Focusing of high order cylindrical vector beams

Topological Charge of Light Fields with a Polarization Singularity

We have studied diverse vector and hybrid light fields, including those with multiple polarization singularities, and have derived relationships for polarization singularity indices based on the familiar Berry formula, which is normally utilized to find the topological charge of a scalar vortex light field. The fields with pure polar-angle-dependent polarization in the beam cross-section are shown to feature either polarization singularity lines outgoing from the center or a single polarization singularity point at the beam center. The fields with pure radial-variable-dependent polarization are shown to have no polarization singularities and zero polarization index. The vector fields with both polar-angle- and radial-variable-dependent polarization are shown to have multiple polarization singularity points that are scattered across the cross-section. A vector field with higher-order radial polarization and a real parameter was also studied and was shown to feature either several polarization singularity lines outgoing from the center or a central singular point, depending on the parameter value. Notably, at different parameter values, the polarization singularity index of such a field can take half-integer, integer, or zero values.

Wavelength-Tunable Vortex Beam Emitter Based on Silicon Micro-Ring with PN Depletion Diode

Herein we propose a design of a wavelength-tunable integrated vortex beam emitter based on the silicon-on-insulator platform. The emitter is implemented using a PN-depletion diode inside a microring resonator with the emitting hole grating that was used to produce a vortex beam. The resonance wavelengths can be shifted due to the refractive index change associated with the free plasma dispersion effect. Obtained numerical modeling results confirm the efficiency of the proposed approach, providing a resonance wavelength shift while maintaining the required topological charge of the emitted vortex beam. It is known that optical vortices got a lot of attention due to extensive telecommunication and biochemical applications, but also, they have revealed some beneficial use cases in sensors. Flexibility in spectral tuning demonstrated by the proposed device can significantly improve the accuracy of sensors based on fiber Bragg gratings. Moreover, we demonstrate that the proposed device can provide a displacement of the resonance by the value of the free spectral range of the ring resonator, which means the possibility to implement an ultra-fast orbital angular momentum (de)multiplexing or modulation.

Spin-Orbital Conversion of a Strongly Focused Light Wave with High-Order Cylindrical-Circular Polarization

We discuss interesting effects that occur when strongly focusing light with m^th-order cylindrical–circular polarization. This type of hybrid polarization combines properties of the m^th-order cylindrical polarization and circular polarization. Reluing on the Richards-Wolf formalism, we deduce analytical expressions that describe E- and H-vector components, intensity patterns, and projections of the Poynting vector and spin angular momentum (SAM) vector at the strong focus. The intensity of light in the strong focus is theoretically and numerically shown to have an even number of local maxima located along a closed contour centered at an on-axis point of zero intensity. We show that light generates 4m vortices of a transverse energy flow, with their centers located between the local intensity maxima. The transverse energy flow is also shown to change its handedness an even number of times proportional to the order of the optical vortex via a full circle around the optical axis. It is interesting that the longitudinal SAM projection changes its sign at the focus 4m times. The longitudinal SAM component is found to be positive, and the polarization vector is shown to rotate anticlockwise in the focal spot regions where the transverse energy flow rotates anticlockwise, and vice versa—the longitudinal SAM component is negative and the polarization vector rotates clockwise in the focal spot regions where the transverse energy flow rotates clockwise. This spatial separation at the focus of left and right circularly polarized light is a manifestation of the optical spin Hall effect. The results obtained in terms of controlling the intensity maxima allow the transverse mode analysis of laser beams in sensorial applications. For a demonstration of the proposed application, the metalens is calculated, which can be a prototype for an optical microsensor based on sharp focusing for measuring roughness.

Practical generation of arbitrary high-order cylindrical vector beams by cascading vortex half-wave plates

A practical direct-view scheme for generating arbitrary high-order cylindrical vector (HCV) beams by cascading vortex half-wave plates (VHPs) is presented. The combination of odd number 2n-1 VHPs for n≥1 can realize (m2n-1-m2n-2+…+m1)-order CV beams, in which m is the order number of VHP and the corresponding subscript 2n-1 represents the arrangement number of VHPs, and the cascading of even number 2n ones can obtain (m2n-m2n-1+…+m2-m1)-order CV beams. All 1-12 order CV beams, including the high-order anti-vortex CV (ACV) beams, are generated only by selectively cascading the VHPs with m=1, 3 and 8. The polarization properties of the generated HCV beams are investigated by measuring the corresponding Stokes parameters. It is experimentally demonstrated that arbitrary HCV beams are effectively achieved by the proposed method. The order numbers of CV beams can be greatly expanded by cascading limited types of VHPs.

Sector sandwich structure: an easy-to-manufacture way towards complex vector beam generation

Complex polarization-phase transformations that are realized using easy-to-manufacture optical elements are considered. The manufacturing technology of such elements is based on the angular discretization of the required polarization and phase distributions, which allows one to make optical elements in the form of sector sandwich structures consisting of polarized and phase plates stacked together. We analyze analytically and study numerically the main types of such sector sandwich structures for the formation of cylindrical polarizations of various orders. New effects are observed, which result in the appearance of complex polarized beams with vortices of various orders, arising after the passage through polarizing plates and their combinations with differently rotated phase plates. The results of the experimental study of the formed beams using a multichannel diffraction filter are consistent with theory.

Orbital angular momentum density characteristics of tightly focused polarized Laguerre-Gaussian beam

The orbital angular moment (OAM) of light has been proved to be useful in plenty of applications. By transmitting the OAM of the focused light field to a particle, it will be orbited around the optical axis. Therefore, it is necessary to study the OAM distribution of the focused light field used to manipulate the particles. In this application, the widely used paraxial approximation is no longer sufficient due to the tightly focused beam. We employ the higher-order Poincaré sphere to represent the Laguerre-Gaussian (LG) beams with arbitrary polarization. Then the Rayleigh-Sommerfeld integral method and the q-parameter method are used to derive the analytical expression of the light field on the focal plane. Based on this, the OAM density expression of the tightly focused LG beam is derived. In the numerical simulation, we study and analyze the unique intensity distributions and OAM distributions of tightly focused linear polarized, radial polarized, and circular polarized LG beams. The results could be leveraged to further explore the applications of the polarized vortex beam.

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

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

Vector Lissajous laser beams

We consider a new type of vector beam, the vector Lissajous beams (VLB), which is of double order (p,q) and a generalization of cylindrical vector beams characterized by single-order p. The transverse components of VLBs have an angular relationship corresponding to Lissajous curves. A theoretical and numerical analysis of VLBs was performed, showing that the ratio and parity of orders (p,q) affect the properties of different components of the electromagnetic field (EF) (whether they be real, imaginary, or complex). In addition, this allows one to engineer the imaginary part of the longitudinal component of the electromagnetic field and control the local spin angular momentum density, which is useful for optical tweezers and future spintronics applications.

Variable transformation of singular cylindrical vector beams using anisotropic crystals

We demonstrated and investigated, both theoretically and experimentally, the transformation of cylindrical vector beams with an embedded phase singularity under the condition of focusing perpendicularly to the axis of the anisotropic calcite crystal. Theoretical and numerical analysis, performed on the basis of decomposing the light field into a set of plane waves for an anisotropic medium, allowed us to study the dependence of the structural transformation of the initial laser beam on the polarisation and phase state in detail. The proposed approach allows one to perform the visual recognition of cylindrically-polarised vector beams of various orders and can be used for the demultiplexing of information channels in the case of polarisation-division multiplexing. The experimentally-obtained results agree with the theoretical findings and demonstrate the reliability of the approach.

Angular momentum properties of hybrid cylindrical vector vortex beams in tightly focused optical systems

Optical angular momenta (AM) have attracted tremendous research interest in recent years. In this paper we theoretically investigate the electromagnetic field and angular momentum properties of tightly focused arbitrary cylindrical vortex vector (CVV) input beams. An absorptive particle is placed in focused CVV fields to analyze the optical torques. The spin-orbit motions of the particle can be predicted and controlled when the influences of different parameters, such as the topological charge, the polarization and the initial phases, are taken into account. These findings will be helpful in optical beam shaping, optical spin-orbit interaction and practical optical manipulation.

Reverse and toroidal flux of light fields with both phase and polarization higher-order singularities in the sharp focus area

Based on the Richards-Wolf formalism, we obtain for the first time a set of explicit analytical expressions that completely describe a light field with a double higher-order singularity (phase and polarization), as well as distributions of its intensity and energy flux near the focus. A light field with the double singularity is an optical vortex with a topological charge m and with nth-order cylindrical polarization (azimuthal or radial). From the theory developed, rather general predictions follow. 1) For any singularity orders m and n, the intensity distribution near the focus has a symmetry of order 2(n - 1), while the longitudinal component of the Poynting vector has always an axially symmetric distribution. 2) If n = m + 2, there is a reverse energy flux on the optical axis near the focus, which is comparable in magnitude with the forward flux. 3) If m ≠0, forward and reverse energy fluxes rotate along a spiral around the optical axis, whereas at m = 0 the energy flux is irrotational. 4) For any values of m and n, there is a toroidal energy flux in the focal area near the dark rings in the distribution of the longitudinal component of the Poynting vector.

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

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

Theoretical investigation on asymmetrical spinning and orbiting motions of particles in a tightly focused power-exponent azimuthal-variant vector field

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.

Optical manipulation using highly focused alternate radially and azimuthally polarized beams modulated by a devil's lens

We propose and demonstrate a novel high numerical aperture (NA) focusing system composed of an annular beam with alternate radially and azimuthally polarized rings, focused by a devil's lens (DL), and further investigate its radiation forces acting upon a Rayleigh particle both analytically and numerically. Strongly focused cylindrical vector beams produce either dark-centered or peak-centered intensity distributions depending on the state of polarization, whereas the DL produces a series of foci along the propagation direction. We exploit these focusing properties and show that by selecting an appropriate truncation parameter in front of the focusing lens, the proposed optical focusing system can selectively trap and manipulate dielectric micro-particles with low or high refractive indices by simply adjusting the radius of the pupil or the beam. Finally, the stability conditions for effectively trapping and manipulating Rayleigh particles are analyzed. The results obtained in this work are of interest in possible applications in optical confinement and manipulation, sorting micro-particles, and making use of a DL.

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

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

Manipulation of dielectric Rayleigh particles using highly focused elliptically polarized vector fields

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.

Parallel confocal microscopy using high-order axially symmetric polarized beams

A novel scheme of parallel confocal microscopy using high-order axially symmetric polarized beams (ASPBs) is proposed. The basic concept of ASPBs is introduced first, then the principle of the scheme is presented, finally some numerical results are shown to verify the feasibility of the scheme. Seen from the results, multiple imaging spots are obtained and the size of spots is about 70% of the spot size in the single lens microscopy, and a kind of high temporal and spatial resolution parallel confocal microscopy is achieved, which may find wide applications in the fields of 3D profile measurement and biomedical imaging.

Elliptic-symmetry vector optical fields

We present in principle and demonstrate experimentally a new kind of vector fields: elliptic-symmetry vector optical fields. This is a significant development in vector fields, as this breaks the cylindrical symmetry and enriches the family of vector fields. Due to the presence of an additional degrees of freedom, which is the interval between the foci in the elliptic coordinate system, the elliptic-symmetry vector fields are more flexible than the cylindrical vector fields for controlling the spatial structure of polarization and for engineering the focusing fields. The elliptic-symmetry vector fields can find many specific applications from optical trapping to optical machining and so on.

Trapping volume control in optical tweezers using cylindrical vector beams

We present the result of an investigation into the optical trapping of spherical microparticles using laser beams with a spatially inhomogeneous polarization direction [cylindrical vector beams (CVBs)]. We perform three-dimensional tracking of the Brownian fluctuations in the position of a trapped particle and extract the trap spring constants. We characterize the trap geometry by the aspect ratio of spring constants in the directions transverse and parallel to the beam propagation direction and evaluate this figure of merit as a function of polarization angle. We show that the additional degree of freedom present in CVBs allows us to control the optical trap strength and geometry by adjusting only the polarization of the trapping beam. Experimental results are compared with a theoretical model of optical trapping using CVBs derived from electromagnetic scattering theory in the T-matrix framework.

Optical trapping of nanotubes with cylindrical vector beams

We use laser beams with radial and azimuthal polarization to optically trap carbon nanotubes. We measure force constants and trap parameters as a function of power showing improved axial trapping efficiency with respect to linearly polarized beams. The analysis of the thermal fluctuations highlights a significant change in the optical trapping potential when using cylindrical vector beams. This enables the use of polarization states to shape optical traps according to the particle geometry, as well as paving the way to nanoprobe-based photonic force microscopy with increased performance compared to a standard linearly polarized configuration.

Nonparaxial and paraxial focusing of azimuthal-variant vector beams

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.

Optical trapping of porous silicon nanoparticles

Silicon nanoparticles obtained by ball-milling of a 50% porosity silicon layer have been optically trapped when dispersed in a water-surfactant environment. We measured the optical force constants using linearly and radially polarized trapping beams finding a reshaping of the optical potential and an enhanced axial spring constant for the latter. These measurements open perspectives for the control and handling of silicon nanoparticles as labeling agents in biological analysis and fluorescence imaging techniques.

Theoretical and experimental studies on tightly focused vector vortex beams

The high-NA focusing properties of vector vortex beams are studied theoretically and experimentally. The vector vortex beams are generated by space-variant segmented subwavelength metallic gratings first. Then the mathematical expressions for the focused fields are derived based on the vector diffraction theory, and some numerical simulations are presented that show that the focused fields are not dark at the center and the focusing spot size of vector vortex beams with high topological charges approaches the diffraction limitation at high NA. Finally, to verify the theoretical analysis, the tightly focused fields are measured based on a confocal microscopy system when the NA of the objective lens is 0.90. The research results confirm the potential of vector vortex beams in some applications, such as optical trapping, laser printing, lithography, and material processing.

A new type of vector fields with hybrid states of polarization

We present an idea based on Poincaré sphere and demonstrate the creation of a new type of vector fields, which have hybrid states of polarization. Such a type of hybridly polarized vector fields have completely different property from the reported scalar and vector fields. The novel vector fields are anticipated to result in new effects, phenomena, and applications.

Nonparaxial propagation of a Gaussian optical vortex with initial radial polarization

We study the nonparaxial diffraction of a Gaussian vortex beam with initial radial polarization and an arbitrary integer topological charge n. Analytical relationships for the radial, azimuthal, and longitudinal components of the E-vector are deduced. At n=0, the azimuthal component of the field equals zero, with the radial and axial components becoming coincident with the relationships reported in [J. Opt. Soc. Am. A 26, 1366 (2009)]. At any n>1, the vortex beam intensity on the optical axis equals zero, whereas at n=1(-1) an intensity peak is found in the focus. Explicit analytical relationships for a Gaussian vortex beam with initial elliptical polarization are also derived. Relationships that describe the nonparaxial radially polarized Gaussian beam are deduced as a linear combination of the Gaussian vortex beams with n=1(-1) and left- and right-hand circular polarization.

Sagnac interferometer method for synthesis of fractional polarization vortices

We present a method for producing laser beams of nonuniform polarization where the polarization direction rotates on a trajectory about the beam propagation direction. Our method uses a Sagnac interferometer that incorporates a spatial light modulator to combine beams that possess oppositely charged phase vortices in order to achieve the desired polarization vortex. We demonstrate the utility of our method by producing polarization vortices characterized by a fractional index, and we compare the results with calculations of the expected fields.