Influence ofDriving Pulse Properties on Third-HarmonicDiffraction from Quasi-BIC Metasurfaces

A scenario of quantum interference in which decaying (quasibound) states interfere with the continuum or with other quasibound states is investigated. The model we adopt as the basis of our analysis consists of two or three antidots in an electronic waveguide. In a perfect waveguide, electron states belong to different subbands and antidots give a transfer between them. For a waveguide with two antidots we have observed interesting phenomena: interference between one subband of the quasibound state and a background second subband, and interference of resonant group states of different subbands. In this case, the zero of the Fano resonance is shifted to the complex plane and the coupling parameter becomes complex. In a waveguide with three antidots, degeneracy of two quasibound states takes place and interference of these states occurs. The Fano interference of two nearly degenerate resonances may bring a full suppression of pair resonances in the transmission. We explain that this is due to the parities of the quasibound states. Our results show that the zero of the Fano resonance due to interference between the quasibound states and the continuum is generally placed in the complex plane. This gives an additional possibility for manipulating conductance resonances in a waveguide by changing the antidot parameters.

High-index dielectric structures have recently been studied intensively for Mie resonances at optical frequencies. These dielectric structures can enable extreme light manipulation, similar to that which has been achieved with plasmonic nanostructures. In the microwave region, dielectric resonators and metamaterials can be fabricated directly using 3D printing, which is advantageous for fabricating structurally complicated 3D geometries. It is therefore especially suitable for the fabrication of subwavelength structures. Here we report theoretical investigations on microwave Fano resonances in 3D-printable dielectric materials and structures. In particular, we propose and analyse 3D-printable, hollow, dielectric resonators with relatively low refractive indices, which exhibit sharp Fano resonances. We can control the interaction between bright and dark modes in a coupled dielectric particle pair by adjusting the inner-hole size, and thus we can increase the radiative Q factors further. We also find that Fano resonances in these hollow dielectric resonators are very sensitive to an index change in the surrounding medium, which could be useful for long-distance environmental sensing. New possibilities and opportunities are opening up with the rapid development of 3D-printing technologies. Our findings and the detailed investigations reported here can provide useful guidelines for future photonic devices based on 3D-printable materials and structures.

The existence of Fano resonances in dynamic resonant tunneling (RT) systems has been investigated. Fano resonances are characterized by the appearance of a 100% reflection coefficient in proximity to a high transmission coefficient. For a Fano resonance to appear, a bound state must exist. On the other hand, a resonant tunneling process is characterized by a high transmission and the existence of a quasi-bound state (QBS) instead of a bound one. It has been shown that, by narrowing the width of the barrier, the resonance energy of the QBS gradually decreases and eventually turns into a bound state. Consequently, in a dynamic RT process, there are two scenarios: either a bound state exists, in which case, Fano resonances exist for any barrier width, or a QBS exists, and the barrier should be narrow enough for the Fano resonance to appear. In both cases, the incoming particle’s frequency must be lower than the oscillating well’s frequency. In this work, these resonances are investigated in detail, and both exactly numerically and approximated analytical expressions are derived for both the weak and strong oscillating amplitude regimes. One of the conclusions is that, when the oscillating frequency is low enough, multiple Fano resonances can appear by varying the barrier’s width. Since these resonances are very sharp and zero transmission can easily be detected, this property can be used as a very accurate method for measuring the barrier’s width, even when the particle’s de-Broglie wavelength is much larger than the barrier’s width.

Fano resonance via bonding and antibonding states in nonadiabatically-pumped double-quantum-well systems

A grating coupled graphene surface plasmon and planar waveguide structure is investigated. A sharp asymmetric profile Fano resonance attributed by the coupling between the graphene plasmon and the waveguide mode can be observed. The physical origin of Fano resonance are analyzed by electric field distribution, and the tunable Fano resonances with different line profiles are demonstrated by varying the Fermi level and the incident angle. The further studies demonstrate the Fano resonance has a potential application in light absorption and the absorption can reach 76% when graphene carrier mobility is 0.5 m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /(Vs). In addition, the Fano resonance could potentially be applied as a self-referenced refractive index sensor due to the decoupled property of Fano resonance and a sensitivity of 5.21 μm/RIU can be achieved. Thus, the Fano resonance we proposed in the work would have great prospects in developing excellent light absorption and refractive index sensor functional devices.

Mechanisms of Fano-resonant biosensing: Mechanical loading of plasmonic oscillators

Interference between different quantum paths can generate Fano resonance. One of the examples is transport through a quasibound state driven by time-dependent scattering potential. Previously it is found that Fano resonance occurs as a result of energy matching in one-dimensional systems. In this work, we demonstrate that when transverse motion is present, Fano resonance occurs precisely at the wavevector matching situation. Using the Floquet scattering theory, we considered the transport properties of a nonadiabatic time-dependent well both in the 2DEG and monolayer graphene structure. Dispersion of the quasibound state of a static quantum well is obtained with transverse motion present. We found that Fano resonance occurs when the wavevector in the transport direction of one of the Floquet sidebands is exactly identical to that of the quasibound state in the well at equilibrium and follows the dispersion pattern of the latter. To observe the Fano resonance phenomenon in the transmission spectrum, we also considered the pumped shot noise properties when time and spatial symmetry secures vanishing current in the considered configuration. Prominent Fano resonance is found in the differential pumped shot noise to the reservoir Fermi energy.

We experimentally demonstrate a planar terahertz Fano metamaterial with an ultrahigh quality (Q) factor of 227. This is achieved by the excitation of the nonradiative dark modes by introducing a tiny asymmetry in the metamaterial structure. The extremely sharp quadrupole and Fano resonances are excited at normal incidence for orthogonal polarizations of the electric field. In order to capture the narrow linewidth of the dark resonance modes, we perform high resolution terahertz time-domain measurements with a scan length of 200 picoseconds and frequency resolution of 5 GHz. These high-Q metamaterials can be used in ultrasensitive label-free terahertz sensing, dense photonic integration, and narrowband filtering.

This thesis will discuss and highlight the importance of the lattice mode in minimising the radiative losses and enhancing the quality factor in metamaterial resonances. The study of lattice modes has been done extensively in plasmonic arrays, and we would like to extend it into the field of terahertz metamaterials. It is particularly important to understand the role of lattices modes when they are coupled to the eigen-structural modes of the metamaterial systems that could be engineered to support, either uncoupled eigen-resonances or strongly coupled modes including Fano resonance at terahertz frequencies. Fano resonance is known for its asymmetric feature and high-quality factor that arises from breaking the symmetry of the constituent resonator in a unit cell. Subsequently, Fano resonance also known to be a consequence of a symmetry broken bound state in the continuum, which at low loss supports ultrahigh quality factors that are difficult to be measured. The lattice modes that are inherent in periodic structures play a pivotal role in mediating the coupling between constituent resonators and can also be utilized to resonantly couple to metamaterial resonance for quality factor enhancement. This mediative coupling is observed in an avoided crossing and can be modelled as two or more coupled oscillators. Likewise, resonant coupling with metamaterial resonance enhances the resonant fields with the help of the trapped surface fields of the lattice mode. Lattice mode coupling to narrow split resonances and Fano resonance was demonstrated and we achieved enhancement of quality factor up an order of magnitude. This proves that radiative losses can be further minimized through optimization of the lattice modes but still is significantly insufficient to achieve an ultrahigh quality factor known to quasi-bound state in the continuum. Quasi-bound state in the continuum known to be excited through structural symmetry breaking have piqued the interest of many, due to its ultrahigh quality factor resonant states. A new concept and model were developed to show that a subwavelength thin dielectric can be used to support and modulate such resonance in a symmetric and metallic split ring resonator. Additionally, we have shown that it could be used as an active ultrafast filter or a micro-fluidic sensor. The lattice mode could also directly excite and support a resonant mode and such modes requiring phase matching conditions, e.g. spoof surface plasmons and guided-mode resonances. These modes are very narrow and can be exploited for low loss application. Therefore, we hope that the lattice mode can be used as an optimising strategy for minimising the radiative loss in metamaterials and that the new proposed device could be used to support an active high quality resonance on any existing symmetric and metallic metamaterial. The development of low-loss THz devices is beneficial for the support of upcoming and future communication devices and technologies.

We designed a multifunctional all-dielectric metasurface employing cuboid structures patterned with bow-tie-shaped nanoholes; it exhibits multiple Fano resonances induced by quasi-bound states in the continuum (quasi-BICs) through structural asymmetry. Among them, several resonant modes demonstrated high quality factors in the range of 103–104, along with near-unity modulation depth and strong spectral contrast. The optical responses were analyzed utilizing the finite-difference time-domain (FDTD) method, with Fano profiles fitted to theoretical models and the BIC-governed modes validated via the inverse-square ratio law. Furthermore, multipolar decomposition and electromagnetic spatial field profiles revealed the origins of the resonance, while LC circuit modeling provided additional physical insight into the Fano profiles. The proposed metasurface also exhibited strong polarization dependence, indicating its potential for active optical switching. Finally, the refractive-index sensing performance, including the potential for detecting Vibrio cholerae in an appropriate environment, reached a sensitivity of 342 nm per RIU and a figure of merit of 217.14 RIU−1. Advancing the control of high-Q quasi-BIC Fano resonances, this study highlights Fano resonators’ potential for refractive-index sensing and active switching.

We present high-quality (high-Q) Fano resonances in all-dielectric metasurfaces consisting of a periodic array of air holes on silicon (Si) film, deposited on the top of quartz substrate. With the control of the radius difference Δr and center distance Δd between the air holes, two asymmetric all-dielectric metasurfaces are proposed to achieve extremely high-Q Fano resonances. Numerical method with finite difference time domain and equivalent circuit model is employed to analyse the excitation mechanism of the sharp Fano resonances. It is shown that the high-Q Fano resonances come from the interference of two Fabry-Perot resonances, resulting in an extremely narrow window. Moreover, we also demonstrate that the high-Q Fano resonances can also be realized as electromagnetic wave is obliquely incident on the symmetric all-dielectric metasurface. Finally, we show the high-Q Fano resonances caused by asymmetric configurations can coexist with the Fano resonances in the symmetric configuration induced by oblique incidence. As a result, a tri-band Fano resonance is obtained. It is expected that our results will provide important mechanisms for tuning and switching a wide variety of optical devices such as angular sensors, filters, switches, and modulators.

Nanostructure-based sensors are capable of sensitive and label-free detection for biomedical applications. However, plasmonic sensors capable of highly sensitive detection with high-throughput and low-cost fabrication techniques are desirable. We utilized the thermal-embossing template-stripping method to fabricate large-area two-layered gold nanoslits on polymer films with low cost and ultrahigh SPR sensitivities. We found that a transverse magnetic-polarized wave in the nanoslits generated extremely sharp and asymmetric Fano resonances in transmission spectra. The full width at half-maximum bandwidth (FWHM) was only 3.88 nm (0.0063 eV) and the wavelength sensitivity was 644 nm/RIU (1.018 eV/RIU) for 650-nm-period nanoslits. In addition, the extremely sharp resonance leads to an ultrahigh intensity sensitivity up to 48117 %/RIU. Compared to previous single-layer SPR sensors, the proposed structure has a much narrower bandwidth as seen in Fig. 1(a) and Fig. 1(b). The figure of merit (FOM) of Fano mode reaches up to 166 (FOME=162). We attribute such high sensitivity to enhanced resonant effects by the second gold layer. It caps the gap plasmon in nanoslits, resulting an enhanced cavity mode. In addition, the outside surface plasmon wave between nanoslits is better confined, resulting an enhanced SPR mode. The strength of Fano coupling between both modes can be tuned by the thickness of gold film and slit width as seen in Fig. 1(c). The optimal Fano coupling is achieved when the gold layer thickness is close to the height of nanoslits. A protein-protein interaction experiment based on the interactions between bovine serum albumin (BSA) and anti-BSA were measured using two-layer gold nanoslits with a 600 nm period. Fig. 1(d) shows the normalized intensity change of as a function of the interaction time for protein-protein interactions. The measured intensity signal is at a wavelength of 810 nm. It is stable with time when the PBS buffer is injected into the microfluidic device. The BSA coated on the gold surface resulted in an intensity change of 13%. For the Anti-BSA, the 375 μg/mL concentration caused an intensity change up to 237%. Using the intensity measurement, the signal-to-noise ratio for Anti-BSA molecules is up to 1185 when the intensity stability is 0.2%.

Using the resonating group method (RGM), we dynamically study the baryon-meson interactions in chiral quark model. Some interesting results are obtained: (1) The Sigma K state has an attractive interaction, which consequently results in a Sigma K quasibound state. When the channel coupling of Sigma K and Lambda K is considered, a sharp resonance appears between the thresholds of these two channels. (2) The interaction of Delta K state with isospin I=1 is attractive, which can make for a Delta K quasibound state. (3) When the coupling to the Lambda K* channel is considered, the N phi is found to be a quasibound state in the extended chiral SU(3) quark model with several MeV binding energy. (4) The calculated S-, P-, D-, and F-wave KN phase shifts achieve a considerable improvement in not only the signs but also the magnitudes in comparison with other's previous quark model study.

The coupled oscillators model has been used for decades to interpret the Fano interference in a variety of systems: optical, plasmonic, and microwave. Hence, Fano resonance can be modeled with a weak or tightly coupled mechanical oscillators system, which provide insight into the interaction dynamics of a radioactive continuum of propagation modes and a discrete state. Therefore, the coupled cantilevers model was implemented in a FEM routine, in order to study and discuss aspects of the Fano resonance. The study of the Fano resonance in coupled cantilevers shows that this model may be applied in the field of micromechanical sensors.

All optical switch based on Fano resonance in metal nanocomposite photonic crystals