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International Journal of Modern Physics B

ELECTROMAGNETICALLY INDUCED NEGATIVE REFRACTIVE INDEX IN DOPED SEMICONDUCTORS AT OPTICAL FREQUENCIES

Adil‐Gerai Kussow, Alkim Akyurtlu

Published Jan 30, 2011• 6 citations
Publisher

Abstract

Based on methods of quantum optics, we discuss the possibility of achieving the negative index of refraction in a semiconductor with donor-like impurities. The quantum states of hydrogen-like donor atom and states of an electron in conduction band constitute a discrete-level atomic medium within the optical range. The coherent coupling of an electric dipole transition with a magnetic dipole transition leads to permeability and permittivity responses and, within some frequency band, ensures the negative refractive index. The magnetic moment between two quasi-atomic states separated by optical frequencies is induced by a low-frequency electromagnetic field. The implementation of this scheme is carried out in tin-doped indium oxide, and the calculations show feasibility of the effect within a broad bandwidth ∼2% with a high figure of merit greater than 10 in the optical regime.

DOI
10.1142/s0217979211057906

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Based on methods of quantum optics, we discuss the possibility of achieving the negative index of refraction in a semiconductor with donor-like impurities. The quantum states of hydrogen-like donor atom and states of an electron in conduction band constitute a discrete-level atomic medium within the optical range. The coherent coupling of an electric dipole transition with a magnetic dipole transition leads to permeability and permittivity responses and, within some frequency band, ensures the negative refractive index. The magnetic moment between two quasi-atomic states separated by optical frequencies is induced by a low-frequency electromagnetic field. The implementation of this scheme is carried out in tin-doped indium oxide, and the calculations show feasibility of the effect within a broad bandwidth ∼2% with a high figure of merit greater than 10 in the optical regime.
The existing Quantum Optics- based models of negative refractive index in atomic-vapor medium (e.g. Ne, Na) require unrealistically strong magnetic response of atoms combined with high atomic density. In contrast to these gas-based models, our approach explores solid-state n-type semiconductor with well-defined hydrogen-like donor atomic states within the band gap. Based on methods of Quantum Optics, we have found that optically transparent indium oxide is negative refractive index material if doped with tin and zinc (In 2-x Sn x/2 Zn x/2 O 3 (zinc-doped ITO)). The desirable negative refractive index effect is due to coherent coupling an electric dipole transition with magnetic transition with proper detunings of the probe and support laser beams (A.-G. Kussow and A. Akyurtlu, Int. J. Mod. Physics (2010)). The calculations demonstrate the feasibility of the effect at ~ 10 THz with extremely high figure of merit FOM >> 10.
We discuss the feasibility of negative refraction with reduced absorption in coherently driven atomic media. Coherent coupling of an electric and a magnetic dipole transition by laser fields induces magnetoelectric cross coupling and negative refraction at dipole densities which are considerably smaller than necessary to achieve a negative permeability. At the same time the absorption gets minimized due to destructive quantum interference and the ratio of negative refraction index to absorption becomes orders of magnitude larger than in systems without coherent cross coupling. The proposed scheme allows for a fine tuning of the refractive index. We derive a generalized expression for the impedance of a medium with magnetoelectric cross coupling and show that impedance matching to vacuum can easily be achieved. Finally we discuss the tensorial properties of the medium response and derive expressions for the dependence of the refractive index on the propagation direction.
A scenario for realizing simultaneously negative permittivity and permeability of a two-photon quantum-coherent atomic vapor is suggested in order to achieve a left-handed atomic medium with a negative refractive index. One of the remarkable features of the present scheme is that it can lead to a controllable manipulation of the negative refractive index of the atomic vapor. Since the electric- and magnetic-dipole allowed transitions of atoms can be excited by visible and infrared lightwaves, the refractive index of the atomic vapor can exhibit its negative refractive index at optical and near-optical frequency bands. This may be a new scheme to fabricate a negatively refracting material based on the quantum optical approach. Such a three-dimensionally isotropic negative refractive index at visible and infrared wavelengths induced by the two-photon-resonant quantum coherence would find a potential application in fabrication of superlenses for perfect imaging and subwavelength focusing.
A new quantum optical mechanism to realize simultaneously negative electric permittivity and magnetic permeability is suggested. In order to obtain a negative permeability, we choose a proper atomic configuration that can dramatically enhance the contribution of the magnetic-dipole allowed transition via the atomic phase coherence. It is shown that the atomic system chosen with proper optical parameters can give rise to striking electromagnetic responses (leading to a negative refractive index) and that the atomic vapour becomes a left-handed medium in an optical frequency band. Differing from the previous schemes of artificial composite metamaterials (based on classical electromagnetic theory) to achieve the left-handed materials, which consist of anisotropic millimetre-scale composite structure units, the left-handed atomic vapour presented here is isotropic and homogeneous at the atomic-scale level. Such an advantage may be valuable in realizing the superlens (and hence perfect image) with left-handed atomic vapour.
A new mechanism for realizing negative refractive index with a four-level atomic system is suggested. The explicit expressions for the electric permittivity and magnetic permeability at probe frequency are presented. It is shown that there is a frequency band in which the four-level photonic-resonant atomic vapour may exhibit simultaneously negative permittivity and permeability, and that such an atomic vapour may become a left-handed material (negatively refracting medium). Compared with the previous schemes to realize negative refraction within the framework of classical electromagnetic theory, the most remarkable features of the present scenario are as follows: (i) isotropic material with microscopic structure units at atomic-scale level, (ii) negative refraction in visible and infrared frequency bands, (iii) controllable manipulation by external fields and (iv) based on quantum coherence in a multilevel atomic system.
We show that negative refraction with minimal absorption can be obtained by means of quantum interference effects similar to electromagnetically induced transparency (EIT). 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 suppress 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 refractive index can be fine-tuned, which is essential for practical realization of subdiffraction-limit imaging. As with EIT, electromagnetically induced chirality should be applicable to a wide range of systems.