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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Negative refractive index in doped semiconductors via electromagnetically induced mixed-parity transitions

Adil‐Gerai Kussow, Alkim Akyurtlu

Published Aug 19, 2010• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.859137

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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.
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 dressed states that are linear combinations of two bare levels of an atom (e.g., an alkali-metal atom) can be realized by a strong-coupling laser beam. As the dressed states have mixed parities, both electric- and magnetic-dipole-allowed transitions can occur between the dressed states and a third level with a definite (pure) parity. It is shown that such dressed-state mixed-parity transitions in an atomic vapor (the concept also applies in the solid state) can give rise to a negative refractive index. The produced negative refractive index is isotropic with atomic-scale microscopic structure units, and the negative real part can emerge in the optical frequency band. Also examined is the case of a fully quantized probe photonic field which interrogates the bottom dressed state and the third-level state. Similarities between the semiclassical approach for the weaker probe field and its fully quantum mechanical second-quantization treatment are discussed in regard to the off-diagonal density matrix element for the reduced $2\ifmmode\times\else\texttimes\fi{}2$ manifold, and its implications for the refractive index.
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.
Abstract—A scheme of double-negative left-handed atomic vapor medium based on dressed-state assisted simultaneous electric and magnetic resonances is suggested. In this mechanism, simultaneous electric- and magnetic-dipole allowed transitions of atoms are driven by an optical wave by taking full advantage of both mixed-parity dressed-state assisted resonance and incoherent population pumping in a quantum-coherent atomic medium (e.g., alkali-metal atomic vapor). Since the simultaneously negative permittivity and permeability can be achieved in a same frequency band, such an atomic vapor will exhibit an incoherent-gain double-negative refractive index that is three-dimensionally isotropic and homogeneous. The imaginary part of the negative refractive index of the present atomic vapor would be drastically suppressed or would become negative because of loss compensation through incoherent population transfer. The quantum-coherent left-handed atomic vapor presented here will have four characteristics: i) three-dimensionally isotropic and homogeneous negative refractive index, ii) double-negative atomic medium at visible (and infrared) wavelengths, iii) tunable negative refractive index based on dressed-state quantum coherence, and iv) high gain due to incoherent pumping action.
We carried out the negative refractive index in the solid medium Er3+:YAlO3 crystal with a Λ-type four-level scheme proposed for atomic vapour by Thommen and Mandel, and Kastel (Phys. Rev. Lett. 2006 96 053601 and 2007 98 069301) based on quantum interference and electromagnetically induced transparency (EIT). The results show that the frequency band with the negative index is much wider (~1 MHz) than reported previously. Usually, Im[n] is always positive, corresponding to absorption, and the figure of merit (FOM, the ratio of real to imaginary, namely |Re[n]/Im[n]|) is only on the order of unity. We achieve FOM = |Re[n]/Im[n]| = 4.6. The corresponding negative Im[n] is related to the stimulated emission of 4I13/2 → 4I15/2 of the rare earth ion Er3+ under external electromagnetic fields. It is concluded that the rare earth ion doped material with abundant energy levels and various electric and magnetic transitions is an outstanding and practical candidate for the electromagnetically induced negative refractive index material.
This research focuses on a coherently driven four-level atomic medium with the aim of inducing a negative index of refraction while taking into consideration local field corrections as well as magnetoelectric cross coupling (i.e.,chirality) within the material's response functions. Two control fields are used to render the medium transparent for a probe field which simultaneously couples to an electric and a magnetic dipole transition, thus allowing one to test the permittivity and permeability of the material at the same time. Numerical simulations show that a negative index of refraction with low absorption can be obtained for a range of probe detunings while depending on number density and the ratio between the intensities of the control fields.