Negative refraction and left-handed electromagnetism in microwave photonic crystals

We demonstrate the negative refraction of microwaves in a metallic photonic crystal prism. The spectral response of the photonic crystal prism, which manifests both positive and negative refraction, is in complete agreement with band-structure calculations and numerical simulations. The validity of Snell's law with a negative refractive index is confirmed experimentally and theoretically. The negative refraction observed corresponds to left-handed electromagnetism that arises due to the dispersion characteristics of waves in a periodic medium. This mechanism for negative refraction is different from that in metamaterials.     

Some remarks regarding electrodynamics of materials with negative refraction

In the following article some electrodynamical problems of materials with negative refraction are considered. In contrast to the usual case when the index of refraction is positive, for these sorts of materials many laws and equations must be recorded differently. Special note is taken of the fact that most of the books and textbooks are written with the so-called “nonmagnetic approach”, which is only valid for nonmagnetic materials (μ = 1). This approach is undoubtedly unfit for material with a negative index of refraction.It is shown that materials with simultaneously negative dielectric and magnetic permeabilities undoubtedly must possess the frequency dispersion. Correlation is brought between phase and group velocities for these sorts of materials.The question is considered in detail about the so-called “overcoming of the diffraction limit” by means of plates from materials with a negative factor of refraction. It is shown that this effect is indeed reduced to the problem of matching between source and receiver of radiation. Such matching is possible by spreading the so-called evanescent modes, for which a diffraction limit does not exist. These modes fade within a distance of the order of the wavelength, and only at such a distance is the transfer of picture details that are smaller than the wavelength possible.     

含负折射率材料的一维光子晶体的光学传输特性

采用光学传输矩阵方法,模拟研究了由正折射率材料和负折射率材料交替组成的一维光子晶体的光学传输特性.计算了这种含负折射率材料的一维光子晶体的透射谱和色散关系.结果表明,在正入射时,含负折射率材料的光子晶体的带隙要比传统的光子晶体要大得多,并具有狭窄的透射带,从光学薄膜理论的色散关系出发解释了形成上述现象的原因.讨论了在不同的偏振模式下,光以中心波长入射时,反射率随着入射角度的变化关系.发现含负折射率材料的一维光子晶体具有更好的角度特性,可以用来实现对中心波长的全方位反射.     

Experimental verification of negative refraction in a double cross metamaterial

We report on microwave experiments with a metamaterial composed of pairs of metallic crosses. The transmission properties of the structure show a left-handed transmission band at frequencies around 10.2 GHz. The validity of the negative effective index of refraction is verified by a Snell’s law refraction experiment performed on a wedge-shaped sample of the metamaterial. A second measurement of a similar wedge made from blank FR4 boards is done for reference. The results of the measurements show positive refraction over the whole measured frequency band for the FR4 wedge as well as the refraction of the incident radiation to negative angles within the designated left-handed frequency band for the metamaterial sample.     

Nonlinear dynamics of negatively refracted light in a resonantly absorbing Bragg reflector

The evolution of nonlinear light fields traveling inside a resonantly absorbing Bragg reflector is studied by use of Maxwell-Bloch equations. Numerical results show that a pulse initially resembling a light bullet may effectively experience negative refraction and anomalous dispersion in the resonantly absorbing Bragg reflector.     

单轴晶体中的负折射现象研究

分析了在各向同性介质和单轴晶体界面实现负折射的最佳条件。计算发现,通过调节光轴角和各向异性参量可以使得负折射现象更为明显,获得最佳光轴角和最大入射临界角。各向异性强的晶体实现负折射的入射角范围可能会很大。讨论了单轴晶体中和负折射率介质中的负折射现象的区别：负折射率介质中的负折射是由负的折射率引起的,单轴晶体中是由于各向异性决定的。同时还发现单轴晶体中的能流负折射现象不能实现Pendry在理论上所预言的完美透镜。     

高斯光束在单轴挛晶界面上的反射与折射

给出了高斯光束入射到挛晶结构的电磁场分布,解出了反射系数和透射系数。根据晶体的色散关系解出了入射角、反射角和折射角关于晶体参量及波矢的方程,并根据角度方程给出了在一定参量下反射角和折射角关于入射角变化的关系图,以图示的方法显示了光束在界面处的异常性质。根据角度关系和反射、透射系数分析了异常光束在界面处能够出现二性折射、负反射、全透射和全反射等光束的奇特性质;分析了出现这些奇特性质对晶体参量和入射角所要求的条件。根据时间平均的能流密度公式,用数值模拟的方法给出了二性折射、全透射和全反射在特定参量下的高斯光束在挛晶内的能流密度分布图及当发生全反射时不同宽度光束在界面处关于入射角的古斯-亨兴(Goos-Hanchen)位移。     

Optical devices based on materials with negative refraction

The Abbe invariant is obtained for media with negative refractive index, which allows calculations of optical devices with elements characterized by negative refraction. Formulas for calculating the source-image distances and the magnification provided by various lenses with negative refraction are derived. Block diagrams are given for the focusator, microscope, and spectrograph in which materials with negative refraction are used. The microscope and focusator magnifications are estimated. The linear dispersion is calculated for the spectrograph in which a plane-parallel plate with negative refraction is used as a spectral element.     

Negative refractive index and anomalous dispersion

Media with negative index of refraction are discussed briefly within Sellmeier model. In particular, dispersion of light waves is found to be anomalous and the corresponding coefficient of material dispersion is found to be negative. In addition, the group index becomes negative.     

Dispersion compensation for a femtosecond self-pumped phase conjugator

Dispersion compensation for a photorefractive self-pumped phase conjugator with femtosecond pulses is analyzed. The self-pumped phase conjugator consists of a pair of dynamic gratings coupled by total internal reflections at the crystal surfaces (cat conjugator). The negative angular dispersions of refraction at the air-crystal interface and the gratings inside the crystal compensate for the positive dispersion of the finite crystal path. The experimental results show that with partial dispersion compensation the width of the self-pumped phase conjugation at 450 nm of femtosecond pulses is narrower than that of the transmitted pulses.     

Index of refraction for cold lithium- and diatomic sodium waves traveling through cold noble gases

In the present paper we propose to measure the index of refraction for diatomic sodium molecules traveling through a cold helium gas. Theoretical calculations of the index of refraction for this system are presented as a function of the molecule velocity and atom gas temperature. Whereas previous theoretical efforts to compute the refractive index have been concerned with atomic systems and atomic matter waves, we extend the investigation to diatomic molecules in the present work. To enable such calculations the potential energy surface for the atom-molecule interaction is calculated ab initio, along with the long range dispersion coefficients for the atom-molecule system. The full close-coupled equations, describing the atom-molecule collisions, are solved numerically to work out the influence of the collisions on the matter waves. We investigate the sensitivity of the results upon changes and inaccuracies in the potential energy surface. Several molecular rotational levels are included in the present study, and the index of refraction is found to depend on the rotational state. In addition, the index of refraction for atomic lithium matter waves traveling through the cold noble gases helium and argon are computed, motivated by a recent experiment with atomic lithium matter waves. Different resonances (glory- and scattering resonances) are identified from the results. Such resonances offer an important opportunity for the comparison of experiment and theory.     

Imaging properties and negative refraction of the metallic photonic crystal at near-infrared frequency

Imaging properties and negative refraction of the two-dimensional metallic photonic crystal (PC) consisting of a triangular lattice of silver rods immersed in a dielectric is studied. It is found that good-quality image spots and negative refraction with an effective refractive index of ?1 can be achieved for the near-infrared frequency through the adjustment of the metallic PC's lattice constant and the permittivity of the background material together. Drude dispersion model is adopted to describe the silver rod and it is found that the influence of the metal's absorption is trivial to debase the quality of the image spot.     

Towards focusing using photonic crystal flat lens

We report on the numerical simulation and fabrication of a two-dimensional flat lens based on negative refraction in photonic crystals. The slab acting as a lens is made of an hole array (operating at the wavelength of 1.5 μm) etched in a InP/InGaAsP/InP semiconductor layer. We first study the key issues for the achievement of a negative refractive index taking advantage of folding of dispersion branches with main emphasis in dispersion properties rather than the opening of forbidden gaps. The diffraction and refraction regimes are analysed according to the comparison of the wave-vector with respect to the relevant dimensions of the hole array. In the second stage, we illustrate technological challenges in terms of e-beam lithography on a sub-micron scale and deep reactive ion etching for an indium phosphide based technology.     

石墨烯基双曲色散特异材料的负折射与体等离子体性质

基于有效介质理论研究了石墨烯/介质周期结构的电磁性质, 研究发现这种复合结构的等频面在太赫兹和远红外波段为双曲线, 可用来实现石墨烯基双曲色散特异材料. 通过改变石墨烯的费米能级、介质层厚度和单元结构中石墨烯的层数, 可很容易地调节双曲色散存在的频段. 由于等频面的双曲色散特性, 石墨烯基双曲色散特异材料在远低于截止频率的范围内, 对斜入射的电磁波具有负的能量折射率和正的相位折射率, 并支持局域体等离子体模式. 基于衰减全反射结构, 研究了体等离子体的激发, 探索了体等离子体在可调的光学反射调制器中的应用.     

Hyperbolic metamaterial using chiral molecules

We theoretically investigate the intra-band transitions in Mobius molecules.Due to the weak magnetic response,the relative permittivity is significantly modified by the presence of the medium while the relative permeability is not.We show that there is hyperbolic dispersion relation induced by the intra-band transitions because one of the eigen-values of permittivity possesses a different sign from the other two,while all three eigen-values of permeability are positive.We further demonstrate that the bandwidth of negative refraction is 0.165 eV for the H-polarized incident light,which is broader than the ones for inter-band transitions by 3 orders of magnitude.Moreover,the frequency domain has been shifted from ultra-violet to visible domain.Although there is negative refraction for the E-polarized incident light,the bandwidth is much narrower and depends on the incident angle.     

Experimental verification and simulation of negative index of refraction using Snell's law

We report the results of a Snell's law experiment on a negative index of refraction material in free space from 12.6 to 13.2 GHz. Numerical simulations using Maxwell's equations solvers show good agreement with the experimental results, confirming the existence of negative index of refraction materials. The index of refraction is a function of frequency. At 12.6 GHz we measure and compute the real part of the index of refraction to be -1.05. The measurements and simulations of the electromagnetic field profiles were performed at distances of 14lambda and 28lambda from the sample; the fields were also computed at 100lambda.     

Alternative approach to realize all-angle negative refraction and far-field imaging effects via two-dimensional all-solid photonic crystals

We systematically investigate the band structures, equifrequency surfaces, and the intensity distributions of Poynting vector in two-dimensional Si/SiO₂ all-solid photonic crystals with different lattice types. It is found that all-angle negative refraction with effective refractive index of nearly ? 1 and far-field imaging effects can be achieved from all-solid photonic crystals. And more important thing is that, the all-solid photonic crystals can realize all-angle negative refraction at lower frequencies and provide far-field images with higher quality compared with normal air–dielectric photonic crystals. Such improved performance provides an alternative approach to realize all-angle negative refraction in super-lens and super-prisms applications.     

Wave refraction in negative-index media: always positive and very inhomogeneous

We present the first treatment of the refraction of physical electromagnetic waves in newly developed negative index media (NIM), also known as left-handed media (LHM). The NIM dispersion relation implies that group fronts refract positively even when phase fronts refract negatively. This difference results in rapidly dispersing, very inhomogeneous waves. In fact, causality and finite signal speed always prevent negative wave signal (not phase) refraction. Earlier interpretations of phase refraction as "negative light refraction" and "light focusing by plane slabs" are therefore incorrect, and published NIM experiments can be explained without invoking negative signal refraction.     

周期性层状铁氧体-电介质复合材料中导模模式的有效负折射率

运用等效传输线法研究了周期性层状铁氧体-电介质/金属复合材料导模模式的有效折射率.通过对复合材料导模模式的色散特性和有效折射率的分析和计算，发现负折射率只能出现在TE模式激励下的某一频带内.在负折射率频带内的电磁损耗与复合材料中介电材料的性质密切相关，减小介电损耗可以有效降低复合材料的损耗，但过分小的介电损耗则会导致负折射率的消失. 关键词： 负折射率 导模模式 等效传输线法