Nonlinear Hilbert Boundary Value Problem of Negative Index for Nonlinear Elliptic Complex Equation

This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k + iλ_k)Z^k],Z∈Γ:|z|=1 k--1 in which the index is negative. By establishing a priori estimate and using the imbdding method combined with the the Newton interation procedure, it is proved that the above problem is solvable and the solution is unique in C^l+a(g) ,O<a<].

Flat lenses constructed by graded negative index-based photonic crystals with tuned configurations

Flat lenses are designed by means of graded negative refractive index-based photonic crystals （PCs） constructed using air-holes tuned with different shapes. By gradually modifying the filling factor along the transverse direction, we obtain the graded negative index-based lenses for the purpose of focusing an incident plane wave. The finite-difference and timedomain （FDTD） algorithm is adopted for numerical calculation. Our calculation results indicate that these lenses can finely focus incident plane waves. Moreover, for the same size of air-holes, the focusing properties of the lens with rectangular air-holes are better than those with the other shaped air-holes. The graded negative index PCs lenses could possibly enable new applications in optoelectronic systems.

Tunability of graded negative index-based photonic crystal lenses for fine focusing

Graded negative refractive index-based photonic crystal （PC） lenses are designed by gradually modifying the sizes of air holes along the transverse direction for focusing the incident plane wave. To study the tunability of the graded negative index-based PC, we introduce filling factor A, gradually tune the filling factor, and use the finite-difference and time-domain （FDTD） algorithm for numerical calculation. Our calculation results indicate that the focal length and the spot size increase with A increasing. For the same A value, the focal length of a PC with elliptical air holes is the longest, and those of PC with square and rectangular air holes are the shortest. Moreover, when the focal length is greater than 1 ~xm, the focal parameters of the PC are highly insensitive to the variation of A. When the focal length is less than 1 gm, the PC lenses have higher transmittances and all well focus with a beam spot size breaking the diffraction limit. This feature possibly makes the graded negative index-based PC lenses have some new applications in optoelectronic systems.

Optical bistability induced by quantum coherence in a negative index atomic medium

Bistability behaviors in an optical ring cavity filled with a dense V-type four-level atomic medium are theoretically investigated. It is found that the optical bistability can appear in the negative refraction frequency band, while both the bistability and multi-stability can occur in the positive refraction frequency bands. Therefore, optical bistability can be realized from conventional material to negative index material due to quantum coherence in our scheme.

Guided resonance in negative index photonic crystals: a new approach

The behavior of a negative refraction photonic crystal slab irradiated with out-of-plane incident beam is an unexplored subject.In such an experimental configuration,guided mode resonance appears in the reflection spectrum.We show that,in this case,the light coupled inside the photonic crystal is backpropagating.A relationship with the negative index properties is established using a new approach in which the guided resonance is recovered by modeling the photonic crystal layer with a simple Lorentz resonator using the Fresnel reflection formula.

Negative-index dispersion and accidental mode degeneracy in an asymmetric spoof-insulator-spoof waveguide

It has been recently demonstrated that negative-index dispersion and mode degeneracy can be achieved by manipulating a spoof-insulator-spoof（SIS） waveguide. In this paper, we propose a new SIS waveguide, which is composed of two spoof surface plasmon polaritons（SSPPs） waveguides drilled with periodic rhomboidal grooves. Both the symmetric and asymmetric cases are investigated. Our simulation results show that the asymmetric SIS waveguides are more significant.By tailoring the tilt of the rhomboidal grooves, the negative-index dispersion can be achieved and the microwave band gap（MBG） can be effectively modulated. At a critical tilt, there appears an accidental mode degeneracy at the edge of the first Brillouin zone. The excitation and propagation of the two coupled modes sustained by the asymmetric SIS waveguides are also demonstrated.

How to realize a negative refractive index material at the atomic level in an optical frequency range?

The theoretical mechanism for realizing a negative refractive index material in an optical frequency range with an atomic gas system of electromagnetically induced transparency (EIT) is studied. It is shown that under certain conditions such a dense gas can exhibit simultaneously negative permittivity and negative permeability, and negligibly small loss.

A new class of negative refractive index transmission line

We propose a new class of negative refractive index transmission line in which ideal operational amplifiers are applied to form the periodically loaded negative-impedance-converted inductors and capacitors. The phase response of the new trans-mission line is opposite to that of a positive refractive index conventional transmission line. Unlike the existing negative refractive index transmission line,the new negative refractive index transmission line is non-dispersive and thus can lead to many novel applications such as designing new broadband devices.

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.

Negative refractive index in a four-level atomic system

A closed four-level system in atomic vapour is proposed, which is made to possess left handedness by using the technique of quantum coherence. The density matrix method is utilized in view of the rotating-wave approximation and the effect of a local field in dense gas. The numerical simulation result shows that the negative permittivity and the negative permeability of the medium can be achieved simultaneously （i.e. the left handedness） in a wider frequency band under appropriate parameter conditions. Furthermore, when analysing the dispersion property of the left-handed material, we can find that the probe beam propagation can be controlled from superluminal to subluminal, or vice versa via changing the detuning of the probe field.

Science Letters:Lattice type transmission line of negative refractive index

In this letter,we introduce a novel passive transmission line of negative refractive index(i.e.,left-handedness)based on identical symmetrical lattice type structures thus called "lattice type transmission line"(LT-TL).The dispersion characteristic and the transmission response of the proposed LT-TL are analyzed.While all the other left-handed passive transmission lines are of high pass,the present passive left-handed transmission line is of low pass.Compared with a conventional transmission line,the LT-TL has a phase shift of 180° in the entire wide pass-band.

Role of shape of hole in transmission and negative refractive index of sandwiched metamaterials

Transmission and negative refractive index （NRI） of metal-dielectric-metal （MDM） sandwiched metamaterial perfo- rated with four kinds of shapes of holes are numerically studied. Results indicate that positions of all transmission peaks of these kinds of holes are sensitive to the shape of the hole. Under the same conditions, the circular hole can obtain the maximum NRI and the rectangular hole can obtain the maximum frequency bandwidth of NRI. Moreover, the figure of merit （FOM） of the circular hole is the maximum too. As a result, we can obtain a higher NRI and FOM metamaterial by drilling circular hole arrays on MDM metamaterial.

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.

Study on Microcavity Organic Light-emitting Devices Containing Negative Refractive Index Dielectric Layer

A new structure containing negative refractive index dielectric layer（NRlDL） is introduced into microcavity. The properties of the new mierocavity organic light-emitting devices（MOLEDs） are investigated. In the experiment, the transfer matrix method is adopted. The dependence of reflectance and transmittance on the refractive index and thickness of NRIDL are analyzed in detail. Compared with the electroluminescence spectra of non-NRIDL diodes, the line widths of the spectra of the MOLEDs are narrower and all the peaks enhance. The results show that the new structure is beneficial to improve the performance and reduce the thickness of microcavity devices.

Optical Negative-Index Metamaterial Using CSRR by Incidenting the Light Horizontally at Near-Infrared Domain

Metamaterial structure based on cascaded split ring resonators (CSRR) is proposed in order to produce a negative refractive index in terahertz regime at near-infrared range. We have incident light horizontally instead of incidenting it perpendicular. We have measured the negative refractive index, permeability and permittivity by using the S-parameter analysis. Furthermore, it is found out that negative refractive index, permeability and permittivity are dependent upon the width of the wire and the gap between resonators at near-infrared range. This work will be helpful for the fabrication and design of double negative metamaterials structure having negative permeability, permittivity and negative refractive index for in plane applications.

Effect of Different Plasmonic Nano-Inclusion on Double Negative-Semiconductor Photonic Crystal in Visible Region:Gain Assistance and All-Angle Negative Refraction

A gain assisted double negative- Metallo-semiconductor photonic crystal （DN-MSPC） for visible light with effect of different plasmonic （Al, Ag, Au, Cu） nanorod inclusion, is presented. Negative real values of both permeability （μ） and permittivity （ε） with extremely low imaginary values for visible light is obtained by applying Coupled dipole approximation. All-Angle negative refraction is obtained by applying surface plasmon polariton excitation （SPPE） in DN-MSPC operating in a dispersion regime with anti-parallel refracted wave vector and Poynting vector. Index matched to the incident light and compensated losses due the gain assistance leads the light amplification in the designed structure. Furthermore, extremely high left-handed transmission efficiency （〉99%） is also investigated. Demonstration of near and far-field resonance patterns reveal the nano-photonic device applications potential i.e. highly directional optical nanoantenna, filter, etc.

Effect of continuous negative pressure water supply on the growth, development and physiological mechanism of Capsicum annuum L.

Effects of continuous negative pressure water supply on water consumption, growth and development, as well as physiological mechanism and quality of Capsicum annuum L. were investigated in this paper. Meanwhile, the optimal negative pressure water supply conditions for growth of C. annuum L. were screened out to achieve the goals of water conservation, high yield and high quality, thus providing theoretical foundation for its field production. The pot experiment within the greenhouse was utilized; the continuous negative pressure water supply was adopted; the four treatments, artificial watering（CK）, –5 k Pa（T1）, –10 k Pa（T2）, and –15 k Pa（T3） were set; and the daily water consumption, yield, as well as the biomass, nitrate reductase, root activity, vitamin C, capsaicin, and nutrient uptakes of nitrogen（N）, phosphorus（P） and potassium（K） during various stages of its growth were determined. Compared with CK, when the water supply pressure was controlled at –5 to –15 k Pa in the experiment, the total water consumption of C. annuum L. reduced by 53.42 to 67.75%, the total water consumption intensity reduced by 54.29 to 67.14%, and the water use efficiency increased by 12.66 to 124.67%. The N accumulation in a single strain of C. annuum L. from the color turning stage to the red ripe stage increased by 15.99 to 100.55%, respectively, compared with that of CK; the P accumulation increased by 20.47 to 154.00% relative to that of CK, and the K accumulation increased by 64.92 to 144.9% compared with that of CK. Compared with CK, C. annuum L. yield was remarkably improved by 13.79% at T1, and contents of vitamin C, capsaicin as well as carotenoids at all growth stages were enhanced by 13.42–147.01%, 11.54–71.01%, and 41.1–568.06%, respectively. Nitrate reductase activity, root activity and chlorophyll（a＋b） were markedly increased by 335.78–500%, 79.6–140.68% and 114.95–676.19%, respectively, from immature stage to full ripe stage. Adopting the continuous negative pressure water supply for C. annuum L. has a significant water-saving effect, and the water supply pressure being stable at –5 k Pa contributes to its growth and development, improves yield, enhances root activity, promotes nutrient uptake, and improves its quality, thus achieving the effects of water conservation, high yield, high quality and high efficiency.

Forecasting of Thunder/Lightning Potential

In this paper, the characteristics of thunderstorms in Zibo City were ana- lyzed. The thunderstorms could be divided into cold-front thunderstorm, upper trough （shear line） type thunderstorm and cold-vortex thunderstorm. We also screened out the atmosphere parameters that were highly correlated to the occurrence of thunder/ lightning. They were treated as the predictors. Each possible influencing factor was analyzed on the lightning day correspondingly. Their threshold values were also de- termined. Among them, the parameter that had the highest neutralizing capacity was treated as negative index. For different type of thunderstorm weather, the negative index was different. The application of negative indexes was also discussed. We hope to provide a valuable basis for the accurate forecasting of thunder/lightning.

Ghost resonance in anisotropic materials:negative refractive index and evanescent field enhancement in lossless media

We show that dielectric waveguides formed by materials with strong optical anisotropy support electromagnetic waves that combine the properties of propagating and evanescent fields.These“ghost waves”are created in tangent bifurcations that“annihilate”pairs of positive-and negative-index modes and represent the optical analogue of the“ghost orbits”in the quantum theory of nonintegrable dynamical systems.Ghost waves can be resonantly coupled to the incident evanescent field,which then grows exponentially through the anisotropic media—as in the case of negative index materials.As ghost waves are supported by transparent dielectric media,the proposed approach to electromagnetic field enhancement is free from the“curse”of material loss that is inherent to conventional negative index composites.

Properties of Defect Modes in Periodic Lossy Multilayer with Negative-Index-Materials

Employing the characteristic matrix method, this study investigates transmission properties of onedimensional defective lossy photonic crystals composed of negative and positive refractive index layers with one lossless defect layer at the center of the crystal. The results of the study show that as the refractive index and thickness of the defect layer increase, the frequency of the defect mode decreases. In addition, the study shows that the frequency of the defect mode is sensitive to the incidence angle, polarization, and physical properties of the defect layer, but it is insensitive to the small lattice loss factor. The peak of the defect mode is very sensitive to the loss factor, incidence angle, polarization, refractive index, and thickness of the defect layer. This study also shows that the peak and the width of the defect mode are affected by the numbers of the lattice period and the loss factor. The results can lead to designing new types of narrow filter structures and other optical devices.