Universal behaviour of high-Q Fano resonances in metamaterials: terahertz to near-infrared regime
© The Author(s) 2018
Received: 20 January 2018
Accepted: 15 February 2018
Published: 21 February 2018
The observation of Fano resonance phenomena is universal across several branches of physics. Photonics is one of the most important areas of physics that mainly deals with the control of light propagation and localization through its interaction with natural and artificially engineered media. In an era of miniaturization, manipulation of light at micro-nanoscales has assumed unprecedented significance due to its potential to satisfy the mankind with disruptive future technologies. In this work, we present our study on the universality of high quality factor Fano resonances in planar metamaterials across terahertz and infrared parts of the electromagnetic spectrum. The narrow linewidth asymmetric Fano resonant metamaterials have tremendous potential to find applications in micro-nanoscale flat lasers, sensors, and ultra-resolution spectrometers.
In recent years, the field of plasmonics and metamaterials have enabled a seemingly new and innovative direction in the optics and photonics community, promising the conceptualization of subwavelength inventions with advanced and exceptional functionalities [1–3]. Metamaterials  are composed of periodic arrangements of artificially engineered meta-atoms whose optical and physical properties are determined by its size, shape and geometry. Meta-atoms are the building blocks of the metamaterials with artificial properties of atoms. When the ensembles of meta-atoms interact with the incident electromagnetic waves, fascinating optical and physical properties non-existent in natural materials are manifested, which allow them to have the ability to guide, modulate or slow down light. The occurrence of strong light-matter interactions in metallic nano- to micro-structures is beneficial for applications in sensors [5–8], absorbers [9, 10], nanolasers , photoswitches [11–15, 16] and slow-light devices . However, metallic subwavelength structures entail extremely high losses due to absorption, especially at higher frequency regime of the electromagnetic spectrum where the energies are transferred into optical and acoustic phonons . Radiative and non-radiative losses render the operation of metamaterial devices inefficient and hence impractical. As such, several solutions were proposed to reduce the inherent losses dominant in metamaterials which involve replacing metals with highly doped semiconductors  or superconductors , or to compensate losses by integrating metamaterials with optical gain medium [21, 22].
Apart from introducing new plasmonic materials or optical gain into the system, geometric tailoring of the subwavelength structures offers an additional platform to mitigate radiative losses. In general, the symmetry of a metamaterial system exhibits a broad dipole resonance that can be excited by the far-field of the propagating electromagnetic wave in free space. However, breaking the symmetry of a unit cell induces a sharp asymmetric lineshape which is forbidden in a perfectly symmetric system. This sharp asymmetric lineshape which is also known as Fano resonance  arises from the destructive interference between a bright (continuum) mode and a dark (discrete) mode. The bright mode is superradiant and appears as a broad dipole resonance in the spectrum. As the bright mode has a finite dipole moment whose polarization of the conduction electrons are aligned similarly to the polarization of the electromagnetic field, it can strongly couple with the electromagnetic field. Therefore, energies are transferred between the conduction electrons and the oscillating fields of the propagating electromagnetic wave which are then scattered to the far-field, contributing to the radiative losses in the system. The dark mode which is subradiant in nature, can only be excited indirectly through near-field coupling with the superradiant bright mode, which in turn interferes back with the superradiant bright mode to produce Fano resonance. This process suppresses the radiative losses in Fano resonators and the overall losses are mainly contributed by non-radiative losses due to resistive heating (especially at high frequencies). In metals, free conduction electrons are constantly moving in random motion among the cloud of positive lattice ions. When the free conduction electrons collide with the lattice ions or another free electron, energy is lost non-radiatively to the environment in the form of heat due to resistive heating in metallic Fano resonators. However, at low frequencies, Drude metals have a higher conductivity and so non-radiative losses can be reduced, which leads to radiative losses contributing as the main loss mechanism. In summary, the sharp asymmetric lineshape of Fano resonance is more prominent at terahertz frequency as compared to infrared frequency due to lower non-radiative losses.
Numerous designs of the unit cell in Fano system have been proposed, whereby the symmetry of the unit cell is broken either (in a single-particle system) by altering the geometry of the unit cell  or (in a dual-particle system) by moving one of the sub-unit cell [25, 26] or modifying the dimension/geometry of the sub-unit cell [27–29] relative to the other neighbouring sub-unit cell to induce the sharp asymmetric lineshape. Fano resonance has also been demonstrated in multi-particle system such as the dolmen structure (the unit cell itself possesses asymmetry) , or in the heptamer (a special case of symmetric structure) [31, 32] whereby Fano resonance is a result of out-of-phase interactions between the bodies of particles. The degree of asymmetry of the unit cell is determined by asymmetry parameter which is a dimensionless parameter and it is defined relative to its specific Fano system. In addition, Fano resonance is most easily excited in positive Fano structures when the polarization of the electric field incident onto the unit cell is parallel to the symmetry breaking axis of the unit cell.
Fano resonance in optical metamaterial system is highly attractive, primarily because at the resonance frequency, it has strong electromagnetic field confinement within the structures and an extremely narrow linewidth which also dictates its quality (Q) factor. Q-factor is often used as a dimensionless parameter to characterize the strength of damping on the metamaterial resonators. For a metamaterial system with heavy damping, the resonance will not be able to sufficiently survive the energy lost through radiative and non-radiative pathways which cause the resonance linewidth to be largely broadened, and vice versa. Therefore, Q-factor helps to determine how much of the energy is being lost or confined, which allows further refinements to be made to optimize the performance of the metamaterial system. Albeit the abundance of discussion on Fano system, there remains a void in the systematization of the Q-factors for different asymmetry parameters in complementary structures across the near-infrared (NIR) to terahertz (THz) regime. It has been observed in several works that the Q-factor of Fano system decays exponentially with increasing asymmetry parameter [33–35]. However, the similarity in the decay trend of the Q-factor ubiquitous in Fano system has received less attention and remains an essential part of understanding the implications of radiative and non-radiative losses. Hence, if a standard system of decay trends under different situations could be developed, it could serve as a guide for appropriate optimization and fabrication of scalable and functional metamaterial-based devices. In this work, we performed numerical calculations on a complementary asymmetric dipole bars, and by proportionally scaling the dimensions we induced Fano resonance at different frequency regimes ranging from NIR to THz. The Q-factors at different regimes were evaluated and fitted with an exponential decay function to extract the decay constants. Our results further show that for the smallest asymmetry parameter, the decay constant of the Q-factor obtained as a function of the Fano resonance frequency from NIR to THz regime is the largest. We also observed that the decay constant of the Q-factor obtained as a function of asymmetry parameter is largest at the NIR Fano resonance frequency and then decreases (with saturation) towards THz Fano resonance frequency. Both distributions display similar trend which tend towards an exponential decay behaviour.
Numerical simulations based on finite-differential time-domain (FDTD) technique were performed using commercially available electromagnetic simulation software, computer simulation technique (CST) Microwave studio using the frequency domain solver. Unit cell boundary conditions were imposed in the periodic directions of x and y, and the incident plane wave source is excited from the Zmax direction with the electric field polarized along the symmetry axis of the asymmetric dipole bars as shown in Fig. 1. Throughout the interested regions of the electromagnetic spectrum, the quartz substrate is modelled as loss free and assigned with a permittivity of 2.25. The aluminium is modelled as a lossy metal in the THz regime with DC conductivity of σ = 3.56 × ×107 S/m, and permittivity values of aluminium in the optical regime were taken from the data measured by Palik .
3 Results and discussion
In conclusion, the universal behaviour of Fano resonance in symmetry-broken resonators is investigated in asymmetric dipole bars. Sharp asymmetric and strong resonant lineshape were observed with Q-factor of at least 20 from the near-infrared to terahertz regime. Positive and complementary structures follow closely to the Babinet’s Principle for electromagnetic fields. A standard system based on exponential decay function has been developed to characterize the behaviour of Q-factor under varying asymmetry parameter or Fano resonance frequency. Decay constants obtained from the exponential fittings provide insights into the rate at which energy is stored under different conditions. This work will be more extensive if a larger superset can be established based on varying materials or geometries, and further evaluated based on their decay trends. The process may be tedious but once a standard system is developed, it would enable smart designing of the metamaterial structure to tailor its Q-factor by itself through machine learning techniques. The standard system is beneficial and useful for the realization of scalable and “smart” metadevices across a wide spectral range.
RS conceived the idea and supervised the work. WXL performed the simulations. RS and WXL wrote the manuscript together. Both authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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Funding and acknowledgements
This work is supported by research grants from Singapore Ministry of Education Grant No. MOE2015-T2-2-103.
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