Fano interference and resonances in open systems

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.

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.

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 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.

In this work, we investigate electron transport across a carbon molecular junction consisting of a C60 molecule attached to two semi-infinite metallic open-end CNT leads in the coherent regime. Here, we put emphasis on topology of the molecular-electrode interface and gate voltage, and obtain the electrical transmission through the CNT/C60/CNT structure, using the Green’s function method in the framework of a nearest neighbor tight-binding approximation. To this end, three different ways of coupling C60 fullerene through one, five, and six carbon atoms to the CNT-leads in the direction of the longitudinal axis of the tube have been considered. Also, the current-voltage characteristic is calculated in the Landauer-Büttiker formalism at room temperature. It is shown that the number of contact points between the electrodes and the molecule can play an important role in the electrical transport. Also, the bond dimerization and a gate voltage shift the molecular levels, where by adjusting the related parameters the electron conduction can be controlled. Our results show that the proposed structure gives rise to the resonance states and quasi-bound states (Fano resonances) close to −2.63 eV. These antiresonance states are related to the active region and independent from the coupling strength between the device and the leads. The numerical results may serve as important components of nanocircuits.

Fano resonance in graphene anti-dot and periodic graphene anti-dot arrays

Quasi-bound states in the continuum in dielectric metasurfacessupport sharp Fano resonances that emerge from the interference betweenbrightand dark modes. We exploit this modal interplay to demonstrate tunablethird-harmonic emission, controlled through the driving pulse’swavelength and intensity. Our experiments show imbalances in third-harmonicdiffraction patterns and non-Gaussian third-harmonic spectral featuresthat exhibit strong variations near the Fano resonance. We explainthe observations via a coupled-oscillator model that captures theinterplay between the driving field and the nonlinear response ofthe modes, explaining our observations and providing a predictiveframework for optimizing the third-harmonic diffraction efficiency.These results establish pulse-engineered metasurfaces as a powerfulplatform for nonlinear wavefront shaping and frequency conversionapplications while simultaneously serving as a warning that pulseproperties play a vital role in metasurface function design.

We experimentally demonstrate dielectric metasurfaces that support spatially tailored dark modes (quasi-Bound States in the Continuum) and mold optical wavefronts only at narrowband Fano resonances, while leaving the rest of the spectrum unaffected.

Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs chaotic), and is often instrumental to identify classical-to-quantum correspondence. Here, we study, both theoretically and experimentally, the statistics of chaotic resonances in an optical microcavity with a mixed phase space of both regular and chaotic dynamics. Information on the number of chaotic modes is extracted by counting regular modes, which couple to the former via dynamical tunneling. The experimental data are in agreement with a known semiclassical prediction for the dependence of the number of chaotic resonances on the number of open channels, while they deviate significantly from a purely random-matrix-theory-based treatment, in general. We ascribe this result to the ballistic decay of the rays, which occurs within Ehrenfest time, and importantly, within the time scale of transient chaos. The present approach may provide a general tool for the statistical analysis of chaotic resonances in open systems.

Owing to radiation losses, resonances in open systems, i.e. solution domains which extend to infinity in at least one direction, are generally complex valued. However, near symmetric centred objects in ducted domains, or in periodic arrays, so-called trapped modes can exist below the cut-off frequency of the first non-trivial duct mode. These trapped modes have no radiation loss and correspond to real-valued resonances. Above the first cut-off frequency isolated trapped modes exist only for specific parameter combinations. These isolated trapped modes are termed embedded, because their corresponding eigenvalues are embedded in the continuous spectrum of an appropriate differential operator. Trapped modes are of considerable importance in applications because at these parameters the system can be excited easily by external forcing. In the present paper directly computed embedded trapped modes are compared with numerically obtained resonances for several model configurations. Acoustic resonances are also computed in two-dimensional models of a butterfly and a ball-type valve as examples of more complicated geometries.

We experimentally demonstrate near-infrared to ultraviolet (UV) wavelength conversion in an As2S3-based metasurface that is strongly enhanced by the excitation of a quasi-bound states in the continuum resonance near 1064 nm. We report the all-optical, ultrafast tunability of the QBIC resonance and the third harmonic induced by Kerr effects. These results give rise to a range of novel applications for UV sensors and lasers.

The possibility for the existence of unstable bound states of the S11 nucleon resonance N$^*$(1535) and nuclei is investigated. These quasibound states are speculated to be closely related to the existence of the quasibound states of the eta mesons and nuclei. Within a simple model for the N N$^*$ interaction involving a pion and eta meson exchange, N$^*$-nucleus potentials for N*-$^3$He and N*-$^{24}$Mg are evaluated and found to be of a Woods-Saxon like form which supports two to three bound states. In case of N*-$^3$He, one state bound by only a few keV and another by 4 MeV is found. The results are however quite sensitive to the N N$^*$ $\pi$ and N N$^*$ $\eta$ vertex parameters. A rough estimate of the width of these states, based on the mean free path of the exchanged mesons in the nuclei leads to very broad states with $\Gamma \sim$ 80 and 110 MeV for N*-$^3$He and N*-$^{24}$Mg respectively.

Label-free molecular detection plays a vital role in the terahertz (THz) field but remains limited by weak light-matter interaction and narrow detection bandwidth, especially for trace analytes. Here, we propose a dielectric metasensor that synergistically couples guided mode resonance and quasi-bound states in the continuum to achieve multimodal enhancement. On this basis, three multiplexing strategies-geometric scaling, incident angle modulation, and waveguide thickness adjustment-are implemented to provide broadband adaptability and structural tolerance. Numerical simulations demonstrate that the "angle multiplexing-thickness compensation" hybrid mechanism narrows the scanning range while effectively enhancing both the resolution and the intensity of fingerprint recognition, with a maximum signal enhancement of 10.69 dB. The method offers a promising pathway for the practical application of THz metasensing in high-throughput biosensing, chemical analysis, and environmental monitoring.

Cavity optomechanical systems have become a topic of great interest in recent years, and the coupled-cavity model is also a classic theoretical framework. This paper aims to construct a coupledcavity optomechanical system to study induced transparency, Fano resonance, and fast-slow light effects in such a system. By transferring phenomena typically studied in a single optical cavity to a coupled-cavity system, we analyze specific phenomena detected in optical and microwave cavities, such as transmission and absorption spectra, to investigate induced transparency. We also examine Fano resonance in the model by varying detuning, and study fast-slow light effects through group velocity. This paper first constructs the corresponding physical model, as shown in Figure 1. Based on the theoretical model, a reasonable Hamiltonian is proposed. By introducing appropriate dissipation and fluctuation noise terms, the Langevin equations of motion are derived. Next, the Langevin equations are linearized, and the resonant terms are retained to obtain <i>O</i><sub>+</sub> . The amplitude of the field modes is then derived using the input-output relations. Following the experimental data from referenced literature, a numerical simulation program is implemented in Mathematica. By substituting the relevant parameters and performing calculations, the results are obtained through simulation. For the first time, the interactions among photons, magnons, microwaves, and phonons— as well as the interplay between photons in the two cavities—are investigated in a coupled cavity optomagnomechanical system. Electromagnetically induced transparency (EIT), Fano resonance, and fast-slow light effects are studied in this coupled-cavity optomagnomechanical framework. Phenomena typically examined in a single optical cavity are extended to the coupled-cavity system, with specific observations analyzed separately in the optical and microwave cavities. When <i>δ</i>=<i>ω</i><i><sub>b</sub></i>, the absorption spectrum splits, and the absorption peak decreases from its maximum to its minimum. This phenomenon arises from the disruption of quantum interference effects. The resonance condition suppresses the generation of Fano resonance. At the resonant frequency <i>ω</i><i><sub>0</sub></i>, the group delay is greater than zero, indicating slow-light propagation, and this effect is enhanced with increasing coupling strength. Additionally, a group delay of τ is achieved. Meanwhile, on either side of the resonant frequency, the group delay peaks exhibit a decreasing positive value and an increasing negative value, respectively, signifying a gradual weakening of the slow-light effect and a corresponding enhancement of the fast-light effect. This paper investigates the MIT, MMIT, and OMIT windows in a coupled-cavity optomagnomechanical (OMM) system under a strong control field and weak probe field. The MMIT phenomenon is observed through nonlinear phonon-magnon interactions. Additionally, the photon-magnon interaction in the microwave cavity leads to MIT, while OMIT is achieved via the radiation pressure interaction between photons and nonlinear phonons in the optical cavity. The frequency of the probe field is tuned to interact with both the microwave and optical cavities. When the probe field couples with the microwave cavity, its absorption at the resonant frequency is significantly suppressed under optomechanical coupling, resulting in a pronounced optical switching effect on transmission. We analyze the asymmetric Fano resonance phenomenon, which reflects the existence of quantum interference mechanisms within the system and influences the fast- and slow-light conversion processes. Furthermore, by selecting appropriate coupling parameters, not only can the fast- and slow-light effects be enhanced, but dynamic switching between them can also be achieved.

A comparative study of vibrational predissociation dynamics is presented. Two collinear models of the van der Waals complex are used with a realistic medium-strength coupling parameter. The predissociation rates are calculated by four different approaches: an accurate quantum mechanical method by the complex-scaling technique, first-order approximations in the diabatic (FOD) and adiabatic (FOA) basis, and purely classically. It is shown that FOA within the improved semiclassical Landau method provides an excellent description of the dynamical tunnelling of the system from all the quasibound states into continuum; at the same time, FOD yields noticeably higher rates though the transition probabilities are very low. At low excitation energies of the van der Waals bond, the classical description yields zero rates in accord with the KAM theorem. At higher excitation energies, the classical rates are higher than the quasiclassical rates since the classical system dissociates via the diffusion through the holes...