Wavelength dependence of focusing properties of two-dimensional photonic quasicrystal flat lens

We investigated the wavelength dependence of the focusing properties of a germanium-cylinder-based two-dimensional (2D) decagonal Penrose-type photonic quasicrystal (PQC) flat lens for the first time, to the best of our knowledge. We found that near the second bandgap and in the high-frequency side (between the bandgap boundary and the first light intensity peak) of the pass band, the flat lens can exhibit a focusing effect for a point light source and that the focusing wavelengths can directly be drawn from the photonic band structure. For all the focusing wavelengths, the summation of the object distance and the image distance is less than the thickness of the flat lens when the object distance is half the thickness of the flat lens. As the wavelength increases, the image distance, the image quality, and the effective refractive index of the flat lens increase, whereas the image power of the point light source decreases. The effective refractive index of the flat lens is less than -1.     

Flat acoustic lens by acoustic grating with curled slits

We design a flat sub-wavelength lens that can focus acoustic wave. We analytically study the transmission through an acoustic grating with curled slits, which can serve as a material with tunable impedance and refractive index for acoustic waves. The effective parameters rely on the geometry of the slits and are independent of frequency. A flat acoustic focusing lens by such acoustic grating with gradient effective refractive index is designed. The focusing effect is clearly observed in simulations and well predicted by the theory. We demonstrate that despite the large impedance mismatch between the acoustic lens and the matrix, the intensity at the focal point is still high due to Fabry–Perot resonance.     

On the use of NR-PC flat lens for square target detection and imaging by lens-combined scanning scheme

In the paper, target detection and imaging from refraction photonic crystal (NR-PC) slab lens is studied by the finite-difference time-domain (FDTD) method. Numerical simulation shows that, there is a transmission peak with a value far greater than unit, resulting from the mini-forbidden bands and resonance excitation at the resonance frequency of 0.3068 (a/λ). When a target is placed at the focus point (F₂) of the NR-PC lens, its image and great amplitude could be formed in the vicinity of the point source through the focusing of backscattered optical wave from the target. Further investigation demonstrates that the lens-combined scanning scheme provides higher refocusing resolution than lens-fixed and non-dynamic scanning scheme for square target detection and imaging.     

Sub-wavelength imaging with a left-handed material flat lens

We study numerically, by means of the pseudospectral time-domain method, the unique features of imaging by a flat lens made of a left-handed metamaterial that possesses the property of negative refraction. We confirm the earlier finding that a left-handed flat lens can provide near-perfect imaging of a point source and a pair of point sources with clear evidence of sub-wavelength resolution. We illustrate the limitation of the resolution in the time-integrated image due to the presence of surface waves.     

Effects of wave propagation anisotropy on the wave focusing by negative refractive sonic crystal flat lenses

<正>In this study,wave propagation anisotropy in a triangular lattice crystal structure and its associated waveform shaping in a crystal structure are investigated theoretically.A directional variation in wave velocity inside a crystal structure is shown to cause bending wave envelcpes.The authors report that a triangular lattice sonic crystal possesses six numbers of a high symmetry direction,which leads to a wave convergence caused by wave velocity anisotropy inside the crystal.However,two of them are utilized mostly in wave focusing by an acoustic flat lens.Based on wave velocity anisotropy,the pseudo ideal imaging effect obtained in the second band of the flat lens is discussed.     

Determination of the focusing power of flat lenses using the radiovisor

Focusing of electromagnetic radiation of a point source with a wavelength of 3 cm by flat negative-refraction lenses formed by a hexagonal structure of metal cylindrical rods was studied. The spatial distribution of microwave field of H polarization in the lens focal plane was recorded by a radiovisor screen which converts it into a visible image. The full width at half maximum of the focal spot distribution at optimum focusing did not exceed half the emission wavelength.     

Numerical research on properties of optical-wave target detection and imaging from NR-PC flat lens

The characteristics of optical-wave target detection and imaging from a negative-refraction photonic crystal (NR-PC) flat lens are studied with a two-dimensional (2D) finite-difference time-domain (FDTD) method in the paper. The results show that there exists a transmission peak, with a value far greater than unit, resulting from the influence of the mini-forbidden bands and resonance excitation effect at resonance frequency. Also, the refocusing of backscattered optical wave from the target leads to its image with a sub-wavelength lateral resolution and great amplitude as long as the target is placed at the focus of the NR-PC flat lens. Therefore, the NR-PC flat lens will find many implications in optical area, especially in the detection and imaging of small targets.     

X‐ray focusing by the system of refractive lens(es) placed inside asymmetric channel‐cut crystals

An X‐ray one‐dimensionally focusing system, a refracting–diffracting lens (RDL), composed of Bragg double‐asymmetric‐reflecting two‐crystal plane parallel plates and a double‐concave cylindrical parabolic lens placed in the gap between the plates is described. It is shown that the focal length of the RDL is equal to the focal distance of the separate lens multiplied by the square of the asymmetry factor. One can obtain RDLs with different focal lengths for certain applications. Using the point‐source function of dynamic diffraction, as well as the Green function in a vacuum with parabolic approximation, an expression for the double‐diffracted beam amplitude for an arbitrary incident wave is presented. Focusing of the plane incident wave and imaging of a point source are studied. The cases of non‐absorptive and absorptive lenses are discussed. The intensity distribution in the focusing plane and on the focusing line, and its dependence on wavelength, deviation from the Bragg angle and magnification is studied. Geometrical optical considerations are also given. RDLs can be applied to focus radiation from both laboratory and synchrotron X‐ray sources, for X‐ray imaging of objects, and for obtaining high‐intensity beams. RDLs can also be applied in X‐ray astronomy.     

Focusing of a Flat Left-Handed Metamaterial Lens in a Heterogeneous and Lossy Medium

For applications such as near-field target detection and tumor hyperthermia with a fiat left-handed metamaterial （LHM） lens, a microwave will be focused in the heterogeneous and lossy medium. Different from the focusing of a fiat LHM lens in vacuum as reported in most previous studies, the medium loss and heterogeneity will affect the focusing performance of the LHM lens. Numerical simulations indicate that the medium loss will degrade the focusing resolution, while the heterogeneity of random variability within ±30% will affect the focusing resolution to a limited extent. Both the loss and heterogeneity of the medium will shift the focal point away from the image plane. When focusing in a medium with different permittivity values, an LHM lens will also have different focusing resolutions due to different electric thicknesses.     

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions.     

Scatterer radius dependence of focusing properties in two-dimensional photonic quasicrystal flat lens

The focusing properties of a germanium decagonal photonic quasicrystal flat lens with different scatterer radii have been analyzed. For different wavelengths and polarization modes, the lenses have different scatterer radius thresholds resulting in different focusing properties. For a point source of light in the transverse-electric mode, we found dual-focusing occurs along the symmetry axis within a range of scattering radii. As scatterer radius increases, the dual-focusing image power and far-field-focusing image quality diminish, whereas near-field-focusing image quality, dual-focusing image distance, and the summed object-image distance all increase.     

Image resolution and the properties of optical-wave target detection and imaging by using the NR-PC flat lens

We used the method of two-dimensional (2D) finite-difference time-domain (FDTD) to study the characteristics of optical-wave target detection and imaging from negative-refraction photonic crystal (NR-PC) flat lens in the paper. The theory of image resolution was introduced. The results show that there exists a transmission peak, with a value far greater than unit, resulting from the influence of the mini-forbidden bands and resonance excitation effect at resonance frequency. And, the refocusing of backscattered optical wave from the target leads to its image with a sub-wavelength lateral resolution and great amplitude as long as the target is placed at the focus of the NR-PC flat lens. And the application of NR-PC flat lens can be extended in optical area, especially in the detection and imaging of small target.     

On the cylinder air holes of NR-PC double flats lens group with active impurities for lightwave target detection and imaging

In the paper, the influence of the cylinder air holes of negative-refraction photonic crystal (NR-PC) double flats lens group with active impurities on the performance of lightwave target detection and imaging are studied with finite-difference time-domain (FDTD) method. Firstly, we conclude the focusing imaging circuit diagram of NR-PC flat lens with the Snell extension law and geometrical optics principle. Then we use NR-PC flat lens to detect target with dynamic scanning system according to that. Numerical simulations indicate that significant enhancement of the scattering signal can be obtained due to the use of the NR-PC flat lens. We further research the influence of active impurities on target detecting by using NR-PC double flats lens group with cylinder air holes. We use NR-PC flat with active impurities instead of the perfect ones. By using dynamic scanning scheme, we find that it could improve the lateral resolution of target scanning through introducing appropriate active impurities. In conclusion, our investigation optimized the performance of the small target detection and imaging system, and provided the basis for converting an idealized LHM lens into a physically realizable NR-PC double flats lens group.     

Fourier optics approach to imaging with sub-wavelength resolution through metal-dielectric multilayers

Metal-dielectric layered stacks for imaging with sub-wavelength resolution are regarded as linear isoplanatic systems — a concept popular in Fourier optics and in scalar diffraction theory. In this context, a layered flat lens is a one-dimensional spatial filter characterised by the point spread function. However, depending on the model of the source, the definition of the point spread function for multilayers with sub-wavelength resolution may be formulated in several ways. Here, a distinction is made between a soft source and hard electric or magnetic sources. Each of these definitions leads to a different meaning of perfect imaging. It is shown that some simple interpretations of the PSF, such as the relation of its width to the resolution of the imaging system are ambiguous for the multilayers with sub-wavelenth resolution. These differences must be observed in point spread function engineering of layered systems with sub-wavelength sized PSF.     

Negative refractive behavior of a two-dimensional negative-index photonic crystals using a wave vector diagram method

We have theoretically studied the negative refractive behavior and the focusing effect in a two-dimensional square-lattice photonic crystal made of air rods in a dielectric background. Detailed explanations are given for the effect of the negative refraction, and the imaging of the plano-concave lens is shown by the use of a wave vector diagram formalism. The typical negative refractive behavior is demonstrated by considering the Bloch mode with the wave vector inside the first Brillouin zone, because only those wave vectors inside the first Brillouin zone of multiple Brillouin zones have a definite meaning. The single propagating beam is analyzed by the use of the wave vector diagram formalism following the folding of the wave vectors. Good-quality focusing of a plane wave can be realized by using a photonic crystal plano-concave lens, while a plane wave is formed by a point source placed at the focal point. Our results are in good agreement with the experimental ones shown for a negative-index plano-concave lens by Vodo et al. [Appl. Phys. Lett. 86 (2005) 201108]. Finally, we also have shown the focusing behavior of a plane wave and a Gaussian pulse by a plano-concave lens structure with high-index modulation instead of air in the concave region.     

Negative Refraction and Near-Field Imaging of an Elliptical-Rod Photonic Crystal Slab in the Second Band

Negative refraction and imaging properties of the electromagnetic wave through a two-dimensional photonic crystal （PC） slab, which consists of a square lattice of elliptical dielectric rods immersed in the air background, is studied by the plane-wave expansion method and the finite-difference time-domain method. A point source placed in the vicinity of the PC slab can form a good-quality image spot through the PC slab for the incident frequencies within the second photonic band. The calculated result also shows that negative refraction occurs in this kind of PC slab.     

All angle negative refraction with the effective phase index of-1

We theoretically studied a left-hand structure based on a two-dimensional (2D) photonic crystal (PC)with a negative refractive index. The propagation of electromagnetic waves in the proposed PC structure is investigated through dispersion characteristic analysis and numerical simulation of field pattern. The designed PC structure can exhibit all angle negative refraction, and the corresponding effective refractive indices along all directions are almost same and close to the ideal value of -1. A flat lens formed from such a PC has been designed and its imaging properties have been investigated systematically.     

Theoretical demonstration of the hybrid focusing points of sonic crystal flat lenses and possible applications

We demonstrate the hybrid focusing points of sonic crystals for a multi-source array applied to flat sonic crystal lenses. The contributions of different point source couples form hybrid focusing points. Ray-trace analyses are conducted for acoustic flat lenses with multi-source configurations. The finite-difference time-domain (FDTD) simulation of flat lenses with multi-source configurations demonstrates the establishment of pure and hybrid focusing points in a pyramidal constellation. The number of focusing points in the pyramidal constellation depends on the number of point sources. We propose an acoustic device for fine-tuning the location of a far-field hybrid focusing point and discuss its benefits for acoustic energy focusing application.     

对光声成像系统中声透镜的二元声学研究

基于二元声学的方法提出了一种折射／衍射混合声透镜设计方案,该声透镜在对光声信号进行二维成像时体现出了极大的优越性,与单声透镜相比,除了有实时成像、成像焦深较大且可以利用时间分辨技术实现层析成像的优点外,还可以利用二元声学透镜独特的色散特性校正单声透镜的轴向色差,可以极大提高成像的分辨力。通过计算机模拟了有一定带宽的点声源通过该声透镜像面上的点扩展函数,与经单声透镜的结果比较,可以看出点扩展函数弥散斑得到明显改善,极大地消除色差对成像质量的影响。     

单层超薄高效圆极化超表面透镜

针对超表面在透镜方面的应用, 本文设计了一种交叉极化透射聚焦超表面, 实现了将圆极化波转化为交叉极化波的同时聚焦电磁波的功能. 设计了一款旋转型单元, 单元为一层且厚度仅为1.5 mm, 分析了旋转型单元提供不同相移的原理并设计了相邻单元相移差为60°的相位梯度超表面, 在中心频率f=15 GHz附近发生奇异折射, 折射角与理论计算结果一致, 验证了设计单元的有效性, 基于该单元设计了尺寸为90 m mm×90 mm、单元数为15×15 的透射型聚焦超表面, 在中心频率f=15 GHz附近, 左旋圆极化平面波照射时, 透射波聚焦于L=40 mm 的实焦点且透射波为照射波的交叉极化波. 该超表面透镜效率高、厚度薄且为单层, 易于加工, 相对于传统透镜, 优势明显, 在操控电磁波、改善透镜性能方面有潜在应用价值.