Focusing properties of spirally polarized hollow Gaussian beam

Focusing properties of spirally polarized hollow Gaussian beam (HGB) are investigated theoretically by vector diffraction theory in this article. Results show that the optical intensity in focal region of spirally polarized HGB can be altered considerably by the beam order, numerical aperture of the focusing system, and spiral parameter that indicates the polarization spiral degree of the spirally polarized HGB. Spiral parameter can induce focal pattern change in axial direction remarkably, while beam order and numerical aperture affect radial foal pattern more obviously. The tunable principle of the focal pattern by spiral parameter differs very considerably under condition of different numerical aperture and beam order. Many novel focal patterns may occur in focal pattern evolution. It was also found that focal shift and focal depth can be altered significantly by spiral parameter and beam order.     

Tight focusing effect of annular obstructed incident beam in the focal region of high NA lens

Focusing properties of the azimuthally polarized axisymmetric Bessel-modulated Gaussian beam with Quadratic Bessel Gaussian (QBG beam) and annular aperture are investigated theoretically by vector diffraction theory. Simulation results show that the intensity distribution in focal region of the azimuthally polarized axisymmetric QBG beam can be shifted along optical axis considerably by changing parameter (C). On introducing annular aperture (δ), focal pattern at the focus extends along optical axis. In this paper, we have shown the generation of focal hole and focal shifting in the axial direction of incident beam propagating through aligned optical system which is suitable for application such as optical manipulation and optical trapping.     

Tight focusing effect of annular obstructed Bessel-modulated Gaussian beam

Based on vectorial diffraction theory, the effect of annular apodization on tightly focused azimuthally polarized Bessel-modulated Gaussian beam (QBG) are investigated theoretically. The numerical results show that the intensity distribution in focal region of the incident beam can be altered considerably by changing beam parameter (μ) and introducing annular apodization (δ). Beam parameter induces the focal splitting in transverse direction, while annular apodization leads to change in focal pattern along optical axis of the focusing system. More interesting, the focal splitting may be in continuous in certain case of incident beam propagating through aligned optical system which is suitable for application such as optical manipulation and optical trapping.     

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.     

Spirally polarized axisymmetric Bessel-modulated Gaussian beam

Focusing properties of the spirally polarized axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) are investigated theoretically by vector diffraction theory. Calculation results show that intensity distribution in focal region can be altered considerably by beam parameter μ and spiral parameter C that indicates polarization spiral degree. For certain real value μ, focal spot can evolve from one focal spot to one focal ring, spherical crust focal shape, then two focal rings on increasing spiral parameter C. It was found that under condition of different μ, evolution principle of focal pattern differs very remarkably on increasing C. And some novel focal shapes may appear, including rhombic shape, quadrangular shape, two-spherical crust focus shape, two-peak shape, one dark hollow focus, two dark hollow focuses pattern, triangle dark hollow focus.     

Effect of annular apodization and pupil beam parameter in the focal region of high NA lens

Focusing properties of the radially polarized axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) and annular aperture are investigated theoretically by vector diffraction theory. Simulation results show that the intensity distribution in the focal region of the radially polarized axisymmetric QBG beam can be adjusted considerably by small beam parameter (μ) and annular aperture (δ). When μ increases, the focal spot may change to focal hole and changes focal pattern remarkably. On introducing annular aperture, focus can split or extends along the optical axis for different μ. In this paper, we have shown the generation of the focal spot, dark focal spot, focal split and increase in focal depth in the axial direction of the incident beam propagating through the aligned optical system.     

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.     

Focal properties of cylindrically polarized axisymmetric Bessel-modulated Gaussian beams by a high NA parabolic mirror

Focusing properties of the cylindrical vector axisymmetric Bessel-modulated Gaussian beam with quadratic radial phase dependence (QBG beam) in high numerical aperture parabolic mirror system is investigated theoretically by vector diffraction theory. Results show that intensity distribution in focal region can be altered considerably by beam parameter μ and polarization angle. The tightly focused cylindrically polarized axial symmetric Bessel-modulated Gaussian beams by a high numerical aperture parabolic mirror have possible applications in particle acceleration, optical trapping and manipulating, single molecule imaging and high resolution imaging microscopy.     

Focal shift in radially polarized hollow Gaussian beam

Focal shift in radially polarized hollow Gaussian beam (HGB) with radial wavefront distribution is investigated theoretically. The wavefront phase distribution is cosine function of radial coordinate. Simulation results show that the intensity distribution in focal region of the radially polarized HGB can be adjusted considerably by the beam order of HGB n and cosine parameter C that indicates the phase change degree. On increasing C, focus can shift along optical axis and focal pattern changes remarkably. Focus may move in different direction under different condition. Focal shift distance fluctuates on increasing C, and fluctuation amplitude also increases simultaneously. In addition, threshold value of C for focal shift from one side to the other side of the paraxial focal plane differs for different n.     

Effect of complex phase plate on tight focusing of azimuthally polarized double ring shaped beam

Based on the vector diffraction theory, the effect of complex phase plate on the intensity distribution of TEM₁₁ mode azimuthally polarized Laguerre–Gaussian beam in the focal region of high NA lens is investigated theoretically. It is observed that a properly designed complex phase plate can generate a subwavelength focal hole having FWHM of 0.332λ with an extended focal depth of 54.4λ. We also observe that by using properly designed complex phase plate generates novel focal patterns including splitting of focal holes and multi focus are obtained. The author expects such investigation is worthwhile for optical manipulation and material processing technologies.     

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.     

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.     

Focus shaping of tightly focused TEM11 mode cylindrically polarized Laguerre Gaussian beam by diffractive optical element

We study the focus shaping of tightly focused TEM₁₁ mode cylindrically polarized Laguerre Gaussian beam with high numerical aperture lens axicon system is investigated theoretically by vector diffraction theory. The intensity pattern at the focus can be tailored by appropriately adjusting the rotation angle. We show that the high NA lens axicon system can generates a sub wavelength focal spot, focal hole, focal splitting and flat-topped focal shapes with extended depth of focus.     

Tight focus of an azimuthally polarized and amplitude-modulated annular multi-Gaussian beam

We investigate the focusing properties of an azimuthally polarized and amplitude modulated annular multi Gaussian beam by a high numerical aperture (NA) lens based on vector diffraction theory. We observe that our proposed system generates a subwavelength focal hole of 0.46λ having large uniform focal depth of 36λ without any annular obstruction. This kind of nondiffracting focal hole is called dark channel, which may have applications in atom optical experiments, such as with atomic lenses, atom traps, and atom switches.     

Tightly focusing of linearly polarized vortex beams through a dielectric interface

Based on vectorial Debye theory, the tightly focusing properties of linearly polarized vortex beams through a dielectric interface are studied. Then the intensity distribution in the focal region is investigated in detail by numerical calculations. The focal shifts induced by the mismatch of the refractive indices across the interface has been found. And the dependence of focal shifts and spot size of the focused field on the probe depth and numerical aperture of the objective are presented. Furthermore, the characteristic of intensity pattern of the cross section of the focused field is illustrated, finding that the intensity pattern rotates with the propagation of beams.     

Study on propagation properties of a radially polarized partially coherent dark hollow beam through a high numerical aperture lens

In recent years the partially coherent beams have attracted very much due to novel properties and its applications. In this paper the tight focusing properties of radially polarized partially coherent dark hollow beam (DHB) through a high numerical aperture lens are investigated numerically based on vectorial Debye theory in detail. The result shows that the optical intensity distribution in the focal region directly fluctuates due to small change in coherence length and high numerical aperture angle of the focused radially polarized partially coherent DHB.     

Tight Focusing of Radially and Azimuthally Polarized Vortex Beams through a Dielectric Interface

Based on vectorial Debye theory, tight focusing of radially and azimuthally polarized vortex beams passing through a dielectric interface are studied. The intensity distribution in the focal region is illustrated by numerical calculations. We show the influence of numerical-aperture （NA） on the full-width at half maximum （FWHM） of the focal spot or the focal hole. It has been found that compared with the azimuthally polarized Besse~Gaussian （BG） beams, the longitudinal component in the z direction of the radially polarized BG beams has no influence on the FWHM of the focal spot and hole, but enhances the total light intensity.     

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.     

Smallest focal hole

We study theoretically routes toward the most confined dark channel that can be obtained using high angular aperture focusing. One possible solution is to use a radially polarized beam combined with an optical singularity. Another possibility is to use an azimuthally polarized light beam combined with an annular aperture or a phase filter. Our results suggest that a focal hole of full-width at half maximum of approximately 0.3λ₀/NA is achievable, where λ₀ is the wavelength in vacuum and NA is the numerical aperture of the focusing system. Finally, we show that by letting a phase-shifted plane wave and a focused scalar wave interfere only one point in the focal plane will exhibit zero intensity. Advantages and disadvantages of the schemes are discussed.     

Effect of annular obstruction on tight focusing of partially coherent radially polarized Vortex beam

Based on vectorial Debye theory, the effect of annular apodization of tightly focused partially coherent radially polarized vortex beams in the focal field of high NA lens is studied. The intensity distribution in the focal region is illustrated by numerical calculations. It is found that the focal depth of the generated focal segment strongly dependent on the source coherence length for unobstructed case and the presence of annular aperture reduces the variation of focal depth with source coherence length.