Vector propagation of radially polarized Gaussian beams diffracted by an axicon

On the basis of the vectorial Rayleigh diffraction integrals and stationary-phase method, the analytic expression describing the vectorial field distribution of radially polarized Gaussian beams diffracted by an axicon is derived. The theoretical analysis and simulation calculation show that the radial component of the diffraction field is the propagation-invariant first-order Bessel beam when the radially polarized Gaussian beam illuminates the axicon. However, the longitudinal component possesses no such behavior because of its intrinsic r dependence, and its central intensity is the maximum. The longitudinal component is related to the open angle and index of the axicon, which has to be considered when the open angle and index are large. For a small open angle and index, the longitudinal component can be neglected, and the scalar approximation is valid.     

On the wavefront spacing of focused, radially polarized beams

We analyze the phase behavior of strongly focused, radially polarized electromagnetic fields. It is shown that, under certain circumstances, the spacing between successive wavefronts can be either greater or smaller than that of a plane wave of the same frequency. Also, this spacing can be significantly larger than that which is predicted for a linearly polarized field that is focused by the same system.     

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.     

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.     

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.     

Generation of three-dimensional dark spots with a perfect light shell with a radially polarized Laguerre-Gaussian beam

The theoretical analyses in this paper show that a highly focused double-ring radially polarized Laguerre-Gaussian beam with a topological charge of 1 (R-LG(11)) can generate a small three-dimensional (3D) dark spot surrounded by an almost 100% uniform light shell in all directions. The cleanness and size of the 3D dark spot, the uniformity and strength of the light shell surrounding the dark spot, and the light efficiency all depend on the truncation parameter β of the R-LG(11) beam and the numerical aperture (NA) of the system. When β=1.6 and the NA is close to its utmost, an almost 100% uniform light shell surrounding the 3D dark spot can be achieved and the dark spot is very clean. If the NA is lowered but β is increased to 1.95, we can also achieve an almost 100% uniform light shell and light efficiency can reach 90%, but the disadvantage is that the center of the dark spot is not too clean. A not-too-clean 3D dark spot, if the light shell surrounding it is very uniform, is acceptable for many applications. Therefore, 3D dark spots surrounded by a high uniform light shell, generated by simply adjusting the truncation parameter of the R-LG(11) beam and the NA of the system, are useful for superresolution fluorescence microscopy, dark spot microscopy, and the dark spot trap.     

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.     

Correction of spherical and azimuthal aberrations in radially polarized beams from strongly pumped laser rods

Spherical aberration of heavily pumped Nd:YAG rods was corrected by use of spherical relay optics selected to add conjugate amounts of aberration. Wavefront measurements showed elimination of spherical aberration. Correction of spherical aberration allowed 250 W of power to be generated in a radially polarized, birefringence-free oscillator (60% more power than without correction). Scale-up of wavefront maintenance was demonstrated in a two-rod amplifier module (6.3 kW electrical pump power). Radial polarization and spherical aberration correction together eliminated the main aberrations in uniformly pumped rod-based lasers. Rotating adjacent pump chambers substantially reduced the multifold aberrations induced by nonuniformity of the azimuthal pumps. DeltaM2 in the radially polarized beam was 0.3 and 1.4 with and without aberration correction, respectively, in each two-pump chamber module. Analysis predicts further improvements when higher-order aberration correction is applied.     

Radiation forces of highly focused radially polarized hollow sinh-Gaussian beams on a Rayleigh metallic particle

Based on the vector diffraction theory, the tight focusing properties of radially polarized hollow sinh-Gaussian (HsG) beams are theoretically studied. It is found that the radially polarized HsG beams can form a longitudinally polarized sub-wavelength focal spot. Moreover, the radiation forces acting on a Rayleigh metallic particle are calculated for the case where the radially polarized HsG beams are applied. Compared with the use of conventional Gaussian beams, the high-order radially polarized HsG beams can largely enhance the radial trap stiffness and broaden the axial trap distance. The influence of the beam order m on the focusing properties and trap stiffness is investigated in detail.     

亚波长径向偏振光栅的设计

针对现有电力光学电流传感中法拉第旋转角的非线性测量、解调模式的光强依赖性等问题,本文设计了一种环型亚波长偏振光栅,其光栅矢量径向分布,可将偏振光的偏振分布转化为光斑强度分布并与偏振面同步旋转。应用琼斯矩阵对其偏振特性进行分析,运用严格耦合波理论对光栅进行仿真分析与优化设计,并制备了辐射状的环型铝金属光栅。测试结果表明,光栅TM光的透过率大于80%、整体消光比大于100,可实现对光偏振态的直接检测,并具有线性测量范围大、测量结果不依赖于光的绝对强度等优点,可用于基于图像分析的偏振检测技术。     

Intracavity generation of radially polarized CO2 laser beams based on a simple binary dielectric diffraction grating

We present experimental results on the intracavity generation of radially polarized light by incorporation of a polarization-selective mirror in a CO(2)-laser resonator. The selectivity is achieved with a simple binary dielectric diffraction grating etched in the backsurface of the mirror substrate. Very high polarization selectivity was achieved, and good agreement of simulation and experimental results is shown. The overall radial polarization purity of the generated laser beam was found to be higher than 90%.     

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.     

Eigenfields and output beams of an unstable Bessel-Gauss resonator

We evaluate the eigenfields of an unstable Bessel-Gauss resonator (UBGR) by use of the transfer-matrix method in which the transverse profiles and their corresponding losses of the UBGR are considered as the eigenvectors and eigenvalues of a transfer matrix so that the dominant mode fields and their losses of the UBGR can be readily extracted in terms of the matrix eigenvalue algorithm. Moreover, based on the eigenfields across two mirrors that resulted from the transfer-matrix method, we simulate the field distributions in the cavity and the propagation of output beams by means of the angular spectrum method. The computation results show that the UBGR easily produces a fundamental Bessel-Gauss mode of good quality, and the output beams retain the original Bessel-Gauss distribution during propagation.     

Axial separation of orthogonally polarized focal field components due to a radially polarized beam

In this paper, we investigate the field distribution in the focal volume of an aberrated radially polarized beam. Using two different forms of the vectorial diffraction theory, we show that the presence of defocus in the beam displaces both the axially and the radially polarized fields parallel to the optical axis of the focusing lens, while the presence of spherical aberration primarily shifts the longitudinally polarized field only. This facilitates axial separation of the two orthogonally polarized field components, resulting in a significant boost to the ratio of the peak longitudinally polarized field to the peak laterally polarized field in the focal plane. We further show that with an appropriate combination of oppositely signed defocus and spherical aberration, the energy density in the focal volume due to the longitudinally polarized field can be caused to peak at the focal plane. The results obtained are expected to be beneficial to the applications requiring a stronger longitudinally polarized focal field relative to the laterally polarized focal field component.     

Formation of a sub-wavelength longitudinally polarized beam using a radially polarized controllable dark-hollow beam

On the basis of vector diffraction theory, the tightly focusing properties of radially polarized controllable dark-hollow (CDH) beams are examined theoretically. Calculation results demonstrate that by choosing the initial parameters of the proposed light beams suitably, a sub-wavelength (0.422λ) longitudinally polarized light beam with high beam quality (82.2%) can be formed without any filters. Meanwhile, we find that a relatively long depth of focus benefits from larger beam order. The dependence of the focal spot size on the parameters such as truncation parameter, variation constant, and beam order is also explored in detail. Moreover, an alternative method to generate the CDH beams is proposed.     

Generation of nondiffracting beams through an opaque disk

A new method of generating nondiffracting beams is presented. It consists of focusing a Gaussian beam in the vicinity of an opaque disk. A beam is generated whose central peak is surrounded by a wide number of bright rings (approximately 250). After collimation, the beam propagates without changing the rings' radii, similar to a diffraction-free beam. The central peak can conserve its dimension over more than 5 m. The diameter of the central peak is adjusted by choosing the focal length of the collimating lens. Experimental results are well predicted by our theoretical developments that simulate exactly the paraxial diffraction.     

Concentric ring metal grating for generating radially polarized light

A subwavelength concentric ring metal grating for visible light (λ=632.8?nm) is designed and fabricated by electron-beam lithography to transform circularly polarized light into radially polarized light. Experimental results are compared to theoretical predictions and the advantages and disadvantages of the element with alternative methods are discussed.     

Highly focused spirally polarized beams

The features of spirally polarized light beams focused by high-numerical-aperture systems are investigated in the nonparaxial regime by means of Debye theory with a multipole expansion technique. General expressions of the expanding coefficients are given, as well as the electric field distributions across the focal plane. Numerical examples are presented for the case of spirally polarized beams of the donut type. Comparisons with recent experimental results are also shown.     

Rotation of nanowires with radially higher-order Laguerre-Gaussian beams produced by computer-generated holograms

In this paper, the influence of radially higher index p of Laguerre-Gaussian (LG) beams on the rotation of nanowires is studied. Radially higher-order LG beams are produced by computer-generated holograms, which are displayed on a spatial light modulator. A series of experiments on manipulating ZnO nanowires was performed on our holographic optical tweezers platform. The experiments demonstrated that radially higher-order LG beams could effectively rotate nanowires along the innermost bright ring of themselves. Compared with radially low-order LG beams, they have larger torques exerted on nanowires and can make nanowires rotate more quickly.     

Quality improvement of partially polarized beams

Improvement of the beam-quality parameter of partially polarized beams is investigated. We focus on the use of a Mach-Zehnder-type interferometric arrangement with crossed polarizers. The analysis has been carried out within the framework of the intensity moment formalism. Conditions are given under which the beam-quality parameter is optimized.