vectorial VCSELs integrated with a single layer of beam shaping metasurface bypass the requirements of multiple cascaded optical components, and thus have the potential to promote the advancements of ultracompact, lightweight, and scalable vector beams sources, enriching and expanding the applications of VCSELs in optical communications, laser manipulation and processing, information encryption, and quantum optics.

Dynamic Phase and Polarization Modulation Using Two-Beam Parallel Coding for Optical Storage in Transparent Materials

In this paper, we propose and experimentally demonstrate a parallel coding and two-beam combining approach for the simultaneous implementation of dynamically generating holographic patterns at their arbitrary linear polarization states. Two orthogonal input beams are parallelly and independently encoded with the same target image information but there is different amplitude information by using two-phase computer-generated holograms (CGH) on two Liquid-Crystal-on-Silicon-Spatial-Light Modulators (LCOS SLMs). Two modulated beams are then considered as two polarization components and are spatially superposed to form the target polarization state. The final linear vector beam is created by the spatial superposition of the two base beams, capable of controlling the vector angle through the phase depth of the phase-only CGHs. Meanwhile, the combined holographic patterns can be freely encoded by the holograms of two vector components. Thus, this allows us to tailor the optical fields endowed with arbitrary holographic patterns and the linear polarization states at the same time. This method provides a more promising approach for laser data writing generation systems in the next-generation optical data storage technology in transparent materials.

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.

Control of transverse mode in a He-Ne laser using an astigmatic resonator

The realization of output of the controllable transverse mode in a laser resonator has always been the key problem in applications of lasers. At present, the theory of optical resonators for passive resonators is relatively mature, but the non-uniformity of gain media greatly affects the output of the laser transverse mode for astigmatic resonators in operation; especially for gas lasers, controllable high-order modes have not been studied. To realize the theory of an astigmatic passive resonator of a gas laser as a good approximation of an active resonator, this paper develops the theory of selecting the laser eigenmode through an astigmatic resonator, and verifies that the two-dimensional tilt of the cavity mirror can break the axial symmetry. Controllable output of the laser mode is realized in real time and conveniently for the first time, to the best of our knowledge. This scheme is not only common to all kinds of lasers, but also has important research significance for the high-order modes required for real-time and rapid regulation of gas lasers under operating conditions.

Radially self-accelerating Stokes vortices in nondiffracting Bessel-Poincaré beams

We theoretically propose and experimentally generate the nondiffracting Bessel-Poincaré beams whose Stokes vortices radially accelerate during propagation. To this end, we design the Bessel beams whose intensity is specified to be uniformly distributed along the longitudinal direction. By superposing two such Bessel beams having different helical phases and mutually orthogonal polarizations, the synthesized vector beam is endowed with the polarization singularity that can rotate about the optical axis, while the total intensities maintain their profiles. Radially self-accelerating Stokes vortices in the resulting beam can be manipulated by adjusting the predefined parameters in the constituent beams.

Compact vectorial optical field generator using a single phase-only spatial light modulator

In this study, we demonstrate a compact vectorial optical field generator for any coherent light, including femtosecond laser beams. The apparatus utilizes a single Köster prism for both beam splitting and recombining. A phase-only spatial light modulator is used as a diffractive optical element to encode the two complex fields that recombine after being converted to orthogonal polarizations, generating an arbitrary vectorial optical field. We apply this setup to shape focused femtosecond pulses in producing patterned structures.

Flexibly modulated Poincaré sphere vector optical field in input and focal planes

We theoretically design and experimentally generate the flexibly modulated Poincaré sphere vector optical field (PS-VOF), which can be constructed by flattening the Poincaré sphere surface. This new kind of PS-VOF provides additional degrees of freedom to modulate the spatial structure of polarization based on Poincaré sphere. The focal property of the PS-VOF is further studied, and we focus on studying the polarization coverage of the Poincaré sphere in the focal plane. In focusing process, the conversion and annihilation of spin angular momentum are presented. In addition, when the proportion of right-handed polarizations from the northern hemisphere of the Poincaré sphere satisfies Golden ratio (0.618) in the input plane, a full PS-VOF with high quality can be achieved in the focal plane. We hope this study of PS-VOF in both input and focal planes can enrich the family of VOFs, provide a new avenue in studying VOFs based on the Poincaré sphere, and can be potentially applied in the regions with sensitivity to polarizations.

Twin curvilinear vortex beams

We report on a novel curvilinear optical vortex beam named twin curvilinear vortex beams (TCVBs) with intensity and phase distribution along a pair of two- or three-dimensional curves, both of which share the same shape and the same topological charge. The TCVBs also possess the character of perfect optical vortex, namely having a size independent of topological charge. We theoretically demonstrate that a TCVB rather than a single-curve vortex beam can be created by the Fourier transform of a cylindrically polarized beam. The behavior of TCVBs generated through our method is investigated by simulation and experiment, including interference experiments for identifying the vortex property of the TCVBs. The TCVBs may find applications in optical tweezers, such as trapping low refractive index particles in the dark region between two curves and driving them moving along the curvilinear trajectory.

Formation of polarization-dependent optical vortex beams via an engineered microsphere

In this work, we propose a method that can realize switchable spatial arrangement of the donut-shaped focusing beams through an engineered microsphere, tuned by changing the polarization state of an incident light. In this polarization-dependent light manipulation, the engineered microsphere is designed and fabricated by focused ion beam (FIB). We simulate and experimentally characterize the focus performance of the engineered microsphere. Under the light incidence with radial polarization, multiple focused donut beams are formed along optical axis. By adding an additional linear polarizer with a rotatable relative angle, the pair of donut beams can be re-arranged in the same transverse plane and stay close to each other. Experimental results and numerical simulation are in good agreement. Such tunable polarization-dependent micro-optics can be used for multiplane imaging applications.

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.

Controlled negative energy flow in the focus of a radial polarized optical beam

The controlled and continuous negative energy flow (from negative to positive) on the optical axis in the focal region is obtained by adjusting the polarization distribution of the input second-order radially polarized beam (the polarization topological charge is equal to 2). Moreover, the similar evolution of negative energy flow also can be achieved for the tightly focused vector beams with polarization topological charge -2. It is because both the beams with polarization topological charges 2 and -2 can possess the same polarization and spin flow density distributions with the help of the polarization modulation. The results provide a potential method for modulating the effects induced by the spin-orbit coupling in tight focusing of optical beam.

High-efficiency non-diffractive generator of arbitrary vectorial optical fields with minimal optical elements

Tailoring electromagnetic waves has a wide range of applications, such as optical trapping, focus engineering, imaging, laser cutting, and optical communication. To do so, the spatial distribution of at least one of the four degrees of freedom of electromagnetic waves, amplitude, phase, polarization ratio, and retardance, must be modified. Arbitrary vectorial optical fields (VOF) can be engineered by spatially modulating all four degrees of freedom simultaneously. However, existing dynamic vectorial optical field generators (VOF-Gens) require intensive alignment and many optical elements in order to achieve high efficiency. Here, we design a dynamic VOF-Gen that can generate arbitrary VOFs using only five optical elements. Experimentally, we demonstrated an efficiency of 72%, the highest ever demonstrated.

Modifying Bessel beam profiles with a spherulite-based radial polarizer

We present a radial polarizer prepared by growing a thickness-constrained spherulite from an oleoresin polymer. As an insert between crossed linear polarizers, the fabricated device is used to alter the intensity profile of an incident zero-order Bessel beam. Radially polarized output beams have an intensity profile with a pronounced singularity at the center. Beams may be rotated by a simple reorientation of the crossed polarizers. Experimental results with our radial polarizer correspond to a transformation of the Bessel beam order from l=0 to l=2.

Optical singularities and Möbius strip arrays in tailored non-paraxial light fields

A major current challenge in the field of structured light represents the development from three- (3d) to four-dimensional (4d) electric field structures, in which one exploits the transverse as well as longitudinal field components in 3d space. For this purpose, non-paraxial fields are required in order to be able to access visionary 3d topological structures as optical cones, ribbons and Möbius strips formed by 3d polarization states. We numerically demonstrate the customization of such complex topological structures by controlling generic polarization singularities in non-paraxial light fields. Our approach is based on tightly focusing tailored higher-order vector beams in combination with phase vortices. Besides demonstrating the appearance of cones and ribbons around the optical axis, we evince sculpting arrays of Möbius strips realized around off-axis generic singularities.

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.

Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge

In this paper, we have introduced a new class of partially coherent vector vortex beams, named radially polarized multi-Gaussian Schell-model (MGSM) vortex beam, carrying the vortex phase with tunable topological charges (i.e., both integral and fractional values) as a natural extension of the radially polarized MGSM beam. The tight focusing properties of the radially polarized MGSM vortex beam passing through a high numerical aperture (NA) objective lens are investigated numerically based on the vectorial diffraction theory. Numerical results show that the focal intensity distributions of the radially polarized MGSM vortex beam can be shaped by regulating the structure of the correlation functions and the topological charge of vortex phase. In contrast with the integral vortex beam, the most intriguing property of the fractional vortex beam is that the focal intensity distribution at the focal plane can be nonuniformity and asymmetry, while such unique characteristics will vanish when the spatial coherence length is sufficiently small. Furthermore, some focal fields with novel structure, such as a focal spot with nonuniform asymmetric or an anomalous asymmetric hollow focal field, can be formed by choosing suitable fractional values of topological charge and spatial coherence length. Our results will be useful for optical trapping, especially for trapping of irregular particles or manipulation of absorbing particles.

Manipulating the transmission of vector beam with spatially polarized atomic ensemble

Vector beams (VBs) with potential applications are successfully utilized in many fields as light sources with a spatially-varying polarization profile in recent years. Here, we study the transmission of a VB by manipulating atomic polarization via the optical pumping effect. By using hybridly and radially polarized beams as pump and probe beams in a counter-propagating configuration, we observe a four-petal pattern intensity distribution of probe beam, and the four-petal pattern rotates with the polarization state orientation of the pump beam. The results show a polarization dependent absorption in the atomic media. We experimentally demonstrate the absorption characteristics under different polarization combinations of pump and probe beams. The Jones matrix method is used to explain this phenomenon and the simulations are consistent with the experimental observation. Our results may provide a sound foundation for applications in optical manipulation and quantum information in atomic ensembles.

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.

Electrically driven generation of arbitrary vector vortex beams on the hybrid-order Poincaré sphere

We propose a simple, efficient, and fast tunable method to generate arbitrary vector vortex beams on the hybrid-order Poincaré sphere in an electrically driven way. The scheme incorporates the tunability and switching capabilities of liquid crystals into dielectric metasurfaces to form an efficient vector vortex beam generator. By applying certain voltages on the liquid crystal phase retarder, the generator converts a linearly polarized Gaussian beam into any desirable vector vortex beams. We demonstrate that the evolution route of the corresponding vector vortex states is just a closed circuit on the hybrid-order Poincaré sphere when the phase retardation varies from 0 to 2π. Several special cases are selected to demonstrate our scheme, and the experimental results coincide well with the theoretical predictions.

Inverse method to engineer uniform-intensity focal fields with arbitrary shape

We present an inverse method to engineer uniform-intensity focal fields with arbitrary shape. Amplitude, phase, and polarization states, as adjustable parameters, are used to seek the desired focal fields in the non-iterative computational procedure. Our method can be applied to the cases with low and moderate numerical aperture (NA), in which case the feasibility and validity of our approach have been demonstrated in theory, simulation and experiment, respectively. For the case of higher NA, simulated results based on the Richards-Wolf diffraction integral are shown. We also made some discussions on the experiments with the higher NA. Our method should have wide applications in optical micro machining, optical trapping and so on.

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.

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.

Generation of optical vortex array along arbitrary curvilinear arrangement

We propose an approach for creating optical vortex array (OVA) arranged along arbitrary curvilinear path, based on the coaxial interference of two width-controllable component curves calculated by modified holographic beam shaping technique. The two component curve beams have different radial dimensions as well as phase gradients along each beam such that the number of phase singularity in the curvilinear arranged optical vortex array (CA-OVA) is freely tunable on demand. Hybrid CA-OVA that comprises of multiple OVA structures along different respective curves is also discussed and demonstrated. Furthermore, we study the conversion of CA-OVA into vector mode that comprises of polarization vortex array with varied polarization state distribution. Both simulation and experimental results prove the performance of the proposed method of generating a complex structured vortex array, which is of significance for potential applications including multiple trapping of micro-sized particles.

Topological charge measurement of concentric OAM states using the phase-shift method

We proposed a method to measure orbital angular momentum (OAM) states by using a multi-zone pure phase grating with the phase-shift technique. In free-space optical communication systems, the topological charges (TCs) of concentric OAM beams are usually detected for decoding, since the diameter of the OAM beam relates to the transmission distance. Two typical concentric OAM beams, concentric Laguerre-Gaussian beams and perfect vortex beams, were generated as incident beams, and the diffraction patterns can be separated by implementing a pure phase grating in the Fourier plane of a 4-f system. By counting the corresponding diffraction fringes, we can identify the TCs of the two OAM states. The simulation results show that the diffraction angles of the concentric OAM beams can be controlled and two concentric OAM states can be measured simultaneously.

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.

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.

Polarisation structuring of broadband light

Spatial structuring of the intensity, phase and polarisation of light is useful in a wide variety of modern applications, from microscopy to optical communications. This shaping is most commonly achieved using liquid crystal spatial light modulators (LC-SLMs). However, the inherent chromatic dispersion of LC-SLMs when used as diffractive elements presents a challenge to the extension of such techniques from monochromatic to broadband light. In this work we demonstrate a method of generating broadband vector beams with dynamically tunable intensity, phase and polarisation over a bandwidth of 100 nm. We use our system to generate radially and azimuthally polarised vector vortex beams carrying orbital angular momentum, and beams whose polarisation states span the majority of the Poincaré sphere. We characterise these broadband vector beams using spatially and spectrally resolved Stokes measurements, and detail the technical and fundamental limitations of our technique, including beam generation fidelity and efficiency. The broadband vector beam shaper that we demonstrate here may find use in applications such as ultrafast beam shaping and white light microscopy.

Shaping of optical vector beams in three dimensions

We present a method of shaping three-dimensional (3D) vector beams with prescribed intensity distribution and controllable polarization state variation along arbitrary curves in three dimensions. By employing a non-iterative 3D beam-shaping method developed for the scalar field, we use two curved laser beams with mutually orthogonal polarization serving as base vector components with a high-intensity gradient and controllable phase variation, so that they are collinearly superposed to produce a 3D vector beam. We experimentally demonstrate the generation of 3D vector beams that have a polarization gradient (spatially continuous variant polarization state) along 3D curves, which may find applications in polarization-mediated processes, such as to drive the motion of micro-particles.

On-demand tailored vector beams

We introduce an effective optical system to produce optical beams with arbitrary, inhomogeneous polarization states. Using our system, we are capable of generating vector beams with discretionarily chosen transverse complex fields in a straightforward way. We generate several different instances of well-known vector beams and the less common spirally polarized vector beams, as well as a full Poincaré beam. We visually show the continual transition between azimuthally and radially polarized beams via a collection of spirally polarized beams. We experimentally determine the polarization states of the generated beams and quantitatively assess the performance of our system. We find that the measured polarization distributions accurately coincide with the intended input polarization distributions.

Dynamic modulation of Poincaré beams

Generation of complex Poincaré beams is enabled by amplitude and phase modulation accompanied by simultaneous spatially polarization structuring. A holographic system to tailor complex light fields and optical angular momentum structures forecasts promising applications in quantum communication and optical trapping. Experimental results are presented together with simulations of complex Poincaré beams embedding different types of polarization singularities. Additionally, parameters of the dynamic polarization modulation system are discussed and analyzed to demonstrate the enormous capability of the method.

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.

Adding a spin to Kerker's condition: angular tuning of directional scattering with designed excitation

We describe a method to control the directional scattering of a high-index dielectric nanosphere, which utilizes the unique focusing properties of an azimuthally polarized phase vortex and a radially polarized beam to independently excite inside the nanosphere a spinning magnetic dipole and a linearly polarized electric dipole mode normal to the magnetic dipole. We show that by simply adjusting the phase and amplitude of the field on the exit pupil of the optical system, the scattering of the nanosphere can be tuned to any direction within a plane, and the method works over a broad wavelength range.

Amplitude and phase beam shaping for highest sensitivity in sidewall angle detection

In integrated circuits manufacturing, specific structures are used as tools to evaluate the quality of the lithographic process, and the shape of these structures is often described by a few parameters, of which in particular the sidewall angle suffers from considerable inaccuracies. Using scalar diffraction theory, we investigate whether a properly shaped cylindrically focused probing beam could increase the ability to detect tiny changes in this angle in the case of a cliff-like structure, modeled as a phase object. This paper describes the theoretical formulation used to calculate the optimized beam and compares its performance with the case of a focused plane wave.

Spin-dependent manipulating of vector beams by tailoring polarization

We examine the spin-dependent manipulating of vector beams by tailoring the inhomogeneous polarization. The spin-dependent manipulating is attributed to the spin-dependent phase gradient in vector beams, which can be regarded as the intrinsic feature of inhomogeneous polarization. The desired polarization can be obtained by establishing the relationship between the local orientation of polarization and the local orientation of the optical axis of waveplate. We demonstrate that the spin-dependent manipulating with arbitrary intensity patterns can be achieved by tailoring the inhomogeneous polarization.

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.

Reverse engineering approach to focus shaping

We propose and experimentally demonstrate an inverse design for the complete shaping of the optical focal field with the prescribed distribution of intensity, phase, and polarization. The input field that yields the desired focal field is obtained through a fast noniterative calculation procedure, in which the focal field is configured at will and then back-propagates to the input plane. The experiments have verified that all parameters of the focal field can be controlled simultaneously and independently. Furthermore, using this inverse design, we generate in focal region a kind of "perfect polarization vortex" field that has a shape independent of the topological charge of vortex. This target-oriented scheme holds the potential for applications requiring a complex focal field.

Transverse spin angular momentum of tightly focused full Poincaré beams

We show theoretically that by tightly focusing a full Poincaré beam one can create states of light whose average spin angular momentum (SAM) is purely transverse. Moreover, the transverse SAM is significantly increased if a narrow annular aperture is inserted into the Poincaré beam. In this case the state with transverse SAM can exist over an extremely long distance along the optical axis. To avoid diffraction on the aperture and increase the light conversion efficiency we employ the phenomenon of conical diffraction in biaxial crystals to convert a Gaussian beam into a ring-shaped beam, with a high ratio of the ring radius to its width.

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.