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Recently, the emergence of transverse orbital angular momentum (OAM) as a novel characteristic of light has captured substantial attention, and the significance of adjustable OAM orientation has been underscored due to its pivotal role in the interaction between light and matter. In this work, we introduce a novel approach to manipulate the orientation of photonic OAM at subwavelength scales, leveraging spatiotemporal coupling. By tightly focusing a wavepacket containing dual spatiotemporal vortices and a spatial vortex through a high numerical aperture lens, the emergence of intricate coupling phenomena leads to entangled and intricately twisted vortex tunnels. As a consequence, the orientation of spatial OAM deviates from the conventional light axis. Through theoretical scrutiny, we unveil that the orientation of photonic OAM within the focal field is contingent upon the signs of the topological charges in both spatiotemporal and spatial domains. Additionally, the absolute values of these charges govern the precise orientation of OAM within their respective quadrants. Moreover, augmenting the pulse width of the incident light engenders a more pronounced deflection angle of photonic OAM. By astutely manipulating these physical parameters, unparalleled control over the spatial orientation of OAM becomes achievable. The augmented optical degrees of freedom introduced by this study hold considerable potential across diverse domains, including optical tweezers, spin-orbit angular momentum coupling, and quantum communication.

The third-order topological insulators based on three-dimensional (3D) photonic crystals (PCs) have hardly been achieved because the nontrivial bandgap in 3D PCs is difficult to form. In this Letter, we elaborately construct 3D Su-Schrieffer-Heeger lattice in which the periodic modulation of refractive index is uniform in three axis directions. The high-order topological PCs are characterized by the nontrivial bulk polarizations and the mirror eigenvalues. Such a structure can achieve topological 1-codimensional surface states, 2-codimensional hinge states, and 3-codimensional corner states. More importantly, it is found for the first time, to the best of our knowledge, that the topological states exhibit a degeneration behavior, i. e., the corner, and hinge state, or corner and surface states coexist at nearly the same frequency, but maintain their own mode properties. The multiple topological states in 3D PCs as well as the degeneration of topological states will open a new window for the study of topological photonics.

Vortex beams carrying optical angular momentum (AM) could drive the orbital motion of a small particle around the optical axis. In general, the orbital rotation speed of trapped particles increases linearly with the increasing laser power. Beyond the linear optics regime, in this work, we investigate both the optical force and torque on a two-photon absorbing Rayleigh particle produced by the tightly focused femtosecond-pulsed circularly polarized vortex beam. Different from the trapping dynamics of particles without two-photon absorption (TPA), it is shown that the orbital motion of trapped particles with TPA accelerates nonlinearly as the laser power increases. Moreover, the orbital motion acceleration of trapped particles is proportional to the TPA coefficient. The corresponding underlying mechanism is discussed in detail. Our results may find interesting applications in the characterization of the optical nonlinearity of a single nanoparticle, and AM manipulation and particle transportation in the nonlinear optics regime.

Aluminum (Al) plasmonic nanostructures have recently demonstrated remarkable optical nonlinear phenomena, such as enhanced second harmonic (SH) generation. However, the relatively weak field enhancement resulted from large optical losses associated with aluminum nanostructures in combination with the difficulties in controlling the emission polarization pose as a challenge for SH enhancement and tuning. In this paper, we show that the SH emission of aluminum nanostructures can be efficiently enhanced with the polarization properties simultaneously tunable by using metal-insulator-metal (MIM) nanostructures, constituting of Al cross nanoantenna arrays on top of Al mirrors with a SiO 2 spacing layer. Specifically, femtosecond laser beam with a linear polarization parallel to one arm illuminates on the structure while the orthogonal arms were physically modified by the laser-induced photothermal reshaping technique to control the SH radiation by the plasmonic resonances. Under the resonance at the SH wavelength, we observed one order of magnitude larger emission enhancement compared to that at the off-resonant condition. Interestingly, the polarization states can be well manipulated simultaneously by controlling the resonances of the orthogonal arms. The enhanced SH conversion and tunable polarization states pave the way for the development of nonlinear optical sources and advanced functional metasurfaces.

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.

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in plenty of applications. In this work, we propose and experimentally demonstrate the generation of a second-order full Poincaré (FP) beam and its application in two-dimensional (2D) flattop beam shaping with spatially variant polarization under a high numerical aperture focusing condition. In addition, the force mechanism of the focal field with 2D flattop beam profile is numerically studied, demonstrating the feasibility to trap a dielectric Rayleigh particle in three-dimensional space. The results show that the additional degree of freedom provided by the FP beam allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force exerted on a dielectric Rayleigh particle. The findings reported in the work may find useful applications in laser micromachining, optical trapping, and optical assembly.

We generate a new kind of azimuthal-variant vector field with a distribution of states of polarization (SoPs) described by the square of the azimuthal angle. Owing to asymmetrical SoPs distribution of this localized linearly polarized vector field, the tightly focused field exhibits a double half-moon shaped pattern with the localized elliptical polarization in the cross section of field at the focal plane. Moreover, we study the three-dimensional distributions of spin and orbital linear and angular momenta in the focal region. We numerically investigate the gradient force, radiation force, spin torque, and orbital torque on a dielectric Rayleigh particle produced by the tightly focused vector field. It is found that asymmetrical spinning and orbiting motions of trapped Rayleigh particles can be realized by the use of a tight vector field with power-exponent azimuthal-variant SoPs.

The nonlinear ellipse rotation usually occurs when an elliptically polarized beam propagates through an isotropic nonlinear medium owing to the existence of χ1221(3). Here we report the radial-variant nonlinear ellipse rotation of a vector beam with structured elliptical polarization through isotropic Kerr nonlinearities. Due to the interaction of elliptically polarized vector beams (EPVBs) with isotropic nonlinear media, the distributions of both the orientation angle and the ellipticity angle of beams at the far-field observational plane exhibit multiple concentric ring structures with the circularly symmetry. Numerical simulations show that the self-diffraction intensity pattern, the distribution of the state of polarization, and the spin angular momentum (SAM) distribution of an EPVB could be manipulated by tuning both the isotropic optical nonlinearity and the chirality parameter of the vector beam, which may find direct applications in polarization-control optical switching, SAM manipulation, and optical polarization encoding or detection.

We propose a simple and flexible method to create identical multiple focal spots with three-dimensional arbitrary shifting without moving lenses or laser beams. The incident cylindrical vector (CV) beam superposed with predesigned phase and amplitude modulations is tightly focused by a single lens. The multiple focal spots with predetermined number and positions are generated and the identical intensity distribution as well as the polarization distribution for each individual focal spot is demonstrated. We also present a three-dimensional dynamic shifting with four identical focal spots along Pyramid-like trajectory by continuously regulating the phase and amplitude modulations on the incident CV beam. Furthermore, multiple focal spots with unique intensity profile can also be achieved when proper diffractive optical element (DOE) is associated in the focusing system. These engineered focal fields may find potential applications in 3D laser printing, moving multiple particles trapping and manipulations.

The polarization rotation of hybridly polarized beams passing through a uniaxial crystal whose optical axis is orthogonal to the beam axis is theoretically and experimentally investigated. Based on the existing theory, analytical expressions of hybridly polarized beams in uniaxial crystals orthogonal to the optical axis are derived. Simulation results show that the distributions of the intensity patterns, the states of polarization, and the spin angular momentum of hybridly polarized beams in uniaxial crystals depend strongly on the beam radius, the propagation distance in the crystal, and the ratio of the extraordinary refractive index to the ordinary refractive index. The experimental investigations observed the polarization rotation behavior of hybridly polarized beams in rutile crystal, which are in good agreement with the theoretical predictions. The presented work opens up novel approaches for manipulating the polarization rotation of the structured light field by anisotropic crystals in the linear optics regime, which has potential applications in material characterization, polarization-sensitive sensing, and all-optical switching.

Structured intense laser interacting with matter will result in a variety of novel nonlinear optical effects, modulate the light propagation behavior, and change the structural property of a material. In this work, we theoretically investigate the spatial self-phase modulation (SSPM) effect, nonlinear ellipse rotation, and spin angular momentum (SAM) flux redistribution of hybridly polarized vector beams through isotropic Kerr nonlinearities. Experimentally, we observe the SSPM effect of the femtosecond-pulsed hybridly polarized vector beam in carbon disulfide at 800 nm, which is in agreement with the theoretical predictions. Our results show that the SSPM intensity pattern, the distribution of state of polarization (SoP), and the SAM flux of a hybridly polarized vector beam could be manipulated by tuning the isotropic optical nonlinearity, which may find interesting applications in nonlinear mechanism analysis, nonlinear optical characterization, and SAM manipulation.

The propagation and focusing properties of light beams continue to remain a research interest owning to their promising applications in physics, chemistry and biological sciences. One of the main challenges to these applications is the control of polarization distribution within the focal volume. In this work, we propose and experimentally demonstrate a method for generating a focused beam with arbitrary homogeneous polarization at any transverse plane. The required input field at the pupil plane of a high numerical aperture objective lens can be found analytically by solving an inverse problem with the Richard-Wolf vectorial diffraction method, and can be experimentally created with a vectorial optical field generator. Focused fields with various polarizations are successfully generated and verified using a Stokes parameter measurement to demonstrate the capability and versatility of proposed technique.

Metallic nanoparticles have fascinated scientists for over a century and are now heavily utilized in biomedical sciences and engineering. Due to its noncontact and holding nature, optical trapping is suitable to be combined with various applications to manipulate metallic nanoparticles. However, stable trapping of resonant metallic nanoparticles remains challenging due to the strong axial scattering force and severe optical heating effect. In this work, we propose novel optical tweezers constructed around a 4Pi focusing system that is capable of manipulating metallic nanoparticles even under the resonant condition. By properly modulating the spatial distribution of the illumination and adjusting the focusing condition, specific numbers of spherical spots with controllable locations can be generated in the focal region, providing multiple probes to interrogate the sample properties. Besides, stable three-dimensional optical trapping can be formed since the axial scattering force is canceled by the counter-propagating light. The greatly enhanced optical force arising from the extremely high focusing efficiency of the 4Pi focusing system enables to avoid the overheating effect by reducing the input power without destroying the mechanical stability. Moreover, complex motion trajectory of the metallic nanoparticles can be realized via introducing specific phase modulation to the illumination sequentially. The technique demonstrated in this work may open up new avenues for optical manipulation and their applications in various scientific fields.

Orbital angular momentum (OAM) is an intrinsic property of light that has attracted increasing attention recently. In a wide range of applications that involve OAM, it is often crucial to discern the OAM states with high fidelity. In this Letter, we propose a novel method to extend the detectable range of the OAM states by adopting a multi-sector metahologram. The incident light carrying OAM would be focused by the metahologram into surface plasmon waves with separated propagation directions that are spatially sampled by multiple subwavelength detectors. Through quantizing and mapping the detector signals into a lookup table, a wide range of OAM states could be distinguished. The principle reported in this Letter may find important applications in optical communications and information processing with the OAM states.

Based on the inverse Faraday effect, the light-induced magnetization field distributions are investigated for a 4π tight focusing configuration with azimuthally polarized beams. It is found that a superlong (16λ) magnetization chain, composed of 19 subwavelength (0.44λ) spherical spots with longitudinal magnetization field, can be achieved in the focal volume of the objective. Moreover, the magnetic force on a magnetic particle or particle trains produced by tightly focused azimuthally polarized beams are calculated and exploited for the stable trapping of magnetic particles. These unique focal field distributions may find potential applications in confocal microscopy, atom control, and magneto-optical data storage.

In this work, we proposed a novel strategy to manipulate the behavior of the metallic nanoparticle under the resonant condition by using engineered azimuthally polarized optical field. Through optimizing the spatial phase distribution of the illumination, the optical force can be tailored to support stable optical trapping while avoiding trap destabilization caused by optical overheating effect simultaneously. Besides, the resonant particle can be stably trapped at predefined location in 3 dimensional space, or revolves around the beam axis with characteristics that can be holistically controlled in terms of both trajectory and rotation direction. The technique demonstrated in this work may open up new avenues for optical manipulation.

Light fields with structured polarization distribution interacting with structured media will result in many novel optical effects in both the linear and nonlinear regimes. In this work, we report a theoretical investigation of both vectorial self-diffraction behaviors and polarization evolution characteristics of a radially polarized beam induced by anisotropic Kerr nonlinearity. By taking the polarization-orientation dependence of the third-order refractive nonlinearity, we study the far-field vectorial self-diffraction patterns of the radially polarized beam using the vectorial Rayleigh-Sommerfeld formulas. Numerical results reveal that the self-diffraction patterns with a four-fold rotational symmetry exhibit hybrid states of polarization. Moreover, the interaction of radially polarized beams with the anisotropic nonlinear Kerr media leads to the redistribution of the spin angular momentum (SAM) flux in the far-field plane. The presented work opens up new avenues for varying polarization and SAM through anisotropic optical nonlinearity.

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

Generation of vectorial optical fields with arbitrary polarization distribution is of great interest in areas where exotic optical fields are desired. In this work, we experimentally demonstrate the versatile generation of linearly polarized vector fields, elliptically polarized vector fields, and circularly polarized vortex beams through introducing attenuators in a common-path interferometer. By means of Richards-Wolf vectorial diffraction method, the characteristics of the highly focused elliptically polarized vector fields are studied. The optical force and torque on a dielectric Rayleigh particle produced by these tightly focused vector fields are calculated and exploited for the stable trapping of dielectric Rayleigh particles. It is shown that the additional degree of freedom provided by the elliptically polarized vector field allows one to control the spatial structure of polarization, to engineer the focusing field, and to tailor the optical force and torque on a dielectric Rayleigh particle.

Based on the vectorial Rayleigh-Sommerfeld integrals, the analytical expressions for azimuthal-variant vector fields diffracted by an annular aperture are presented. This helps us to investigate the propagation behaviors and the focusing properties of apertured azimuthal-variant vector fields under nonparaxial and paraxial approximations. The diffraction by a circular aperture, a circular disk, or propagation in free space can be treated as special cases of this general result. Simulation results show that the transverse intensity, longitudinal intensity, and far-field divergence angle of nonparaxially apertured azimuthal-variant vector fields depend strongly on the azimuthal index, the outer truncation parameter and the inner truncation parameter of the annular aperture, as well as the ratio of the waist width to the wavelength. Moreover, the multiple-ring-structured intensity pattern of the focused azimuthal-variant vector field, which originates from the diffraction effect caused by an annular aperture, is experimentally demonstrated.

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

We present and demonstrate a novel method for engineering the radial-variant polarization on the incident field to achieve a needle of transversally polarized field without any pupil filters. We generate a new kind of localized linearly-polarized vector fields with distributions of states of polarization (SoPs) describing by the radius to the power p and explore its tight focusing, nonparaxial focusing, and paraxial focusing properties. By tuning the power p, we obtain the needle-like focal field with hybrid SoPs and give the formula for describing the length of the needle. Experimentally, we systematically investigate both the intensity distributions and the polarization evolution of the optical needle by paraxial focusing the generated vector field. Such an optical needle, which enhances the light-matter interaction, has intriguing applications in optical microma-chining and nonlinear optics.

Based on the vectorial Rayleigh-Sommerfeld formulas under the weak nonparaxial approximation, we investigate the propagation behavior of a lowest-order Laguerre-Gaussian beam with azimuthal-variant states of polarization. We present the analytical expressions for the radial, azimuthal, and longitudinal components of the electric field with an arbitrary integer topological charge m focused by a nonaperturing thin lens. We illustrate the three-dimensional optical intensities, energy flux distributions, beam waists, and focal shifts of the focused azimuthal-variant vector beams under the nonparaxial and paraxial approximations.

We explore the peculiar interference behaviors of the vector fields in the Young's two-slit configuration. The interference patterns have a chessboard structure in the middle region and depend on the topological charge and the initial phase of the input vector field. The results have potential applications such as characterizing the topological properties of the arbitrary vector fields.

We investigate the far-field vectorial self-diffraction behavior of a cylindrical vector field passing though an optically thin Kerr medium. Theoretically, we obtain the analytical expression of the focal field of the cylindrical vector field with arbitrary integer topological charge based on the Fourier transform under the weak-focusing condition. Considering the additional nonlinear phase shift photoinduced by a self-focusing medium, we simulate the far-field vectorial self-diffraction patterns of the cylindrical vector field using the Huygens-Fresnel diffraction integral method. Experimentally, we observe the vectorial self-diffraction rings of the femtosecond-pulsed radially polarized field and high-order cylindrical vector field in carbon disulfide, which is in good agreement with the theoretical simulations. Our results benefit the understanding of the related spatial self-phase modulation effects of the vector light fields, such as spatial solitons, self-trapping, and self-guided propagation.

We have fabricated the complicated two-dimensional subwave-length microstructures induced by the femtosecond vector light fields on silicon. The fabricated microstructures have the interval between two ripples in microstructures to be around 670-690 nm and the depth of the grooves to be about 300 nm when the pulse fluence of 0.26 J/cm2 is slightly higher than the ablated threshold of 0.2 J/cm2 for silicon under the irradiation of 100 pulses. The ripples are always perpendicular to the direction of the locally linear polarization. The designable spatial structure of polarization of the femtosecond vector light field can be used to manipulate the fabricated microstructure.

The physics behind the spin (polarization)-dependent electromagnetic hot-spot phenomenon is due to the presence of the geometric phase resulting from the optical spin-orbit interaction in the interaction of light with the subwavelength microstructures. Unlike the tiny spin-dependent shift of light associated with the usual spin-Hall effect of light, here we present the distinct polarization-dependent angular shift by employing an array of subwavelength metallic apertures. More importantly, this novel electromagnetic precession is accompanied by the extraordinary optical transmission phenomenon and offers the exciting possibilities for novel applications for subwavelength structured metallic systems., (© 2011 Optical Society of America)

Based on the simplified five-level rate-equation theory, we investigate the hybrid third-order optical nonlinear processes which combine the instantaneous nonlinearity and the one-photon absorption induced excited-state nonlinearity. We obtain the analytical third-order nonlinear absorption and refraction coefficients originating from the singlet and triplet excited-state effects. We explore the photodynamic process and give the corresponding level diagram in the nanosecond, picosecond, and femtosecond regimes. We develop the pulse-duration-dependent Z-scan theory for characterizing the simultaneous instantaneous nonlinearity and cumulative effect of the excited-state nonlinearity. We also demonstrate the validity of the presented theory to analyze the experimental results.

Based on five-level rate-equation theory, we develop the laser-pulse-duration dependence of two-photon-absorption-induced singlet and triplet excited-state absorptions (ESAs). We present analytical expressions for the effective three-photon absorption coefficients caused by both singlet and triplet ESAs under the pulsed excitation on time scales from femtoseconds to microseconds. We demonstrate that the triplet ESA is predominant with longer laser pulses (microseconds to tens of nanoseconds) and that the resultant nonlinear absorption (NLA) can be adequately interpreted by a simplified four-level model. Under the excitation of picosecond laser pulses, generally speaking, the competition between singlet and triplet ESAs is observable. In this instance, the photodynamics of the system can be understood by a five-level model. In the femtosecond regime, however, a three-level model is validated in the prediction of NLA, because the triplet ESA becomes negligible.

By treating laser-induced optical Kerr nonlinearity as a noninstantaneous decaying process, we present the pulse-duration-dependent Z-scan analytical expressions for an arbitrary aperture and an arbitrary nonlinear magnitude. This theory has the capacity to characterize the third-order nonlinear refraction induced by a laser pulse with its temporal duration being much longer than or comparable to the recovery time of the nonlinear effect. Through Z-scan measurements at different pulse durations, the nonlinear refractive coefficient and the recovery time could be determined unambiguously and simultaneously. Furthermore, the theory can be utilized to confirm whether the measured optical Kerr nonlinearity is instantaneous or noninstantaneous with respect to the given pulse duration.

We report both linear and nonlinear optical properties of a ferroelectric thin film of polycrystalline BiFeO(3) deposited on a quartz substrate. The linear refraction index and absorption coefficient of the film are determined as a function of light wavelength by optical transmittance measurements. By performing Z-scan experiments with femtosecond laser pulses at a wavelength of 780 nm, the third-order nonlinear refraction index and two-photon absorption (2PA) coefficient are measured to be 1.5 x 10(-4) cm(2)/GW and 16 cm/GW, respectively. The results indicate that the thin film of polycrystalline BiFeO(3) is a promising candidate for applications in nonlinear photonic devices.

We report experimental investigations of optical nonlinearities and nonlinear dynamics in acetone solution of 2,4,5-Trimethoxy-4- nitrochalcone. By performing Z-scans with femtosecond laser pulses at low excitation intensity, two-photon absorption (2PA) and third-order nonlinear refraction are measured. As laser excitation intensity exceeds a critical value, however, the interplay between third- and fifth-order nonlinearities is observed. It is also confirmed that fifth-order processes mainly originate from 2PA-induced excited-state nonlinearities by conducting femtosecond time-resolved degenerate pump-probe measurements. All the nonlinear parameters are determined unambiguously in the near infrared region of the 2PA cross-section, second-order hyperpolarizability, excited-state absorption cross-section, excited-state refraction cross-section, lifetime of excited states induced by 2PA, and critical population of the excited states in 2,4,5-Trimethoxy-4-nitrochalcone molecule.

We report a theoretical investigation of laser-pulse-duration dependence of excited-state nonlinearities induced by two-photon absorption (2PA). We investigate the spatiotemporal characteristics of the transmitted pulses caused by 2PA-induced excited-state absorption, which strongly depends on laser pulse duration. By taking into account 2PA cross-section, excited-state photophysical properties, as well as laser pulse duration, we quantitatively determine the effective fifth-order nonlinearities caused by excited-state absorption and refraction. The results are capable of predicting the magnitude of 2PA-induced excited-state nonlinearities on the time scales where laser pulse duration is less than or comparable to the lifetime of 2PA-induced excited states. We also develop Z-scan theories for quickly yet unambiguously estimation of 2PA coefficient, third-order nonlinear refraction index, and excited-state absorption and refraction cross-sections.