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Journal of Physics B Atomic Molecular and Optical Physics

The electromagnetically induced negative refractive index in the Er3+:YAlO3crystal

Chunxu Liu, Jisen Zhang, Junye Liu, Guang Jin

Published Apr 21, 2009• 12 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/42/9/095402

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•Jan 1, 2007•0 citations
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.
We first calculated the negative refractive index on the solid Er3+:YAlO3 crystal with a Λ-type four-level scheme proposed for atomic vapour by Thommen and Mandel and Kastel using quantum interference and electromagnetically induced transparency (EIT). It is shown that the frequency band with the negative index is wider (~1 MHz) than that reported previously. Usually,Im[n] is always positive,corresponding to absorption,and the ratio of refraction to absorption,|Re[n]/Im[n]|,is only of the order of unity. In our case the ratio |Re[n]/Im[n]|=4.6,which indicates that the absorption has been well suppressed by EIT approach. The negative Im[n] may be related to the stimulated emission of 4I13/2→4I15/2 of rare earth ion Er3+. It indicates that the rare earth ion doped material with abundant energy levels and various electric and magnetic transitions is an outstanding and practical candidate for electromagnetically induced negative refractive index material.
The electromagnetically induced left-handedness with zero absorption and large negative refractive index was investigated in a solid Er3+:YAG crystal with a four-level system proposed for an atomic medium. It was found that the frequency region with simultaneous negative permittivity and negative permeability, the zero absorption intervals, and the maximum values of the negative refractive index can be adjusted by changing the signal field, the coherent field, as well as the concentration of Er3+ ion in crystal. It is shown that wider zero absorption intervals with a higher index of refraction can be easily obtained when the signal field is only off resonance. The slab fabricated by the left-handed solid medium Er3+:YAG crystal with zero absorption may be a practical candidate for designing perfect lenses.
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.
In this work, we study the generation of a negative refractive index based on electromagnetically induced transparency (EIT) in a Rb four-level N-type atomic gas medium. We derive analytic expressions for the relative permittivity and relative permeability of the medium according to the parameters of the probe, pump, and signal laser fields. We then investigate the variation of the real parts of the relative permittivity and relative permeability with respect to the intensity and frequency of the pump and signal laser fields. In the presence of the pump laser beam, the medium becomes transparent to the probe laser beam even in the resonant region. At the same time, the real parts of the relative permittivity and relative permeability are simultaneously negative (i.e., the medium exhibits a negative refractive index) in the EIT spectral domain. In the presence of the signal laser beam, the EIT effect occurs over two different frequency domains of the probe beam, so a negative refractive index is also generated in these two frequency domains. The investigation of the real parts of the relative permittivity and relative permeability with intensity and frequency of the pump and signal laser fields allowed us to find the laser parameters for the appearance of the negative refractive index, which can be useful for experimental observations.
In this paper, we present the study on negative refractive index in an inhomogeneously broadened four-level inverted-Y atomic medium based on electromagnetically induced transparency (EIT). The expressions of the relative permittivity and the relative permeability are derived under Doppler broadening. For this four-level system, we have found two frequency bands of negative refractive index in an optical region corresponding to two EIT windows. The influences of coupling and signal laser fields as well as temperature on frequency bands of negative refractive index are investigated. Our research can be convenient for experimental implementation with real atomic media under different temperatures.
We propose a scheme for realizing negative refractive index in a V-type four-level atomic system. It is shown that the negative refractive index can be achieved in a wide frequency band based on the effect of quantum coherence. It is also found that the frequency band of negative refractive index and the absorption property of left-handed material are manipulated by the pump and control fields. Furthermore, left-handed material with reduced absorption is possible by choosing appropriate parameters. (c) 2006 Elsevier B.V. All rights reserved.