Bessel beams: Effects of polarization

An approximation to a Bessel beam produced by tightly focusing linearly polarized light is known to produce a smaller central lobe than focusing plane polarized light. This is because the plane polarized wave gives a broad central lobe caused mainly by a parasitic longitudinal field component. It is known that this problem can be overcome by focusing radially polarized light. Here we demonstrate that other polarization distributions based on a linear combination of transverse electric (TE1) and transverse magnetic (TM1) fields can give a beam even narrower than for the radially polarized case. Special cases of this combination are identified, corresponding to the smallest width (TE1), and the maximum peak intensity compared with the side lobes (electric dipole polarization). Axially-symmetric forms can be generated by illumination with elliptically polarized light. A particular case is azimuthal polarization with a phase singularity, which is equivalent to TE1. For a semi-angular aperture of 60°, the TE1 case gives a central lobe width 9% narrower than for radially polarized illumination, while for plane polarized illumination it is 12% wider than the radially polarized case.     

Second harmonic generation polarization microscopy with tightly focused linearly and radially polarized beams

Second harmonic generation microscopy was conducted on rat-tail tendons with linearly and radially polarized beams. Transverse and axial field components were generated in the focal region through tight focusing of linearly and radially polarized. It was found that the generated SHG signals could not be qualitatively explained with a scalar approximation to the electric field at the focus. Only by accounting for the interactions of the axial and transverse components of the electric field interacting through the nonlinear susceptibility χ⁽²⁾ tensor could the SHG images be explained. For the case of collagen we find that the SHG signal varies as a function of the analyzer angle with a cos² or sin² dependency for linearly polarized beams. For tightly focused radially polarized beams we find that the output SHG is radially polarized after collimation and is independent of the analyzer angle.     

High-numerical-aperture focusing of radially polarized doughnut beams with a parabolic mirror and a flat diffractive lens

Recently, Dorn et al. [Phys. Rev. Lett. 91, 233901 (2003)] demonstrated the significance of radially polarized doughnut beams in obtaining very small focal spots (with an area of approximately 0.26 lambda2) with high-numerical-aperture (NA) aplanatic microscope objectives. We propose two simple alternative ways to focus such radially polarized beams: a parabolic mirror and a flat diffractive lens. Because of their large apodization factor for a high NA, a significant further reduction in spot area (up to a factor of 1.76 at a NA of 1) compared with the aplanatic system can be achieved.     

Efficient extracavity generation of radially and azimuthally polarized beams

We demonstrate an efficient transformation of a linearly polarized Gaussian beam to a radially or an azimuthally polarized doughnut (0,1)* Laguerre-Gaussian beam of high purity. We use a spatially variable retardation plate, composed of eight sectors of a lambda/2 retardation plate, to transform a linear polarization distribution to radial/azimuthal distribution. We transformed an Nd:YAG Gaussian beam with M(2)=1.3 to a radially and azimuthally polarized (0,1)* Laguerre-Gaussian beams with M(2)=2.5 and degree of radial/azimuthal polarization of 96-98%.     

Investigation of Near-Field Imaging Characteristics of Radial Polarization for Application to Optical Data Storage

Radially polarized incident light can generate a more confined longitudinal electric field on a focal plane in near-field (NF) optics than focusing circularly polarized light. Using this phenomenon, it is feasible to reduce beam spot size on storage media to increase the areal density of optical data storage. A radially polarized beam generates a beam spot which is 20% more confined on the 1st surface of medium than that of circularly polarized light. However, the peak intensity of total electric field sharply decreases and its transverse component is much more dominant inside the media stack. This confirms that radially polarized optics can be a candidate not for an NF recording system but for an NF read-only memory (ROM) system. Potentially, the results could be useful to understand the effect of radial and circular polarizations inside and outside medium for various applications of NF optics.     

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%.     

Longitudinal field modes probed by single molecules

We demonstrate that a strong longitudinal, nonpropagating field is generated at the focus of a radially polarized beam mode. This field is localized in space and its energy density exceeds the energy density of the transverse field by more than a factor of 2. Single molecules with fixed absorption dipole moments are used to probe the longitudinal field. Vice versa, it is demonstrated that orientations of single molecules are efficiently mapped out in three dimensions by using a radially polarized beam as the excitation source. We also show that there is no momentum or energy transport associated with the longitudinal field.     

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.     

少周期飞秒准径向偏振光的超快瞬变聚焦矢量场

研究了基于腔外螺旋相位调制获取高峰值功率飞秒准径向偏振光的方法,结果表明该方法所产生的并非完全纯净的径向偏振光,其径向分量决定了聚焦后纵场的分布,而径向和角向分量共同影响了横场的分布.根据Richard-Wolf矢量衍射理论模拟得到不同纯度下的少周期飞秒准径向偏振光在焦点附近的电场的时空矢量分布,发现其具有中心对称和震荡衰减特点,载波包络相位将对聚焦场的矢量时空分布产生显著影响,从而对飞秒脉冲与电子在聚焦场中的相互作用产生影响.研究结果可为进一步的激光粒子加速分析以及偏振转换器的设计提供依据.     

Three-dimensional multiple optical cages formed by focusing double-ring shaped radially and azimuthally polarized beams

We propose and simulate a method for generating a three-dimensional(3D) optical cage in the vicinity of focus by focusing a double-ring shaped radially and azimuthally polarized beam. Our study shows that the combination of an inner ring with an azimuthally polarized field and an outer ring with a radially polarized field and a phase factor can produce an optical cage with a dark region enclosed by higher intensity. The shape of the cage can be tailored by appropriately adjusting the parameters of double-mode beams. Furthermore, multiple 3D optical cages can be realized by applying the shift theorem of the Fourier transform and macro-pixel sampling algorithm to a double-ring shaped radially and azimuthally polarized beam.     

Achievement of longitudinally polarized focusing with long focal depth by amplitude modulation

The longitudinal component of a focused beam is split into two parts along the optical axis to obtain a longitudinally polarized long focal depth using amplitude filtering based on Euler transformation and a radially polarized Bessel-Gaussian beam. Numerical results indicate that long focal depth and FWHM can be easily achieved with 9λ and 0.8λ, respectively. A radially polarized beam can be converted into a longitudinally polarized beam with a conversion efficiency of 51.0%. It can therefore be believed that the proposed scheme can be widely used to generate a longitudinally polarized beam for particle acceleration, laser cutting, and optical trapping.     

Analytical vectorial structure of radially polarized light beams

Starting from the vector angular spectrum of the electromagnetic beam, the analytical vectorial structure of the radially polarized beams (RPBs) is presented. The energy flux distributions of the RPBs are demonstrated. The physical pictures of the RPBs are well illustrated from the vectorial structure. This particular electromagnetic field is entirely transverse magnetic, and on axis it only has a longitudinal (z) electric-field component (i.e., no transverse electric field and no magnetic field at all on axis).     

Optimization of focusing of linearly polarized light

We show that, by adding a π-phase shift to one-half of a linearly polarized beam, the roles of the transversal and longitudinal field components of the focused beam are interchanged, resulting in better focusing of the longitudinal component in the direction perpendicular to the phase jump line. For this component the scheme produces a spot with FWHM >15% smaller than a spot generated with either linearly or radially polarized light for any NA. The scheme has a similar advantage when applied to circularly polarized light, and it holds for both a plane wave and a realistic case of a Gaussian incident beam. This technique may find applications when using recording media responsive to the longitudinal field only, particularly in read/write for optical storage where the resolution in one transverse dimension is most important.     

Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects

Production and amplification of radially and azimuthally (tangentially) polarized laser beams are demonstrated. Based on the different focusing between radially and tangentially polarized light in thermally stressed isotropic laser rods, Nd:YAG laser oscillators were developed to produce low-loss stable oscillation in a single polarization. Pure radially polarized light at 70 W with M2 = 2 and on-axis impure radially polarized light at 150 W with M2 = 2.5 were achieved. The radially polarized beams were then amplified while good beam quality and polarization purity were retained. Complete elimination of thermal-birefringence-induced aberrations was demonstrated. This should allow much better beam quality from rod-based high-power lasers.     

Tight Focusing of Radially and Azimuthally Polarized Vortex Beams through a Dielectric Interface

Based on vectorial Debye theory, tight focusing of radially and azimuthally polarized vortex beams passing through a dielectric interface are studied. The intensity distribution in the focal region is illustrated by numerical calculations. We show the influence of numerical-aperture （NA） on the full-width at half maximum （FWHM） of the focal spot or the focal hole. It has been found that compared with the azimuthally polarized Besse~Gaussian （BG） beams, the longitudinal component in the z direction of the radially polarized BG beams has no influence on the FWHM of the focal spot and hole, but enhances the total light intensity.     

非均匀关联径向偏振部分相干光的产生

从理论和实验两方面对非均匀关联径向偏振部分相干光的产生进行了研究.理论上,基于相位关联与相干度的联系,推导出了非均匀关联径向偏振部分相干光的2×2阶交叉谱密度矩阵及相干度分布.实验上,利用一个相位型液晶空间光调制器的不同区域,对入射的完全相干的径向偏振光的两个正交偏振分量分别加载随机相位调制,并实验测量了这种光束的相干度分布及其对光强分布的影响.实验结果验证了光束相干度的非均匀关联结构,并且通过改变随机相位的高斯调制半宽可以改变光束的相干性分布.研究表明,随着随机相位的高斯调制半宽的增加,光束中两点间的相干度逐渐减小,其光强分布由圆环状逐渐变化为类平顶的光强分布.这种非均匀关联的径向偏振部分相干光在激光微操纵和材料加工等领域具有一定的潜在应用价值.     

Simple Nd:YAG laser generates vector and vortex beam

We report a simple Nd:YAG laser that emits radially polarized beam with helical wavefront. The laser cavity consists of a piece of laser crystal and a plane output coupler, and there is no additional polarization component inside it. The pump light is converted into annular profile through de-focal coupling into a multi-mode fiber. For the continuous-wave(CW) operation, the laser emits radially polarized vortex beam, and it is observed that the helical wavefront of the laser beam is switched from right handedness to left handedness when the output coupler is tilted slightly. For the Q-switched operation under the insertion of a Cr4t:YAG saturable absorber inside the cavity, we obtain radially polarized outputs with left-handedness helical wavefront. By tilting the laser crystal slightly, the laser output switches to azimuthal polarization at pump power larger than 4.5 W and left-handedness helical wavefront of laser beam is preserved.     

Focusing property of a double-ring-shaped radially polarized beam

The intensity distributions of a tightly focused radially polarized beam that has a double-ring-shaped transverse mode pattern were calculated based on vector diffraction theory. The distribution of the longitudinal component near the focus varied drastically with the degree of truncation of the incident beam by a pupil. When the ratio of the pupil radius to the beam radius was approximately 1.3, the longitudinal component disappeared at the focal point, owing to destructive interference. This dark area surrounded by an intense light field was of the order of the wavelength, with excellent intensity symmetry.     

Experimental verification on tightly focused radially polarized vortex beams

The theoretical and experimental results of tightly focused radially polarized vortex beams are demonstrated. An auto-focus technology is introduced into the measurement system in order to enhance the measurement precision, and the radially polarized vortex beams are generated by a liquid-crystal polarization converter and a vortex phase plate. The focused fields of radially polarized vortex beams with different topological charges at numerical apertures （NAs） of 0.65 and 0.85 are measured respectively, and the results indicate that the total intensity distribution at focus is dependent not only on the NA of the focusing objective lens and polarization pattern of the beam but also on the topological charge l of the beam. Some unique focusing properties of radially polarized vortex beams with fractional topological charges are presented based on numerical calculations. The experimental verification paves the way for some practical applications of radially polarized vortex beams, such as in optical trapping, near-field microscopy, and material processing.     

Propagation and parametric characterization of the polarization structure of paraxial radially and azimuthally polarized beams

Analytical expressions are provided for describing the free-space evolution of the polarization structure of paraxial beams whose electric-field vector at some transverse plane exhibits either a radially or an azimuthally polarized behavior. At each transverse plane, the polarization distribution across the beam profile is characterized by means of two sets of parameters, namely, the so-called (local) radial Stokes representation, and the (overall) percentage of the irradiance associated with the radial and azimuthal field components. The propagation laws for these sets of parameters are also shown. As an illustrative example, a radially polarized beam is analized whose wavefront contains a spiral phase factor.