Negative group velocity in left-handed materials

We discuss linear and nonlinear optical wave propagation in a left-handed medium (LHM) or medium of negative refraction (NRM). We use the approach of characterizing the medium response totally by a generalized electric polarization [with a dielectric permittivity $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\varepsilon}}(\ensuremath{\omega},\stackrel{\ensuremath{\rightarrow}}{k})]$ that can be decomposed into curl and noncurl parts. The description has a one-to-one correspondence with the usual approach characterizing the LHM response with a dielectric permittivity $\ensuremath{\varepsilon}<0$ and a magnetic permeability $\ensuremath{\mu}<0.$ The latter approach is less physically transparent in the optical frequency region because the usual definition of magnetization loses its physical meaning. Linear wave propagation in a LHM or NRM is characterized by negative refraction and negative group velocity that could be clearly manifested by ultrashort pulse propagation in such a medium. Nonlinear optical effects in a LHM can be predicted from the same calculations adopted for ordinary media using our general approach.

We investigate extraordinary features of optical parametric amplification of Stokes electromagnetic waves that originate from the three-wave mixing of a backward phonon wave with negative group velocity and two ordinary electromagnetic waves. Such properties were earlier shown to exist only in plasmonic negative-index metamaterials that are very challenging to fabricate. Nonlinear optical photonic devices with properties similar to those predicted for negative-index metamaterials are proposed.

This study reports on negative group velocities in a lumped transmission line, where capacitors and inductors connected to resistors are placed in the series and shunt branches of the periodic line, respectively. The propagation characteristics of the left-handed transmission line are examined along with two methods. The first method consists of analysing the lumped-element ladder network by solving in the time domain a system of differential equations derived from the Kirchhoff's voltage and current laws. In the second method, transmission matrix of the unit cell is applied to obtain the dispersion diagram from which the time group delay induced by the periodic network is derived as a function of frequency. Also, non-analytical input signals are considered, whereby transient effects occur at both ends of modulated half-sine wave packets propagating under negative group delay (NGD) regime of the left-handed line. NGD effects arise from ohmic dissipation due to the resistors which establish a frequency range in which NGD propagation is allowed. This finding is numerically demonstrated by injecting into the line modulated Gaussian wave packets, for which the negative time delays determined from the numerical solution of circuit equations and from the dispersion relation are in good agreement.

The high-frequency electromagnetic waves reflected from a perfect electric conductor (PEC) elliptical surface placed in homogeneous, reciprocal, and isotropic medium with high value of chirality parameter are analyzed. Negative phase velocity (NPV) and positive phase velocity (PPV) can be obtained by properly adjusting the value of chirality parameter. For the value of only PPV can propagate in the elliptical reflector and out of this range both PPV and NPV are supported by the elliptical reflector in chiral medium. The line plots are given which illustrate the reflected waves at different values of chirality parameter .

A new field of physics has appeared with the emergence of materials known as "left handed materials" (LHM) or "metamaterials". These materials show very particular characteristics. Their index of refraction has a negative value, which results in the reversal of Snellpsilas law. Whereas, in traditional material the Poynting vector S always forms a right-handed triplet with E and H (S = E nland H). In the left handed media, the Poynting vector S and the wave vector K are in opposite directions. Thus, the wave moves in the direction opposite to the direction of the energy flow: phase speed and group speed are anti-parallel. Therefore, a left-handed media is artificial and does not exist in nature. Indeed, when these materials are inserted into a guided wave device, one obtains the backward-wave effect. The goal of this work is to study more in details this physical phenomenon. To undertake this study, this paper presents also the design of a 10 GHz beam-scanning CPW-Antenna fabricated on metamaterial support.

We analyze the electromagnetic field of a moving point charge in the presence of a 'left-handed' medium (LHM). First, the case of uniform motion of the charge in infinite LHM was considered. Using complex function theory methods, we decomposed the total field into a 'quasi-Coulomb' field, a wave field (Cherenkov radiation) and a 'plasma trace'. In addition, an effective numerical algorithm was developed for the total field computation, and typical plots were presented. It was shown that the wave field in LHM lags behind the charge more so than it does in ordinary medium. Furthermore, we investigated a charge intersecting the interface between vacuumlike medium and LHM. Asymptotic expressions for the field components were obtained and algorithms for their computation were developed. The spatial radiation can be separated into three distinct components, corresponding to ordinary transition radiation with a relatively large magnitude, Cherenkov radiation and reversed Cherenkov-transition radiation (RCTR). Rigorous conditions for generating RCTR were obtained: RCTR in the vacuum area was found to be the double threshold effect in both frequency and charge velocity domain. The RCTR decay in vacuum due to the losses in LHM was studied. Areas of the RCTR significance were determined and were found tomore » be sufficiently large for observation. Possible applications to the beam diagnostics and the characterization of metamaterials were suggested.« less

Analysis of electromagnetic planewave propagation in a medium which is a spatiotemporally homogeneous, temporally nonlocal, isotropic, chiral medium in a comoving frame of reference shows that the medium is both spatially and temporally nonlocal with respect to all non‐co‐moving inertial frames of reference. Using the Lorentz transformations of electric and magnetic fields, we show that plane waves which have positive phase velocity in the comoving frame of reference can have negative phase velocity in certain non‐co‐moving frames of reference. Similarly, plane waves which have negative phase velocity in the comoving frame can have positive phase velocity in certain non‐co‐moving frames. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2640–2643, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22810

Superluminal group velocities, i. e., velocities greater than the speed of light in vacuum, infinite or even negative, have been experimentally observed in the optical, electronic, and microwave domains. Such velocities in no way contradict special relativity because group velocity does not represent, in general, the velocity of a signal or information. Although it may seem counterintuitive, superluminal phenomena and the resulting negative-group-delay (NGD) effects find a variety of applications such as ultra-wide-band phase shifters, high-speed microelectronic interconnections, pulse shaping, delay control, dispersion compensations, and wave-packet switching, for instance. This paper reports on negative group velocities in a lumped C-L line, where capacitors C and inductors L connected to resistors are placed, respectively, in the series and shunt branches of the periodic line. The NGD effects are induced by ohmic dissipation due to the resistors which establish a frequency range in which NGD propagation is allowed. This finding is numerically demonstrated by injecting into the line a 180 kHz modulated Gaussian pulse, with a full width at half maximum of 22.20 μ«, for which the negative time delay of −1.26 μs determined from the numerical solution of circuit equations is in good agreement with that predicted by the analytical dispersion relation of the periodic structure.

Although there have been many discussions on negative group velocity (NGV), disagreements over its counter-intuitive explanations are still on the way. In this paper, it is proposed that the negative group velocity is just a component of the actual wave group, which has to be accompanied by a positive group velocity (PGV) component. A composite wave with the NGV component propagates forward in the form of a tumbling vortex as an attenuated or evanescent wave. Negative group velocity exists only in the anomalous dispersion band with resonance absorption. This wave group model is confirmed by the NGV characteristics of spoof surface plasmon polaritons (SSPPs) of spiral-shaped periodic units. In this case, the PGV and NGV waves are formed by the resonance coupling of periodic cells, and the composite SSPP modes have both resonance absorption attenuation and vortex cancellation attenuation.

Bandgap merging and backward wave propagation in inertial amplification metamaterials

Active control of the group velocity in optical fibres is demonstrated, allowing long delays, faster-than-light propagation and even negative velocity, for which the peak of a pulse exits the fibre before entering the input end

Through the calculation of time-varying error probability, we show that a reduction in signal latency can be obtained in a practical active medium with negative group velocity (negative group delay) in the presence of noise.

The problem of joint oscillations of a thin infinite cylindrical Kirchoff-Love shell is considered. The free vibrations of the system are found. The propagating waves and energy flux are analyzed. Much attention is given to the exploration of waves with negative group velocity in the neighborhood of the bifurcation point of dispersion curves. The asymptotics of dispersion curves are used in the neighborhood of the bifurcation point for this case. The interval of system parameters (the relation of lengths of circle waves and lengths of waves along cylinder to the relative thickness of the cylinder) is estimated when the negative group velocity arises. The range of frequencies and wavenumbers where this effect is observed is also estimated. The difference in the kinds of asymptotics for the regular case and the case of bifurcation is discussed. The analysis of arising effects is carried out in terms of kinematic and dynamic variables and in terms of energy flux. Relative advantages and disadvantages of these approaches are discussed. Comparison of the contributions of various mechanisms of energy transmission in the shell to the integral energy flux is performed. A special role of the rotational component in the occurrence of a subzero integrated energy flux is analyzed. The dependence of subzero energy flux and dynamic and kinematic variables on the relative thickness of the shell, the mode number and other parameters of the system is considered. The proportionality of the energy flux and its components for various modes is analyzed. The possible fields of application of the obtained effects are established.

Model‐independent derivation of macroscopic Maxwell equations is made from a general microscopic Lagangian of coupled light‐matter system. For both microscopic and macroscopic responses, we need only the susceptibility (χcd) connecting transverse (T‐) current density and T‐vector potential, in contrast to the traditional descrition via electric and magnetic susceptibilities, or e and μ, as independent parameters. The dispersion equation of a plane wave in a uniform macroscopic medium is not (ck/ω)2 = eμ, but (ck/ω)2 = 1 + (4πc/ω2)χcd, which may seriously affects the arguments of left‐handed materials (LHM). An alternative definition of LHM “materials with negative group velocity” is recommended as a consequence of this theory.

Characterization of a planar NID chiral interface under negative and/or positive phase velocity conditions