Theoretical and experimental studies on tightly focused vector vortex beams

The high-NA focusing properties of vector vortex beams are studied theoretically and experimentally. The vector vortex beams are generated by space-variant segmented subwavelength metallic gratings first. Then the mathematical expressions for the focused fields are derived based on the vector diffraction theory, and some numerical simulations are presented that show that the focused fields are not dark at the center and the focusing spot size of vector vortex beams with high topological charges approaches the diffraction limitation at high NA. Finally, to verify the theoretical analysis, the tightly focused fields are measured based on a confocal microscopy system when the NA of the objective lens is 0.90. The research results confirm the potential of vector vortex beams in some applications, such as optical trapping, laser printing, lithography, and material processing.     

Vector wave analysis for nonnormal incident rays in epimicroscopic refractive index profile measurements

We have investigated the effects of nonnormal incident rays in calculating the refractive index profile of a dielectric sample using the reflectance measurement data obtained with a scanning confocal epimicroscope and also by solving three-dimensional vector wave equations for linearly polarized light. The numerically calculated reflection data of tightly focused Gaussian beams with different numerical apertures (NAs) on planar surfaces with various refractive indices confirm that the reflectance increases with an increase in the NA of a focusing objective lens. This is due to the nonnormal incident ray components of a Gaussian beam. We have found that the refractive index obtained with the assumption of a normal incident beam is far from the real value when the NA of a focusing lens becomes larger than 0.5, and thus the variation in the reflectance for different angular components in a Gaussian beam must be taken into consideration while using a larger NA lens. Errors in practical refractive index calculation for an optical fiber based on a normal incident beam in reflectance measurements can be as large as 1% in comparison to real values calculated by our three-dimensional vector wave equations.     

Excitation with a focused, pulsed optical beam in scattering media: diffraction effects

To gain a better understanding of the spatiotemporal problems that are encountered in two-photon excitation fluorescence imaging through highly scattering media, we investigate how diffraction affects the three-dimensional intensity distribution of a focused, pulsed optical beam propagating inside a scattering medium. In practice, the full potential of the two-photon excitation fluorescence imaging is unrealized at long scattering depths, owing to the unwanted temporal and spatial broadening of the femtosecond excitation light pulse that reduces the energy density at the geometric focus while it increases the excitation energy density in the out-of-focus regions. To analyze the excitation intensity distribution, we modify the Monte Carlo-based photon-transport model to a semi-quantum-mechanical representation that combines the wave properties of light with the particle behavior of the propagating photons. In our model the propagating photon is represented by a plane wave with its propagation direction in the scattering medium determined by the Monte Carlo technique. The intensity distribution in the focal region is given by the square of the linear superposition of the various plane waves that arrive at different incident angles and optical path lengths. In the absence of scattering, the propagation model yields the intensity distribution that is predicted by the Huygens-Fresnel principle. We quantify the decrease of the energy density delivered at the geometric focus as a function of the optical depth to the mean-free-path ratio that yields the average number of scattering events that a photon encounters as it propagates toward the focus. Both isotropic and anisotropic scattering media are considered. Three values for the numerical aperture (NA) of the focusing lens are considered: NA = 0.25, 0.5, 0.75.     

Highly convergent focusing of light based on rotating dipole polarization

Focusing properties of transverse circular polarization modes that bring light to a small focal spot are investigated. Two particular illumination polarization distributions are discussed. Rotating electric dipole polarization results in a central lobe diameter 8% smaller than for the circularly polarized aplanatic case at a NA of 0.95 in air and is also smaller than for radial polarization at NAs less than 0.90. Azimuthal polarization with a phase singularity of charge unity results in a small central lobe width that is smaller than that produced by focusing radially polarized light, having a width that is 17% smaller than for circularly polarized illumination at a NA of 0.95.     

远距离高精度多普勒位移测量

通过泛函、激光散斑理论和随机过程各态遍历的研究,导出激光多普勒信号强度与聚焦光斑直径、接收透镜通光口径、光电接收器响应等参数间的关系,在此基础上设计出一种适用于远距离处面内位移测量的光路。此光路将高斯光束束腰聚焦在被测体上,实现最小聚焦光斑和平面波叠加,此外采用大口径透镜接收散射光,用响应度高的光电接收器转换光电信号等措施获得高强度高信噪比的测量信号。将此光路用于 100m 处面内位移(49.70mm)测量,其精度可达 2%。此设计方法能用于振动或地震波的高精度检测。     

Comparison of simulated quenching algorithms for design of diffractive optical elements

We compare the performance of very fast simulated quenching; generalized simulated quenching, which unifies classical Boltzmann simulated quenching and Cauchy fast simulated quenching; and variable step size simulated quenching. The comparison is carried out by applying these algorithms to the design of diffractive optical elements for beam shaping of monochromatic, spatially incoherent light to a tightly focused image spot, whose central lobe should be smaller than the geometrical-optics limit. For generalized simulated quenching we choose values of visiting and acceptance shape parameters recommended by other investigators and use both a one-dimensional and a multidimensional Tsallis random number generator. We find that, under our test conditions, variable step size simulated quenching, which generates each parameter's new states based on the acceptance ratio instead of a certain theoretical probability distribution, produces the best results. Finally, we demonstrate experimentally a tightly focused image spot, with a central lobe 0.22-0.68 times the geometrical-optics limit and a relative sidelobe intensity 55%-60% that of the central maximum intensity.     

Generating radial or azimuthal polarization by axial sampling of circularly polarized vortex beams

A laser beam with circular polarization can be converted into either radial or azimuthal polarization by a microfabricated spiral phase plate and a radial (or azimuthal)-type linear analyzer. The resulting polarization is axially symmetric and is able to produce tightly focused light fields beyond the diffraction limit. We describe in detail the theory behind the technique and the experimental verification of the polarization both in the far field and at the focus of a high numerical aperture lens. Vector properties of the beam under strong focusing conditions were observed by comparing the fluorescence images corresponding to the focal intensity distribution for both radial and azimuthal polarizations. The technique discussed here may easily be implemented to a wide range of optical instruments and devices that require the use of tightly focused light beams.     

Optical characteristics of femtosecond laser micromachined periodic structures in Si <100>

A frequency doubled Ti:sapphire laser of 400 nm wavelength, 160 fs pulse width, and 1 kHz repetition rate, combined with a high resolution computer-controlled X-Y stage, was used to direct write periodic structures on Si <100>. Laser pulses of approximately 130 nJ energy were focused using an objective lens of 0.65 NA. Laser micromachining yielded lines of 700 nm width and ablation depths of 600 nm. One- and two-dimensional periodic structures of 5 and 5x5 microm spacing were fabricated, and the structures were characterized by using optical and atomic force microscopy. The light diffraction characteristics of the periodic 1D and 2D patterns were examined. The diffraction properties of the 1D structures were highly dependent upon the light polarization orientation with respect to the micromachining direction.     

Effect of material dispersion on the focusing of isodiffracting ultrashort pulses by a lens

Abstract

Based on the Fourier transform, the focusing of isodiffracting ultrashort pulses by a lens is studied, where the material dispersion of first, second and higher order is taken into account, respectively. Numerical calculation results for spatial and temporal intensity distributions, photon flux and energy density of focused isodiffracting ultrashort pulses are given and illustrated. It is shown, compared to the dispersion-free case, that the first-order dispersion leads to a broadening of the pulse form, photon flux and energy density, and a decrease of their peak values. The second-order dispersion results in a further broadening of the pulse form and photon flux, and a further decrease of their peak values, whereas the higher-order dispersion plays a relatively minor role.     

Controlling the contribution of the electric field components to the focus of a high-aperture lens using binary phase structures

We show that the contribution of the electric field components into the focal region can be controlled using binary phase structures. We discuss differently polarized incident waves, for each case suggesting easily implemented binary phase distributions that ensure a maximum contribution of a definite electric field component on the optical axis. A decrease in the size of the central focal spot produced by a high numerical aperture (NA) focusing system comes as the result of the spatial redistribution of the contribution of different electric field components into the focal region. Using a polarization conversion matrix of a high NA lens and the numerical simulation of the focusing system in Debye's approximation, we demonstrate benefits of using asymmetric to polar angle ? binary phase distributions (such as arg[cos ?] or arg[sin 2?]) for generating a subwavelength focal spot in separate electric field components. Additional binary structure variations with respect to the azimuthal angle also make possible controlling the longitudinal distribution of light. In particular, the contribution of the transverse components in the focal plane can be reduced by the use of a simple axicon-like structure that serves to enhance the NA of the lens central part, redirecting the energy from focal plane. As compared with the superimposition of a narrow annular aperture, this approach is more energy efficient, and as compared with the Toraldo filters, it is easier to control when applied to three-dimensional focal shaping.     

二元光学在强激光波面整形中的应用

文章首先介绍了二元光学波面整形器件的理论基础。在分析GS、YG等正反迭代算法存在问题的基础上,提出三种优化算法,即全局/局部联合搜索算法（GLUSA）、爬山-模拟退火混合算法及多分辨率的混合优化算法。以惯性约束核聚变中光束匀滑为例,进行了二元光学器件的位相设计,获得了良好的位相结构与焦斑性能。采用旋转镂空掩膜板制作了准连续位相器件,并利用CCD与多种光强衰减片进行焦斑光强测量。实验结果表明：获得了较好的顶部均匀性、陡边、小旁瓣、高主瓣能量利用率以及光斑中心没有锐脉冲的光强分布。     

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.     

Scatter-ratio test for lens surface-quality measurement

The surface quality of an optical lens can be quantitatively measured using a scatter ratio test. A collimated light beam is focused by the test lens upon an opaque spot. A detector behind the spot measures light scattered past the spot. The spot is then displaced to the side so that total energy out of the lens is measured by the detector. The scatter ratio is the ratio of the two detector outputs. The test is shown to be reproducible and insensitive to operator effects. It is shown to be an effective process control tool for detecting changes in surface finish. The relationship between stylus measurements of lens surface roughness and the scatter ratios is shown.     

Effects of primary spherical aberration, coma, astigmatism, and field curvature on the focusing of ultrashort pulses: Gaussian illumination and experiment

We analyze the spatiotemporal intensity of Gaussian temporal envelope pulses with initial durations of 200 fs and a carrier wavelength of 810 nm at the paraxial focal plane of an achromatic doublet lens for a well-collimated incoming pulse beam by using the Seidel aberration theory for thin lenses with the stop at the lens. We analyze the effect of these aberrations in the focusing of ultrashort pulses for Gaussian illumination and present experimental results for 200 fs pulses focused by a near-IR achromatic doublet.     

Tight focusing properties of hybridly polarized vector beams

We theoretically investigate the tight focusing properties of hybridly polarized vector beams. Some numerical results are obtained to illustrate the intensity, phase, and polarization of tightly focused hybridly polarized vector beams. It is shown that the shape of the focal pattern may change from an elliptical beam to a ring focus with increasing radial index. The phase distribution around the tightly focused ring is shown to be the helical phase profile, indicating that the radial-variant spin angular momentum of hybridly polarized vector beams can be converted into the radial-variant orbital angular momentum.     

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.     

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.     

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.     

Subwavelength focusing using a hyperbolic medium with a single slit

A hyperbolic dispersion medium with a planar surface that can be used for subwavelength focusing is proposed. By combining the hyperbolic medium in a single slit with diffraction limit width, a laser beam could be focused to a subwavelength spot in the near field. Compared to a conventional superlens, the subdiffraction focusing in this work has higher optical throughput. Using a planar hyperbolic medium, which is actually alternating silver/dielectric multilayers, we showed that the focusing resolution of the designed device is down to ~λ/5 using green light illumination (at a wavelength of 514.5 nm).