Nikitas Papasimakis and Nikolay I. Zheludev
Inspired by the study of atomic resonances, researchers have developed a new type of metamaterial. Their work paves the way toward compact delay lines and slow-light devices.
Metamaterials—crystalline-like sub-wavelength arrangements of electromagnetic resonators—can exhibit exotic optical properties, such as negative refraction and cloaking, most of which have no counterpart in natural media. Metamaterial structures could one day be used to develop a wide variety of devices with enhanced and unusual functions, ranging from super-lenses to electromagnetic cloaks. Metamaterials are also expected to play a key role in the development of all-optical data processing chips.
Now, a new direction has emerged in metamaterial research. Scientists are looking to realize narrow, low-loss resonances and strongly dispersive behavior in planar, two-dimensional structures of sub-wavelength thickness by using interference effects that suppress radiation leakage. These advances will greatly expand the metamaterial playground to encompass sensors, compact delay lines and coherent light-emitting devices.
At the core of this new approach lies an intriguing analogy with the famous quantum phenomenon of electromagnetically induced transparency (EIT). Following the first observation by Fedotov et al. that the electromagnetic response of certain metamaterials provides “another classical analog of the narrow resonances observed in electromagnetically induced transparency,” recent studies show that, by mimicking this quantum phenomenon, the dispersive properties of such planar metamaterials can lead to slow-light propagation and long pulse delays in the microwave, terahertz and optical parts of the spectrum.
Typical three-level atomic system used in demonstrations of EIT. The ground state is coupled to the excited state, where absorption occurs via a probe beam. A pump beam couples the metastable state to the excited state, while transitions from the metastable to the ground state are not allowed. Interference between the two transitions leads to a vanishing probability for the atoms to be found in the excited state; consequently, absorption is minimized.
(Top) A characteristic probe absorption spectrum of an atomic medium under EIT conditions. The broad absorption peak experienced by the probe beam is split in two by a narrow dip when the pump is applied. (Bottom) This results in a very sharp variation of the refractive index, which is responsible for long pulse delays and slow-light behavior.
Mechanical analog of an atomic EIT system. The first oscillator is subject to friction and corresponds to the atom under the influence of the probe beam (external force F), while the second stands for the coupling to the pump beam. Under certain conditions, the first oscillator remains still, thus eliminating dissipation in the system.
Fano resonances: electromagnetically induced transparency and dynamical damping
A typical approach to achieving sharp spectral features involves the so-called Fano resonances that occur due to the interference of different excitation pathways. In the simplest case, Fano interference requires a quasi-bound state coupled to a continuum—which results in two channels of excitation, a direct one and an indirect one through the quasi-bound state. Constructive and destructive interference of these two channels leads to very narrow resonance lineshapes. Such resonances are used in the well-known phenomenon of EIT, where a pump and probe beam are applied at different dipole transitions of an atom vapor that share the same excited state; transitions between the two ground states are not allowed.
The resulting destructive interference of quantum probability amplitudes inhibits absorption and leads to a narrow transparency window in the spectrum of the otherwise opaque atomic medium. As a result, the probe beam can propagate without losses. This resonant transmission peak is accompanied by sharp normal dispersion, which can lead to a dramatic reduction in group velocity and a significant enhancement of nonlinear interactions.
However, scientists’ observations of EIT in atomic gases were restricted to the available atomic resonances, and the work necessitated optical pumping and often cryogenic temperatures. Such requirements severely hinder practical applications, particularly with respect to integration. These obstacles were soon overcome by the realization that the essential physics behind EIT are actually classical, and similar behavior can be observed in very simple systems, such as coupled spring-mass oscillators.
This insight led to the implementation of induced transparency effects in classical optical systems—for example, coupled optical resonators, photonic bandgap crystals and photonic crystal waveguides—that are robust and do not require special experimental conditions. The operation frequency is directly related to the geometry of the structure and can be varied in a wide spectral range through scaling. Nevertheless, in all approaches to classical EIT, the structure extends along the propagation direction of the incident wave, which imposes restrictions on the minimum dimensions of the medium.
Metamaterial-induced transparency
In the case of metamaterials, we used Fano resonances in a planar array of asymmetrically split-ring “meta-molecules” that consist of two arcs with different lengths in order to minimize scattering losses and achieve high-quality resonances. Indeed, breaking the symmetry of the split-ring leads to two closely spaced resonances, each of which corresponds to strong excitation of one of the two arcs. When excited by an incident electromagnetic wave, the two arcs support currents oscillating in-phase, apart from a narrow frequency range, where an anti-symmetric current configuration is established due to the coupling of the two resonances.
As a consequence, these anti-symmetric currents radiate fields that interfere destructively, allowing the incident wave to propagate without losses, as signified by a narrow transparency window in the transmission spectrum of the metamaterial. This resonant mode has a long lifetime due to its weak coupling to free-space radiation and therefore appears to be “trapped” in the vicinity of the metamaterial surface—hence the term “trapped mode.” An important consequence of causality restrictions is that, at the metamaterial resonance, the transmission band is accompanied by steep normal dispersion, providing for low group velocities and slow light behavior.
In fact, we showed in a recent study that similar resonances can also be observed experimentally in a bi-layered structure. In this case, the two metamaterial layers can be either identical or very similar, and they are separated by a small sub-wavelength distance along the propagation direction. This displacement allows the two layers to be excited with opposite phases at a specific frequency, hence leading to the elimination of scattering losses by destructive interference of the re-radiated fields originating from each layer.
