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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

The focusing property of vector Bessel-Gauss beams by a high numerical aperture objective

The rich available transverse intensity structure of vector Bessel-Gauss beams make it important to probe into the focusing property by high numerical aperture objective. In this paper, we obtain the analytical expressions of azimuthally, radially and longitudinally polarized components in the focal area of the objective after tight focusing. Theoretical analysis and the numerical simulation show that, the transverse intensity distributions of the focused beams still have doughnut-like structure, two separate peak structure and circularly aligned array structure. The focused beam spots obtained by an objective with annular aperture usually have smaller spots than with circular aperture. The focused beam of the vector Bessel-Gauss beam with lowest mode number m = 0 is a radially and azimuthally polarized doughnut-like beam with no longitudinal component. These properties and results are useful in optical trapping and particle alignment.     

Focal shift of cylindrical vector axisymmetric Bessel-modulated Gaussian beam with radial variance phase wavefront

Axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) has attracted much attention recently. In this paper, the focal shift of the cylindrical vector QBG beam with radial variance phase wavefront is investigated theoretically by vector diffraction theory. Results show that focus shifts considerably by changing the phase parameter C that indicates the radial phase variance speed. Under condition of small beam parameter μ of cylindrical vector QBG beam, there is one focal peak that shifts far away from optical aperture on increasing C. When μ increases, there may occur two focal peaks that also shift remarkably on increasing C. And it was found that the dependence of focal shift distance on increasing phase parameter is linear. Phase parameter adjusts the focal shift distance, while, polarization angle does not affect focal shift obviously.     

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%.     

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 hyperbolic-cosine-Gaussian beam

Vector beams have attracted much interest recently. In this paper, focusing properties of the radially polarized hyperbolic-cosine-Gaussian beam are investigated. Simulation results show that the focal depth increases with increasing cosine parameter in the cosine term of the beam, while focal spot decreases simultaneously, namely, superresolution occurs. Focal depth increase velocity is quicker for larger cosine parameter, while the transverse focal spot shrinks more quickly for smaller cosine parameter. In addition, for two-portion concentric piecewise radially polarized hyperbolic-cosine-Gaussian beam with π phase shift in center circle portion, focal pattern evolves considerably with increasing cosine parameter, and the evolution principle differs for different radius of the center circle portion. Focal splitting and novel focal spots may appear. This kind of vector beam can be used in optical storage, optical manipulation, and lithography.     

Sharply focusing a radially polarized laser beam using a gradient Mikaelian’s microlens

Focusing a radially polarized annular Gaussian beam with a gradient Mikaelian’s microlens is simulated using a radial version of the FDTD method (finite-difference time domain), in which Maxwell’s equations in the cylindrical coordinates are solved in the MATLAB 7.0 environment. We show that the focal spot size (the area with larger-than half-maximum intensity) can be made as small as 0.126λ², with focal spot diameter being 0.40λ.     

Sharper focus for a radially polarized light beam

We experimentally demonstrate for the first time that a radially polarized field can be focused to a spot size significantly smaller [0.16(1)lambda(2)] than for linear polarization (0.26lambda(2)). The effect of the vector properties of light is shown by a comparison of the focal intensity distribution for radially and azimuthally polarized input fields. For strong focusing, a radially polarized field leads to a longitudinal electric field component at the focus which is sharp and centered at the optical axis. The relative contribution of this component is enhanced by using an annular aperture.     

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.     

Cylindrical vector axisymmetric Bessel-modulated Gaussian beam

Focusing properties of the cylindrical vector axisymmetric Bessel-modulated Gaussian beam with quadratic radial dependence (QBG beam) in high numerical aperture 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. Polarization angle may adjust transverse intensity distribution, for instance from one focal spot to one ring shape. While μ alters axial intensity distribution remarkably, focal splitting may occur with tunable focal shift, and real value μ also may induce local intensity minimum. For certain case, with increasing imaginary value μ, transverse focal spot shrinks accompanied with higher full width half maximum of axial intensity distribution.     

Sharper focal spot below λ/4 of azimuthally polarized illumination phase-encoded by the binary 0/π phase plate

The intensity distribution in the focal region for the azimuthally polarized beam phase-encoded by the binary 0/π phase plate is calculated on the basis of the vector diffraction theory. With the annular pupil aperture employed, the resolution of the focal spot will be improved remarkably. We demonstrate a sharper focal spot with full width at half maximum (FWHM) of 0.223λ (below λ/4), significantly smaller that of linear, circular and radial polarization beam under the same condition. The focusing phenomena for illumination beam with various polarization status and beam shapes are analyzed explicitly. This analysis could have potential applications in confocal microscopy and two-photo microscopy for polarization difference imaging.     

Quasi Bessel beam by Billet's N-split lens

This study utilizes the focal property of a classical Billet's split lens to create more focal points by splitting the lens. This approach distributes the focal points circularly on the focal plane. This study explores the characteristics of beam propagation and analytically derives the asymptotic characteristics of beam propagation based on the stationary phase approximation and the moment-free Filon-type method. Results show that the unique Billet's N-split lens can generate a quasi Bessel beam if the number of splitting N is large enough, e.g., N ≧ 24. This study also explores the diffraction efficiency of corresponding quasi Bessel beam and the influence of aperture size. The potential advantage of proposed split lens approach is that, unlike the classical means of annular aperture, this simple lens approach allows a much larger throughput in creating the Bessel beam and hence the Bessel beam could have more optical energy.     

大数值孔径光子筛偏振特性研究

根据角谱理论建立不同偏振照明条件下的光子筛矢量衍射模型。在此基础上,对入射光分别为线偏振光、径向偏振光、切向偏振光三种特殊偏振状态下的光子筛聚焦光强分布进行了模拟分析。研究结果表明,对于大数值孔径光子筛,入射光的偏振特性将对光子筛聚焦光强分布产生巨大影响。线偏振光将使聚焦光斑沿偏振方向拉伸,切向偏振光产生的聚焦光斑具有"中空"结构,而径向偏振光所产生的聚焦光斑呈较为规则的圆形,且其焦深优于线偏照明情况。在激光直写及高分辨成像等光子筛典型应用中采用径向偏振照明将进一步提高系统分辨力。