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Physica Scripta

Negative refractive index enhancement with zero absorption in a concentric chiral metal-atomic nanoshell

Haq Nawab, Majid Khan, Fazal Ghafoor

Published Apr 17, 2024• 2 citations

Abstract

Abstract We investigate the electromagnetic chirality and negative refraction in a concentric nanoshell of a chiral metal sphere and a chiral atomic shell. The medium of the atomic shell with a four-level system is driven by a laser field and an incoherent pump field in a diamond configuration. We show that the electric and magnetic absorption spectra connecting through the chiral coefficients of the respective dipole moments of the two media, produce five and three lines spectral profiles. We explain that the spectral lines separated by dips are the manifestation of the classical (quantum) coherence effect of the wave field excitation in the medium of the metal sphere (atomic shell), and the interaction of the respective dipole moments at the interface of the two media. Furthermore, we show negative refraction with zero absorption without requiring permittivity (ϵ) and permeability (μ) simultaneously negative, where for all values of the incident wavelength, Re [μ] ≈ 1, representing a strong chiral electromagnetic behavior. Consequently, the negative refractive index enhances sufficiently beyond n = −1 for a wide range of parameters depending on the coupling parameters, chiral coefficients, and the radii ratio of the concentric metal-atomic nanoshell.

DOI: 10.1088/1402-4896/ad4012

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Abstract We investigate the electromagnetic chirality and negative refraction in a concentric nanoshell of a chiral metal sphere and a chiral atomic shell. The medium of the atomic shell with a four-level system is driven by a laser field and an incoherent pump field in a diamond configuration. We show that the electric and magnetic absorption spectra connecting through the chiral coefficients of the respective dipole moments of the two media, produce five and three lines spectral profiles. We explain that the spectral lines separated by dips are the manifestation of the classical (quantum) coherence effect of the wave field excitation in the medium of the metal sphere (atomic shell), and the interaction of the respective dipole moments at the interface of the two media. Furthermore, we show negative refraction with zero absorption without requiring permittivity (ϵ) and permeability (μ) simultaneously negative, where for all values of the incident wavelength, Re [μ] ≈ 1, representing a strong chiral electromagnetic behavior. Consequently, the negative refractive index enhances sufficiently beyond n = −1 for a wide range of parameters depending on the coupling parameters, chiral coefficients, and the radii ratio of the concentric metal-atomic nanoshell.

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.

Optical properties of a concentric silver-atomic medium nanoshell are investigated based on the quasi-static and Maxwell-Garnett approximations. We consider the atomic medium as Λ-type three-level atoms driven simultaneously by a coupling field and a probe field. It is shown that the strong coupling between atoms and sphere plasmon of silver core emerges of multiple-mode and ultra narrow-band absorption spectra by controlling the permittivity of the atomic medium. In particular, coherent driving of the coupling field allows us to manipulate surface plasmon resonances, including frequency shift and bandwidth modification. Furthermore, we demonstrate that selective absorption enhancement of different modes can be achieved by tuning the radius of the core and the shell. These absorption properties yield potential applications of the nanoshells as ultracompact tunable nonlinear optical devices.

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.

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 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.