Focusing of radially and azimuthally polarized beams through a uniaxial crystal

We calculated and measured the difference between focal positions of radially and azimuthally polarized beams after passing through a uniaxial crystal. Calculations were carried out on the basis of the ray optics and the vector diffraction theory. The results of the calculations were in good agreement with those of the experiment. In addition, we discussed the polarization selection in a hemispherical laser cavity that was used for the generation of a radially polarized beam by use of the birefringence of a c-cut Nd:YVO4 laser crystal [Opt. Lett. 31, 2151 (2006)]. The stability range of the laser cavity length for the generation of a radially polarized beam was also in good agreement with the differences mentioned above.     

Structure of optical singularities in coaxial superpositions of Laguerre-Gaussian modes

We investigate optical singularities in coaxial superpositions of two Laguerre-Gaussian (LG) modes with a common beam waist from the viewpoints of a general formulation of phase structure, experimental generation of various superposition beams, and evaluation of the generated beams' fidelity. By applying a holographic phase-amplitude modulation scheme using a phase-modulation-type spatial light modulator, output fidelity beyond 0.960 was observed under several typical conditions. Additionally, an elliptic-type folded singularity, which provides a different class of phase structures from familiar helical singularities, was predicted and observed in a superposition involving two LG modes of both radially and azimuthally higher orders.     

Generation of radially polarized beams with an image-rotating resonator

We show how a passive image-rotating optical resonator can be used to convert a linearly polarised, lowest-order Gaussian beam into a radially polarized beam. The image and polarization rotation of the cavity removes the frequency degeneracy of the modes, making it possible to select the radially polarized mode by cavity tuning. With the addition of gain, the same cavity should operate as a radially polarized laser when injection seeded at the proper wavelength.     

Excitation isotropy of single CdSe/ZnS nanocrystals

We study the dimensionality of the excitation transition dipole moment for single CdSe/ZnS core-shell nanocrystals using azimuthally and radially polarized laser modes. The comparison of measured and simulated single nanocrystal excitation patterns shows that single CdSe/ZnS quantum dots possess a spherically degenerated excitation transition dipole. We show that the dimensionality of the excitation transition dipole moment distribution is the same for all individual CdSe/ZnS nanocrystals, disregarding the difference in core size and irrespective of variations in the local environment. In contrast to the emission transition dipole moment, which is oriented in one plane, the excitation transition dipole moment of a single CdSe/ZnS quantum dots possesses an isotropy in three dimensions.     

Sharper focal spot formed by higher-order radially polarized laser beams

The intensity distributions near the focal point for radially polarized laser beams including higher-order transverse modes are calculated based on vector diffraction theory. For higher-order radially polarized mode beams as well as a fundamental mode (R-TEM01*) beam, the strong longitudinal component forms a sharper spot at the focal point under a high-NA focusing condition. In particular, double-ring-shaped radially polarized mode (R-TEM11*) beams can effectively reduce the focal spot size because of destructive interference between the inner and the outer rings with pi phase shift. Compared with an R-TEM01* beam focusing in a limit of NA=1, the full width at half-maximum values of the focal spot for an R-TEM11* beam are decreased by 13.6% for the longitudinal component and 25.8% for the total intensity.     

Representation and focusing properties of higher-order radially polarized Laguerre–Gaussian beams

A method based on higher-order Poincaré sphere was proposed to represent the states of polarization of higher-order radially polarized Laguerre–Gaussian (LG) vectorial beams (VBs). And the focusing properties of such LG beams of different radial orders focused by a high-NA lens were discussed. By tuning the ratio of the pupil radius to the waist of the incident beams, some cage-like or needlelike electric intensity field is generated in the focal region for several specific LG VBs with high order. Modulated by diffractive optical elements, the shape of the focal field shows novel behaviors such as splitting of cage-like modes, which provides potentially a more flexible control over micro-particles.     

Focal shift in focused radially polarized ultrashort pulsed laser beams

Beginning with a beam coherence polarization (BCP) matrix, we obtain an analytical intensity expression for radially polarized ultrashort pulsed laser beams that pass through an apertureless aplanatic lens. We also investigate the intensity distribution of radially polarized beams in the vicinity of the focus. The focal shift of these beams is studied in detail. The focal shift depends strongly on Z(F) that coincides with pi times the Fresnel number.     

Reflection and transmission of strongly focused light beams at a dielectric interface

The reflection and transmission of tightly focused azimuthally, radially and linearly polarized electromagnetic wave beams with subwavelength spot size and wavefront curvature at a dielectric interface are investigated. For a given wavefront radius, the existence of the optimal radius of beam spot corresponding to a minimal reflectance and maximal transmittance is shown. Significant lateral shift in the transmitted intensity peak is revealed for strongly focused azimuthally and radially polarized beams that are normally incident to an interface. The reflection and transmission of transverse-electric- and transverse-magnetic- polarized extremely narrow wave beams which are obliquely incident on the dielectric interface is analysed. Disappearance of the Brewster angle and total internal reflection effects for the strongly focused beams are predicted. The change in beam profile after reflection and transmission for different polarizations, incident beam spots and incidence angles are analysed.     

Quasimode theory of quantum optical processes in photonic band gap materials

This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.     

Modal properties of an external diode-laser-array cavity with diffractive mode-selecting mirrors

Coupled mode theory is used to describe the behavior of an external laser cavity consisting of a diode laser array and a diffractive mode-selecting mirror. The mirror is designed to establish a uniform-amplitude, uniform-phase fundamental mode. Coupled mode theory is then used to study the behavior of higher-order modes. We show that the maximum discrimination against higher-order modes occurs when the round-trip cavity length satisfies certain Talbot relations. In addition, this high modal discrimination can be maintained for arrays with large numbers of lasers without incurring significant loss in the fundamental mode.     

Polarization states and output powers of a CO(2) laser with an electro-optic phase retarder

We study the power output and polarization state of a CO(2) laser that contains both passive polarization-sensitive elements (Brewster plates) and an active phase-retarding electro-optic modulator (CdTe crystal). The theoretical threshold condition (i.e., the retardation required to extinguish the laser) is obtained from a cavity round-trip Jones matrix. We show that adding extra Brewster plates may be counterproductive in that the required retardation voltage increases. We calculated the output power, which depends on the saturated gain properties of the active media, by iterative modeling, with the elliptically polarized light propagated repeatedly around the cavity. We compare the theory with results from a folded rf-excited waveguide CO(2) laser (Laser Ecosse Model CM3500). Theory and experiment are in fair agreement for low powers. As expected, at high powers there are extra difficulties in modeling the cavity behavior, probably because of distortions induced in and by the crystal.     

Tight focusing of radially and azimuthally polarized vortex beams through a uniaxial birefringent crystal

Under the approximation of small birefringence, the properties of radially and azimuthally polarized vortex beams tightly focused through a uniaxial birefringent crystal are investigated. The contour plots of intensity distribution near the focus and in the real focal plane are illustrated by performing numerical calculations. The dependence of the focal shift on numerical aperture and birefringence are analyzed. Moreover, the Strehl ratio in the real focal plane as a function of birefringence is also analyzed. It is revealed that the variation of birefringence has no influence on the focal shift and the Strehl ratio of azimuthally polarized vortex beams.     

Average characteristics of partially coherent electromagnetic beams

Average characteristics of partially coherent electromagnetic beams are treated with the paraxial approximation. Azimuthally or radially polarized, azimuthally symmetric beams and linearly polarized dipolar beams are used as examples. The change in the mean squared width of the beam from its value at the location of the beam waist is found to be proportional to the square of the distance in the propagation direction. The proportionality constant is obtained in terms of the cross-spectral density as well as its spatial spectrum. The use of the cross-spectral density has advantages over the use of its spatial spectrum.     

基于4π聚焦系统的电磁矢量光学斯格明子的产生

光学斯格明子为实现结构光场以及时空光场的拓扑属性提供了新的研究方法与研究思路。本文在4π聚焦系统中,通过对两对入射柱矢量光束进行偏振与相位调控,实现了聚焦光场纵向分量与横向分量的独立控制,在焦平面上得到了Néel型与Bloch型的电磁矢量光学斯格明子。在4π聚焦系统内调控两对反向传播的径向偏振光时,焦平面处将产生Néel型的电场矢量斯格明子。将其中一对替换为角向偏振光时,焦平面处将同时产生Bloch型的电场矢量斯格明子与相位超前π/2的磁场矢量斯格明子。本工作为进一步研究自由空间中微纳尺度电磁矢量光学斯格明子与物质的相互作用提供了理论基础。

     

On propagation-invariant and self-imaging intensity distributions of electromagnetic fields

Propagation-invariant azimuthally and radially polarized fields are examined. The orthogonality of these fields in every point of space is used to form propagation-invariant intensity distributions outside the scope of scalar theory. The same principle is then used to form self-imaging electromagnetic fields with non-self-imaging scalar components.     

Form-birefringent space-variant inhomogeneous medium element for shaping point-spread functions

We experimentally characterize the properties of an element that generates a doughnutlike point-spread function by converting the linearly polarized incident field to radially or azimuthally polarized light utilizing space-variant inhomogeneous medium (SVIM) form-birefringent subwavelength structures. To fabricate the high-aspect-ratio SVIM structures, we developed a chemically assisted ion-beam-etching process that permits control of the fabricated form-birefringent structure profile to optimize the effect of birefringence and the impedance mismatch on the substrate-air interface. Fabricated elements perform efficient polarization conversion for incident angles as large as 30 degrees, where the extinction ratio is found to be better than 4.5. The intensity distribution in the far field shows that our SVIM device generates a doughnut point-spread function that may prove useful for various applications.     

Creation of subwavelength light needle,equidistant multi-focus,and uniform light tunnel

A versatile method is presented for the creation of ultra-long subwavelength light needles with high-purity longitudinal polarization, uniform light tunnels of variable length and with narrow dark channel, or coaxially equidistant multi-focus with prescribed number and spacing. This is achieved by modulating the radially or azimuthally polarized vector beams using the same kind of amplitude apodization filter under a high numerical aperture aplanatic lens system. These peculiar focusing patterns may suit a variety of potential applications, such as optical trapping, particle acceleration, atom optical experiments, and near-field scanning optical microscopy.     

双层管结构中扭转模态传播特性的理论分析与实验研究

通过分析不同的应力和位移边界条件得到了三种不同双层管结构中扭转模态的频散方程。不同结构中频散方程的阶次也不相同。并进行数值求解,得到相应的频散曲线。对不同双层管结构中扭转模态尤其是T(0,1)模态的主要传播特性进行了分析。然后,利用厚度剪切压电陶瓷片分别在这三种不同的管结构中进行了激励接收扭转模态的实验。实验结果与理论分析较为吻合。结果表明,利用全局矩阵法可以得到不同双层管结构的扭转模态频散方程,并且其频散曲线可用作模态选取的理论指导,用于这些管结构的缺陷检测。     

Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer

A principal scheme for an external cavity technique for changing the polarization of a laser beam based on a modified Sagnac interferometer is proposed. The modified Sagnac interferometer includes standard optical components: a displacement polarizing beam splitter, an angle reflector, and a Dove prism. The radially polarized beams, obtained with the help of the developed scheme, allow the generation of a longitudinally polarized electric field by sharp focusing. The phase correction of radially polarized modes of higher orders leads to increasing the longitudinal field in the focus of the beam.     

Non-diffractive Vector Bessel Beams

Abstract

The non-diffractive vector Bessel beams of an arbitrary order are examined as both the solution to the vector Helmholtz wave equation and the superposition of vector components of the angular spectrum. The transverse and longitudinal intensity components of the vector Bessel beams are analysed for the radial, azimuthal, circular and linear polarizations. The radially and azimuthally polarized beams are assumed to be formed by the axicon polarizers used with the initially unpolarized or linearly polarized light. Conditions in which the linearly polarized Bessel beams can be approximated by the scalar solutions to the wave equation are also discussed.