Dark Hollow Focus Research Articles

Tight focusing properties of spirally polarized LG (1,1)* beam with High NA Parabolic mirror

The tight focusing of double ring shaped spirally polarized beam with high NA Parabolic mirror system is analyzed numerically based on the vector diffraction theory. Calculation results show that intensity distribution in focal region can be altered considerably on changing the spiral parameter (C) and pupil to beam ratio (β) of the incident double ring shaped beam. Many novel focal patterns such as focal spot, dark hollow focus and flat top profile of sub wavelength scale are achieved by proper tuning β and C.

Focal shift of radial varying polarized Bessel-Gauss beam with radial phase modulation

Focusing shift of Bessel-Gauss (BG) beam with radial varying polarization is investigated by vector diffraction theory in this article. The radial phase modulation is given by a function of radial direction angle θ and m. It was found that the focal shift only can be altered considerably by the phase modulation parameter m, and the focus region intensity shape is variable with the change of the others parameters except m, turning into different shapes such as multiple intensity rings, dark hollow focus without the focus shift. There is an interesting phenomenon that the focus shifts along with the horizontal axis when the phase modulation parameter m is changing, and the shifts distance is linearity to the variation of the phase modulation parameter m.

Focusing properties of Lorentz-Gaussian beam with trigonometric function modulation

Wavefront distribution of linearly polarized Lorentz-Gaussian beam was modulated with trigonometric functions, and focusing properties of the modulated beam were investigated by vector diffraction theory. The complex wavefront modulation includes sine function phase distribution and cosine amplitude distribution with one modulation parameter. Results show that the focal intensity distributions can be altered considerably by modulation parameter and the beam parameters. And the effect of numerical aperture on focal pattern evolution is weaker than that of modulation parameter and the beam parameters. Under condition of different beam parameters, the focal pattern evolves differently, and many novel focal patterns can appear, including two-peak focal pattern and shallow dark hollow focus, which may be employed to construct tunable optical traps.

Investigating the focus shaping of the TEM11* beam with radial varying polarization

In this article, based on vector diffraction theory the focusing properties of double ring shaped higher order Laguerre–Gauss beam with radial varying polarization are investigated numerically. The numerical simulations show that the evolution of some interesting focal spot, focal split and focal patterns in the focal region by changing polarization rotation angle under tight focusing through the high NA lens. It is also shown that a subwavelength focal hole with a quite long depth of focus, multiple focal holes are achieved near the focus, when tuning β (is the ratio of the pupil radius to the beam waist) in the focal plane for different modes under tight focusing through the high NA lens. We found that when tuning, beam parameter or the polarization rotation angle of the incident beam, it is possible to generate some interesting novel focal patterns, including multiple intensity rings, dark hollow focus and cylindrical crust focus. Such kind of beams plays an important role in optical trapping, laser cutting and optical manipulation applications.

Effect of Pupil Beam in the Focal Region of High Numerical Aperture Objective Lens

In this article, based on vector diffraction theory the focusing properties of double ring shaped higher order Laguerre - Gauss beam with radial varying polarization are investigated numerically. The numerical simulations show that the evolution of some interesting focal spot, focal split and focal patterns in the focal region by changing polarization rotation angle under tight focusing through the high NA lens. It is also shown that a subwavelength focal hole with a quite long depth of focus, multiple focal holes are achieved near the focus, when tuning β (is the ratio of the pupil radius to the beam waist) in the focal plane for different modes under tight focusing through the high NA lens. We found that when tuning, beam parameter or the polarization rotation angle of the incident beam, it is possible to generate some interesting novel focal patterns, including multiple intensity rings, dark hollow focus and cylindrical crust focus. Such kind of beams plays an important role in optical trapping, laser cutting and optical manipulation applications.

To construct a stable and tunable optical trap in the focal region of a high numerical aperture lens

Based on the diffraction theory, the focusing properties of a radially polarized quadratic Bessel–Gaussian beam (QBG) with on-axis radial phase variance wavefront are investigated theoretically in the focal region of a high numerical aperture (NA) objective lens. The phase wavefront C and pupil beam parameter μ of QBG are the functions of the radial coordinate. The detailed numerical calculation of the focusing property of a QBG beam is presented. The numerical calculation shows that the beam parameter μ and phase parameter C have greater effect on the total electric field intensity distribution. It is observed that under the condition of different μ, evolution principle of focal pattern differs very remarkably on increasing C. Also, some different 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, and triangle dark hollow focus, which find wide optical applications such as optical trapping and nanopatterning.

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.And some novel focal patterns may occur, including focal spot, one ring focus, and dark hollow focus, which is very important in optical tweezers technique.

Focusing of linearly polarized Lorentz–Gauss beam with one optical vortex

Focusing properties of linearly polarized Lorentz–Gauss beam with one on-axis optical vortex was investigated by vector diffraction theory. Results show that the focal pattern can be altered considerably by charge number of the optical vortex and the beam parameters. Many novel focal patterns may occur, such as dark hollow focus, multiple-peak focal pattern, and dark hollow focus chain. For certain beam parameter, the focal pattern changes more remarkably in the direction perpendicular to the incident polarized direction than that in polarized direction. Especially, there is one clear relation between the intensity distributions along the direction perpendicular to the polarized direction and the charge number of the optical vortex, which may be used as one measurement method of charge number.

Subwavelength dark hollow focus of spirally polarized axisymmetric Bessel-modulated Gaussian beam

Dark hollow focus plays an important role in many optical systems. In this paper, dark hollow focal shaping of spirally polarized axisymmetric Bessel-modulated Gaussian beam is investigated by vector diffraction theory in detail. Results show that the dark hollow focus can be altered considerably by beam parameter and spiral parameter that indicates polarization spiral degree. One dark hollow focus and two dark hollow foci pattern may occur for certain spiral parameter, and the transverse size of dark hollow focus can be less than the diffraction limit size of bright focus. In addition, there may also appear two triangle dark hollow foci that are connected by one dark line focus.

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.

Focusing of concentric piecewise vector Bessel–Gaussian beam

The focusing properties of a concentric piecewise vector Bessel–Gaussian beam are investigated in this paper. The beam consists of three portions: the center circular portion and outer annular portion are radially polarized, while the inner annular portion is generalized polarized with tunable polarized angle. Numerical simulations show that the evolution of focal pattern is altered considerably with different Bessel parameters in the Bessel term of the vector Bessel–Gaussian beam. The polarized angle also affects the focal pattern remarkably. Some interesting focal patterns may appear, such as two-peak, dark hollow focus; ring focus; spherical shell focus; cylindrical shell focus; and multi-ring-peak focus, and transverse focal switch occurs with increasing polarized angle of the inner annular portion, which may be used in optical manipulation.

Focusing properties of concentric piecewise cylindrical vector beam

The focusing properties of a concentric piecewise cylindrical vector beam is investigated theoretically in this paper. The beam consists of three portions with different and changeable phase retardation and polarization. Numerical simulations show that the evolution of the focal shape is very considerable by changing the radius and polarization rotation angle of each portion of the vector beam. And some interesting focal spots may occur, such as two- or three-peak focus, dark hollow focus, ring focus, and two-ring-peak focus. Corresponding gradient force patterns are also computed, and novel trap patterns, including cup shell shape trap with one trap at its each side along axis, rectangle shell shape trap with one trap at its each side, dumbbell optical trap, spherical shell optical trap, may occur, which shows that the concentric piecewise cylindrical vector beam can be used to construct controllable optical tweezers.