Focusing surface plasmons on Er3+ ions through gold planar plasmonic lenses

Gold plasmonic lenses consisting of a planar concentric rings-groove with different periods were milled with a focused gallium ion beam on a gold thin film deposited onto an Er³⁺-doped tellurite glass. The plasmonic lenses were vertically illuminated with an argon ion laser highly focused by means of a 50× objective lens. The focusing mechanism of the plasmonic lenses is explained using a coherent interference model of surface plasmon-polariton (SPP) generation on the circular grating due to the incident field. As a result, phase modulation can be accomplished by the groove gap, similar to a nanoslit array with different widths. This focusing allows a high confinement of SPPs that can excite the Er³⁺ ions of the glass. The Er³⁺ luminescence spectra were measured in the far-field (500?C750?nm wavelength range), where we could verify the excitation yield via the plasmonic lens on the Er³⁺ ions. We analyze the influence of the geometrical parameters on the luminescence spectra. The variation of these parameters results in considerable changes of the luminescence spectra.     

Single-layer metal nanolenses with tight foci in far-field

In simulations we analyze performance of plasmonic nanolenses made of a single metal layer. We consider the nanolenses in two configurations. In the first, the nanolens is a free-standing silver layer with no hole on the optical axis and double-sided concentric corrugations. In the second, the nanolens has a set of slits instead of grooves. This necessitates integrating the annular metal elements with a dielectric matrix. We examine the following parameters of the nanolenses: film thickness, diameter of an on-axis stop, and lattice constant of slits or double-sided concentric grooves, as well as depth and width of grooves. Due to radially polarized illumination lenses have foci of full widths at half maxima (FWHMs) better than half a wavelength, though foci formed by propagating waves do not decrease beyond the diffraction limit. Due to proper geometry of slits or double-sided grooves lenses have focal lengths of the order of a few wavelengths. Transmission of light through lenses with double-sided narrow grooves reaches 30% while through ones with slits exceeds 80%.     

Subwavelength beam manipulation via multiple-metal slits coupled by disk-shaped nanocavity

A novel plasmonic structure consisting of three nano-scaled slits coupled by nano-disk-shaped nanocavities is pro- posed to produce subwavelength focusing and beam bending at optical frequencies. The incident light passes through the metal slits in the form of surface plasmon polaritons （SPPs） ,and then scatters into radiation fields. Numerical simulations using finite-difference time-domain （FDTD） method show that the transmitted fields through the design example can gener- ate light focusing and deflection by altering the refractive index of the coupled nanocavity. The simulation results indicate that the focal spot is beyond the diffraction limit. Light impinges on the surface at an angle to the optical axis will add an extra planar phase front that interferes with the asymmetric phase front of the plasmonic lens, leading to a larger bending angle off the axial direction. The advantages of the proposed plasmonic lens are smaller device size and ease of fabrication. Such geometries offer the potential to be controlled by using nano-positior!i0g systems for applications in dynamic beam shaping and scanning on the nanoscale.     

介质填充型二次柱面等离激元透镜的亚波长聚焦

本文提出了一种亚波长聚焦的表面等离激元透镜,该透镜由二氧化硅填充金膜纳米狭缝阵列组成,金膜的出射表面为二次柱面.表面等离激元在狭缝入口处激发并沿狭缝传输,在狭缝出口转变为带有一定相位延迟的自由空间传播的光波.通过对透镜结构参数的控制,可以调节来自各狭缝的光波间的相对相位,使它们在设定的焦点处进行相长干涉,从而实现聚焦效果.本文用时域有限差分法数值计算了二次柱面等离激元透镜的聚焦特性.数值模拟结果表明,所设计的孔径为2μm的透镜,能够实现微米级焦距和焦深、且焦斑半高宽低至0.4倍波长的亚波长聚焦.该表面等离激元透镜结构简单紧凑、尺寸小,有利于光子器件的集成,在集成光学、光学微操纵、超分辩率成像、光存储、生化传感等相关领域有潜在的应用价值.     

Beam bending through compound structure with two subwavelength metallic slits in each period

To provide a more practical, easy-to-implement method to achieve directional modulation with a plasmonic lens, beam manipulation method via compound metallic gratings with two subwavelength slits filled with different dielectrics inside each period is proposed and numerically investigated by finite-difference time-domain (FDTD) method. Compared with conventional metal-grating based structures, phase retardation is tuned by the Fabry-Pérot (FP) resonant condition and light bending is achieved by constructing a carefully designed, curved phase front for the plasmonic lenses. Our designs have advantages in ease of fabrication and capability to perform in the far field. With these advantages, the designs are expected to be valuable in applications such as plasmonic circuits and photonic communication.     

Plasmonic planar lens based on stack of metal–insulator–metal waveguides with height tuning

We introduce a technique capable of focusing electromagnetic (EM) waves through plasmonic nanoslits symmetrically arranged along the indented semi-circular surface in silver background. The EM transports through the tuning slits in the form of surface plasmon polaritons (SPPs), and gets the required phase retardations to focus at the focal plane. Due to the subwavelength nature of planar metallic lens, we present the rigorous electromagnetic analysis by using two dimensional (2D) finite difference time domain (FDTD) method. These height-modulated slits with uniform width are demonstrated to have unique advantages in beam manipulation. In combination with previous studies, it is expected that our structure with small number of slits could lead to realization of optimum designs of plasmonic nano-lens.     

Focusing of elliptically polarized Gaussian beams through an annular high numerical aperture

Based on the vectorial Debye theory,the focusing properties of the Gaussian beam through an annular high numerical aperture are studied numerically,including the intensity,the phase and the orbital angular momentum properties.Then the influence of certain parameters on the focusing properties is also investigated.It is shown that sub-wavelength elliptical light spots can be obtained.And there exists a vortex in the longitudinal component of the focused field even though the incident beam is Gaussian beam,indicating that the spin angular momentum of the elliptically polarized Gaussian beam is converted into the orbital angular momentum by the focusing.     

Optical phase front control in a metallic grating with equally spaced alternately tapered slits

A technique capable of focusing and bending electromagnetic （EM） waves through plasmonic gratings with equally spaced alternately tapered slits has been introduced. Phase resonances are observed in the optical response of transmission gratings, and the EM wave passes through the tuning slits in the form of surface plasmon polaritons （SPPs） and obtains the required phase retardation to focus at the focal plane. The bending effect is achieved by constructing an asymmetric phase front which results from the tapered slits and gradient refractive index （GRIN） distribution of the dielectric material. Rigorous electromagnetic analysis by using the two-dimensional （2D） finite difference time domain （FDTD） method is employed to verify our proposed designs. When the EM waves are incident at an angle on the optical axis, the beam splitting effect can also be achieved. These index-modulated slits are demonstrated to have unique advantages in beam manipulation compared with the width-modulated ones. In combination with previous studies, it is expected that our results could lead to the realization of ootimum designs for plasmonic nanolenses.     

径向偏振光下的长焦、紧聚焦表面等离子体激元透镜

表面等离子体激元透镜(plasmonic lens, PL)是一种通过激发和操控表面等离子体激元 (SPPs), 突破衍射极限, 实现亚波长紧聚焦的纳米光子器件. 如何实现高效率的紧聚焦及调控, 一直是研究PL的重点. 如果选取电矢量沿径向振动的径向偏振光作为PL的入射光, 可从各个方向激发SPPs, 提高紧聚焦的能量效率. 本文提出了一种在径向偏振光激发下的长焦深、长焦距、亚波长紧聚焦的表面等离子体激元透镜, 该透镜由中心T 形微孔、阶梯形同心环和同心环结构组成. 本文首先利用有限元方法数值分析了中心微孔-同心环结构透镜的聚焦特性, 结果显示径向偏振光由底部入射可高效激发SPPs, 并且中心微孔透射光与散射至自由空间的SPPs由于多光束干涉形成了紧聚焦. 为进一步压缩焦斑、增加焦距、加深焦深、改善透镜聚焦特性, 本文引入中心T形微孔-阶梯形同心环结构, 从而对阶梯表面的SPPs同时提供了相位调制和传播方向的控制. 经过参数优化, 该透镜结构实现了光斑焦深、半高宽、焦距分别是入射光波长的2.5倍、0.388 倍、3.22倍的亚波长紧聚焦; 而且该透镜具有结构紧凑、尺寸小、易于集成的优点, 满足了纳米光子学对于器件微型化和高度集成化的要求. 该研究结果在纳米光子集成、近场光学成像与探测、纳米光刻等相关领域具有潜在的应用价值.     

Compound plasmonic vortex generation based on spiral nanoslits

In view of wide applications of structured light fields and plasmonic vortices, we propose the concept of compound plasmonic vortex and design several structured plasmonic vortex generators. This kind of structured plasmonic vortex generators consists of multiple spiral nanoslits and they can generate two or more concentric plasmonic vortices. Different from Laguerre–Gaussian beam, the topological charge of the plasmonic vortex in different region is different. Theoretical analysis lays the basis for the design of radially structured plasmonic vortex generators and numerical simulations for several examples confirm the effectiveness of the design principle. The discussions about the interference of vortex fields definite the generation condition for the structured vortex. This work provides a design methodology for generating new vortices using spiral nanoslits and the advanced radially structured plasmonic vortices is helpful for broadening the applications of vortex fields.     

Optically trapping Rayleigh particles by using focused partially coherent multi-rotating elliptical Gaussian beams

By investigating the cross-spectral density of partially coherent multi-rotating elliptical Gaussian beams(REGBs) that propagate through a focusing optical system, we obtain the radiation force on a Rayleigh particle.The radiation force distribution is studied under different beam indexes, coherence widths, and elliptical ratios of the partially coherent multi REGBs. The transverse and the longitudinal trapping ranges can increase at the focal plane by increasing the beam index or decreasing the coherence width. The range of the trapped particle radii increases as the elliptical ratio increases. Furthermore, we analyze the trapping stability.     

The coherent radiation fraction of low‐emittance synchrotrons

In this work the coherence properties of the synchrotron radiation beam from an X‐ray undulator in a fourth‐generation storage ring are analyzed. A slightly focused X‐ray beam is simulated using a wavefront propagation through a non‐redundant array of slits and the mutual coherence function is directly obtained and compared with the Gaussian–Schell approximation. The numerical wave propagation and the approximate analytical approaches are shown to agree qualitatively, and it is also shown that, when the coherent fraction is selected by a finite aperture before the focusing element, even achromatic focusing systems like total reflection mirrors become slightly chromatic. This effect is also well accounted for in the Gaussian–Schell model. The wavefront propagation simulation through the non‐redundant array was repeated with an imperfect mirror demonstrating that, although the wavefront is distorted, its coherent length is practically unchanged.     

基于轴棱锥产生近似无衍射Mathieu光束的新方法

提出了一种基于轴棱锥产生零阶近似无衍射Mathieu光束的新方法,利用轴棱锥聚焦具有椭圆高斯振幅调制的平面波,得到近似零阶无衍射Mathieu光束.根据椭圆高斯平面波经轴棱锥衍射的衍射积分公式,对光强分布进行了数值模拟,依据几何光学模型计算了近似无衍射Mathieu光束的最大无衍射距离,并设计了实验对理论模拟的结果进行了验证.实验采用柱透镜和准直扩束系统变换圆高斯光束产生具有椭圆高斯振幅调制的平面波,用轴棱锥聚焦该平面波后得到近似无衍射Mathieu光束,实验结果与理论模拟和计算相符.     

Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere

The propagation of an elliptical Gaussian beam (EGB) through an astigmatic ABCD optical system in a turbulent atmosphere is investigated. An analytical formula for the average intensity of an EGB and a generalized tensor ABCD law for the generalized complex curvature tensor are derived. As an application example, we derived an analytical formula for the average intensity of an elliptical flat-topped beam propagating through an astigmatic ABCD optical system in a turbulent atmosphere. As a numerical example, the focusing properties of an EGB focused by a thin lens in a turbulent atmosphere are studied. It is found that the focused beam at the focal plane becomes a circular Gaussian beam when the atmospheric turbulence is strong enough, and the beam width of the circular Gaussian beam is determined by atmospheric turbulence strength, focal length of the thin lens, and wavelength of the initial beam but is independent of the initial beam widths (i.e., initial intensity distribution).     

Scintillation index of elliptical Gaussian beam in turbulent atmosphere

A tensor method is used to formulate the on-axis scintillation index for an elliptical Gaussian beam (EGB; astigmatic Gaussian beam) propagating in a weak turbulent atmosphere. Variations of the on-axis scintillation of an EGB are studied. It is interesting to find that the scintillation index of an EGB can be smaller than that of a circular Gaussian beam in a weakly turbulent atmosphere under certain conditions and is closely related to the ratio of the beam waist size along the long axis to that along the short axis of the EGB, the wavelength, and the structure constant of the turbulent atmosphere.     

Modeling of astigmatic-elliptical beam shaping during fs-laser waveguide writing including beam truncation and diffraction effects

In this work, we report a model for accurately calculating the focal volumes corresponding to astigmatic elliptical beams used in fs-laser waveguide writing. The model is based on the use of the ABCD matrix formalism for the propagation of a Gaussian beam. The code includes the effects of propagation on the astigmatic elliptical beam, and the effects of beam truncation and diffraction at the entrance pupil of the focusing objective due to beam clipping when overfilling the pupil. The results predict that for a given astigmatism value and propagation distance it is possible to efficiently suppress the astigmatic focus closer to the surface. This explains previous experimental results where single structure waveguides with controllable aspect-ratio were fabricated using astigmatic-elliptical beams. Furthermore, we investigate the respective roles of astigmatism and beam propagation, as well as the strong impact of truncation and diffraction effects caused by clipping the beam at the pupil of the focusing optics. Finally, based on the results from our model, we present some practical considerations in terms of beam propagation and phase wrapping constraints.     

Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass

In the present work, we have analyzed the use of elliptical beam shaping along with low numerical aperture focusing optics in order to produce circular cross-section waveguides in different materials at large processing depths by direct femtosecond laser writing (100 fs, 800 nm, 1 kHz). A variable slit located before the focusing optics allows to generate a nearly elliptical beam shape and also to reduce the effective numerical aperture of the beam along the shat axis of the ellipse. The focusing optics allows to focus the beam deep inside the sample, which is translated at a constant speed transversely to the writing beam direction. The influence of several experimental parameters (energy per pulse, slit width, processing depth) on the properties of the produced waveguides has been analyzed. The influence of the intrinsic properties of the material (refractive index, composition) has been analyzed by comparing results obtained in fused silica and Er:Yb co-doped phosphate glass. The results obtained show that this approach leads to the successful production of deep subsurface (up to 7 mm) waveguides with circular cross-sections. Preliminary results using chirped pulses in the phosphate glass suggest that temporal pulse shaping can be used as an additional parameter to optimize the guided mode symmetry.     

Comparison of subwavelength focusing properties of diffraction and Fresnel zone plate plasmonic planar lenses

The subwavelength focusing properties of diffractive plasmonic planar lenses (DPLs) and Fresnel zone plate plasmonic planar lenses (FZPs) have been compared in this paper. To that end, we use the same lens material, incident wavelength, thickness and focal length for comparison. Both DPLs and FZPs consist of central circular slits surrounded by transparent and opaque zones and can get clear focusing performances. By using the rigorous electromagnetic numerical method, the fields in the focal region are analyzed in detail, and our results demonstrate that FZP can generate higher transmission efficiency, and higher peak field intensity at the focal plane. Focusing polarization properties of the lens illuminated by linearly polarized state, are calculated and analyzed also. The numerical results show that both the DPL and the FZP produce asymmetrical focal spot distributions with a low f-number. To the FZP, the full-width at half-maximum (FWHM) varies from 256 nm (along y-axis) to 516 nm(along x-axis) and to the DPL, the FWHM varies from 256 nm(along y-axis) to 580 nm(along x-axis), respectively. But for a high f-number, the asymmetrical performance of the focal spot will be reduced due to complicated electromagnetical field interferences and micro waveguide effect. Otherwise, the DPL can get a higher depolarization effect than the FZP does.     

Electrical beam steering with metal-anisotropic-metal structure

In this numerical study, we present and demonstrate a compact, electrical plasmonic beam-steering device composed of anisotropic material. The splitting angle can be modulated by the external electric or magnetic field. The physical principle of this phenomenon is evaluated from the phase of surface plasmon polaritons and Fabry-Perot (F-P) resonance in slits. Our numerical simulations with finite-difference time-domain (FDTD) technique reveals that wide-angle (±27°) beam steering can be achieved. Moreover, the efficiency increases when increasing the steering angle. A special characteristic of the presented structure gives an opportunity to be used as an efficient element in a high integrated optical device for miniaturization and tuning purposes.     

Semianalytical theory of focusing synchrotron radiation by an arbitrary system of parabolic refracting lenses and the problem of nano-focusing

It has been shown that an arbitrary system of parabolic refracting lenses does not change the shape of the Gaussian wave function of a synchrotron radiation beam. Only three parameters of the wave function change, for which the recurrent formulas are derived. These formulas allow one to perform quickly and accurately the calculation of optical properties of an arbitrary system of lenses. The parameters of the radiation beam calculated by the developed method have been compared to the results of the theory of continuously refracting lens. It has been shown that both approaches give surprisingly close values. The problem of focusing the beam to a nanometer size is discussed. A two-lens system has been proposed, which can provide a five-fold increase in the number of photons inside the focus, although we failed to decrease the beam size.