Controlling the contribution of the electric field components to the focus of a high-aperture lens using binary phase structures

Spin-Orbital Conversion with the Tight Focus of an Axial Superposition of a High-Order Cylindrical Vector Beam and a Beam with Linear Polarization

In this paper, spin-orbital conversion in the tight focus of an axial superposition of a high-order (order m) cylindrical vector beam and a beam with linear polarization is theoretically and numerically considered. Although such a beam does not have a spin angular momentum in the initial plane and the third projection of its Stokes vector is equal to zero, subwavelength local regions with a transverse vortex energy flow and with the non-zero third Stokes projection (the longitudinal component of the spin angular momentum) are formed in the focal plane for an odd number m. This means that such a beam with an odd m has regions of elliptical or circular polarization with alternating directions of rotation (clockwise and counterclockwise) in the focus. For an even m, the field is linearly polarized at every point of the focal plane, and the transverse energy flux is absent. These beams can be used to create a micromachine in which two microparticles in the form of gears are captured in the focus of the beam into neighboring local areas in which the energy flow rotates in different directions, and therefore, these gears will also rotate in different directions.

Experimental estimation of the longitudinal component of a highly focused electromagnetic field

The detection of the longitudinal component of a highly focused electromagnetic beam is not a simple task. Although in recent years several methods have been reported in the literature, this measure is still not routinely performed. This paper describes a method that allows us to estimate and visualize the longitudinal component of the field in a relatively simple way. First, we measure the transverse components of the focused field in several planes normal to the optical axis. Then, we determine the complex amplitude of the two transverse field components: the phase is obtained using a phase recovery algorithm, while the phase difference between the two components is determined from the Stokes parameters. Finally, the longitudinal component is estimated using the Gauss's theorem. Experimental results show an excellent agreement with theoretical predictions.

Generation of Multiple Vector Optical Bottle Beams

We propose binary diffractive optical elements, combining several axicons of different types (axis-symmetrical and spiral), for the generation of a 3D intensity distribution in the form of multiple vector optical ‘bottle’ beams, which can be tailored by a change in the polarization state of the illumination radiation. The spatial dynamics of the obtained intensity distribution with different polarization states (circular and cylindrical of various orders) were investigated in paraxial mode numerically and experimentally. The designed binary axicons were manufactured using the e-beam lithography technique. The proposed combinations of optical elements can be used for the generation of vector optical traps in the field of laser trapping and manipulation, as well as for performing the spatial transformation of the polarization state of laser radiation, which is crucial in the field of laser-matter interaction for the generation of special morphologies of laser-induced periodic surface structures.

Formation of hybrid higher-order cylindrical vector beams using binary multi-sector phase plates

Nowadays, the well-known cylindrical vector beams (CVBs) – the axially symmetric beam solution to the full-vector electromagnetic wave equation – are widely used for advanced laser material processing, optical manipulation and communication and have a great interest for data storage. Higher-order CVBs with polarisation order greater than one and superpositions of CVBs of various orders (hybrid CVBs) are especially of interest because of their great potential in contemporary optics. We performed a theoretical analysis of the transformation of first-order CVBs (radially and azimuthally polarised beams) into hybrid higher-order ones using phase elements with complex transmission functions in the form of the cosine or sine functions of the azimuthal angle. Binary multi-sector phase plates approximating such transmission functions were fabricated and experimentally investigated. The influence of the number of sectors and a height difference between neighbouring sectors, as well as the energy contribution of the different components in the generated hybrid higher-order CVBs were discussed in the context of polarisation transformation and vector optical field transformation in the focal region. The possibility of polarisation transformation, even in the case of weak focusing, is also demonstrated. The simple structure of the profile of such plates, their high diffraction efficiency and high damage threshold, as well as the easy-to-implement polarisation transformation principle provide advanced opportunities for high-efficient, quickly-switchable dynamic control of the generation of structured laser beams.

Generation of a dark spot beyond the diffraction limit with a radially polarized vortex beam

We propose and demonstrate that a dark spot can be generated by a radially polarized beam with a first-order vortex after phase modulation by an optimal binary phase element. The distance between two mainlobe intensity peaks along the radial direction is 0.62λ on the focal plane. The proposed system is easy to implement in practice and has low energy loss, since it uses phase-only modulation. Then, the fluorescent spot is calculated for stimulated emission depletion microscopy when a radially polarized beam works as the pump beam. The FWHM of the fluorescent spot can achieve 0.008λ for a saturated case. This is much smaller than that achieved using a circular polarized vortex erase beam (0.0422λ) or an azimuthally polarized erase beam with optimizing amplitude-phase modulation (0.0279λ).

New hybrid genetic particle swarm optimization algorithm to design multi-zone binary filter

The binary phase filters have been used to achieve an optical needle with small lateral size. Designing a binary phase filter is still a scientific challenge in such fields. In this paper, a hybrid genetic particle swarm optimization (HGPSO) algorithm is proposed to design the binary phase filter. The HGPSO algorithm includes self-adaptive parameters, recombination and mutation operations that originated from the genetic algorithm. Based on the benchmark test, the HGPSO algorithm has achieved global optimization and fast convergence. In an easy-to-perform optimizing procedure, the iteration number of HGPSO is decreased to about a quarter of the original particle swarm optimization process. A multi-zone binary phase filter is designed by using the HGPSO. The long depth of focus and high resolution are achieved simultaneously, where the depth of focus and focal spot transverse size are 6.05λ and 0.41λ, respectively. Therefore, the proposed HGPSO can be applied to the optimization of filter with multiple parameters.

Optical encryption in the longitudinal domain of focused fields

We develop a method for encoding information in the longitudinal component of a focused field. Focused beams display a non-zero contribution of the electric field in the direction of propagation. However, the associated irradiance is very weak and difficult to isolate from the transverse part of the beam. For these reasons, the longitudinal component of a focused field could be a good choice for encoding and securing information. Using the Richards and Wolf formalism we show how to encrypt information in the longitudinal domain of the focal area. In addition, we use quantum imaging techniques to enhance the security and to prevent unauthorized access to the information. To the best of our knowledge, this is the first report on using the longitudinal component of the focused fields in optical security.

Vortex phase elements as detectors of polarization state

We suggest vortex phase elements to detect the polarization state of the focused incident beam. We analytically and numerically show that only the types of polarization (linear, circular, or cylindrical) can be distinguished in the low numerical aperture (NA) mode. Sharp focusing is necessary to identify the polarization state in more detail (direction or sign). We consider a high NA micro-objective and a diffractive axicon as focusing systems. We show that the diffractive axicon more precisely detects the polarization state than does the micro-objective with the same NA.

Experimental implementation of tightly focused beams with unpolarized transversal component at any plane

The aim of this paper is to provide a formal framework for designing highly focused fields with specific transversal features when the incoming beam is partially polarized. More specifically, we develop a field with a transversal component that remains unpolarized in the focal area. Special attention is paid to the design of the input beam and the development of the experiment. The implementation of such fields is possible by using an interferometric setup combined with the use of digital holography techniques. Experimental results are compared with those obtained numerically.

Generation of hollow beam with radially polarized vortex beam and complex amplitude filter

The generation of hollow beams with a long focal depth from a radially polarized Bessel-Gaussian beam with a second-order vortex phase and an amplitude filter is theoretically investigated by Richards-Wolf's integral. The null intensity on the optical axis is achieved by introducing the second-order vortex. The long focal depth is a result of the amplitude filtering based on the cosine function and Euler transformation. Numerical results indicate that the focal depth of a hollow beam is improved from 0.96λ to 2.28λ with a slight increase of the transverse size for the simplest amplitude filter design. The intensity distribution twist phenomenon of the x- and y-polarized components around the optical axis due to the introducing of the vortex phase is also discussed. It is believed that the proposed scheme can be used to achieve particle acceleration and optical trapping.

Study of polarization properties of fiber-optics probes with use of a binary phase plate

We conduct a theoretical and experimental study of the distribution of the electric field components in the sharp focal domain when rotating a zone plate with a π-phase jump placed in the focused beam. Comparing the theoretical and experimental results for several kinds of near-field probes, an analysis of the polarization sensitivity of different types of metal-coated aperture probes is conducted. It is demonstrated that with increasing diameter of the non-metal-coated tip part there occurs an essential redistribution of sensitivity in favor of the transverse electric field components and an increase of the probe's energy throughput.

Synthesis of highly focused fields with circular polarization at any transverse plane

We develop a method for generating focused vector beams with circular polarization at any transverse plane. Based on the Richards-Wolf vector model, we derive analytical expressions to describe the propagation of these set of beams near the focal area. Since the polarization and the amplitude of the input beam are not uniform, an interferometric system capable of generating spatially-variant polarized beams has to be used. In particular, this wavefront is manipulated by means of spatial light modulators displaying computer generated holograms and subsequently focused using a high numerical aperture objective lens. Experimental results using a NA = 0.85 system are provided: irradiance and Stokes images of the focused field at different planes near the focal plane are presented and compared with those obtained by numerical simulation.

Spatial filtering nearly eliminates the side-lobes in single- and multi-photon 4pi-type-C super-resolution fluorescence microscopy

Super-resolution microscopy has tremendously progressed our understanding of cellular biophysics and biochemistry. Specifically, 4pi fluorescence microscopy technique stands out because of its axial super-resolution capability. All types of 4pi-microscopy techniques work well in conjugation with deconvolution techniques to get rid of artifacts due to side-lobes. In this regard, we propose a technique based on spatial filter in a 4pi-type-C confocal setup to get rid of these artifacts. Using a special spatial filter, we have reduced the depth-of-focus. Interference of two similar depth-of-focus beams in a 4π geometry result in substantial reduction of side-lobes. Studies show a reduction of side-lobes by 46% and 76% for single and two photon variant compared to 4pi - type - C confocal system. This is incredible considering the resolving capability of the existing 4pi - type - C confocal microscopy. Moreover, the main lobe is found to be 150 nm for the proposed spatial filtering technique as compared to 690 nm of the state-of-art confocal system. Reconstruction of experimentally obtained 2PE - 4pi data of green fluorescent protein (GFP)-tagged mitocondrial network shows near elimination of artifacts arising out of side-lobes. Proposed technique may find interesting application in fluorescence microscopy, nano-lithography, and cell biology.

Strengthening the longitudinal component of the sharply focused electric field by means of higher-order laser beams

We study the sharp focusing of differently polarized low-order and high-order beams, including Bessel and Laguerre-Gaussian (LG) modes, to compare them using several criteria: the size of a light spot, the intensity ratio of the central peak and sidelobes, and the intensity of the longitudinal electric field component. The experiments performed using the near-field microscopy techniques are in general agreement with the results of the numerical simulation. We have validated the growth of the longitudinal component in the focus for high-order modes at moderate NA=0.6-0.8, and essential lower sidelobes of Bessel modes, in comparison with LG modes.

On the physical realizability of highly focused electromagnetic field distributions

A method to evaluate the physical realizability of an arbitrary three-dimensional vectorial field distribution in the focal area is proposed. A parameter that measures the similarity between the designed (target) field and the physically achievable beam is provided. This analysis is carried out within the framework of the closest electromagnetic field to a given vectorial function, and the procedure is applied to two illustrative cases.

Diffraction of convergent spherical waves with all possible polarization states using the Luneburg integral method

We present a complete electromagnetic study, which includes electric, magnetic, and Poynting vector fields of diffracted convergent spherical waves under all possible polarization states compatible with Maxwell's equations. Exit pupil boundary conditions for these polarizations were obtained by means of Hertz potentials. Using these boundary conditions, two-dimensional Luneburg diffraction integrals for the three components of electric and magnetic fields were formulated, and after some approximations, we showed that the complete electromagnetic description of the inhomogeneous polarization states of spherical waves is reduced to the knowledge of seven one-dimensional integrals. The consistency of the method was tested by comparison with other previously reported methods for linearly polarized (LP), TE, and TM polarizations, while the versatility of the method was showed with the study of nonstandard polarization states, for example, that resulting from the superposition of TE and TM dephased spherical waves, which shows a helicoidal behavior of the Poynting vector at the focalization region, or the inhomogeneous LP state that exhibits a ring structure for the Poynting vector at the focal plane.

Optimization of focusing of linearly polarized light

We show that, by adding a π-phase shift to one-half of a linearly polarized beam, the roles of the transversal and longitudinal field components of the focused beam are interchanged, resulting in better focusing of the longitudinal component in the direction perpendicular to the phase jump line. For this component the scheme produces a spot with FWHM >15% smaller than a spot generated with either linearly or radially polarized light for any NA. The scheme has a similar advantage when applied to circularly polarized light, and it holds for both a plane wave and a realistic case of a Gaussian incident beam. This technique may find applications when using recording media responsive to the longitudinal field only, particularly in read/write for optical storage where the resolution in one transverse dimension is most important.