Nonreciprocal negative refraction in a dense hot atomic medium

We investigate the electromagnetic properties of a four-level dense atomic gas medium with Doppler effect.It is shown that the relative permittivity and relative permeability of the medium can be negative simultaneously with low absorption in the same detuning interval on account of electromagnetically induced transparency.Furthermore,with the suitable parameters,the nonreciprocal negative refraction can be obtained due to the Doppler effect,and the nonreciprocity frequency band can be regulated by adjusting the temperature,the intensity of the control field and the atomic density in this hot atomic medium.

Frequency bands of negative refraction in finite one-dimensional photonic crystals

We have discussed theoretically the negative refraction in finite one-dimensional （1D） photonic crystals （PCs） composed of alternative layers with high index contrast. The frequency bands of negative refraction are obtained with the help of the photonic band structure, the group velocity and the power transmittance, which are all obtained in analytical expression. There shows negative transverse position shift at the endface when negative refraction occurs, which is analysed in detail.

Theoretical Investigation of Negative Refraction in Metallic and Ferromagnetic Composites

A new design of LHM (left-handed material) is suggested, in which the wave vectork and the energy flowS (the Poynting vector) are in the opposite direction. Metallic cores or lines are coated with ferromagnetic layers to obtain negative permittivity and permeability. This design may bring some improvements over the binary design, such as higher homogeneity, smaller volume size, lower power loss, higher convenience and economy. The analytical expressions for the permittivity ε and permeability μ are shown to be negative in certain direction and frequency regions. Two specific structures are theoretically discussed and proved to be left-handed. Key words left-handed materials - negative refraction - NIM - LHM - artificial crystal CLC number O 438 Foundation item: Supported by the National Natural Science Foundation of China (10344002)Biography: SU Hua (1978-), male, Master candidate, research direction: information optics.

Negative refractions by triangular lattice sonic crystals in partial band gaps

This study numerically demonstrates the effects of partial band gaps on the negative refraction properties of sonic crystal. The partial band gap appearing at the second band edge leads to the efficient transmissions of scattered wave envelopes in the transverse directions inside triangular lattice sonic crystal, and therefore enhances the refraction property of sonic crystal. Numerical simulation results indicate a diagonal guidance of coupled scattered wave envelopes inside crystal structure at the partial band gap frequencies and then output waves are restored in the vicinity of the output interface of sonic crystal by combining phase coherent scattered waves according to Huygens＇ principles. This mechanism leads to two operations for wavefront engineering： one is spatial wavefront shifting operation and the other is convex-concave wavefront inversion operation. The effects of this mechanism on the negative refraction and wave focalization are investigated by using the finite difference time domain （FDTD） simulations. This study contributes to a better understanding of negative refraction and wave focusing mechanisms at the band edge frequencies, and shows the applications of the slab comer beam splitting and SC-air multilayer acoustic system.

Electromagnetic chirality-induced negative refraction with the same amplitude and anti-phase of the two chirality coefficients

This paper suggests a scheme of electromagnetic chirality-induced negative refraction utilizing magneto-lectric cross coupling in a four-level atomic system. The negative refraction can be achieved with the two chirality coefficients having the same amplitude but the opposite phase, without requiring the simultaneous presence of an electric-dipole and a magnetic-dipole transition near the same transition frequency.

Coherent control of negative refraction based on local-field enhancement and dynamically induced chirality

This paper studies the electromagnetic response of a coherently driven dense atomic ensemble to a weak probe. It finds that negative refraction with little absorption may be achieved in the presence of local-field enhanced interaction and dynamically induced chirality. The complex refractive index governing the probe refraction and absorption depends critically on the atomic density, the steady population distribution, the coherence dephasings, and the frequency de- tunings, and is also sensitive to the phase of the driving field because the photonic transition paths form a close loop. Thus, it can periodically tune the refractive index at a fixed frequency from negative to positive values and vice versa just by modulating the driving phase. Moreover, the optimal negative refraction is found to be near the probe magnetic resonance, which then requires the electric fields of the probe and the drive being on two-photon resonance due to the dipole synchronisation.

Asymmetry in Negative Refraction of Nonlinear Waves

Recently, inwardly propagating waves （called antiwaves, AWs） in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves （normal waves, NWs） and the other AWs. In this paper we find that negative refraction （NR） in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source with proper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes （both positive and negative refractions） nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.

Existing conditions of full bandgaps and absolute negative refraction in metallic-dielectric photonic crystal

This paper has theoretically studied the characteristic frequencies of band structures in two-dimensional metallic- dielectric photonic crystals. It is demonstrated that a large filling fraction benefits the existence of absolute photonic band gap, while a smaller filling fraction benefits an absolute negative refraction band. In addition, it also finds that the relation between the cut-off frequency of E-polarized wave and the filling fraction exceeding 10% is content with a linear increasing function, whose coefficients are exponential to the normalized lattice constant. These investigations have significant implications for tuning the operational frequencies to desired applications and manufacturing photonic crystals.

Wider frequency domain for negative refraction index in a quantized composite right–left handed transmission line

The refraction index of the quantized lossy composite right-left handed transmission line（CRLH-TL） is deduced in the thermal coherence state. The results show that the negative refraction index（herein the left-handedness） can be implemented by the electric circuit dissipative factors（i.e., the resistances R and conductances G） in a higher frequency band（1.446 GHz≤ ω ≤ 15 GHz）, and flexibly adjusted by the left-handed circuit components（Cl, Ll） and the right-handed circuit components（Cr, Lr） at a lower frequency（ω = 0.995 GHz）. The flexible adjustment for left-handedness in a wider bandwidth will be significant for the microscale circuit design of the CRLH-TL and may make the theoretical preparation for its compact applications.

Negative refraction in ferromagnetic materials under external magnetic field:a theoretical analysis

We present a detailed theoretical analysis on the possibilities and conditions for negative permeability and negative refraction occuring in the magnetic materials with both pronounced magnetic and dielectric responses to electromagnetic waves. The results indicate that the permeability is always positive for 5 = （2q ＋0.5）π （5 is the initial phase difference of magnetic components hx and hy of incident electromagnetic wave, q is integer）, which means that it is difficult to realize negative refraction. However, for 5 = 2qπ, 5 = （2q ＋ 1）π, or 5 = （2q - 0.5）π, the negative permeability occurs at some range of free procession frequency, which means that the refraction can become negative under certain conditions. Further analysis reveals that for general positive permittivity there are various opportunities for realizing the negative refraction provided that some requirements are met. One concludes also that the refractive index for δ = 2qπ case is similar to 5 = （2q ＋ 1）π The only difference between two cases of δ = 2qπ and 5 = （2q ＋ 1）π is that the x-direction for δ = 2qπ corresponds to the y-direction for 5 = （2q ＋ 1）π and the y-direction for 5 = 2qπ corresponds to the x-direction for δ = （2q ＋ 1）π. The results are valuable for designing and analysing the complex negative refraction of magnetic materials.

Negative Refraction in a Lossy Plasma Layer

NeEative refraction at the interface between air and a lossy plasma layer is theoretically analyzed based on the inhomogeneous wave theory. The phenomenon of negative refraction, which arises from the negative refraction angle, can occur when a transverse magnetic wave is incident from air to the lossy plasma layer under certain conditions. The formula of the negative refraction angle is derived, and the dependences of the negative refraction angle on the angle of incidence, frequency of incidence, and lossy plasma layer are analytically investigated. The parameter dependences of the effects are calculated and discussed.

Foreword for the Special Issue——International Workshop on Metamaterials and Negative Refraction

Electromagnetic properties of materials are often described using the concept of refraction index. The re- fraction index of a natural material is always positive. However, some artificially designed materials-so-called metamaterials-can act as negative-index media （NIM）.

Negative refraction based on purely imaginary metamaterials

By introducing a new mechanism based on purely imaginary metamaterials （PIMs）, we reveal that bidirectional negative refraction and planar focusing can be obtained using a pair of PIM slabs, over- coming the unidirectional limit in parity-time （PT）-symmetric systems. Compared with PT-symmetric systems, which require two different types of materials, the proposed negative refraction can be realized using two identical media. In addition, asymmetric excitation with bidirectional total transmission is observed in our PIM system. Therefore, a new way to realize negative refraction with properties that are unavailable in PT-symmetrie systems is presented.

Realization of absolute negative refraction index by a photonic crystal using anisotropic dielectric material

A method to realize absolute negative refraction index -1 with a two-dimensional （2D） photonic crystal is presented by introducing dielectric anisotropy in the photonic crystal material. The band structures of E-polarization mode and H-polarization mode can be adjusted by changing the parameters of materials. Thus the two modes with different polarizations have the same negative refraction index -1 for the same frequency. The results are demonstrated by numerical simulation based on the finite-difference time-domain （FDTD） method.

Negative refraction with absorption suppressed by electromagnetically induced transparency in a left-handed atomic system

This paper intends to realize negative refraction with absorption suppressed by the electromagnetically induced transparency (EIT) in a dense four-level atomic system.Without the two equal transition frequencies responding to the probe field,the atomic system displays a negative refraction with the simultaneously negative permittivity and negative permeability (left-handedness).The response of the probe field is amplified and propagates transparency in some frequency extents.Therefore,our aim for searching the low-loss negative refraction can be achieved in the scheme,given the main applied limitation of the negative refractive materials is the large amount of dissipation and absorption.However,an excessive signal field intensity would increase the absorption near the resonance in our scheme.

Numerical simulations of negative-index refraction in a lamellar composite with alternating single negative layers

Negative-index refraction is demonstrated in a lamellar composite with epsilon-negative （ENG） and mu-negative （MNG） materials stacked alternatively. Based on the effective medium approximation, simultaneously negative effective permittivity and permeability of such a lamellar composite are obtained theoretically and further proven by full-wave simulations. Consequently, the renowned left-handed metamaterial comprising split ring resonators and wires is interpreted as an analogy of such ENG-MNG layers. In addition, beyond the effective medium approximation, the propagating field squeezed near the ENG/MNG interface is demonstrated to be left-handed surface waves with backward phase velocity.

Negative Refraction at a Lossy Interface and a Bold Hypothesis via Complex Frequency

We investigate the negative refraction effect at a planar interface of a highly absorptive material,where the direct experimental verification is difficult because of the loss-induced skin depth effect. An apparent contradiction occurs when we try to determine the group velocity direction by the method of equifrequency contours(EFCs) in detail. This contradiction forbids any physical solution to be found for negative refraction.We conclude that this paradox is mainly caused by the definition of complex wavevector ■which is conventionally adopted in the case of complex permittivity. The complex wavevector may result in ambiguously defined optical path, which limits the application of the classical Snell’s law. We propose a bold suggestion that the complex wavevector■ should be replaced by a complex frequency■ . Therefore, the optical path can always be defined as real. The proposed hypothesis is capable of resolving the contradiction about the loss-induced negative refraction,and the obtained theoretical prediction fits well with the reported experimental results.

Analysis of influence factors of negative refraction phenomenon in particulate composite

The effective optical constants that describe the interaction between electromagnetic wave and particulate composite are calculated based on effective medium theory and Mie theory.The negative refractive phenomenon is compared between the Ge-particle-dispersed LiTaO 3 composites and Ag-particle-dispersed LiTaO 3 composites.It is indicated that the negative refraction phenomenon for semiconductor Ge particulate composite occurs in higher frequency range than that of noble Ag particulate composite.By take the Ge particulate composite as an example,the influence of size and number density of spherical particles on the negative refraction phenomenon is analyzed.It is indicated that the frequency range where negative refraction phenomenon occurs can be shifted to higher frequency by adjusting these two influencing factors.

Direct and real-time sub-wavelength resolution photoacoustic imaging method based on acoustic lens with negative refractive index

The signal processing technology based on material with negative refractive index provides researchers with the latest ideas. As a new nondestructive bio-photonic technology, photoacoustic tomography is a kind of imaging method based on the differences of optical absorption within the biological organization However, photoacoustic tomography by the scanning sensor or by the sensors array at present has its inherent disadvantages that may lead to poor real-time performance and high cost in the imaging process. The characteristics of acoustic lens with negative refractive index such as focusing, filtering and directional control on acoustic wave, are very suitable for solving the problem in photoacoustic tomography. With an analysis on the nega-tive quality response of acoustic lens and the advantages of negative refractive imaging, we proposed an approach using the lens to change the current photoacoustic imaging methods. The experiment showed that the imaging effectiveness of photoacoustic tomography by the designed lens is very impressive that the pressure distribution of the absorber is basically consistent with the image of the absorber. In addition, the result of 0. 6 times wavelength in the experimental image is demonstrated on sub-wave-length photoacoustic imaging through the lens designed in this work.

The largest negative refractive angles in uniaxial bicrystals

Using the Maxwell＇s equations, we carry out theoretical analysis on the maximum incident and refractive angles at which negative refraction can be realized at the interfaces associated with conventional uniaxial media. In the numerical analysis, the largest incident and refractive angles at which refraction arises are obtained by optimizing directions of the optical axis of the uniaxial bicrystal. Meanwhile, the optical parameters of the ordinary uniaxial bicrystals （including homogeneity- junction and heterogeneity-junction） are given, and some representative laser wavelengths, the largest incident and refractive angles are obtained. The relation between the largest incident angles （or refractive angles） and refractive index is also discussed.