Generation of multiple focal holes by tightly focused azimuthally polarized double-ring-shaped beam with complex phase mask

We study the focusing properties of a tight focusing of double ring shaped azimuthally polarized beam through complex phase mask (CPM) with high NA objective lens, based on vector diffraction theory. A novel design to generate an azimuthally polarized subwavelength focal hole having FWHM of 0.332λ with long focal depth of about 18.8λ is illustrated numerically. Apart from generating focal hole with long focal depth, it is observed that a properly designed CPM also generates multiple focal hole segments useful for laser cutting, microscopy and the manipulation of optical traps of low refractive index particles.     

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.     

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.     

Focusing properties of cylindrical vector vortex beams with high numerical aperture objective

Focused by a high numerical-aperture objective in free space, the cylindrical vector beam phase-encoded by vortex phase plate with higher topological charge was capable to generate the doughnut-shaped spot in the vicinity of the focal region. The width of the dark focal spot was manipulated by the phase plate with different topological charge. The relationship between the properties of the focal spot and the vortex phase plate was explicitly analyzed for the input beam with different cylindrical vector polarization. Furthermore, the experimental verification was undertaken at the incidence beam λ = 635 nm with the radial and azimuthal polarization. The experimental results are in excellent agreement with the theoretical calculation.     

Quantum phase transition in XY spin chain with three-site interaction studied in terms of Loschmidt echo and Berry phase

By means of the Loschmidt Echo (LE) and Berry Phase (BP) calculations, quantum phase transition (QPT) of an XY spin chain with three-site interaction (α) in a transverse magnetic field (λ) is studied. Both the LE and BP?s λ derivative present anomaly behaviors at the critical regions λ₁,λ₂ and λ₃. The model is in the Ferromagnetic phase as λ>λ₁=1+α and in the Spin Liquid I phase as −1+α<λ<1+α. λ₁ and λ₂ are independent on the anisotropy parameter γ. But, the anisotropy interaction can shift the critical line λ₃ between the Spin Liquid II phase and the Ferromagnetic phase. The present work suggests that QPT of the XY spin chain with three-site interaction can be characterized by exploring the dynamical behaviors of the LE and BP.     

Formation of sub-half-wavelength focal spot with ultra long depth of focus

We theoretically demonstrate the creation of sub-wavelength focal spot with ultra long depth of focus (DOF) non-diffracting. To achieve a sub-half-wavelength focal spot (0.4λ) with modulation, extended DOF (over 9.5λ) in vacuum, an integration of amplitude phase encoding, cylindrical polarization and the combination of dual-beams is utilized. Further analysis also predicts that a flattop intensity distribution along z axis can be observed around the ideal focus point.     

零相关位相板准远场应用的数值研究

对零相关位相板匀滑准远场散斑的特性进行了数值模拟,并与使用随机位相板(配合二单元 偏振控制板)的情形进行了比较.结果表明,尽管零相关位相板是针对入射场为平面波和作为 远场应用而设计的,但在准远场应用中,当离焦距离不超过0002355λf²/d2,入射场的振幅随机起伏不超过10%和位相随机起伏不超过λ/2０的情况下,其 散斑的光强起伏仍明显低于采用随机位相板的情形.因而,零相关位相板在准远场应用中仍 能有效地匀滑散斑. 关键词： 零相关位相板 准远场散斑匀滑 激光聚变     

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.     

Investigation on high power phase compensation of strong aberrations via stimulated Brillouin scattering

The strong wave-front aberrations compensated by stimulated Brillouin scattering phase conjugate mirror (SBS-PCM) in a high power laser were investigated experimentally. The wave-front fluctuation of the 10 Hz 500 mJ Nd:YAG laser is 0.5λ. Transmitting through a random phase plate (RPP), it increases to 8.6λ. While using SBS-PCM in place of a high reflection mirror, the distortion induced by the RPP is compensated, and the wave-front fluctuation becomes 0.9λ. At the same time, obvious breakdown phenomena in the SBS cell were observed, and the reflectivity is unstable. A rotating wedge plate is introduced into the phase conjugating mirror to make the focus of the SBS cell rotate and optical breakdown is avoided effectively. The reflectivity becomes stable around about 70% and the instability is changed from ±4.1% to ±0.9%. Besides, the compensated wave-front fluctuation is only 0.6λ, which is near to the original wave-front distribution. The results show that the reflectivity of the SBS-PCM is very high and stable when there are no other nonlinear effects such as optical breakdown. Thus the compensating effects for strong wave-front errors are perfect.     

Formation of periodic surface nanostructures on Ti:Al2O3 crystals using femtosecond laser pulses

Periodic surface nanostructures are observed on Ti³⁺:Al₂O₃ single crystals that have been irradiated by a single focused beam from a femtosecond pulsed laser (wavelength: 800 nm; pulse duration: 130 and 152 fs). Atomic force microscopy images of single-ablated zones and modified structures created by fixing and translating samples through the focal region of a linearly polarized laser beam reveal self-organized periodic surface nanostructures (ripples) with a subwavelength spacing, which are oriented perpendicular to the electric-field vector of the laser beam. The period of the subwavelength ripples obtained by linearly polarized laser irradiation varies from ∼λ/5 to 2λ/5 (λ: incident laser wavelength) depending on the laser pulse energy. This phenomenon can be explained by assuming that the incident light field interferes with the electric field of electron plasma waves propagating inside the material; this interference periodically modulates the electron plasma density and modifies the surface ablation. In addition, for the first time, we observe screw-shaped nanostructures in the focal spot of circularly polarized beam irradiation. The morphology of these nanostructures appears to reflect the circular polarization of the laser light.     

Analysis of transmittance enhancement for a slab lens formed by sub-wavelength holes array on the metallic film

By investigating the transmittance and phase characteristics of the square holes on the metallic film, we find that the transmittance fluctuates with center distance between holes and appears resonant peaks, which attributes to the surface wave enhanced transmission phenomenon while the corresponding phase retardation through holes keeps constant. Based on this phenomenon, the slab lens can be optimized to a high transmittance by modulating the center distance of the holes. Design results show that the light intensity values at the focal spot of the slab lens can be enhanced from 3 to 14.5 in intensity scale when the center distance changes from 1.25λ to 0.95λ.     

Check of the T-invariance principle in 635 MeV pn-scattering

The “polarization-asymmetry” relation resulting from the T-invariance of strong interactions has been tested in a 635 MeV pn double-scattering experiment.No effects of T-invariance violation have been observed within the accuracy obtained of some percent in the angular range of (34–124)°. The T-odd scattering phase λ₁ has been obtained as λ₁=0.01 ± 0.02, which exceeds the accuracy of determining the λ₂ phase of pp-scattering at other energies.     

Laser treatment of Si-Al2O3 two-layer target

The laser treatment of two-layer Si-Al₂O₃ target at λ=1064 nm and P=170 W in a N₂+O₂ atmosphere by electron microscopy, atomic force microscopy, X-ray microanalysis, and IR-spectroscopy was investigated. It is established that in the stage of fracture of a silicon plate, the ablation products were silicon clusters into which, when passing over, oxygen and nitrogen diffused. On collective plate, a SiO_xN composite film formed. In the stage of fracture of an alumina plate, the oxidation of silicon in the channel zone and the interaction of Al and Si oxides, accompanied by their nitration, occurred. In this stage, evolved oxide vapors and ejected mullite drops deposit on the SiO_xN film. On collective plate, mullite nanowhiskers grew from mullite drops by the vapor-liquid-solid body mechanism.     

New omega vortex identification method

A new vortex identification criterion called W-method is proposed based on the ideas that vorticity overtakes deformation in vortex.The comparison with other vortex identification methods like Q-criterion and λ_2-method is conducted and the advantages of the new method can be summarized as follows:(1) the method is able to capture vortex well and very easy to perform;(2) the physical meaning of W is clear while the interpretations of iso-surface values of Q and λ_2 chosen to visualize vortices are obscure;(3)being different from Q and λ_2 iso-surface visualization which requires wildly various thresholds to capture the vortex structure properly, W is pretty universal and does not need much adjustment in different cases and the iso-surfaces of W=0.52 can always capture the vortices properly in all the cases at different time steps, which we investigated;(4) both strong and weak vortices can be captured well simultaneously while improper Q and λ_2 threshold may lead to strong vortex capture while weak vortices are lost or weak vortices are captured but strong vortices are smeared;(5) W=0.52 is a quantity to approximately define the vortex boundary. Note that, to calculate W, the length and velocity must be used in the non-dimensional form. From our direct numerical simulation, it is found that the vorticity direction is very different from the vortex rotation direction in general 3-D vortical flow,the Helmholtz velocity decomposition is reviewed and vorticity is proposed to be further decomposed to vortical vorticity and non-vortical vorticity.     

Tight focusing of circularly polarized beam over high NA lens axicon with a diffractive optical element

We propose to use diffractive optical element in combination with high NA lens axicon to achieve a high depth of focus when illuminated by a circularly polarized beam. With this kind of system, the focal depth is increased to 12.816λ and the magnetic spot size is reduced to 0.3764λ. However, in the conventional lens with same NA, the FWHM of the magnetic spot is found to be 0.4308λ and its corresponding magnetization depth is only 0.888λ. The author expects that such a high focal depth strong longitudinal magnetic field with large magnetization depth can be widely used in high density magneto optic recording, laser machining, laser cutting and the scanning near-field magnetic microscope.     

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.     

N-point functions and low-energy scattering by N centres

The scattering of a low-energy particle by a potential of a small range is known to be described satisfactorily by the s-wave alone. In the present paper we give a method of describing low-energy scattering by N potentials with the aid of N waves. For this purpose, a special system of Laplacian eigenfunctions is suggested. The scattering amplitude depends on only N parameters, irrespective of overlapping of potentials. The physical significance of these parameters δ_λ, λ=1,2,…N, is shown by exp (2iδ_λ)=S_λ where S_λ is the eigenvalue of the S matrix. The parameters δ_λ may be obtained by direct methods and perturbation theory.The low-energy scattering by an arbitrary configuration of N centres is discussed. The differential cross-section is averaged over all orientations of the configuration and radially about the direct beam, giving it as a function of the scattering angle. This formula may be used for the phase shift analysis.     

Lattice (Φ 4)4 effective potential giving spontaneous symmetry breaking and the role of the Higgs mass

We present a critical reappraisal of the available results on the broken phase ofλ(Φ ⁴)₄ theory, as obtained from rigorous formal analyses and from lattice calculations. All the existing evidence is compatible with Spontaneous Symmetry Breaking but dictates a trivially free shifted field that becomes controlled by a quadratic hamiltonian in the continuum limit. As recently pointed out, this implies that the simple one-loop effective potential should become effectively exact. Moreover, the usual naive assumption that the Higgs mass-squaredm _h ² is proportional to its “renormalized” self-couplingλ _R is not valid outside perturbation theory: the appropriate continuum limit hasm _h finite and vanishingλ _R . A Monte Carlo lattice computation of theλ(Φ ⁴)₄ effective potential, both in the single-component and in theO(2)-symmetric cases, is shown to agree very well with the one-loop prediction. Moreover, its perturbative leading-log improvement (based on the concept ofλ _R ) fails to reproduce the Monte Carlo data. These results, while supporting in a new fashion the peculiar “triviality” of theλ(Φ ⁴)₄ theory, also imply that, outside perturbation theory, the magnitude of the Higgs mass does not give a measure of the observable interactions in the scalar sector of the standard model.     

Extending the depth of focus with high NA lens axicon

Based on vectorial Debye theory, tight focusing of x-polarized beam with high NA lens axicon is studied. The high NA lens axicon utilizes spherical aberration to duplicate the performance of an axicon and to create an extended focal line. The intensity distribution in the focal region is illustrated by numerical calculations. We show that the high NA lens axicon system can generates a sub wavelength beam (0.826λ) with depth of focus around 10λ.     

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.