Negative refraction of ultra-short electromagnetic pulses

We study pulse propagation across a boundary that separates an ordinary medium from a medium with simultaneously negative dielectric permittivity and magnetic permeability. Solving Maxwell’s equations with two spatial coordinates (one longitudinal, one transverse) and time we find negative refraction as the wave packet undergoes significant and unusual shape distortions. The pulse acquires and maintains a chirp as it traverses the interface, as expected, but with a sign that is opposite to the chirp attained upon traversal into a positive-index material. Both a direct calculation of the spatial derivative of the instantaneous, local phase of the pulse and a Fourier analysis of the signal reveal the same inescapable fact: that inside a negative-index material, a transmitted, forward-moving wave packet is indeed a superposition of purely negative wave vectors. The central findings of this paper are a confirmation that causality is not violated in the short-pulse regime, and that energy and group velocities never exceed the speed of light in vacuum.     

Chiral planar waveguide for guiding single-mode backward wave

Single-mode backward wave is shown to be guided in a planar dielectric waveguide with a strong chiral core. The significant difference of such a waveguide from the traditional one is the guidance of single-mode backward wave, without using negative permittivity and/or negative permeability. In the design, we generalize the idea of total internal reflection to the chiral medium and make a numerical analysis on the reflection with oblique incidence. We deduce rigorously a general solution of incident wave on the boundary of two arbitrary chiral magneto-electric media. We observe that the impedance matching can eliminate the coupling between two eigenwaves in chiral media. With strong chiral core and the matched impedance with cladding, one eigenwave becomes a backward wave and can be guided without transferring to the other eigenwave. If a single-mode propagation condition is satisfied, we will get single-mode backward guided wave. A special interface has been designed to prevent the forward wave entering the waveguide from the source.     

Electric and magnetic losses and gains in determining the sign of refractive index

Within the framework of classic electromagnetic theories, we have studied the sign of refractive index of optical medias with the emphases on the roles of the electric and magnetic losses and gains. Starting from the Maxwell equations for an isotropic and homogeneous media, we have derived the general form of the complex refractive index and its relation with the complex electric permittivity and magnetic permeability, i.e. , in which the intrinsic electric and magnetic losses and gains are included as the imaginary parts of the complex permittivity and permeability, respectively, as  = _r + i_i and μ = μ_r + iμ_i. The electric and magnetic losses are present in all passive materials, which correspond, respectively, to the positive imaginary permittivity and permeability _i > 0 and μ_i > 0. The electric and magnetic gains are present in materials where external pumping sources enable the light to be amplified instead of attenuated, which correspond, respectively, to the negative imaginary permittivity and permeability _i < 0 and μ_i < 0. We have analyzed and determined uniquely the sign of the refractive index, for all possible combinations of the four parameters _r, μ_r, _i, and μ_i, in light of the relativistic causality. A causal solution requires that the wave impedance be positive Re{Z} > 0. We illustrate the results for all cases in tables of the sign of refractive index. One of the most important messages from the sign tables is that, apart from the well-known case where simultaneously  < 0 and μ < 0, there are other possibilities for the refractive index to be negative n < 0, for example, for _r < 0, μ_r > 0, _i > 0, and μ_i > 0, the refractive index is negative n < 0 provided μ_i/_i > μ_r/_r.     

Tunable negative index metamaterial using yttrium iron garnet

A magnetic field tunable, broadband, low-loss, negative refractive index metamaterial is fabricated using yttrium iron garnet (YIG) and a periodic array of copper wires. The tunability is demonstrated from 18 to 23 GHz under an applied magnetic field with a figure of merit of 4.2 GHz/kOe. The tuning bandwidth is measured to be 5 GHz compared to 0.9 GHz for fixed field. We measure a minimum insertion loss of 4 dB (or 5.7 dB/cm) at 22.3 GHz. The measured negative refractive index bandwidth is 0.9 GHz compared to 0.5 GHz calculated by the transfer function matrix theory and 1 GHz calculated by finite element simulation.     

Total reflection of electromagnetic waves propagating from an isotropic medium to an indefinite metamaterial

The existence conditions for total reflection and the corresponding critical angle at the interface separating an isotropic medium and an indefinite metamaterial for TE- and TM-polarized electromagnetic waves are obtained. For different kinds of indefinite metamaterial, there appear different total reflection phenomena. Particularly, the anomalous total reflection in which the incident angle is smaller than the critical angle and the Brewster’s angle can be smaller than the critical angle can occur for anti-cutoff medium. Furthermore, the omnidirectional total reflection exists for the always cutoff medium and anti-cutoff medium. The total reflection depends on the thickness of indefinite metamaterial when the indefinite metamaterial is finite, and the photon tunneling phenomenon can occur when the thickness of indefinite metamaterial is smaller than wavelength.     

Abrupt change of reflectivity from the strongly anisotropic metamaterial

The wave reflection from a non-magnetic anisotropic metamaterial, whose principal elements of the permittivity tensor have different signs, is investigated in this paper. It is found that, if the orientation of the optical axis is properly chosen, an extremely small change of the transverse wave number will lead to a dramatically change of the reflectivity at the glancing incidence. The physical insight for this abrupt change of reflectivity is also given by the analysis of the imaginary part of the k-surface. Since the metamaterial discussed here have been experimental realized from GHz to optical frequencies, the proposed abrupt change property of reflectivity may find some potential applications in various calibration devices, because of its extremely sensitivity to the transverse wave number.     

Anomalous wave propagation in quasiisotropic media

Based on boundary conditions and dispersion relations, the anomalous propagation of waves incident from regular isotropic media into quasiisotropic media is investigated. It is found that the anomalous negative refraction, anomalous total reflection and oblique total transmission can occur in the interface associated with quasiisotropic media. The Brewster angles of E- and H-polarized waves in quasiisotropic media are also discussed. It is shown that the propagation properties of waves in quasiisotropic media are significantly different from those in isotropic and anisotropic media.     

Polarization-sensitive propagation in an anisotropic metamaterial with double-sheeted hyperboloid dispersion relation

The polarization-sensitive propagation in the anisotropic metamaterial (AMM) with double-sheeted hyperboloid dispersion relation is investigated from a purely wave propagation point of view. We show that TE and TM polarized waves present significantly different characteristics which depend on the polarization. The omnidirectional total reflection and oblique total transmission can occur in the interface associated with the AMM. If appropriate conditions are satisfied, one polarized wave exhibits the total refraction, while the other presents the total reflection. We find that the opposite amphoteric refractions can be realized by rotating the principle axis of AMM, such that one polarized wave performs the negative refraction, while the other undergoes positive refraction. The polarization-sensitive characteristics allow us to construct two types of efficient polarizing beam splitters under certain achievable conditions.     

Unique properties of microwave in interlayer exchange-coupled trilayer ferromagnetic films associated with negative imaginary part of permeability

Based upon Landau-Lifshitz equation and Maxwell's equations, we theoretically investigated properties of normally incident microwave propagation in interlayer exchange-coupled trilayer ferromagnetic film. It is found that, near resonance frequency of optic mode, imaginary part of permeability of one ferromagnetic layer is smaller than zero unusually, i.e., the ferromagnetic layer may be taken as an active medium. Thus a number of unique electromagnetic properties are presented, such as, the ferromagnetic layer becomes a left-handed material near low side of the resonance frequency of optic mode, and both phase velocity and time-averaged Poynting flow of the usually defined forward wave are negative simultaneously near high side of the resonance frequency. This work provides a feasible active medium to demonstrate the unique microwave properties.     

A polarization-dependent wide-angle three-dimensional metamaterial absorber

In this paper, a polarization-dependent wide-angle three-dimensional metamaterial absorber with a near-unity absorbance was presented. The metamaterial absorber structure is composed of coplanar electric and magnetic resonators. By carefully adjusting the structural dimensions, less-than-unity ε and/or μ can be realized. To match the impedance of free space, the structural dimensions were adjusted so that ε=μ, which guarantees minimum reflection. Since the resonance-based structure is made of metallic resonators and lossy substrates, the imaginary part of refractive index is large, which guarantees strong absorption of transmitted waves. Full-wave simulations confirmed the effectiveness of the proposed three-dimensional metamaterial absorber.     

Electromagnetically induced negative refraction in an atomic system with spontaneously generated coherence

We propose a new scheme for realizing left-handed electromagnetic properties in a coherently driven four-level system. At the presence of spontaneously generated coherence and the local field effect, both dielectric permittivity and magnetic permeability may have negative real parts of the same order in a small frequency band. Thus, one can achieve the negative refractive index and then manipulate it by modulating the coherent field or changing the atomic density. With incoherent pumping applied to have more remarkable spontaneously generated coherence, one can further obtain a wider frequency band of negative refraction and simultaneously reduce the accompanied absorption.     

Lamellar model of the left-handed metamaterials composed of metallic split-ring resonators and wires

Left-handed materials composed of split ring resonators (SRRs) and wires are investigated in the viewpoint of lamellar composite with epsilon-negative (ENG) and mu-negative (MNG) materials staked alternatively. Several configurations of the SRR-wire metamaterial are numerically simulated to confirm its left-handed response as an analogy to the ENG-MNG lamellar model.     

Simultaneously Large and Opposite Lateral Beam Shifts for TE and TM Modes on a Double Metal-Cladding Slab

We report simultaneously large and opposite Goos-Hanchen shifts for TE and TM beams on a double metalcladding slab. Theoretical examination shows that both positive and negative lateral shifts are in two orders of the wavelength. It is also found that the magnitude of the lateral beam shift strongly depends on the thickness of the upper metal layer. The optimal thickness of the upper metal layer for zero reflection is found to be the critical thickness above which a negative beam shift occurs. Numerical calculations are in good agreement with the theoretical results.     

Positive and Negative Lateral Shifts from an Anisotropic Metamaterial Slab Backed by a Metal

The lateral shift of a light beam at the surface of an anisotropic metamaterial (AMM) slab backed by a metal is investigated. Analytical expressions of the lateral shifts are derived using the stationary-phase method, in the case that total reflection does and does not occur at the first interface. The sign of the lateral shift in two situations is discussed, and the necessary conditions for the lateral shift to be positive or negative are given. It is shown that the thickness and physical parameters of the AMM slab and the incident angle of the light beam strongly affect the properties of the lateral shift. Numerical results validate these conclusions. The lossy effect of the metamaterial on the lateral shift is also investigated.     

Independent Modulation of Omnidirectional Defect Modes in Single-Negative Materials Photonic Crystal with Multiple Defects

Single-negative materials based on photonic crystal with multiple defect layers are designed and the free modulation of defect modes is studied. The results show that the multi-defect structure can avoid the interference between the defect states. Therefore, the designed double defect modes in the zero effective-phase gap can be adjusted independently by changing the thickness of different defect layers. In addition, the two tunable defect modes have the omnidirectional characteristics. This multi-defect structure with above-mentioned two advantages has potential applications in modern optical devices such as tunable omnidirectional filters.     

Rigorous electromagnetic analysis of dual-closed-surface microlens arrays

In this paper, we investigated the focal performance of the dual-closed-surface microlens arrays (DCSMAs) based on rigorous electromagnetic theory and boundary element method (BEM) in the case of TE polarization. The DCSMAs are designed with different substrate thickness and different distance between microlenses. DCSMAs designed according to different wavelengths are surveyed. The DCSMAs with different incident angles are also studied. Several focusing performance measures, such as the focal spot size, the focal position on the preset focal plane, the diffraction efficiency and the normalized transmitted power, are presented. Numerical results indicate the DCSMAs with different parameters can implement focusing beams and the focal performance of DCSMAs is easily influenced by the substrate thickness and the incident wavelength. Furthermore, the optimal thickness for the maximal diffraction efficiency of the DCSMAs is given. It is expected that the DCSMAs may be used as a parallel processing device in micro-optics systems.     

Giant and negative bistable shifts for one-dimensional photonic crystal containing a nonlinear metamaterial defect

In this Letter, we investigate giant and negative bistable lateral shifts for a light beam transmitted through a one-dimensional photonic crystal containing a nonlinear metamaterial defect. It is shown that there exists a typical S-shaped curve of the normalized input-output intensity. The hysteresis of lateral shift, resulting from the reshaping effect (constructive and destructive interferences of each plane wave components undergoing different phase shifts) is dependent on the nonlinear defect, the incident intensity and incidence angle. Numerical simulations are also made for the validity of stationary phase approach. All these phenomena lead to potential applications in integrated optics and optical switches.     

Amphoteric-like refraction in a two-dimensional photonic crystal

High-index contrast photonic crystals possess an intricate photonic band structure that is responsible for surprising phenomena as the surperprism effect, self-collimation, power splitting or negative refraction. Recently, it was reported that at the interface between an isotropic medium and a uniaxial crystal (or between two uniaxial crystals) a phenomenon known as amphoteric refraction, that is, positive as well as negative refraction, can take place. By means of a equifrequency contours analysis and finite-difference time-domain simulations, we show that a two dimensional photonic crystal can also present amphoteric refraction by properly choosing the lattice orientation and the termination. However, total transmission is difficult to achieve because a Bloch mode is excited inside the photonic crystal and the coupling efficiency from this mode to an external plane wave is lower than one.     

A Zone Plate as a Tunable Terahertz Filter

A broadband tunable terahertz filter based on a zone plate is demonstrated in our terahertz time domain spec- trometer. The central bandpass frequency covers the whole spectral range of the terahertz wave emitted from a ZnTe emitter, from 0.5 THz to 2.5 THz, and can be tuned continuously by simply moving the zone plate along the terahertz beam path. The peak transmission is about 40% and the bandwidth varies from 0.16 THz to 0.25 THz at different bandpass frequencies when the aperture size is kept constant.