Metasurface-based circular polarizer with a controllable phase and its application in holographic imaging.

A diatomic circular polarizer based on a single-layered metasurface is proposed. This metasurface circular polarizer carries the controllable phase besides the desired circular dichroism, which is different from the existing circular polarizers. The diatoms contain two nanoholes equivalent to half-wave plates with a specified cross angle and a fixed phase difference. The alternative circular polarization transmission of this circular polarizer depends on the relative angular position of diatoms, and the controllable phase of this circular polarizer can be adjusted through rotating nanoholes. The generation of the optical vortex and holographic imaging verifies the polarization and phase manipulation of the diatomic circular polarizer. The numerical simulations and the experimental measurement give the powerful verification. Simple design, compact structure, and poly-functionality enable the wide applications of circular polarizer in integrated and polarized optics.

Correction: Lu et al. Performance Analysis of Metalenses Based on Three Kinds of Phase Compensation Techniques. Nanomaterials 2021, 11, 2091.

There was an error in the original publication [...].

Versatile Integrated Polarizers Based on Geometric Metasurfaces.

We propose versatile integrated polarizers based on geometric metasurfaces. Metasurface polarizer consists of an L-shaped hole array etched on a silver film, and it can simultaneously generate several polarization states, including linear polarization, circular polarization, elliptical polarization, or even hybrid polarization. Meanwhile, the combination of output polarization states changes with the illumination polarization type. The theoretical analysis provides a detailed explanation for the generation of the integrated polarization states. The well-designed metasurface polarizers may generate more complex polarization modes, including vector beams and vector vortex beams. The theoretical and simulated results confirm the polarization performance of the proposed integrated metasurface polarizers. The compact design of metasurface polarizers and the controllable generation of versatile polarization combinations are a benefit to the applications of polarization light in optical imaging, biomedical sensing, and material processing.

Performance Analysis of Metalenses Based on Three Kinds of Phase Compensation Techniques.

The phase delays introduced by anisotropic nanounits include propagation phase delay, resonant phase delay and geometric phase delay. Various phase devices can be formed based on the metasurfaces consisting of anisotropic nanounits and the phase devices of the same kind function have different performances because of different working modes. In this paper, metalenses and vortex metalenses are chosen as examples to compare the optical performance of metasurface phase devices based on three kinds of phase compensation techniques. We design separately three kinds of metalenses and vortex metalenses using the cross nanoholes, L-shaped nanohole and V-shaped nanoholes and simulate numerically their intensity and phase distributions. Additionally, the results show the differences among these elements in structure complexity, polarization dependence, working efficiency and phase uniformity. The comparison for three kinds of metalenses clearly shows the merits of different phase compensation techniques and this work must be helpful for expanding the practical applications of metasurfaces.

Metasurface circular polarizer based on rotational symmetric nanoholes.

A circular polarizer is proposed based on a single layered metasurface. This metasurface circular polarizer is composed of L-shaped nanoholes etched on the silver film. The L-shaped nanoholes are rotational symmetric, and the special symmetric structure determines the polarization selection transmission of the metasurface. The theoretical analysis elaborates the design process of the metasurface circular polarizer. The proposed metasurface circular polarizers have good polarization selective transmittance, and more interestingly, they take on the opposite circular dichroism at different wavebands. The numerical simulations and experiment measurement confirm the circular dichroism of the proposed circular polarizers. The compact design, ultrathin thickness and available performance can expand the applications of the metasurface circular polarizers in the integrated optics.

Uniform theory of plasmonic vortex generation based on nanoholes.

In view of the wide applications of plasmonic vortices, a uniform theory of plasmonic vortex generation is advanced based on a metasurface consisting of nanometric rectangular holes. Rectangular holes may be located on one circle, two concentric circles, one spiral or two parallel spirals. The key problem in generating the plasmonic vortex is to construct a spiral phase, which can be excited by single or double holes. Theoretical analysis for generation of the plasmonic vortex is implemented in terms of the radiation model of dipoles and the propagation rule of surface plasmon polaritons. Several practical examples are presented and theoretical predictions are verified by the generated plasmonic vortices. The proposed theory is of benefit to the design of plasmonic vortex generators and the applications of plasmonic vortices.

α spiral nanoslit and the higher order plasmonic vortex generation.

In view of the conciseness of a spiral nanoslit and the limited order of the generated vortex, a kind of nanometer spiral, named α spirals, is proposed to generate a higher order plasmonic vortex. Theoretical analysis provides the basis for the advancement of an α spiral. The proposed spiral can generate the plasmonic vortex and the extreme order of the generated vortex depends on parameter α. The numerical simulations express the valid region of the plasmonic vortex generated by the α spiral. Discussions about the validity range of the α spiral nanoslit and the influence of the film material are beneficial to generate a high order vortex. This work builds a platform for the generation of the higher order plasmonic vortex using the simple spiral nanostructure and it can extend the potential applications of higher order plasmonic vortices.

Polarization controllable plasmonic focusing based on nanometer holes.

Two kinds of plasmonic lenses are proposed based on phase compensation. Each kind of plasmonic lens is comprised of four sets of nanohole arrays, and two sets of face-to-face nanohole arrays are planar symmetric. The adjustment of separation and the rotation angle of holes compensates, respectively, for the phase difference of the surface plasmon polaritons reaching to the focal spot. The different design principles make the proposed plasmonic lenses show the different polarization dependence focusing. Two or four foci of the first kind of plasmonic lens and two controllable foci focusing of the second kind of plasmonic lens can be utilized as optical switch and logic judgment. Theoretic analysis, numerical calculations and experiment measurement verify the focusing performance of our proposed plasmonic lenses. The focusing functionality and versatility of our proposed structures are helpful for extending the applications of plasmonic lenses in integrated optics.

Metalens based on constructive interference.

A metalens consisting of nanometer rectangular holes etched on silver film is proposed, and the focusing effect is actualized in the visible region. The rectangular holes are arranged on concentric circles, and the fields excited by these holes constructively interfere due to having the same propagation phase. The propagation phase is obtained by optimizing the sizes of the rectangular holes and the radii of the circles. This metalens can focus linearly or circularly polarized light, and numerical simulations and experimental measurement confirm its focusing performance. The proposed metalens has the advantages of flexible design, loose constraint to incident polarization, low-cost equipment, and simpler experimental operation, and we believe it will be useful to applications in optical integration and visible light imaging.

Multifocal metalens with a controllable intensity ratio.

A multifocal metalens is proposed based on the optical metasurface consisting of subwavelength gratings etched on silver film. The larger transmission of grating makes the proposed metalens have high focusing efficiency, and the exquisite design of the metasurface enables the metalens to focus the light at multiple spots with the controllable intensity ratio. The intensity ratio of focal spots is controlled by adjusting grating structures. The numerical simulations give the good presentation, and the experiment measurement provides the favorable verification for the performance of the proposed multifocal metalens in light focusing and beam splitting. The advantages of the multifocal metalens, including simple design, compact structure, high efficiency, and the controllable focusing, are a benefit to its applications in optical integration and micromanipulation.

Generation of vector beams using spatial variation nanoslits with linearly polarized light illumination.

Vector beams (VBs) that possess nonuniform polarization distributions in space have various applications. In view of the utilization of the circularly polarized light in generating VBs based on the metallic structures, this paper proposes an approach to generate VBs using metallic nanoslits with linearly polarized light illumination. These nanoslits are located on two concentric circular orbits, and the nanoslits on the inner circle are perpendicular to the ones in the outer circle. The linearly polarized light is effectively changed into the rotational symmetric VBs by rotating these orthogonal nanoslits, and the polarization order of the VBs can be adjusted by changing the rotation angles of nanoslits. The detailed theoretical analysis provides the basis for the conversion from the linearly polarized light to the VBs. Numerical simulations and experimental measurement demonstrate the performance of VB generators. This paper's proposed method has advantages that include ultrathin and compact structure, convenient operation and immediate conversion from linear polarization to VBs, and easier expansion of VB applications.

Fresnel diffraction of fractal grating and self-imaging effect.

Based on the self-similarity property of fractal, two types of fractal gratings are produced according to the production and addition operations of multiple periodic gratings. Fresnel diffractions of fractal grating are analyzed theoretically, and the general mathematic expressions of the diffraction intensity distributions of fractal grating are deduced. The gray-scale patterns of the 2D diffraction distributions of fractal grating are provided through numerical calculations. The diffraction patterns take on the periodicity along the longitude and transverse directions. The 1D diffraction distribution at some certain distances shows the same structure as the fractal grating. This indicates that the self-image of fractal grating is really formed in the Fresnel diffraction region. The experimental measurement of the diffraction intensity distribution of fractal grating with different fractal dimensions and different fractal levels is performed, and the self-images of fractal grating are obtained successfully in experiments. The conclusions of this paper are helpful for the development of the application of fractal grating.

Near-field interference of slit doublet.

We study the physical mechanism of near-field interference of slit doublet and explore the distinctive phenomena in near-field interference of slit doublet. The average electric field and average energy-flow density are chosen to describe the near-field distribution rules of the electromagnetic field. The numerical calculations for near-field interference of slit doublet under different illumination conditions are performed according to the finite-difference time-domain method, and the distinctive characteristics of the near-field interference of slit doublet are provided. They include the polarization dependence, the distortion of fringes, and the bifurcation of the fringes. These characteristics are completely different from those of the far-field interference. With the aid of the interference of two slits and of slit and groove, the physical mechanism of polarization dependence of near-field interference is investigated. The fringe distortion of the electric field and the fringe bifurcation of the energy-flow density reflect the amplitude and phase variations of the electromagnetic field. The influences of the slit parameters and the base material on the near-field interference of slit doublet are also discussed. These results may provide us with new insights into the underlying physics of interaction between complex nanostructures and electromagnetic waves.

Talbot effect of quasi-periodic grating.

Theoretic and experimental studies of the Talbot effect of quasi-periodic gratings are performed in this paper. The diffractions of periodic and quasi-periodic square aperture arrays in Fresnel fields are analyzed according to the scalar diffraction theory. The expressions of the diffraction intensities of two types of quasi-periodic gratings are deduced. Talbot images of the quasi-periodic gratings are predicted to appear at multiple certain distances. The quasi-periodic square aperture arrays are produced with the aid of a liquid crystal light modulator, and the self-images of the quasi-periodic gratings are measured successfully in the experiment. This study indicates that even a structure in short-range disorder may take on the self-imaging effect in a Fresnel field.

Evolutions of speckles on rough glass/silver surfaces with film thickness.

This paper reports experimental studies on speckles produced by the rough silver films. The speckles on the rough glass/silver surfaces are measured with a microscopic imaging system. The structures of speckle patterns have the characteristics of fractals and multi-scaled sizes. We find that with the increase of the silver film thickness, the contrast of the speckles increases, and the intensity probability density functions gradually transit to exponential decay. We calculate the global and the local correlation functions of the speckle patterns, and find that both the fractal exponent and correlation length of the small-sized speckles decrease with the thickness of the silver films. We use the mechanisms of rough dielectric interface scattering and random surface plasmon waves to give the preliminary explanations for the evolutions of the speckles.

Polarization dependence of the quasi-Talbot effect of the high-density grating.

Diffractions by the one-dimensional high-density grating in the near field with TM and TE polarization illuminations are studied, and the diffraction intensity distributions are calculated with the finite-difference time-domain technique. The calculation results show that the diffractions of the high-density grating with different polarization illuminations are different. The quasi-Talbot image of the grating depends on the polarization of the incident wave, and the existence condition of the quasi-Talbot image of the grating in the near field also changes with the polarization of the incident wave. We present explanations based on the vector distribution of the energy flow density. These studies on the polarization dependence of the quasi-Talbot imaging of the high-density grating are helpful for the application of the grating to near-field photolithography.

Optical scattering analysis of the diffraction distortion of a two-dimensional reflection grating.

Theoretical and experimental studies of the diffraction of a two-dimensional reflection grating are performed in this paper. Based on the theory of optical scattering, the light field in the Fraunhofer diffraction region is deduced, and the general expression of the diffraction field is given in the form of the wave vectors of the diffracted wave and the incident wave. Then the coordinate of the diffraction order is obtained. The calculation results show that the diffraction distortion of the grating appears when the grating is illuminated by the oblique incident light wave and the distortion is restricted on the diffraction of the grids varying along the direction perpendicular to the plane of incidence. The orbit equation satisfied by the distortion diffraction orders is presented. The experimental results verify adequately this diffraction distortion rule of the grating, and they agree very well with the theoretical results.

Quasi-Talbot effect of the high-density grating in near field.

On the basis of the finite-difference time-domain technique, the diffraction of the high-density grating in the near field is developed, and the gray-scale pattern of the diffraction intensity distribution of a one-dimensional grating is presented. A detailed analysis shows that the near-field diffraction of the grating is the result of the diffraction of a single slit, the interference of two evanescent waves from neighboring slits, and the interference of the homogeneous waves from the slits. Through many numerical calculations, the condition for obtaining the quasi-Talbot imaging of the grating in the near field is explored, i.e., the period of the grating d is larger than the incident wavelength lambda but smaller than 4lambda. The influence of the opening ratio of the grating on the quasi-Talbot imaging of the grating in the near field is also discussed. This study of the near-field diffraction of the high-density grating may be helpful for understanding the diffraction characteristics of subwavelength structures, and the quasi-Talbot imaging of the high-density grating will contribute to the application of the grating in near-field photolithography.

Diffraction of a one-dimensional phase grating in the deep Fresnel field.

We analyze theoretically the diffraction of phase gratings in the deep Fresnel field on the basis of the theory of scalar diffraction and Green's theorem and present the general formula for the diffraction intensity of a one-dimensional sinusoidal phase grating. The numerical calculations show that in the deep Fresnel region the diffraction distribution can be described by designating three characteristic regions that are influenced by the parameters of the grating. The microlensing effect of the interface of the phase grating provides the corresponding explanation. Moreover, according to the viewpoint that the diffraction intensity distribution is the result of the interference of the diffraction orders of the grating, we find that the diffraction patterns, depending on the carved depth of the phase grating, are determined by the contributing diffraction orders, their relative power, and the quasi-Talbot effect of the phase grating, which results from the second meeting of the diffraction orders carrying most of the power of the total field, as in the case of the amplitude grating.

Quasi-Talbot effect of a grating in the deep Fresnel diffraction region.

Based on the theory of scalar diffraction, the diffraction of gratings in the deep Fresnel diffraction region is developed, and the general formula of the diffraction intensity of the one-dimensional grating is presented by using the Hankel function. Through numerical calculations, some interesting diffraction phenomena are found. In the deep Fresnel diffraction region, the dominant effects, with increasing propagation distance from the grating, are, in order, the geometrical effect, the quasi-geometrical effect, and the interference and diffraction effects. Furthermore, the diffraction intensities vary periodically in the diffraction effect region with increasing propagation distance. Quasi-Talbot imaging of the grating exists in the interference and diffraction regions, and the intensity distributions most similar to the structure of the grating are not at the exact Talbot distances. These phenomena in the deep Fresnel diffraction region are distinct from those in the Fresnel diffraction region. The formation origin of quasi-Talbot imaging of the grating is also discussed, and the numerical calculations powerfully verify the theoretical results.