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.

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.

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.

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.

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.

Aberration-free two-thin-lens systems based on negative-index materials

Since the complete correction of all five monochromatic Seidel aberrations for a singlet lens with random shape or a two-thin-lens system is unprocurable merely by using the conventional positive-index materials both in theory and practice, this paper proposes that when one or both of the two lenses is/are made from negative-index materials, an imaging system composed of a pair of spherical thin lenses is possible to form a real image, in air, free from all five monochromatic Seidel aberrations. The calculated numerical solutions to the structural parameters of such lens systems possessing superior performance are provided and examples of them are illustrated for the given combinations of the two lenses＇ refractive indices, including an ultimately-remote imaging system.

Reflection and Refraction on the Boundary of a Left-Handed Material with a Hyperbolic Dispersion Relation

Wave reflection and refraction at the interface between a normal media and a one-dimensional left-handed material （1 DLHM） with a hyperbolic dispersion relationship is studied. It is found that in a special case that the boundary is perpendicular to one asymptotic line of the hyperbola, phase matching cannot be achieved unless the 1 DLHM is regarded to be intrinsically lossy. After introducing a small loss factor to the 1 DLHM, a reasonable solution for the phase matching is obtained. According to the analytical result, a wave confined to a thin layer near the boundary is found, which can be excited at the interface as a reflected wave or a refracted wave attenuating drastically away from the boundary inside the 1 DLHM in both cases.Wave reflection and refraction at the interface between a normal media and a one-dimensional left-handed material （1 DLHM） with a hyperbolic dispersion relationship is studied. It is found that in a special case that the boundary is perpendicular to one asymptotic fine of the hyperbola, phase matching cannot be achieved unless the 1 DLHM is regarded to be intrinsically lossy. After introducing a small loss factor to the 1 DLHM, a reasonable solution for the phase matching is obtained. According to the analytical result, a wave confined to a thin layer near the boundary is found, which can be excited at the interface as a reflected wave or a refracted wave attenuating drastically away from the boundary inside the 1 DLHM in both cases.

Impacts of Refraction Index Mismatch on Performance of Target Detection and Imaging by Using Flat LHM Lens

Refraction index mismatch between fiat left-handed metamaterial （LHM） lens and its surrounding medium generally destroys the focusing of flat LHM lens and degrades the performance of near-field target detection by using fiat LHM lens. For LHM lens of refraction index mismatch within ±30%, numerical simulations demonstrate that lenses with large refraction index may suffer less resolution degradation than lenses with small refraction index, and the enhancement of refocused microwave backscattered from target can be subsided by up to approximately 5.5 dB. The refraction index mismatch will also shift the target position in the reconstructed image so that theoretical prediction of target position needs to be modified.

Refraction Light Control by Constructing Output Interface Topography of Metal Waveguide Arrays

We investigate a nanoscale metal waveguide array （MWGA） structure and demonstrate that negative refraction effect exists from the visible to infrared frequency. Our numerical analysis shows that this effect is related to output interface of MWGAs. Refraction light would have different directions on the gradient shaped output surface as a result of phase retardation control by waveguide thickness. Finite-difference time-domain analysis shows that more sharp superdiffraction limit imaging can be obtained by constructing convex-like output interface topography.

Band rules for the frequency spectra of three kinds of aperiodic photonic crystals with negative refractive index materials

By means of the theory of electromagnetic wave propagation and transfer matrix method, this paper investigates the band rules for the frequency spectra of three kinds of one-dimensional （1D） aperiodic photonic crystals （PCs）, generalized Fibonacci GF（p, 1）, GF（1,2）, and Thue Morse （TM） PCs, with negative refractive index （NRI） materials. It is found that all of these PCs can open a broad zero-n gap, TM PC possesses the largest zero-n gap, and with the increase of p, the width of the zero-n gap for GF（p, 1） PC becomes smaller. This characteristic is caused by the symmetry of the system and the open position of the zero-n gap. It is found that for GF（p, 1） PCs, the possible limit zero-n gaps open at lower frequencies with the increase of p, but for GF（1,2） and TM PCs, their limit zero-n gaps open at the same frequency. Additionally, for the tbree bottom-bands, we find the interesting perfect self-similarities of the evolution structures with the increase of generation, and obtain the corresponding subband-number formulae. Based on 11 types of evolving manners Qi （i = 1, 2,... , 11） one can plot out the detailed evolution structures of the three kinds of aperiodic PCs for any generation.