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Optics Letters

Negative refraction in terbium at ultraviolet frequencies

Zachary Noel Buckholtz, Deniz D. Yavuz

Published Aug 10, 2020• 4 citations
Publisher

Abstract

One of the key challenges in the development of negative index metamaterials is creating a sufficiently strong magnetic response in the material. Rare-earth ions can contain a strong optical magnetic response even in the ultraviolet region of the spectrum, which can be enhanced using magneto-electric cross-coupling. Using energies, transition strengths, and linewidths from atomic structure software, along with realistic inhomogeneous broadenings and densities in a solid, we simulate a negative index scheme using a terbium crystal at a wavelength of 282 nm.

DOI
10.1364/ol.400358

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One of the key challenges in the development of negative index metamaterials is creating a sufficiently strong magnetic response in the material. Rare-earth ions can contain a strong optical magnetic response even in the ultraviolet region of the spectrum, which can be enhanced using magneto-electric cross-coupling. Using energies, transition strengths, and linewidths from atomic structure software, along with realistic inhomogeneous broadenings and densities in a solid, we simulate a negative index scheme using a terbium crystal at a wavelength of 282 nm.
Abstract : In this project, our long-term goal is to demonstrate the first negative refraction in atomic systems. Although the concept of negative refraction remained an academic curiosity for a long time, it is now well-understood that negative refraction may have important and far-reaching practical implications. The key challenge in observing negative refraction in the optical region of the spectrum is the weakness of the magnetic response. Our central experimental result during this project has been the first observation of Rabi flopping of a magnetic dipole transition in the optical region of the spectrum. We have performed this experiment using the 7F0-5D1 transition of europium ions in a cryogenically cooled doped crystal. This is a major result; we have shown for the firs time that an electron can interact sufficiently strongly with the magnetic field of a light wave and coherently move between the levels. Another important result during this project was the proposal for a new type of materials that exhibit negative refraction. Because of these achievements, observing negative refraction and left-handed electromagnetic waves in atomic systems seem within reach for the first time.
We present a scheme that achieves negative refraction with low absorption in far-off resonant atomic systems. The scheme utilizes Raman resonances and does not require the simultaneous presence of an electric-dipole transition and a magnetic-dipole transition near the same wavelength. We show that two interfering Raman tran-sitions coupled to a magnetic-dipole transition can achieve a negative index of refraction with low absorption through magnetoelectric cross-coupling. We confirm the validity of the analytical results with exact numerical simulations of the density matrix. We also discuss possible experimental implementations of the scheme in rare-earth metal atomic systems.
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 suggest a scheme for obtaining negative refraction that does not require the simultaneous presence of an electric-dipole and a magnetic-dipole transition near the same transition frequency. The key idea of the scheme is to obtain a strong electric response by using far-off-resonant Raman transitions. We propose to use a pair of electric-dipole Raman transitions and utilize magneto-electric cross coupling to achieve a negative index of refraction without requiring negative permeability. The interference of the two Raman transitions allows tunable negative refraction with low absorption.
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.
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.