Sign of refractive index and group velocity in left-handed media

Pokrovsky, A.; Efros, Alexander L.

doi:10.1016/s0038-1098(02)00553-7

Cited by 49 publications

(26 citation statements)

References 12 publications

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“…Using thermodynamic arguments, it was shown that in a left-handed passive medium the real and imaginary parts of the index of refraction must have opposite signs [13]. This sign condition is not valid here since we deal with active media.…”

Section: 053601 (2006) P H Y S I C a L R E V I E W L E T T E R S mentioning

confidence: 93%

“…Using typical values 10 8 Hz, 13 10 7 Hz, jd 34 j ' 10 ÿ29 Cm, and 12 ' B , negative permittivity and negative permeability at ÿ0:1 are obtained for a density N > 10 25 at=m 3 , which is perfectly realistic. Note that it is because we are interested in the vicinity of 12 0 that we need to choose !…”

Section: 053601 (2006) P H Y S I C a L R E V I E W L E T T E R S mentioning

confidence: 99%

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Electromagnetically Induced Left Handedness in Optically Excited Four-Level Atomic Media

2006

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We show that left-handed properties can be electromagnetically induced in a general four-level atomic medium for a finite spectral range. We use an electric (magnetic) atomic transition as an electric (magnetic) resonator to modify the permittivity (permeability), both at the same frequency. The implementation of the four-level model is carried out in atomic hydrogen and neon. In each case the existence of left-handed properties is predicted inside an experimentally reachable domain of parameters. DOI: 10.1103/PhysRevLett.96.053601 PACS numbers: 42.50.Gy, 42.25.Bs, 78.20.Ci The propagation of electromagnetic waves in matter is characterized by the frequency-dependent relative dielectric permittivity " r and magnetic permeability r . Their product defines the index of refraction: " r r n 2 . Lefthanded media are characterized by negative real parts of " r , r [1]. It has been shown that in this case the negative root must be used for the index of refraction n ÿ " r r p[1]. Left-handed media have recently attracted significant attention since it has been discovered that a slab of lefthanded materials is able, for instance, to focus light into a spot much smaller than the wavelength, realizing a ''perfect'' lens [2]. Experimentally, left-handed properties in the microwave domain were obtained with a composite medium made of a periodic array alternation of split ring resonators and continuous wires [3]. Left handedness has been recently analyzed in a three-level medium [4]. However, the proposed scheme requires the conflicting demand that the middle state is involved in both a magnetic transition and an electric transition at the same frequency. An independent study of the same scheme has reached a similar conclusion [5].In this Letter we demonstrate that a four-level medium may be left handed in a restricted domain of parameters. In our model an electric transition and a magnetic transition play the role of an electric resonator and a magnetic resonator, respectively. They involve two different pairs of states, leading to a realistic energy configuration. Explicit calculation predict the occurrence of a left-handed domain in hydrogen and neon gases with Ref" r g < 0 andNumerous works have been carried out over the past 15 years to control the index of refraction by quantum interference. They led, in particular, to electromagnetically induced transparency (EIT) [6], refractive index enhancement [7], and slow light [8]. As the magnetic transition strengths are typically 2 orders of magnitude smaller than the electric transition strengths, the permeability does not change significantly from unity as the frequency of the probe magnetic field reaches a magnetic resonance. Therefore, the modification of the index of refraction is in general due mainly to a modification of the electrical susceptibility. However, a significant change of the permeability can be obtained from a magnetic moment induced by coupled electric transitions [4]. In this Letter we combine the modification of the permeability by an induced magneti...

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Section: 053601 (2006) P H Y S I C a L R E V I E W L E T T E R S mentioning

confidence: 93%

Section: 053601 (2006) P H Y S I C a L R E V I E W L E T T E R S mentioning

confidence: 99%

Electromagnetically Induced Left Handedness in Optically Excited Four-Level Atomic Media

2006

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“…[14]. It reads that the group velocity v g = ∂ω/∂k in an isotropic medium is positive in the regular …”

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confidence: 99%

Dielectric photonic crystal as medium with negative electric permittivity and magnetic permeability

Efros

Pokrovsky

2004

Solid State Communications

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We show that a two-dimensional photonic crystal (PC) made from a non-magnetic dielectric is a left-handed material in the sense defined by Veselago. Namely, it has negative values of both the electric permittivity ǫ and the magnetic permeability µ in some frequency range. This follows from a recently proven general theorem. The negative values of ǫ and µ are found by a numerical simulation.Using these values we demonstrate the Veselago lens, a unique optical device predicted by Veselago. An approximate analytical theory is proposed to calculate the values of ǫ and µ from the PC band structure. It gives the results that are close to those obtained by the numerical simulation. The theory explains how a non-zero magnetization arises in a non-magnetic PC.

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“…On the other hand, in purely dielectric homogeneous media, negative dispersion is obtained only within the absorption bands. A homogeneous material can be simultaneously transparent and characterized by negative dispersion only if it has a nontrivial magnetic permeability 7,8 . Therefore, to obtain this result by homogenizing an intrinsically non-magnetic PC, one has to consider sufficiently large frequencies where the dispersion is negative 9 .…”

Section: Introductionmentioning

confidence: 99%

Applicability of effective medium description to photonic crystals in higher bands: Theory and numerical analysis

Markel

Tsukerman

2016

Phys. Rev. B

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We consider conditions under which photonic crystals (PCs) can be homogenized in the higher photonic bands and, in particular, near the Γ-point. By homogenization we mean introducing some effective local parameters eff and µ eff that describe reflection, refraction and propagation of electromagnetic waves in the PC adequately. The parameters eff and µ eff can be associated with a hypothetical homogeneous effective medium. In particular, if the PC is homogenizable, the dispersion relations and isofrequency lines in the effective medium and in the PC should coincide to some level of approximation. We can view this requirement as a necessary condition of homogenizability. In the vicinity of a Γ-point, real isofrequency lines of two-dimensional PCs can be close to mathematical circles, just like in the case of isotropic homogeneous materials. Thus, one may be tempted to conclude that introduction of an effective medium is possible and, at least, the necessary condition of homogenizability holds in this case. We, however, show that this conclusion is incorrect: complex dispersion points must be included into consideration even in the case of strictly non-absorbing materials. By analyzing the complex dispersion relations and the corresponding isofrequency lines, we have found that two-dimensional PCs with C4 and C6 symmetries are not homogenizable in the higher photonic bands. We also draw a distinction between spurious Γ-point frequencies that are due to Brillouin-zone folding of Bloch bands and "true" Γ-point frequencies that are due to multiple scattering. Understanding of the physically different phenomena that lead to the appearance of spurious and "true" Γ-point frequencies is important for the theory of homogenization.

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Sign of refractive index and group velocity in left-handed media

Cited by 49 publications

References 12 publications

Electromagnetically Induced Left Handedness in Optically Excited Four-Level Atomic Media

Electromagnetically Induced Left Handedness in Optically Excited Four-Level Atomic Media

Dielectric photonic crystal as medium with negative electric permittivity and magnetic permeability

Applicability of effective medium description to photonic crystals in higher bands: Theory and numerical analysis

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