Generating and measuring nondiffracting vector Bessel beams

Quantum ghost imaging of a vector field

Quantum ghost image technique utilizing position or momentum correlations between entangled photons can realize nonlocal reconstruction of the image of an object. In this work, based on polarization entanglement, we experimentally demonstrate quantum ghost imaging of vector images by using a geometric phase object. We also provide a corresponding theoretical analysis. Additionally, we offer a geometrical optics path explanation of ghost imaging for vector fields. The proposed strategy offers new insights into the fundamental development of ghost imaging and also holds great promise for developing complex structured ghost imaging techniques. Our work expanding the principle of ghost imaging to spatially varying vector beams will lead to interesting developments of this field.

Optical vector fields with kaleidoscopic quasicrystal structures by multiple beam interference

An easily accessible approach is proposed to create structured beams with various quasicrystal structures and polarization distributions based on multi-beam interference. By controlling the azimuthally-dependent polarization for Q evenly and circularly distributed beams to be interfered, the intensity and polarization structures for the generated quasicrystal field with Q-fold rotational symmetry are flexibly adjusted. Using the diffraction theory for interfering Q vector Gaussian beams, an analytical wave function is derived to reconstruct the polarization-resolved intensities and the distributions of Stokes parameters measured in the experiment. With good agreement between the numerical and experimental results, the derived wave function is further employed to characterize the propagation-variant states of polarization, providing fundamentally important information for the vector quasicrystal beams.

Helico-conical vector beams

In this work, we propose and demonstrate experimentally a new family of vector beams, the helico-conical vector beams (HCVBs), whose spatial degree of freedom is encoded in the helico-conical optical beams. We use Stokes polarimetry to study their properties and find that upon propagation their transverse polarization distribution evolves from nonhomogeneous to quasihomogeneous, such that even though their global degree of nonseparability remains constant, locally it decreases to a minimum value as z → ∞. We corroborated this quantitatively using the Hellinger distance, a novel metric for vectorness that applies to spatially disjoint vector modes. To the best of our knowledge, HCVBs are the second family of vector beams featuring this behavior, paving the way for applications in optical tweezing or information encryption.

Space-time vector light sheets

We introduce the space-time (ST) vector light sheet. This unique one-dimensional ST wave packet is characterized by classical entanglement (CE), a correlation between at least two non-separable intrinsic degrees-of-freedom (DoFs), which in this case are the spatiotemporal DoFs in parallel with the spatial-polarization DoFs. We experimentally confirm that the ST vector light sheet maintains the intrinsic features of the uniformly polarized ST light sheet, such as near-diffraction-free propagation and self-healing, while also maintaining the intrinsic polarization structure of common vector beams, such as those that are radially polarized and azimuthally polarized. We also show that the vector beam structure of the ST vector light sheet is maintained in the subluminal and superluminal regimes.

Demonstrating Arago-Fresnel laws with Bessel beams from vectorial axicons

Two-dimensional Bessel beams, both vectorial and scalar, have been extensively studied to date, finding many applications. Here we mimic a vectorial axicon to create one-dimensional scalar Bessel beams embedded in a two-dimensional vectorial field. We use a digital micro-mirror device to interfere orthogonal conical waves from a holographic axicon, and study the boundary of scalar and vectorial states in the context of structured light using the Arago-Fresnel laws. We show that the entire field resembles a vectorial combination of parabolic beams, exhibiting dependence on solutions to the inhomogeneous Bessel equation and asymmetry due to the orbital angular momentum associated rotational diffraction. Our work reveals the rich optical processes involved at the interplay between scalar and vectorial interference, opening intriguing questions on the duality, complementarity, and non-separability of vectorial light fields.

Generation of vector beams using synthetic phase holograms

We discuss a class of synthetic phase holograms (SPHs) applied to the generation of vector fields. Each SPH encodes the transverse components of the vector field, modulated by different linear phase carriers. Such components, which are spatially separated by the carriers, are modulated by appropriate orthogonal polarizations. A final stage that makes the components collinear allows the generation of the vector field. We assess the efficiency and accuracy of the different SPHs, in the task of generating vector fields. The proposal is illustrated by the implementation of vector Bessel beams, which are experimentally generated in a setup based on a phase spatial light modulator.

Lossless reshaping of structured light

Structured light concerns the control of light in its spatial degrees of freedom (amplitude, phase, and polarization), and has proven instrumental in many applications. The creation of structured light usually involves the conversion of a Gaussian mode to a desired structure in a single step, while the detection is often the reverse process, both fundamentally lossy or imperfect. Here we show how to ideally reshape structured light in a lossless manner in a simple two-step process using conformal mapping. We outline the core theoretical arguments, and experimentally demonstrate reshaping of arbitrary structured light patterns with correlations in excess of 90%. Further, we highlight when the technique is applicable and when not, and how best to implement it. This work will be a useful addition to the structured light toolkit, and particularly relevant to those wishing to use the spatial modes of light as a basis in classical and quantum communication.

Digital Stokes polarimetry and its application to structured light: tutorial

Stokes polarimetry is a mature topic in optics, most commonly performed to extract the polarization structure of optical fields for a range of diverse applications. For historical reasons, most Stokes polarimetry approaches are based on static optical polarization components that must be manually adjusted, prohibiting automated, real-time analysis of fast changing fields. Here we provide a tutorial on performing Stokes polarimetry in an all-digital approach, exploiting a modern optical toolkit based on liquid-crystal-on-silicon spatial light modulators and digital micromirror devices. We explain in a tutorial fashion how to implement two digital approaches, based on these two devices, for extracting Stokes parameters in a fast, cheap, and dynamic manner. After outlining the core concepts, we demonstrate their applicability to the modern topic of structured light, and highlight some common experimental issues. In particular, we illustrate how digital Stokes polarimetry can be used to measure key optical parameters such as the state of polarization, degree of vectorness, and intra-modal phase of complex light fields.

Polarisation-insensitive generation of complex vector modes from a digital micromirror device

In recent time there has been an increasing amount of interest in developing novel techniques for the generation of complex vector light beams. Amongst these, digital holography stands out as one of the most flexible and versatile with almost unlimited freedom in the generation of scalar and complex vector light fields featuring arbitrary polarisation distributions and spatial profiles. In this manuscript we put forward a novel technique, which relies on the polarisation-insensitive attribute of Digital Micromirror Devices (DMDs). In a prior work where we outlined a new detection scheme based on Stokes projections we alluded to this technique. Here we outline the creation process in full, providing all the details for its experimental implementation. In addition, we fully characterise the performance of such technique, providing a quantitative analysis of the generated modes. To this end, we experimentally reconstruct the transverse polarisation distribution of arbitrary vector modes and compare the ellipticity and flatness of the polarisation ellipses with theoretical predictions. Further, we also generate vector modes with arbitrary degrees of non-separability and determine their degree of concurrence comparing this to theoretical predictions.

Detecting the Extremely Small Angle of an Axicon by Phase-Shifting Digital Holography

Axicon is an optical element that can be used to produce high-quality Bessel beams efficiently. In general, the smaller the base angle of the axicon is, the longer the diffraction-free distance of the generated Bessel beam will be. Therefore, axicon with an extremely small base angle is important for the generation of Bessel beam. However, the measurement of an extremely small base angle is a challenge. Here, we applied the phase-shifting digital holography in the measurement of axicon angle. The errors of the three measured axicons with base angles of 0.5°, 1°, and 1° were 1.94%, 4.43%, and 1.63%, respectively.

Spatial variation of vector vortex beams with plasmonic metasurfaces

The spatial variation of vector vortex beams with arbitrary polarization states and orbital angular momentum (OAM) values along the beam propagation is demonstrated by using plasmonic metasurfaces with the initial geometric phase profiles determined from the caustic theory. The vector vortex beam is produced by the superposition of deflected right- and left-handed circularly polarized component vortices with different helical phase charges, which are simultaneously generated off-axially by the single metasurface. Besides, the detailed evolution processes of intensity profile, polarization distribution and OAM value along the beam propagation distance is analyzed. The demonstrated arbitrary space-variant vector vortex beam will pave the way to many promising applications related to spin-to-orbital angular momentum conversion, spin-orbit hybrid entanglement, particle manipulation and transportation, and optical communication.

Beyond the display: phase-only liquid crystal on Silicon devices and their applications in photonics [Invited]

Existing for almost four decades, liquid crystal on Silicon (LCOS) technology is rapidly growing into photonic applications. We review the basics of the technology, from the wafer to the driving solutions, the progress over the last decade and the future outlook. Furthermore we review the most exciting industrial and scientific applications of the LCOS technology.

Generation of structured light by multilevel orbital angular momentum holograms

Structured light has been created by a myriad of near-and far-field techniques and has found both classical and quantum applications. In the case of orbital angular momentum (OAM), continuous spiral phase patterns in dynamic or geometric phase are often employed with the phase patterns existing across the entire transverse plane. Here, we exploit the uncertain relationship between OAM and angle in order to create structured OAM fields by using multilevel OAM holograms. We show theoretically and experimentally that only a multilevel angular phase contour in the near-field is needed to create structured OAM light in the far-field, exploiting the reciprocal nature of angular momentum and angle. We use this approach to demonstrate exotic 3D structured light control to show the Poynting vector's evolution in such fields and to highlight the physics underlying this phenomenon.

Generation of arbitrary vector vortex beams based on the dual-modulation method

A dual-modulation method that combines a liquid crystal on silicon spatial light modulator with an S-waveplate and a biplate consisting of double quarter-wave plates (DQWPs) or double half-wave plates (DHWPs) is proposed. The method is used to realize the phase and polarization dual modulation of an incident laser beam. This study focuses on the generation of an arbitrary vector vortex beam (VVB) based on the proposed dual-modulation method. The phase and polarization transformation effects of the proposed method are theoretically derived using the Stokes-Mueller matrix algorithm. Correspondingly, an experimental configuration is constructed to generate arbitrary VVBs, and correlation analyses are carried out to quantitatively evaluate the quality of the generated VVBs. The results indicate that the correlation coefficients of the generated VVBs can reach more than 0.94 whether the biplate in the experimental configuration is DQWP or DHWP.

Demonstration of longitudinally polarized optical needles

Longitudinally polarized optical needles are beams that exhibit ultra-long depth of field, subwavelength transverse confinement, and polarization oriented along the longitudinal direction. Although several techniques have been proposed to generate such needles, their scarce experimental observations have been indirect and incomplete. Here, we demonstrate the creation and full three-dimensional verification of a longitudinally polarized optical needle. This needle is produced by generating a radially polarized Bessel-Gauss beam at the focus of a high numerical aperture microscope objective. Using three-dimensional spatial mapping of second-harmonic generation from a single vertically aligned GaAs nanowire, we directly verify such a longitudinally polarized optical needle's properties, which are formed at the focus. The needle exhibits a dominant polarization, which is oriented along the longitudinal direction, an ultra-long depth of field (30 λ), and high spatial homogeneity. These are in agreement with corresponding focal field calculations that use vector diffraction theory. Our findings open new opportunities for manipulation and utilization of longitudinally polarized optical needles.

Propagation of Bessel Gaussian beams through non-Kolmogorov turbulence based on Rytov theory

The average intensity of the Bessel Gaussian beams propagating through the non-Kolmogorov turbulence based on Rytov theory is derived without the quantic approximation in this paper. Therefore, this result is comparatively more accurate than that calculated by the extended Huygens-Fresnel principle, especially when the inner scale of the turbulence is small or the beams width is large. There is an interesting finding which does not exist in Gaussian beams propagation. It is the intensity variation with the inner scale that displays different behaviors when the beams width is different. Moreover, there will be some beams with specific source width, whose average intensities on the axis do not affected by the turbulence after the inner scale increasing to a certain value as their turbulence perturbation is zero. And the beams here become to the flat top beams. In summary, this paper provides an accurate method for the investigation of the Bessel Gaussian beams propagation through the non-Kolmogorov turbulence and improves the theoretical basis for the applications.

Are Bessel beams resilient to aberrations and turbulence?

It is understood from the conical wave picture that Bessel beams may self-heal after certain opaque obstructions, but the extrapolation to transparent phase screens is not self-evident. Here we consider the propagation of Bessel beams through aberrated obstacles and show that the self-healing is not guaranteed, but rather a function of the severity of the aberration. Paradoxically, we explain why strong aberrations may show self-healing while weak aberrations will not, and highlight the parameters that influence this. Finally, we combine aberrations to pass the Bessel beam through turbulence, and debunk the myth that Bessel beams are resilient to such perturbations.

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.

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.

Vector optical field generation based on birefringent phase plate

Vector optical field has recently gained interest in a variety of application fields due to its novel characteristics. Conventional approaches of generating vector optical fields have difficulties in forming highly continuous polarization and suffer from the issue of high energy utilization rates. In order to address these issues, in this study a single optical path was proposed to generate vector optical fields where the birefringent phase plate modulated a linear polarized light into a vector optical field, which was then demodulated to a non-uniform linear polarization distribution of the vector optical field by the polarization demodulation module. Both a theoretical model and numerical simulations of the vector optical field generator were developed, illustrating the relationship between the polarization distribution of the target vector optical field and the depth distribution of the birefringent phase plate. Furthermore, the birefringent phase plate with predefined surface distributions was fabricated by grayscale exposure and ion etching. The generated vector optical field was experimentally characterized, capable of producing continuous polarization with high light energy utilization ratio, consistent with simulations. This new approach may have the potential of being widely used in future studies of generating well-controlled vector optical fields.

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.

Polymorphic beams and Nature inspired circuits for optical current

Laser radiation pressure is a basis of numerous applications in science and technology such as atom cooling, particle manipulation, material processing, etc. This light force for the case of scalar beams is proportional to the intensity-weighted wavevector known as optical current. The ability to design the optical current according to the considered application brings new promising perspectives to exploit the radiation pressure. However, this is a challenging problem because it often requires confinement of the optical current within tight light curves (circuits) and adapting its local value for a particular task. Here, we present a formalism to handle this problem including its experimental demonstration. It consists of a Nature-inspired circuit shaping with independent control of the optical current provided by a new kind of beam referred to as polymorphic beam. This finding is highly relevant to diverse optical technologies and can be easily extended to electron and x-ray coherent beams.

Nondiffracting vector beams where the charge and the polarization state vary with propagation distance

We generate nondiffracting vector beams where the charge and the polarization state vary with the propagation distance. We use reflective geometry where a parallel-aligned spatial light modulator is used to spatially modulate two orthogonal linear polarizations. We encode spiral phases with equal charge but with opposite signs onto the two polarization directions to encode a vector beam and add two axicon phases. Both the charge and the phase shift between the two axicons can be varied along the focus line. We provide experimental results that demonstrate both features.

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.

On the use of structured light in nonlinear optics studies of the symmetry group of a crystal

We put forward a technique that allows to extract information about the symmetry group to which certain nonlinear crystals belong using a single illuminating beam. It provides such information by considering the outcome of a nonlinear optics process characterized by the electric nonlinear susceptibility tensor, whose structure is dictated by such symmetry group. As an example, we consider the process of spontaneous parametric down-conversion, when it is pumped with a special type of Bessel beam. The observation of the spatial angular dependence of the lower-frequency generated light provides direct information about the symmetry group of the crystal. We should stress that the choice of the appropriate illumination is of paramount importance for unveiling the sought-after information.

Nondiffracting Bessel beams with polarization state that varies with propagation distance

We generate nondiffracting Bessel beams whose polarization state varies with propagation distance. We use a reflective geometry where a single parallel-aligned spatial light modulator device is used to spatially modulate two orthogonal linear polarizations with two axicon phase profiles. Then, by adding an extra phase retardation radial profile between these linear states, we are able to modulate the state of polarization along the line focus of the axicon. We provide experimental results that demonstrate the polarization axial control with zero-order and higher order Bessel beams.

Shaping of light beams by 3D direct laser writing on facets of nonlinear crystals

We demonstrate experimentally spatial-mode conversions of light beams generated in a quadratic nonlinear process by micron-scale structures placed on the facets of nonlinear crystals. These structures were printed on the crystal facets using a three-dimensional (3D) direct laser writing system. The functional structures were designed to modify the phase of the beam at specific wavelengths, thereby enabling conversion of a fundamental Gaussian laser beam into different high-order Hermite-Gaussian modes, Laguerre-Gaussian modes, and zeroth-order Bessel beams of the second harmonic. This facet functionalization opens exciting new opportunities for robust and compact beam shaping in a nonlinear interaction without compromising the conversion efficiency.

Creating order with the help of randomness: generating transversely random, longitudinally invariant vector optical fields

We show that it is possible to generate transversely random, diffraction-free/longitudinally invariant vector optical fields. The randomness in transverse polarization distribution complements a previously studied one in intensity of scalar Bessel-type beams, adding another degree of freedom to control these beams. Moreover, we show that the relative transversely random phase distribution is also conserved along the optical axis. Thus, intensity, phase, and polarization of Bessel-type beams can be transversely random/arbitrary while invariant upon propagation. Such fields may find applications in encryption/secure communications, optical trapping, etc.

Fiber propagation of vector modes

Here we employ both dynamic and geometric phase control of light to produce radially modulated vector-vortex modes, the natural modes of optical fibers. We then measure these modes using a vector modal decomposition set-up as well as a tomography measurement, the latter providing a degree of the non-separability of the vector states, akin to an entanglement measure for quantum states. We demonstrate the versatility of the approach by creating the natural modes of a step-index fiber, which are known to exhibit strong mode coupling, and measure the modal cross-talk and non-separability decay during propagation. Our approach will be useful in mode division multiplexing schemes for transport of classical and quantum states.

Visualizing polarization singularities in Bessel-Poincaré beams

We demonstrate that an annulus of light whose polarization is linear at each point, but the plane of polarization gradually rotates by π radians can be used to generate Bessel-Poincaré beams. In any transverse plane this beam exhibits concentric rings of polarization singularities in the form of L-lines, where the polarization is purely linear. Although the L-lines are invisible in terms of light intensity variations, we present a simple way to visualize them as dark rings around a sharp peak of intensity in the beam center. To do this we use a segmented polarizer whose transmission axes are oriented differently in each segment. The radius of the first L-line is always smaller than the radius of the central disk of the zero-order Bessel beam that would be produced if the annulus were homogeneously polarized and had no phase circulation along it.

Generation of terahertz vector beams with a concentric ring metal grating and photo-generated carriers

A scheme for vector terahertz (THz) beam generation is proposed. A subwavelength metal grating is utilized to adjust the polarization of the THz radiation. The amplitude and phase distributions of the THz beam are dynamically regulated by a THz computer-generated hologram (CGH) pattern of the photo-generated carriers. A radially polarized THz beam and a vector THz vortex beam with a topological charge of 1 are generated to demonstrate the validity and the effectiveness of the proposed scheme. Experimental results correspond to the theoretical simulations well. Moreover, the proposed method is applicative for a broadband THz radiation. These results could be applied in the THz sensing, THz imaging, and THz communication in the future.

Detection of Bessel beams with digital axicons

We propose a simple method for the detection of Bessel beams with arbitrary radial and azimuthal indices, and then demonstrate it in an all-digital setup with a spatial light modulator. We confirm that the fidelity of the detection method is very high, with modal cross-talk below 5%, even for high orbital angular momentum carrying fields with long propagation ranges. To illustrate the versatility of the approach we use it to observe the modal spectrum changes during the self-reconstruction process of Bessel beams after encountering an obstruction, as well as to characterize modal distortions of Bessel beams propagating through atmospheric turbulence.

All-digital wavefront sensing for structured light beams

We present a new all-digital technique to extract the wavefront of a structured light beam. Our method employs non-homogeneous polarization optics together with dynamic, digital holograms written to a spatial light modulator to measure the phase relationship between orthogonal polarization states in real-time, thereby accessing the wavefront information. Importantly, we show how this can be applied to measuring the wavefront of propagating light fields, over extended distances, without any moving components. We illustrate the versatility of the tool by measuring propagating optical vortices, Bessel, Airy and speckle fields. The comparison of the extracted and programmed wavefronts yields excellent agreement.

Generation of radially polarized Bessel-Gaussian beams from c-cut Nd:YVO₄ laser

We experimentally demonstrate the generation of radially polarized Bessel-Gaussian beams from a c-cut Nd:YVO₄ laser with a hemispherical cavity configuration by proper mode control. The output beam has an annular-shaped intensity distribution with radial polarization. When the beam is focused, the intensity pattern changes to a multi-ring, which is a typical characteristic of the lowest transverse mode of vector Bessel-Gaussian beam. Higher-order modes of vector Bessel-Gaussian beam are also observed from the same cavity by slightly changing the cavity alignment. The experimental results show a good agreement with the simulation results for both focal and far fields. The present method is a simple and direct way for generating vector Bessel-Gaussian beams.