Tunable Negative Refraction without Absorption via Electromagnetically Induced Chirality

Abstract

We show that negative refraction with minimal absorption can be obtained by means of quantum interference effects similar to electromagnetically induced transparency. Coupling a magnetic dipole transition coherently with an electric dipole transition leads to electromagnetically induced chirality, which can provide negative refraction without requiring negative permeability, and also suppresses absorption. This technique allows negative refraction in the optical regime at densities where the magnetic susceptibility is still small and with refraction/absorption ratios that are orders of magnitude larger than those achievable previously. Furthermore, the value of the refractive index can be fine-tuned via external laser fields, which is essential for practical realization of sub-diffraction-limit imaging. PACS numbers:Negative refraction of electromagnetic radiation [1] is currently a very active area of research, driven by goals such as the development of a "perfect lens" in which imaging resolution is not limited by electromagnetic wavelength [2]. Despite remarkable recent progress in demonstrating negative refraction using technologies such as meta-materials [3,4,5,6] and photonic crystals [7,8,9], a key challenge remains the realization of negative refraction without absorption which is particularly important in the optical regime. Here we propose a promising new approach to this problem: the use of quantum interference effects similar to electromagnetically induced transparency (EIT) [10] to suppress absorption and induce chirality [11] in an ensemble of radiators (atoms, molecules, quantum dots, excitons, etc.).Early proposals for negative refraction required media with both negative permittivity and permeability (ε, µ < 0) in the frequency range of interest. In the optical regime, however, it is difficult to realize negative permeability with low loss, since typical transition magnetic dipole moments (µ a ) are smaller than transition electric dipole moments (d a ) by a factor of the order of the fine structure constant α ∼ 1 137 . As a consequence the magnitude of magnetic susceptibilities χ m are much smaller than that of electric susceptibilities χ e :2 |χ e | ∼ (1/137) 2 |χ e |, where ε = 1 + χ e and µ = 1 + χ m . Recently, Pendry suggested an elegant way to alleviate this problem [13] by using a chiral medium, i.e., a medium in which the electric polarization P is coupled to the free-space magnetic field component H of an incident optical-frequency electromagnetic wave and the magnetization M is coupled to the electric field component E:Here ξ EH and ξ HE are the chirality coefficients, which in general can be complex. These terms lead to additional contributions to the refractive indexAs Pendry noted, such a chiral medium allows n < 0 without requiring negative permeability if there is a positive imaginary part of (ξ EH − ξ HE ) of sufficiently large magnitude. For example, choosing the phases of the complex chirality coefficients such that ξ EH = −ξ HE = iξ, with ξ, ε, µ > 0, the index of refraction ...

Coherent Magnetic Response at Optical Frequencies Using Atomic Transitions

“…We also note that a negative permeability is not necessary to create a left-handed material. For example, using chirality, even a magnetic susceptibility of χ M ≈ 10 −2 is sufficient to induce a negative index of refraction [18,19].…”

“…It was recognized early on that it may also be possible to construct left-handed materials using sharp transitions of atoms or ions [16][17][18][19][20]. When an electron makes a transition from the ground level to an excited level, it can do so by either interacting with the electric field or the magnetic field of light.…”

Coherence-Driven Topological Transition in Quantum Metamaterials

“…More recently, exotic properties such as left-handed electromagnetic responses have been theoretically proposed using dense homogenous atomic vapors with number density N 0 ∼ 10 23 m −3 or higher [17][18][19][20][21]. However, because quantum interference is fragile, the performance of thermal atomic vapors is severely affected by collisional dephasing and Doppler broadening.…”

The thermal effect on the left-handedness of the mesoscopic composite right-Left handed transmission line

“…However, one key obstacle in the applications of left-handed materials is absorption which is particularly important in the optical regime [5,6,7], and significant efforts have been spent to realize low-loss left-handed materials [8,9,10]. Meanwhile, the transmission lines (TLs) are reportedly low dissipation and wide frequency bands for lefthanded materials [11,12,13,14], i.e., the composite right-Left handed transmission lines (CRLH-TLs) [15].…”