（3＋1）-dimensional nonlinear propagation equation for ultrashort pulsed beam in left-handed material

In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evolving-wave approximation, a generalized （3＋1）-dimensional wave equation first order in the propagation coordinate and suitable for both right-handed material （I~HM） and left-handed material （LHM） is derived. By the commonly used Drude dispersive model for LHM, a （3＋1）-dimensional nonlinear Schrodinger equation describing ultrashort pulsed beam propagation in LHM is obtained, and its difference from that for conventional RHM is discussed. Particularly, the self-steeping effect of ultrashort pulse is found to be anomalous in LHM.     

Focusing and phase compensation of paraxial beams by a left-handed material slab

On the basis of angular spectrum representation, a formalism describing paraxial beams propagating through an isotropic left-handed material (LHM) slab is presented. The treatment allows us to introduce the ideas of beam focusing and phase compensation by LHM slab. Because of the negative refractive index of LHM slab, the inverse Gouy phase shift and the negative Rayleigh length of paraxial Gaussian beam are proposed. It is shown that the phase difference caused by the Gouy phase shift in right-handed material (RHM) can be compensated by that caused by the inverse Gouy phase shift in LHM. If certain matching conditions are satisfied, the intensity and phase distributions at object plane can be completely reconstructed at the image plane.     

Propagation properties of the chirped Airy vortex beams through left-handed and right-handed material slabs

We present an investigation on the propagation properties of the chirped Airy vortex(CAi V) beams through slabs of left-handed materials(LHMs) and right-handed materials(RHMs). We discuss the influence of chirped parameter C on the propagation of the CAi V beams through LHM and RHM slabs. Our simulation results show that a maximum accelerated velocity appears during the propagation process. The intensity concentration of the CAi V beams increases with the absolute value of the chirped parameter. The peak intensity of the CAi V beams changes abruptly, and the chirped parameter plays an active role on the difference of the maximum and the minimum. In the energy flow, we find that the effects of the chirped parameter on the strength of the vortex are different at different propagation distances.     

A compact polarization splitter utilizing directional coupler with left-handed material

A compact polarization splitter (PS) with left-handed material (LHM) sandwiched between two right-handed material (RHM) waveguides of a directional coupler (DC) is proposed. Its operation is by setting the coupling length of TM polarization be half that of TE polarization. Theoretic analysis exhibits that the PS with a very small size of 138.4 μm × 18.6 μm can be realized due to the inclusion of LHM even when the RHM with small birefringence is used.     

ABCD matrix formalism for propagation of Gaussian beam through left-handed material slab system

We apply a simple ABCD matrix formalism to investigate beam propagation in left-handed material (LHM) slab systems. Firstly, we derive the expressions for the matrix elements for a single LHM slab. Based on the ABCD matrix, we obtain the field distributions both inside and outside the LHM slab, and the conditions for focusing and phase compensation of the Gaussian beam. Secondly, the derived ABCD law is applied to analyze the propagation properties of Gaussian beams through various cascaded LHM slab systems. The corresponding focusing and phase compensation conditions of the Gaussian beam are also obtained. Our theoretic formalism may be applied as a compact and effective tool for the research of light beam propagation in complex LHM slab systems, since it avoids the complicated integral operation.     

左手介质椭圆光波导基模传播特性

在椭圆柱坐标系中，采用分离变量方法，得出了左手介质椭圆光波导本征方程的近似解，通过数值计算，分析了椭圆波导偏心率、左手介质的电容率、磁导率对椭圆光波导基模传播特性的影响，并将左介质光波导与右手介质光波导基模特性进行对比，得出左手介质光波导的基模特性与右手介质光波导基模特性差别不大的结论.     

非线性左右手媒质界面的Goos-Hänchen位移

 由均匀平面电磁波在左右手媒质界面满足的切向边界条件出发,推导了电磁波由线性传统媒质入射到非线性左手媒质时波的传播特性。利用时间延迟的方法,给出全反射情况下媒质界面非线性Goos-Hänchen位移表达式。分析了非线性左手媒质界面的侧向位移随入射角及入射波电场强度的变化关系,发现入射波场强对传输特性起决定作用:当入射波电场小于临界场强时,调节入射场强可以控制相应的侧向位移;当入射波电场大于临界场强时,不再满足全反射条件,部分入射波透射到非线性介质中。波导中加入非线性介质不仅可以调节侧向位移的大小,且可以实现对入射波场强的控制。     

左手介质矩形波导的吸收特性

采用微扰法研究了左手介质矩形波导的吸收特性。由于色散方程的限制,左手介质波导不能传输基模,它的吸收特性也与右手介质矩形波导明显不同。结果发现, 模式的衰减系数随长宽比(a/b)的增加而减小,而在右手介质波导中结果恰恰相反。除此之外,当不同模式的光波在同一左手介质矩形波导中传输时,每一模式都对应着相邻很近的吸收峰和吸收谷。同时高阶模的衰减系数较低阶模的大。但是,当不同模式的光波在同一右手介质矩形波导中传输时,它们的衰减曲线随着波导宽度的增加而振荡的变化,并且趋近于芯层衰减系数。另外一方面,在右手波导中,高阶模式的衰减系数较低阶模式小。     

附加球面相位引致Airy光束在单轴晶体传输时的两次镜像演化

利用单轴晶体光束传输理论,求得了具有附加球面相位Airy光束在单轴晶体中的传输公式.数值模拟计算结果表明,线偏振附加球面相位Airy光束在晶体中传输时仍为线偏振,但不是传输不变的.粗略地讲,具有附加球面相位的Airy光束在晶体中传输时,近场是传输不变的;而在由晶体寻常与非寻常折射率和球面半径共同确定的两个特定传输距离处,传输光束转换成了取向不同的Gaussian-Airy光束,且高斯依赖的束宽度敏感地与截断因子相关;而当光束依次穿过此两位置时光斑花样先后相对于两横向轴平面做镜像演化,且镜像演化顺序也与晶体寻常和非寻常折射率相对大小密切相关,其总的效果是远场强度花样能恢复原样但花样取向产生了关于对过横平面二、四象限平分平面的镜像演化.这些结果表明,通过恰当选择晶体材料(即折射率)和附加球面相位的半径R,可以调控光束花样的形状、取向及表征各向异性材料的相关性质.     

Numerical analysis of propagation characteristics of electromagnetic wave in lossy left-handed material media

The propagation characteristics of electromagnetic wave in lossy left-handed materials (LHM) are studied using finite-difference time-domain (FDTD) method base on auxiliary differential equation (ADE) technology. The LHM medium is realized with lossy Drude models for both the negative electric permittivity and the negative magnetic permeability. The discretized ADE-FDTD equations are derived in detail. The incident wave used in the simulation is a multiple cycle m-n-m pulses source. The term of Poynting's vector E_xH_y was calculated. These numerical results demonstrate conclusively that the phase velocity direction of electromagnetic wave propagation and the direction of the Poynting vectors are anti-parallel in LHM. The amplitude of electric field is reduced with the enhancive distance of LHM slab. It is also demonstrated that the energy of electromagnetic wave in the LHM slab is obviously attenuated, and the attenuation of energy becomes stronger with the angular plasma frequency ω_p increasing. These results indicate that LHM stealth is effective in theory, and reasonable selection of the large negative index of refraction can greatly enhance its effectiveness.     

Propagation and modulation of Airy beams through a four-level electromagnetic induced transparency atomic vapor

We study the propagation properties of an Airy beam through a four-level electromagnetic induced transparency (EIT) atomic vapor. The analytical expression for the Airy beam passing through the ABCD optical system of the EIT vapor is deduced and employed to analyze the propagation characteristics of the beam. It is shown that both the deflection position and the intensity of the Airy beam can be modulated by the Rabi frequency of the control light. Such a tunable optical behavior may have some potential applications in medicine science.     

The influence on atomic decay by inserting a LHM layer into an ordinary one dimensional multi-layer structure

Inserting left-handed material (LHM) layers into a one dimensional structure can influence the spontaneous emission (SpE) of a two-level atom. This has been investigated, starting from the simplest case of a three-layer system, where we find the reflected field (atom can “see”) passing through LHM layer is stronger than that through the corresponding normal layer. Indeed the induced decay is more strongly influenced by reflected field passing through LHM layer. Based on this and after further analysis of reflectivity, we find that, a quarter photonic crystal (PC) composed of alternately LHM and RHM can inhibit the atomic spontaneous emission more intensely compared to an ordinary PC.     

关于左手性介质几何光学的研究（一）

根据几何光学中的费马原理和完善成像原理研究了光线经过正负折射率界面时的传播特性，推导了单负折射率完善成像的曲面方程，讨论了单块负折射率透镜成像特性的一些缺陷及改进方案，依此指出了最短时间原理的适用范围的局限性和利用左手性介质制作光学器件的优越性，为进一步研究左手性介质的光学特性和相关光学器件设计提供了理论基础.     

A Non-Energy-Concentrating Lens Using Left-Handed Material

In a planar lens made of left-handed material (LHM), the rays converge to a focal point in the material and once again in free space. The problems exhibited by the planar lens are its great thickness, the long optical path length, and energy concentration in the LHM. We examine a bowl-shaped LHM lens with an index n = −1. In this lens, the back is a concave hemispherical surface and the rays never converge in the LHM, but in free space only. We also designed a quantized bowl-shaped LHM lens composed of multiple layers of thin LHM plates of uniform thickness. A bowl-shaped LHM lens quantized with more than 4 bits has a lens function similar to that of a smooth curved lens. The bowl-shaped lens is characterized by its thinness, its short optical path length, and the absence of energy concentration in the LHM. Furthermore, the quantized bowl-shaped LHM lens can be fabricated. Wave propagation through these lenses is numerically simulated using the finite difference time domain (FDTD) method.     

Spatiotemporal airy light bullets in the linear and nonlinear regimes

We demonstrate the realization of intense Airy-Airy-Airy (Airy(3)) light bullets by combining a spatial Airy beam with an Airy pulse in time. The Airy(3) light bullets belong to a family of linear spatiotemporal wave packets that do not require any specific tuning of the material optical properties for their formation and withstand both diffraction and dispersion during their propagation. We show that the Airy(3) light bullets are robust up to the high intensity regime, since they are capable of healing the nonlinearly induced distortions of their spatiotemporal profile.     

关于左手性介质几何光学的研究（二）

利用几何光学方法研究了由左手性介质制成的简单透镜的光学特性.推理分析了左手性介质透镜处球形界面的负折射规律，并依此表明了常用光学公式仍适用于左手性介质.指出了左手性介质透镜相对于用传统介质制作的普通透镜所具备的固有优点，最后证实了利用单块左手性介质透镜即可完全消球差，并相应提供了零球差左手性介质透镜的设计实例.     

基于非分裂FDTD的左手介质电磁特性的研究

为验证左手介质的电磁特性,采用非分裂时域有限差分方法对左手介质的Drude模型进行建模.这种方法不需要对电场和磁场进行分裂,也不需要对PML空间进行特殊处理,吸收边界PML和工作空间可以通过参数转换来完成,并且构造的PML层为有耗介质,进入PML层的透射波将迅速衰减.它是一种准确而有效的分析色散和各向异性介质的方法,通过此方法有效地验证了左手介质的负折射效应、汇聚效应、相位补偿效应,充分验证了左手介质及其反常特性的存在性和此方法分析左手介质的有效性. 关键词： 左手介质 非分裂 时域有限差分 Drude     

非线性左手材料的时域研究

 分析了非线性左手材料模型，推导了非线性左手材料中的时域有限差分法及完美匹配层的计算式。数值模拟了具有Kerr非线性效应的左手材料平板中的电磁波。观察到该材料同样具有电磁聚焦特性。对比线性左手材料，其聚焦点的幅度和位置都会发生偏移。同时改变波源的强度及其到平板边界距离，讨论了不同距离情况下该非线性左手材料平板对电磁波分布的影响。当波源距离材料平板足够远，通过非线性左手材料聚焦的电场强度几乎集中在其外表面。     

Generating mechanism of the energy-stream loops for the evanescent waves in a left-handed material slab

The generating mechanism of the energy-stream loops (ESLs) for the evanescent waves around the interfaces of a left-handed material (LHM) slab has been investigated with a finite-difference time-domain (FDTD) method. The simulations have shown that these ESLs originate from standing waves, attributed to the intervention of counter-propagating evanescent waves. Large numbers of ESLs can appear because of the numerous values of wave vectors k_y. The larger ESLs die out more quickly than the smaller ones in time after the source is switched off, the ESLs shrink continuously with increasing delay, and the oscillated distributions of the evanescent waves between the surfaces can also be validated. It is greatly helpful for the further comprehension on energy fluxes of evanescent waves in the LHM slab.     

Persistence and breakdown of Airy beams driven by an initial nonlinearity

We study the behavior of Airy beams propagating from a nonlinear medium to a linear medium. We show that an Airy beam initially driven by a self-defocusing nonlinearity experiences anomalous diffraction and can maintain its shape in subsequent propagation, but its intensity pattern and acceleration cannot persist when driven by a self-focusing nonlinearity. The unusual behavior of Airy beams is examined from their energy flow as well as the Brillouin zone spectrum of self-induced chirped photonic lattices.