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Physica Scripta

Negative refractive index in a Doppler broadened three-level Λ-type atomic medium

Nguyen Van Ai, Nguyen Huy Bang, Le Van Doai

Published Dec 15, 2021• 5 citations
Publisher

Abstract

Abstract We have achieved a negative refractive index with significantly reduced absorption in a three-level Λ-type atomic gas medium under Doppler broadening. It shows that the conditions for obtaining negative refractive index in the presence of Doppler broadening are very different from those of Doppler broadening absent. In particular, in order to obtain negative refractive index in the case of Doppler broadening the coupling laser intensity must be approximately ten times greater than that when the Doppler broadening is ignored. Meanwhile, the frequency band of negative refractive index with Doppler broadening is significantly expanded (about a hundred times) compared to that without Doppler broadening, however, the amplitude of negative refractive index decreases with increasing temperature (or Doppler width). Even in some cases as temperature (Doppler width) increases, the left-handedness of the material can disappear. In addition, we also show that the amplitude and the frequency band of negative refractive index can be changed by adjusting the intensity and the frequency of coupling laser. Our theoretical investigation can be useful for selection of laser parameters under different temperature conditions to achieve negative refractive index in experimental implementation.

DOI
10.1088/1402-4896/ac437a

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Abstract We have achieved a negative refractive index with significantly reduced absorption in a three-level Λ-type atomic gas medium under Doppler broadening. It shows that the conditions for obtaining negative refractive index in the presence of Doppler broadening are very different from those of Doppler broadening absent. In particular, in order to obtain negative refractive index in the case of Doppler broadening the coupling laser intensity must be approximately ten times greater than that when the Doppler broadening is ignored. Meanwhile, the frequency band of negative refractive index with Doppler broadening is significantly expanded (about a hundred times) compared to that without Doppler broadening, however, the amplitude of negative refractive index decreases with increasing temperature (or Doppler width). Even in some cases as temperature (Doppler width) increases, the left-handedness of the material can disappear. In addition, we also show that the amplitude and the frequency band of negative refractive index can be changed by adjusting the intensity and the frequency of coupling laser. Our theoretical investigation can be useful for selection of laser parameters under different temperature conditions to achieve negative refractive index in experimental implementation.
This work investigates the manipulation of the negative refractive index in a degenerate three-level Λ \Lambda Λ-type atomic system in the presence of an external magnetic field and Doppler broadening. The results show that the bandwidth of the negative refractive index can be significantly broadened by increasing the coupling laser intensity; for example, when Ωc \Omega_c Ωc​ increases from 30γ 30\gamma 30γ to 60γ 60\gamma 60γ, the bandwidth expands from [0.5γ,1.5γ] [0.5\gamma, 1.5\gamma] [0.5γ,1.5γ] to [1.2γ,4γ] [1.2\gamma, 4\gamma] [1.2γ,4γ]. The spectral position can be flexibly tuned by adjusting the magnetic field, shifting toward lower (higher) frequencies for B=−1γc B = -1\gamma_c B=−1γc​ (B=2γc B = 2\gamma_c B=2γc​). Temperature has a pronounced effect on both the range and amplitude; increasing the temperature from 200 K 200\,\mathrm{K} 200K to 400 K 400\,\mathrm{K} 400K narrows the range from [−1.6γc,−0.2γc] [-1.6\gamma_c, -0.2\gamma_c] [−1.6γc​,−0.2γc​] to [−1.1γc,−0.5γc] [-1.1\gamma_c, -0.5\gamma_c] [−1.1γc​,−0.5γc​]. These findings may facilitate experimental realization and potential practical applications of EIT-based negative-index materials.
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.
Multicolor manipulation of negative refraction in a three-level Λ atomic system is theoretically investigated.Based on multicolor coherence, the negative refractive index can be obtained with reduced absorption.The refractive index can also be controlled by changing the sum of the phases of the sidebands in the trichromatic driving fields.By adjusting the sum phase, the refractive index can be varied between negative and positive in two different frequency bands.Furthermore, the frequency band corresponding to the negative refractive index is widened by increasing the intensity and the frequency difference of the trichromatic field.
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.
We propose two dense gas schemes of four-level 'Lambda'-type and V-type atoms based on the effect of quantum coherence. It is shown that under certain conditions the dense gas can simultaneously exhibit negative permittivity and negative permeability, and thus become a negative refractive-index material. Furthermore, by analyzing the absorption property of the left-handed materials, we find that the absoption can be reduced via choosing appropriate parameters. Such schemes might be used to fabricate isotropic and homogeneous left-handed material with vanishing absorption in a wider optical frequency band.
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.