Polarization Shaping for Control of Nonlinear Propagation

Measuring the Optical Concurrence of Vector Beams with an Atomic-State Interferometer

We investigate the transmission of vector beams, correlated in their polarization and spatial degrees of freedom, through cold atoms in the presence of a transverse magnetic coupling field. The resulting phase-dependent dynamics allow us to imprint the spatially varying polarization of a vector beam onto atomic spin polarizations, thereby establishing a direct link between optical space-polarization correlations and atomic-state interference. We find that the resulting absorption profiles show interference fringes whose modulation strength is given by the squared concurrence of the vector beam, letting us identify optical concurrence from a single absorption image. We expect impact across a diverse range of applications, including spintronics, quantum memories, metrology, and clocks.

Spatial self-phase modulation excited by fractional-order linearly polarized vector fields

Compared to the integer-order vector field, the fractional-order vector field has an additional degree of control freedom, which will bring rich photophysical properties and what we believe to be novel nonlinear optical phenomena. In this work, we theoretically and experimentally investigate the focusing, propagation, and spatial self-phase modulation (SSPM) of fractional-order linearly polarized vector fields (FLPVFs). It is shown that the weak focusing field of FLPVF exhibits an asymmetric intensity distribution. Intriguingly, its state of polarization (SoP) has a hybrid polarization distribution. When this focused FLPVF propagates to the far field in free space, its SoP degenerates into a localized linearly polarization distribution. However, after the focused FLPVF passes through an isotropic nonlinear Kerr medium, its SoP exhibits a hybrid polarization distribution. Additionally, unlike the self-diffraction intensity pattern of integer-order linearly polarized vector field (ILPVF) with a concentric multi-ring structure, the SSPM pattern of FLPVF is a symmetry broken self-diffraction intensity pattern. The presented work provides a nonlinear optics approach for manipulating both the SoP and intensity distributions of the light field.

Pseudo-spin-orbit-coupling-based manipulation of vector beams using electromagnetically induced transparency

Based on the electromagnetically induced transparency (EIT) model and the higher-order Poincaré sphere (HOPS) framework, we establish a general paradigm to investigate the paraxial evolution of a vector beam in a tripod EIT system. By quantum-optical analogy, we introduce a formalism with a generalized Pauli-like equation under rotational invariance, in which the pseudo-spin-orbit coupling (PSOC) and the spin-orbit nonseparability of light can coexist. More importantly, we find that both the PSOC-based real and imaginary potentials play a key role in controlling and modulating the nonseparable state of the vector beam to traverse the entire HOPS, where the orientation and ellipticity of the transmitted polarization can be modified by varying the PSOC coefficients. Therefore, an all-optical scheme can be proposed to improve the flexibility for tailoring the space-variant polarization of light in coherent media, where the tunable spatial-polarization multiplexing may be useful in conventional and quantum information processing.

Opto-magnetic resonance single-beam magnetometer driven by vector polarized light

In this paper, we present an analysis of the amplitude variations of the opto-magnetic resonance absorption signals obtained in a single-beam magnetometer driven by radially or azimuthally polarized light (RPL/APL). It is shown that optically polarized atoms driven by cylindrical vector beams obtained only the alignment of atomic multipole moments but not the orientation, which is in good agreement with our simulation and experimental results. In comparison with the plane polarized pump light fields, cylindrical vector beams with much more complete electric vector polarization distribution in the transverse plane, make it unlikely to create the "emptying state " (no-atom populated) among the ground-state Zeeman sublevels for any possible orientation of the applied static magnetic field. These characteristics of the RPL/APL lead to generally smaller atomic population difference and lower response intensity of the transmitted signal. The tensor decomposition of atomic polarized states and the evolution of atomic multipole moments with the sweeping radio frequency (RF) field offer the way to show the magnetic orientation sensitivity of the radially or azimuthally polarized probe light, which possess similar profiles as that of the linearly polarized light, only with a constant phase lag of about π/2 and obvious amplitude differences.

Generation of volumetrically full Poincaré beams

Optical communications, remote sensing, particle trapping, and high-resolution imaging are a few research areas that benefit from new techniques to generate structured light. We present a method of generating polarization-structured laser beams that contain both full and partial polarization states. We demonstrate this method by generating an optical beam that contains every state of partial and full polarization. We refer to this beam as a volumetrically full Poincaré beam to distinguish it from full Poincaré beams, which contain all states of full polarization only. In contrast to methods relying upon spatial coherence to generate polarization-structured beams with partial polarization, our method creates well-collimated beams by relying upon temporal coherence.

Suppression of Nonlinear Optical Rogue Wave Formation Using Polarization-Structured Beams

A nonlinear self-focusing material can amplify random small-amplitude phase modulations present in an optical beam, leading to the formation of amplitude singularities commonly referred to as optical caustics. By imposing polarization structuring on the beam, we demonstrate the suppression of amplitude singularities caused by nonlinear self-phase modulation. Our results are the first to indicate that polarization-structured beams can suppress nonlinear caustic formation in a saturable self-focusing medium and add to the growing understanding of catastrophic self-focusing effects in beams containing polarization structure.

Control of Light-Atom Solitons and Atomic Transport by Optical Vortex Beams Propagating through a Bose-Einstein Condensate

We model propagation of far-red-detuned optical vortex beams through a Bose-Einstein condensate using nonlinear Schrödinger and Gross-Pitaevskii equations. We show the formation of coupled light-atomic solitons that rotate azimuthally before moving off tangentially, carrying angular momentum. The number, and velocity, of solitons, depends on the orbital angular momentum of the optical field. Using a Bessel-Gauss beam increases radial confinement so that solitons can rotate with fixed azimuthal velocity. Our model provides a highly controllable method of channeling a BEC and atomic transport.

Towards higher-dimensional structured light

Structured light refers to the arbitrarily tailoring of optical fields in all their degrees of freedom (DoFs), from spatial to temporal. Although orbital angular momentum (OAM) is perhaps the most topical example, and celebrating 30 years since its connection to the spatial structure of light, control over other DoFs is slowly gaining traction, promising access to higher-dimensional forms of structured light. Nevertheless, harnessing these new DoFs in quantum and classical states remains challenging, with the toolkit still in its infancy. In this perspective, we discuss methods, challenges, and opportunities for the creation, detection, and control of multiple DoFs for higher-dimensional structured light. We present a roadmap for future development trends, from fundamental research to applications, concentrating on the potential for larger-capacity, higher-security information processing and communication, and beyond.

Vector beam polarization rotation control using resonant magneto optics

Vector beam propagation through a four-level tripod atomic system has been investigated. The three transitions of the tripod atomic system are coupled by a strong control field and the two constituent orthogonally polarized components of a weak probe vector beam. An external magnetic field induces anisotropy, creating a difference in the refractive indices of the two polarization components of the beam. This difference in refractive indices varies with the magnetic field strength and directly relates to the polarization orientation at any transverse plane. Thus, the transverse polarization structure can be rotated as desired with appropriate magnetic field strength. We further study the effect of nonlinearity and inhomogeneous broadening on the vector beam's polarization rotation. Therefore, the mechanism of efficient polarization control and manipulation of a vector beam can open up a new avenue for high-resolution microscopy and high-density optical communications.

Polarimetric method of generating full Poincaré beams within a finite extent

A novel polarimetric method of generating a variety of Poincaré beams such as half Poincaré beams and full Poincaré beams using doubly inhomogeneous wave plates (d-plates) is proposed. In this method, every input state of polarization (SoP) through such a d-plate generates a unique Poincaré beam, thereby giving access to a potentially infinite number of them. Furthermore, the generation of full Poincaré beams is presented here as an instance of the geometrical problem of mapping the surface of a sphere onto a plane, and this insight allows one to design d-plates that convert the input SoP to every possible SoP, within a finite region of the beam. A gadget composed of three singly inhomogeneous wave plates for an equivalent realization of these d-plates is also presented.

Atomic Compass: Detecting 3D Magnetic Field Alignment with Vector Vortex Light

We describe and demonstrate how 3D magnetic field alignment can be inferred from single absorption images of an atomic cloud. While optically pumped magnetometers conventionally rely on temporal measurement of the Larmor precession of atomic dipoles, here a cold atomic vapor provides a spatial interface between vector light and external magnetic fields. Using a vector vortex beam, we inscribe structured atomic spin polarization in a cloud of cold rubidium atoms and record images of the resulting absorption patterns. The polar angle of an external magnetic field can then be deduced with spatial Fourier analysis. This effect presents an alternative concept for detecting magnetic vector fields and demonstrates, more generally, how introducing spatial phases between atomic energy levels can translate transient effects to the spatial domain.

Vector optical field with the polarization varying along an arbitrary circular trajectory on the Poincaré sphere

As an inherent feature of vector optical field, the spatial distribution of polarization brings additional degrees of freedom to engineer the optical field and control the interaction between light and matters. Here we focus on the variation of polarization in single vector optical field, which can be defined by the trajectory on the Poincaré sphere. Based on the amplitude-phase-polarization joint modulation method we propose, vector optical field, whose variation of polarization follows arbitrary circular trajectory on the Poincaré sphere, can be generated. Moreover, the tightly focusing behaviors of the vector optical fields with the polarization varying along parallel circles on the Poincaré sphere are compared. Relations between the circular trajectory and the central intensity of the hollow focal field are concluded.

Trans-spectral vector beam nonlinear conversion via parametric four-wave mixing in alkali vapor

Coherent frequency conversion of vector beams (VBs) without distorting their intensity profile or spatial polarization distribution is important for novel applications in quantum and classical regimes. Here, we experimentally and theoretically investigate VB transfer from near-infrared to blue light using a Sagnac interferometer, combining the parametric four-wave mixing process in atomic vapor. The vector probe beam is converted into a completely different wavelength, and the vector mode of the generated blue beam is highly similar to the incident probe beam. These results may provide a feasible solution for communication interfaces in classical and quantum science fields based on atomic ensembles.

Geometric control of vector vortex light beams via a linear coupling system

We demonstrate a novel theoretical platform to realize geometric control of vector vortex states in an optical coupling system. These complex states are characterized by spatially varying polarizations and coupled with vortex phase profiles. It can be mapped uniquely as a point on a higher-order Poincaré sphere. The geometric theory clearly reveals how a tailored phase mismatch profile, together with a suitable coupling, supports state conversion between these higher-order complex light fields, in analogous to the processes appearing in two-level quantum system as well as three-wave mixing process in nonlinear optics. Specifically, in the phase matching condition, it is shown that these complex states carried by an envelope field exhibit periodic oscillations in the course of state evolution; whereas in the phase mismatching condition the oscillations become detuned, leading to noncyclic state evolution. Intriguingly, when using an adiabatic technique for the phase mismatch, robust state conversion between two arbitrary vector vortex light fields can be realized. Our demonstrations provide a fully control over the vector vortex states on the sphere, and we suggest that it would benefit various potential applications both in the classical and the quantum optics.

Spatio-temporal controlled filamentation using higher order Bessel-Gaussian beams integrated in time

We demonstrate a new method for a systematic, dynamic, high-speed, spatio-temporal control of femtosecond light filamentation in BK7 as a particular example of nonlinear medium. This method is based on using coherent conjugate asymmetric Bessel-Gaussian beams to control the far-field intensity distribution and in turn control the filamentation location. Such spatio-temporal control allows every femtosecond pulse to have a unique intensity distribution that results in the generation of structured filamentation patterns on demand. The switching speed of this technique is dependent on the rise time of the acousto-optic deflector, which can operate in the MHz range while having the ability to handle high peak power pulses that are needed for nonlinear interactions. The proposed and demonstrated spatio-temporal control of structured filaments can enable generation of large filament arrays, opto-mechanical manipulations of water droplets for fog clearing, as well as engineered radiofrequency plasma antennas.

Collapse of hybrid vector beam in Rb atomic vapor

In recent years, many researchers have tried to control and design the collapsing behavior of light beams in nonlinear media. Vector beams coupling with spin and orbit angular momentum freedom have attracted more and more attention. In this Letter, we study the collapse of a hybrid vector beam (HVB) propagating through rubidium atomic vapor. First, the HVB collapses into filaments located at positions with linear polarization. As propagation distance in atomic vapor increases, the locations of the filaments switch from positions with linear polarization to those with circular polarization. In this process, the absorption of the medium plays an important role. Results indicate that the absorption can be used as a degree of freedom to modulate the filamentation. Furthermore, by analyzing the polarization angle of an elliptically polarized position on the transverse plane of the HVB, we demonstrate the evolution of polarization distribution of HVB during propagation. Such results could have application in manipulating other structured beams and could be potentially applied to realize optical switches or logic for information processing.

Vector vortex state preservation in Fresnel cylindrical diffraction

The vector vortex light beam, which exhibits a space-variant polarization state and is coupled with orbital angular momentum of light, has been drawing much attention due to its fundamental interest and potential applications in a wide range. Here we reveal both theoretically and experimentally that a diffractive structure having cylindrical symmetry is shown to be transparent for the vector vortex state of light with arbitrary topology. We demonstrate such an intriguing phenomenon in the Fresnel diffraction condition, where the vector Helmholtz wave equation can be utilized in the paraxial regime. Our demonstration has implications in control and manipulation of vector vortex light beams in diffractive optics, and hence, it may find potential applications.

Hybrid order Poincaré spheres for Stokes singularities

Hybrid order Poincaré spheres to represent more general Stokes singularities are presented. Polarization singularities form a subset of Stokes singularities, and therefore induction of these spheres brings completeness. The conventional understanding of Poincaré beams as hybrid order Poincaré sphere beams is also expanded to include more beams. Construction and salient properties of these spheres are explained with illustrations to show their ability to represent more exotic Poincaré beams that have zero total helicity irrespective of their size. Pancharatnam-Berry geometric phase formulation using these new spheres is also possible.

Bessel-like beams with controllable rotating local linear polarization during propagation

Bessel-like beams with controllable rotation of local linear polarization upon propagation are generated, which in fact achieve the evolution of polarization states along the equator of the Poincaré sphere during propagation. Based on the amplitude-phase joint modulation method, the rotation direction and rate of polarizations of the Bessel-like beam can be controlled easily by adjusting the radial indices and intensity ratio of two superposed beams. A rotation angle of $\sim$∼800 deg has been achieved after a propagation distance of 120 mm, corresponding to a rotation rate of $\sim$∼6.7 deg/mm, which is about three times higher than in previous works.

Energy transfer of the tightly focused hybridly polarized vector optical fields with elliptic symmetry in free space

We theoretically and experimentally present hybridly polarized vector optical fields (HP-VOFs) with elliptic symmetry in an elliptic coordinate system. Compared with the traditional cylindrical HP-VOFs, there is an additional degree of freedom for this new kind of vector optical field, which is the interval between the two foci in the elliptic coordinate system. Except for discussing the singularities of the HP-VOFs, we concentrate on studying the energy transfer of the tightly focused HP-VOFs with elliptic symmetry in free space. We summarize the rules of the energy transfer and introduce a reference optical field to explain them. We hope these results can provide a new way to flexibly modulate tightly focused fields, which may be applied in realms such as optical machining, optical trapping, and information transmission.

Control of spatially rotating structures in diffractive Kerr cavities

Turing patterns in self-focussing nonlinear optical cavities pumped by beams carrying orbital angular momentum (OAM) m are shown to rotate with an angular velocity ω=2m/R ² on rings of radii R. We verify this prediction in 1D models on a ring and for 2D Laguerre-Gaussian and top-hat pumps with OAM. Full control over the angular velocity of the pattern in the range -2m/R ²≤ω≤2m/R ² is obtained by using cylindrical vector beam pumps that consist of orthogonally polarized eigenmodes with equal and opposite OAM. Using Poincaré beams that consist of orthogonally polarized eigenmodes with different magnitudes of OAM, the resultant angular velocity is ω=(m _L+m _R)/R ², where m _L,m _R are the OAMs of the eigenmodes, assuming good overlap between the eigenmodes. If there is no, or very little, overlap between the modes then concentric Turing pattern rings, each with angular velocity ω=2m _L,R /R ² will result. This can lead to, for example, concentric, counter-rotating Turing patterns creating an optical peppermill-type structure. Full control over the speeds of multiple rings has potential applications in particle manipulation and stretching, atom trapping, and circular transport of cold atoms and BEC wavepackets.

Anisotropic nonlinear Kerr media: Z-scan characterization and interaction with hybridly polarized beams

The interaction of intense laser with matter gives rise to a variety of novel nonlinear optical effects, reflects the nonlinear optical property of a material, and modulates the light propagation behavior. Herein, we investigate anisotropic Kerr nonlinearities induced by both scalar and vectorial optical fields. Firstly, we present the anisotropic third-order nonlinear refraction indexes related to left-hand and right-hand components, which depend on the ellipticity, the dichroism coefficient, the anisotropy coefficient, as well as the crystal orientation angle. Secondly, we develop the elliptically polarized light Z-scan technique for characterizing third-order nonlinear susceptibility tensor in anisotropic nonlinear Kerr media, which is demonstrated experimentally. Lastly, with the known nonlinear optical parameters, we numerically study both the vectorial self-diffraction behaviors and spin angular momentum (SAM) characteristics of hybridly polarized beams induced by an anisotropic Kerr nonlinearity. It is shown that the anisotropic Kerr nonlinearity offers a new approach to manipulate the polarization-structured light field, which has potential applications in SAM manipulation, three-dimensional crystal orientation, and polarization-sensitive detection and sensing.

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.

Pancharatnam-Berry phase shaping for control of the transverse enhancement of focusing

We show that elongating a tightly focused field in the direction perpendicular to the optical axis is possible. We demonstrate our approach by specially shaping the Pancharatnam-Berry (PB) phase. Moreover, the analytical formulae required to calculate the strength vectors and energy flux of the three-dimensional electromagnetic fields near the focus of an aplanatic optical system are derived using the Richards and Wolf vectorial diffraction methods. Calculations reveal that the transverse enhancement is controllable and depend on the phase index in the PB phase, thereby giving rise to a focus with tunable length and subwavelength width in the focal plane.

Dynamic control of cylindrical vector beams via anisotropy

We demonstrate that the spatially diffractive properties of cylindrical vector beams could be controlled via linear interactions with anisotropic crystals. It is the first time to show experimentally that the diffraction of the vector beams can be either suppressed or enhanced significantly during propagation, depending on the sign of anisotropy. Importantly, it is also possible to create a linear non-spreading and shape-preserving vector beam, by vanishing its diffraction during propagation via strong anisotropy in a crystal. The manageable diffractive effect enables manipulating propagation dynamics of the circular Airy vector beams, i.e., their propagation trajectories can be dynamically controlled by weakening or enhancing self-acceleration of the Airy beam. We further demonstrate that the cylindrical vector beams with initially zero orbital angular momentum can be rotated either clockwise or anticlockwise, relying on the sign of the anisotropy.

Holographically controlled three-dimensional atomic population patterns

The interaction of spatially structured light fields with atomic media can generate spatial structures inscribed in the atomic populations and coherences, allowing for example the storage of optical images in atomic vapours. Typically, this involves coherent optical processes based on Raman or EIT transitions. Here we study the simpler situation of shaping atomic populations via spatially dependent optical depletion. Using a near resonant laser beam with a holographically controlled 3D intensity profile, we imprint 3D population structures into a thermal rubidium vapour. This 3D population structure is simultaneously read out by recording the spatially resolved fluorescence of an unshaped probe laser. We find that the reconstructed atomic population structure is largely complementary to the intensity structure of the control beam, however appears blurred due to global repopulation processes. We identify and model these mechanisms which limit the achievable resolution of the 3D atomic population. We expect this work to set design criteria for future 2D and 3D atomic memories.

Polarization-controlled orbital angular momentum switching in nonlinear wave mixing

We demonstrate polarization-controlled switching of the orbital angular momentum (OAM) transfer in nonlinear wave mixing. By adjusting the input beam geometry, we are able to produce a three-channel orbital OAM, with arbitrary topological charges simultaneously generated and spatially resolved in the second-harmonic wavelength. The use of path and polarization degrees of freedom allows nearly perfect optical switching between different OAM operations. These results are supported by a theoretical model showing very good agreement with the experiments.

Vectorial optical fields: recent advances and future prospects

Driven by their potential applications, vectorial optical fields with spatially inhomogeneous states of polarization within the cross section have drawn significant attention recently. This work intends to review some of the latest development of this rapidly growing field of optics and offer a general overview of the current status of this field in a few areas. Mathematical descriptions of generalized vectorial optical fields are provided along with several special examples. A time-reversal methodology for the creation of a wide variety of exotic optical focal fields with prescribed characteristics within the focal volume is presented. Recently developed methods for the generation of vectorial optical fields that utilize fiber lasers, digital lasers, vectorial optical field generator, metasurfaces or photoalignment liquid crystals are summarized. The interactions of these vectorial optical fields with various micro- and nano-structures are presented and the prospects of their potential applications are discussed. The connection of vectorial optical fields with higher dimensionality in quantum information is summarized.

Spontaneous Formation of Vector Vortex Beams in Vertical-Cavity Surface-Emitting Lasers with Feedback

The spontaneous emergence of vector vortex beams with nonuniform polarization distribution is reported in a vertical-cavity surface-emitting laser (VCSEL) with frequency-selective feedback. Antivortices with a hyperbolic polarization structure and radially polarized vortices are demonstrated. They exist close to and partially coexist with vortices with uniform and nonuniform polarization distributions characterized by four domains of pairwise orthogonal polarization. The spontaneous formation of these nontrivial structures in a simple, nearly isotropic VCSEL system is remarkable and the vector vortices are argued to have solitonlike properties.

Multiple generations of high-order orbital angular momentum modes through cascaded third-harmonic generation in a 2D nonlinear photonic crystal

We experimentally demonstrate multiple generations of high-order orbital angular momentum (OAM) modes through third-harmonic generation in a 2D nonlinear photonic crystal. Such third-harmonic generation process is achieved by cascading second-harmonic generation and sum-frequency generation using the non-collinear quasi-phase-matching technique. This technique allows multiple OAM modes with different colors to be simultaneously generated. Moreover, the OAM conservation law guarantees that the topological charge is tripled in the cascaded third-harmonic generation process. Our method is effective for obtaining multiple high-order OAM modes for optical imaging, manipulation, and communications.