Tight Focusing Properties of Phase Modulated Radially Polarized Laguerre Bessel Gaussian Beam

We propose a new approach for generating a multiple focal spot segment of subwavelength size, by tight focusing of a phase modulated radially polarized Laguerre Bessel Gaussian beam. The focusing properties are investigated theoretically by vector diffraction theory. We observe that the focal segment with multiple focal structures is separated with different axial distances and a super long dark channel can be generated by properly tuning the phase of the incident radially polarized Laguerre Bessel Gaussian beam. We presume that such multiple focal patterns and high intense beam may find applications in atom optics, optical manipulations and multiple optical trapping.     

Tight focusing of phase modulated radially polarized hollow Gaussian beam using complex phase filter

We propose a new approach for generating multiple focal spot segment of sub wavelength size, by tight focusing of phase modulated radially polarized hollow Gaussian beam. The focusing properties are investigated theoretically by vector diffraction theory. We observed that focal segment with multiple focal spots structure separated with different axial distance can be generated by properly tuning the phase of the incident radially polarized hollow Gaussian (HGB) beam. Potential applications of this focal shaping technique are also discussed.     

Sub wavelength multiple focal spot generation of high NA objective lens using diffractive optical element

In this article, based on the vector diffraction theory, the effect of specially designed phase modulating optical element by means of an incident tightly focused azimuthally polarized Bessel Gaussian beam in the focal region of high NA lens is investigated numerically. It is observed, that a specially designed diffractive optical modulation element (DOE) can generate multiple focal spot segment of transversely polarized in the focal region by controlling the angles of DOE. Such kind of sub wavelength transversely polarized focal spots segment may find wide applications in multiple optical traps and optical manipulation technology.     

Generation of sub wavelength focal spot with large depth of focus generated by radially polarized beam

We investigate the focusing properties of a radially polarized Bessel Gaussian beam by a high numerical aperture (NA) lens based on vector diffraction theory. We observe that our proposed system generates a sub wavelength focal spot of 0.42λ having large uniform focal depth of 6.45λ. The authors expect such a long depth of focus have great potential for use in optical, biological, high-resolution and atmospheric sciences.     

Focal shift of radially polarized axisymmetric Bessel modulated Gaussian beam with radial variance phase plate

Focal shift of the radially polarized axisymmetric QBG beam with radial variance phase plate is investigated theoretically by vector diffraction theory. Axisymmetric Bessel modulated Gaussian beam with quadratic radial dependence (QBG beam) has attracted much attention recently. Calculation results show that focus shifts considerably by changing the phase parameter C that indicates the radial phase variance speed. Under condition of beam parameter μ of radially polarized axisymmetric QBG beam, there is one focal spot that shifts far away from optical aperture on increasing C. When increases the value of beam parameter, there may occur two focal peaks that also shift remarkably on increasing C.     

Generation of sub wavelength multiple focal hole segments using azimuthally polarized annular multi-Gaussian beam

We propose a new approach for generating multiple focal hole segment of sub wavelength size, by tight focusing of phase modulated annular multi-Gaussian beam. The focusing properties are investigated theoretically by vector diffraction theory. We observed that focal segment with multiple focal rings structure separated with different axial distance can be generated by properly tuning the phase of the incident azimuthally polarized annular multi-Gaussian beam. Potential applications of this focal shaping technique are also discussed.     

Focusing of radially polarized beam with radial cosine phase wavefront

Radially polarized beam has gained much interest recently due to its properties and applications. In this article, the focusing properties of radially polarized beam with radial cosine phase wavefront are investigated theoretically. Results show that when the radially polarized beam with radial cosine wavefront phase is focused, the focal pattern differs considerably with frequency parameter in the cosine function term. In the high numerical aperture focusing system, focal shift occurs, and novel focal patterns evolve considerably, for instance, from only one peak to two or multiple overlapping peaks. In addition, peak intensity ratio of radially polarized component to longitudinal polarized component in the focal region fluctuates smoothly for low-frequency parameter, then drops sharply, and comes back remarkably with increasing frequency parameter. Simultaneously focal shift increases slowly, and then decreases, suddenly, focal shift sign changes that results from focal switch phenomenon, and then fluctuates.     

Tight Focusing Properties of Radially Polarized Gaussian Beams with Pair of Vortices

The tight focusing properties of a radially polarized Gaussian beam with a nested pair of vortices having a radial wave front distribution are investigated theoretically by the vector diffraction theory.The results show that the optical intensity in the focal region can be altered considerably by changing the location of the vortices nested in a radially polarized Gaussian beam.It is noted that focal evolution from one annular focal pattern to a highly confined focal spot in the transverse direction is observed corresponding to the change in the location of the optical vortices in the input plane.It is also observed that the generated focal hole or spot lead to a focal shift along the optical axis remarkably under proper radial phase modulation.Hence the proposed system may be applied to construct tunable optical traps for both high and low refractive index particles.     

Radially polarized hollow Gaussian beam with on-axis spiral optical vortex

The focusing properties of radially polarized hollow Gaussian beam (HGB) with on-axis spiral optical vortex are investigated theoretically by vector diffraction theory. The phase wavefront of HGB is the function of radial coordinate. Calculation results show that the focusing properties can be altered considerably by beam order of HGB, topological charge of the on-axis optical vortex, and phase parameter that characterizes the radial phase wavefront distribution. Higher topological charge induces focal evolution from one focal spot to annular focal pattern in transverse direction, while phase parameter can lead to focal shift along optical axis remarkably. In addition, focal shift direction can also be adjusted by changing varying direction of phase parameter.     

Tightly focusing of spirally polarized Quadratic Bessel Gaussian beam through a dielectric interface

Based on vector diffraction theory, the tight focusing properties of spirally polarized axisymmetric Bessel-modulated Gaussian beam through a dielectric interface on high numerical aperture (NA) are investigated theoretically. The optical intensity distribution in the focal region of high NA objective lens is investigated in detail by numerical calculations. The results show that the focal shift induced in the focal region is by mismatch of refractive indices across the dielectric interface. It is also found that the optical intensity in focal region of spirally polarized Quadratic Bessel Gaussian (QBG) beam can be altered considerably by changing spiral parameter C that indicates the polarization spiral degree of the incident beam.     

Multifocus with small size, uniform intensity, and nearly circular symmetry

We investigate in detail the focusing properties of the composite vector beam (CVB) composed of two orthogonally linearly polarized beams with inhomogeneous polarization modulation. By optimizing the modulation factor, a multifocus with excellent quality is obtained, where the sizes of each focus are fairly smaller than that of the focusing spot of a radially polarized beam, the uniformity in the intensity of the focal spots is as high as 1, and the distributions of each focal spot have nearly circular symmetry. In order to decrease the power loss of the incident beam, the CVB formed by an annular beam is demonstrated as the substitute for the optimized CVB formed by a Gaussian beam. This work is important for high-resolution and high-speed imaging in biology and micro-nanofabrication.     

Experimental Research on Focusing Property of Radially Polarized Beam Based on Solid Immersion Lens

Realization of a near-field optical virtual probe based on an evanescent Bessel beam is strongly dependent on a radially polarized beam; this makes it essential to study the focusing property of the beam. In this paper, two experimental setups based on a fiber device and a liquid crystal device, respectively, are built to generate a radially polarized beam. This beam and an annular radially polarized beam are focused by means of a high numerical aperture objective and a solid immersion lens (SIL). Near-field distribution of the focus spot, the evanescent Bessel field, is experimentally measured with a scanning near-field optical microscope (SNOM). The full width at half maximum (FWHM) of the central peak of the evanescent Bessel field is about 200 nm in the close vicinity of the bottom surface of SIL. This has potential for use as a near-field optical virtual probe.     

Bessel beams: Effects of polarization

An approximation to a Bessel beam produced by tightly focusing linearly polarized light is known to produce a smaller central lobe than focusing plane polarized light. This is because the plane polarized wave gives a broad central lobe caused mainly by a parasitic longitudinal field component. It is known that this problem can be overcome by focusing radially polarized light. Here we demonstrate that other polarization distributions based on a linear combination of transverse electric (TE1) and transverse magnetic (TM1) fields can give a beam even narrower than for the radially polarized case. Special cases of this combination are identified, corresponding to the smallest width (TE1), and the maximum peak intensity compared with the side lobes (electric dipole polarization). Axially-symmetric forms can be generated by illumination with elliptically polarized light. A particular case is azimuthal polarization with a phase singularity, which is equivalent to TE1. For a semi-angular aperture of 60°, the TE1 case gives a central lobe width 9% narrower than for radially polarized illumination, while for plane polarized illumination it is 12% wider than the radially polarized case.     

Creation of Multiple Subwavelength Focal Spot Segments Using Phase Modulated Radially Polarized Multi Gaussian Beam

Based on the vector diffraction theory,the effect of complex phase filters on intensity distribution of a radially polarized multi Gaussian beam in the focal region of high NA lens is theoretically investigated.It is observed that a properly designed multi belt complex phase filter can generate subwavelength novel focal patterns including splitting of focal spots and generation of multiple focal spot segments such as eight,six and four focal spots along the optical axis are obtained.We expect that such an investigation is useful for optical manipulation and material processing,multiple high refractive index particle trapping technologies.     

Generating and shifting a spherical focal spot in a 4Pi focusing system illuminated by azimuthally polarized beams

We aim to theoretically investigate the focusing property of a 4Pi configuration under the illumination of azimuthally polarized high-order Bessel–Gaussian beams. The radial component is produced in the focal region through the introduction of a spiral phase plate. The focal region differs from the zero radial intensity component of the azimuthally polarized beams without the spiral phase plate. The spherical focal spot is generated by selecting an appropriate annular obstruction. The position of the focal spot can be shifted.     

Evanescent Bessel beam generation through filtering highly focused cylindrical vector beams with a defect mode one-dimensional photonic crystal

We propose a simple setup for generating evanescent Bessel beams using the defect mode of one-dimensional (1D) photonic crystal. The angular selectivity provided by the defect mode mimics the role of an axicon for Bessel beam generation. When an azimuthally polarized beam is strongly focused onto a 1D defect mode photonic crystal interface, an evanescent Bessel beam of the first-order is produced, while an evanescent Bessel beam of the zeroth-order will be created under a radially polarized beam illumination. Switching between a donut shape and a solid focal distribution can be easily realized by controlling the polarization of the illumination. Such a versatile evanescent Bessel beam generation may find potential applications in optical trapping.     

Efficient conversion of a radially polarized beam to a nearly Gaussian beam

We demonstrate an efficient method for transformation of a radially polarized Laguerre-Gaussian beam to a nearly Gaussian beam with much higher beam quality. The method is based on separation of the radially polarized mode into two degenerate modes and coherent addition of the modes after phase flattening. We transformed a high-power Nd:YAG radially polarized (0,1)(*) Laguerre-Gaussian beam with M(2)=2.52 and power of 30 W into a nearly Gaussian beam with M(2)=1.3. As a result, the brightness increased by a factor of approximately 2.5.     

Tight focus of a radially polarized and amplitude- modulated annular multi-Gaussian beam

The focusing of a radially polarized beam without annular apodization ora phase filter at the entrance pupil of the objective results in a wide focus and low purity of the longitudinally polarized component. However, the presence of a physical annular apodization or phase filter makes some applications more difficult or even impossible. We propose a radially polarized and amplitude-modulated annular multi-Gaussian beam mode. Numerical simulation shows that it can be focused into a sharper focal spot of 0.125λ² without additional apodizations or filters. The beam quality describing the purity of longitudinally polarized component is up to 86%.     

Generation of multiple focal spot and focal hole of sub wavelength scale using phase modulated LG (1,1) beam

Based on the vector diffraction theory, the effect of phase modulation on the intensity distribution on tight focusing of cylindrically polarized Laguerre–Gaussian beam in the focal region of high NA lens is investigated theoretically. It is observed that a properly designed complex phase filter can generate multiple focal spot and focal hole segments useful for the manipulation of optical traps.     

Three-dimensional multiple optical cages formed by focusing double-ring shaped radially and azimuthally polarized beams

We propose and simulate a method for generating a three-dimensional(3D) optical cage in the vicinity of focus by focusing a double-ring shaped radially and azimuthally polarized beam. Our study shows that the combination of an inner ring with an azimuthally polarized field and an outer ring with a radially polarized field and a phase factor can produce an optical cage with a dark region enclosed by higher intensity. The shape of the cage can be tailored by appropriately adjusting the parameters of double-mode beams. Furthermore, multiple 3D optical cages can be realized by applying the shift theorem of the Fourier transform and macro-pixel sampling algorithm to a double-ring shaped radially and azimuthally polarized beam.