The study of localized surface plasmons (LSPs) in nanoscale structures is an essential step towards identifying optimal plasmonic modes that can facilitate robust optomechanical coupling and deepen our understanding of light–matter interactions at the nanoscale. This paper investigates, numerically, using the finite element method, LSP modes in a design comprising two coupled nano-ridges deposited on a gold layer with an interposing polymer spacer layer. Such a structure, usually referred to as a particle-on-mirror structure, shows exquisite optical properties at the nanoscale. We first examine the LSP modes of a single nano-ridge through the analysis of its scattering cross-section in the visible and infrared ranges. To enhance the plasmonic response, a thin polymer layer is placed at the middle of the ridge, which introduces additional LSP modes confined within the former. Then, we extend the analysis to the dimer configuration, which exhibits more complex and enhanced plasmonic behavior compared to a single nano-ridge. In particular, the dimer configuration yields LSP resonances with a quality factor enhancement of approximately threefold relative to a single nano-ridge. Furthermore, the presence of the polymer layer within the ridges significantly improves plasmon field localization and the quality factor. These findings underscore the potential of nano-ridge-based structures in advancing optomechanical coupling and offering valuable insights for the development of high-performance acousto-plasmonic devices. In particular, the proposed device could help significantly improve the design of nano-acousto-optic modulators, operating in the visible or in the near-infrared ranges, that require an enhanced light–phonon coupling rate.

Bound states in the continuum (BICs) are zero-width (infinite lifetime) trapped eigenmodes that remain confined in the system even though they coexist with a continuum of extended states. The resulting high-frequency resonances may have significant applications in photonic integrated circuits, filtering, sensing, and laser. In this paper, we demonstrate that a simple design based on a photonic triple-stub cavity can display both Fabry-Pérot (FP) and Friedrich-Wintgen (FW) BICs, and their occurrence is very dependent on the way the cavity is attached to the outside medium by one or two ports. We first consider a symmetric cavity where a stub of length d3 is surrounded by two stubs of length d2, and all stubs are separated by segments of length d1. When the cavity is inserted between two ports, we demonstrate theoretically and validate experimentally the existence of symmetric BICs (S-BIC) and antisymmetric BICs (AS-BIC) of FP type under commensurability conditions between the lengths d1, d2, and d3. The S-BICs and AS-BICs may cross each other, giving rise to a doubly degenerate BIC. By breaking the symmetry of the cavity, AS-BICs and S-BICs can couple together and realize a FW-type BIC where one resonance remains with zero width while the other broadens into a bright mode. By considering two additional configurations where the triple-stub cavity is attached with one or two ports from only one side, additional BICs can be induced inside the structure. By slightly detuning from the BIC condition, the latter transforms into either an electromagnetic-induced transparency/reflection or Fano resonance. Finally, such a triple-stub cavity can be designed to realize near-perfect absorption for some frequencies. All the analytical results, obtained from the Green's function method, have been confirmed experimentally in the radiofrequency domain using coaxial cables. Published by the American Physical Society 2024

We demonstrate a novel approach to inversely design one-dimensional (1D) photonic stubbed systems with targeted topological properties by leveraging the power of deep learning. The process involves developing a data-driven model to accurately predict the geometric parameters of the photonic system based on a label vector that encodes the targeted topological properties. A tandem network comprising an inverse network connected to a pre-trained forward network is trained to efficiently learn the intricate relationship between the system’s topological properties and the corresponding geometry. After training, the model is shown to effectively perform the inverse design task. The study’s outcomes give new perspectives for the design of topological photonic systems.

Bound states in the continuum (BICs) have unique properties and significant applications in photonics. In this paper, we show analytically and experimentally the existence of ( $$N-1$$ ) BICs (multi-BICs) in the flat band of a periodic photonic comb made of N stubs of length $$d_{2}$$ separated by segments of length $$d_{1}$$ . These BICs occur when $$d_{1}$$ and $$d_{2}$$ are taken commensurate at a given frequency, which turn to quasi-BICs (multi-Fano resonances) when $$d_{1}$$ and $$d_{2}$$ are taken slightly different from the BIC position. The signature of BICs and quasi-BICs can be observed in the transmission and density of states (DOS) spectra. We show that BICs are characterized by an infinite Q factor resonances, while quasi-BICs give rise to high-Q factor resonances that grow cubically with N. Our study improves the theoretical comprehension of BICs in stubbed structure and provides useful guidelines for future applications.

We investigate the effect of the next-nearest-neighbor (NNN) interaction on the band structures of one-dimensional (1D) photonic crystal in the context of the Green’s function approach. Substantial effect has been remarked when the length of these intersite couplings changes; in particular, we show the appearance of a periodic set of flat-bands whose flatness get destroyed if the length of the couplings get tuned, giving rise to absolute bandgaps inside the first Brillouin zone. Furthermore, changing the material’s nature of the NNN intersite couplings shows that when the NNN hopping parameter is so small there exists double degenerate nearly flat-bands in the middle of the bandgaps. As the hopping parameter increases, the degeneracy is lifted and the width of the bandgaps decreases until it disappears completely.

We provide theoretical and experimental evidence for the existence of topological Tamm states at the interface between two stubbed photonic crystals (PCs) as a function of the period and length of the stubs. Several works have addressed these states in the well-known Su-Schrieffer-Heeger model, a dimerized chain based on two resonators per unit cell where the opening of a gap at a Dirac cone results in a symmetry inversion of bulk bands between two topologically different crystals. Here, we give a detailed theoretical analysis of a mechanism based on band-edge symmetry inversion around a flat band, i.e., when the width of the pass band vanishes, while using only one resonator (stub) per unit cell. Then, we propose a simple versatile experimental platform to observe such interface states, which is based on coaxial cables operating in the radio-frequency domain. The investigation of these states was performed by using different approaches: (i) the topology of the bands based on the Zak phase and the symmetry of the band-edge modes, (ii) the sign of the reflection phase between each PC and a waveguide, and (iii) the dips or peaks in the reflection and transmission spectra when two finite photonic crystals are connected together either horizontally or vertically along a waveguide. Furthermore, we give a general rule about the existence of interface states when two PCs exhibit two common gaps with a flat band in their middle and different bulk-edge symmetries. Also, we provide closed-form expressions of the geometrical parameters and the frequency for which the interface state becomes bound state in the continuum (BIC). We show that these topological BIC states are stationary states of the cavity between the two PCs, and are very robust to any perturbation on both sides of the cavity. Finally, we show the impossibility of existence of interface states between two PCs with identical periods and different stubs. The theoretical and experimental results are discussed for both Neumann and Dirichlet boundary conditions at the end of the stubs.

Bound states in the continuum (BICs) in open cavities have attracted considerable attention in wave physics due to their ability to confine light and produce high-quality-factor resonances with promising applications for filtering and sensing. One of the most interesting types of BICs is Friedrich-Wintgen (FW) BICs, which result from destructive interference of two interacting modes belonging to the same radiation channel. Here, we investigate theoretically and experimentally FW BICs in a photonic and plasmonic T-shaped cavity made of two horizontal guides of lengths ${d}_{2}$ and ${d}_{3}$ coupled to a vertical stub of length ${d}_{1}$. We demonstrate that the necessary condition for obtaining BICs consists in taking the lengths of the two horizontal guides ${d}_{2}$ and ${d}_{3}$ commensurate. This BIC is a common mode of the guides of lengths ${d}_{2}$ and ${d}_{3}$, such as the electric field vanishes at their connection point with the stub of length ${d}_{1}$; this BIC is independent of ${d}_{1}$ and the infinite waveguide to which the whole cavity will be attached. We show that, depending on ${d}_{1}$, the FW BIC appears as the consequence of the interaction between two eigenmodes of the originally isolated cavity where the width of one mode vanishes giving rise to FW BIC, while the width of the second mode becomes broad. In addition, we show that by slightly deviating from the BIC condition, the latter transforms to either electromagnetically induced transparency (EIT) or reflection or Autler-Townes splitting (ATS) resonances. Both EIT and ATS effects are qualified as a transparency window between two transmission zeros, but with different physical origins. We exploit the Akaike's information criterion test to discern EIT from ATS and distinguish the regime where the EIT or ATS effect dominates. The theoretical results, obtained by means of the Green's function method, are validated both by experimental measurements using coaxial cables in the radiofrequency domain and numerical simulations using metal-insulator-metal plasmonic waveguides operating in the infrared domain. The sensitivity of the PIT (the plasmonic analogue of EIT) resonances to the dielectric inside the waveguides can be used to design a highly sensitive sensor, which makes it suitable for an on-chip optical sensing platform.

A Friedrich–Wintgen bound state in the continuum (FW-BIC) is of particular interest in the field of wave physics phenomena. It is induced via the destructive interference of two modes that belong to the same cavity. In this work, we analytically and numerically show the existence of FW-BIC in a T-shaped cavity composed of a stub of length d0 and two lateral branches of lengths d1 and d2, attached to an infinite waveguide. The whole system consists of metal–insulator–metal (MIM) plasmonic waveguides that operate in the telecommunication range. Theoretically, when d1 and d2 are commensurated, BIC is induced by these two branches. This latter is independent of d0 and the infinite waveguide, where the T structure is grafted. By breaking the BIC condition, we obtain a plasmon-induced transparency (PIT) resonance. The PIT resonance’s sensitivity to the dielectric material of the waveguide may be exploited to design a sensitive nanosensor suitable for sensing platforms, thanks to its very small footprint. A sensitivity of 1400 nm/RIU and a resolution of 1.86×10−2 RIU showed a high level of performance that the designed structure achieved. Moreover, this structure could also be used as a biosensor, in which we have studied the detection of the concentration in the human body, such as Na+, K+, and glucose solutions, and these sensitivities can reach 0.21, 0.28, and 1.74 nm dL/mg, respectively. Our designed structure advances with technology and has good application prospects, working as a biosensor to detect the blood’s hemoglobin level. The analytical results, obtained via Green’s function method, are validated via numerical simulations using Comsol Multiphysics software based on the finite element method.

We investigate the existence of Tamm states at the interface between two one-dimensional (1D) photonic crystals (PCs) through an analysis of local density of states (LDOS) using the Green’s function method. The PCs are made of a comb-like structure consisting of stubs grafted periodically along a waveguide with different geometrical parameters. The Tamm states appear as maxima in the LDOS inside the common bandgaps of the periodic PCs. In addition, we prove the existence of such Tamm states using a topological invariant based on the Zak phase of the bulk band for each PC. The Zak phase is calculated using two different arguments, namely (i) the symmetry of the electric field at the band edge states and (ii) the sign of the reflection phases between each PC and a given waveguide. The Tamm state appears as well-defined resonance in the bandgap frequency area of the transmission spectra through two finite PCs in tandem. Our proposed design can be used as filter and sensor.

We propose the design of three port photonic and plasmonic demultiplexers where filtering toward the two outputs is based on the phenomena of Fano resonances and electromagnetically induced transparency (EIT). We use a Cross-shape resonator in one output and a U-shape resonator composed of two stubs in the other output. We give a theoretical demonstration of the geometrical parameters of both resonators in order to filter one wavelength in one output while leaving the other output unperturbed. These results are confirmed by experimental validation in the radio frequency domain and a numerical simulation in the infrared (IR) domain using plasmonic metal-insulator-metal waveguides. The Cross resonator in the first output can give rise to an EIT resonance, whereas the U-shaped resonator in the second output may exhibit both EIT and Fano resonances depending on the lengths chosen for the stubs. Therefore, different demultiplexing schemes can be proposed such as achieving a Fano resonance in one output and an EIT in the other, or EIT resonances in both outputs. The Fano resonance is obtained by bringing resonance close to transmission zero, whereas the EIT results from the squeezing of resonance between two transmission zeros. When the widths of the resonances tend to zero, they transform to trapped or bound states in the continuum with an infinite lifetime. We show that the crosstalk between the two channels can be reduced to - 82 dB and the sensitivity can reach 2390.8 nm/RIU, RIU is the refractive index units. Finally, we highlight the performance of our design as a high sensitive filter and sensor in the IR domain. In this work, the analytical calculations and demonstrations are performed by using Green's function approach, the experimental verifications are realized by means of coaxial cables operating in the radio frequency range and the numerical simulations are obtained using the finite element method via Comsol Multiphysics software. Published under an exclusive license by AIP Publishing.

The concept of bound states in the continuum (BICs) in a simple cavity attracts much interest in recent works in wave physics. The BICs are perfectly confined modes with an infinite lifetime that reside inside the continuous spectrum of radiative modes, but they remain totally decoupled from it. There exist several types of BICs based on their physical origin: one of the most interesting types is Friedrich-Wintgen (FW) BICs which result from the destructive interference of two resonant modes belonging to the same cavity. Here, we investigate theoretically and experimentally the existence of FW BICs in a side-coupled loop. The cavity is made of a loop of length 2d = d2 + d3 connected to a stub of length d4. The whole cavity is attached vertically to two semi-infinite waveguides by a wire of length d1. We demonstrate that the BICs can be induced either by the loop-stub system or by the two arms of lengths d2 and d3 of the loop for specific geometrical parameters. When a perturbation in the system produces a deviation from the BIC condition, the latter transforms to either electromagnetically induced transparency (EIT) or reflection (EIR) or Autler-Townes splitting (ATS) resonances. Both EIT and ATS exhibit similar features in the transmission spectrum, namely, a transparency window; however, they have different physical origins. Therefore, EIT and ATS resonances are fitted with corresponding analytical model expressions, revealing good agreements. The Akaike's information criterion is then used to quantitatively discern EIT from ATS and the transition from ATS to EIT is also carried out. Our theoretical results are obtained by means of the Green's function method which enables us to obtain the transmission and reflection coefficients, dispersion relations, as well as density of states and scattering matrix. An experimental validation of all these results is performed in the radio-frequency domain using coaxial cables.

We investigate both analytically and numerically the existence of localized surface modes, the so-called plasmonic Tamm states (PTSs), in a new and versatile platform based on a periodic array of metal-insulator-metal (MIM) stubs grafted along a MIM waveguide. By considering a semi-infinite structure in which we modify the length of the segment at the surface, we show the existence of surface states inside the bandgaps of the periodic structure and investigate the dependence of the localized modes as a function of the geometrical parameters and the boundary conditions applied at the surface. Three types of surface boundary conditions are considered, namely, two limiting cases of zero surface impedance (or perfect electric conductor), infinite surface impedance (or perfect magnetic conductor), and a third case where the structure is in contact with a real metal. In the latter case, we show that the existence of the interface state can be demonstrated based on topological arguments using the Zak phase. We also demonstrate that if a finite size comb-crystal is vertically grafted along a horizontal waveguide, the PTSs can be detected from the dips in the amplitudes of transmission and reflection coefficients as well as from the peaks in their delay times and the local density of states (LDOS). Our theoretical study is first performed analytically with the help of a Green’s function method, which allows the calculation of the dispersion relations of the bulk and surface modes and the LDOS, as well as the transmission and reflection coefficients of the plasmonic comb-like structure. Then, these results are confirmed by a numerical simulation utilizing a 2D finite element method. Besides providing a deep physical analysis of the PTSs, our work demonstrates the capability of the analytical method as a predictive approach in more complex structures. The proposed designs in this paper can be useful to realize highly sensitive plasmonic nanosensors.

We investigate the existence of acoustic Tamm states at the interface between two one-dimensional (1D) comblike phononic crystals (PnCs) based on slender tubes and discuss their topological or trivial character. The PnCs consist of stubs grafted periodically along a waveguide and the two crystals differ by their geometrical parameters (period and length of the stubs). We use several approaches to discuss the existence of Tamm states and their topology when connecting two half-crystals. First, we derive a necessary and sufficient condition on the existence of interface states based on the analysis of the bulk band structure and the symmetry of the band edge states. This approach is equivalent to an analysis of the Zak phases of the bulk bands in the two crystals. Indeed, a topological interface state should necessarily exist in any common bandgap of the two PnCs for which the lower (upper) band edges have opposite symmetries. A novelty of our structure consists in the fact that the symmetry inversion results from a band closure (flat band) rather than from a gap closure, in contrast to previous works. Then, such interface states are revealed through different physical quantities, namely: (i) the local density of states (LDOS), which exhibits a high localization around the interface; (ii) sharp peaks in the transmission spectra in the common bandgap when two finite crystals are connected together; (iii) the phases of the reflection coefficients at the boundary of each PnC with a waveguide, which have a direct relationship with the Zak phases. In addition, we show that the interface states can transform to bound states in the continuum (BICs). These BICs are induced by the cavity separating both PnCs and they remain robust to any geometrical disorder induced by the stubs and segments around this cavity. Finally, we show the impossibility of interface states between two connected PnCs with different stub lengths and similar periods. The sensitivity of these states to interface perturbations can find many practical applications in PnC sensors.

We study analytically and numerically the design of plasmonic demultiplexers based on Fano and plasmonic induced transparency (PIT) resonances. The demultiplexers consist of T-shaped structures with an input waveguide and two output waveguides. Each output contains two waveguide stubs grafted either at the same position or at two different positions far from the input waveguide. We derive closed form analytical expressions of the geometrical parameters allowing a selective transfer of a single mode in one waveguide without affecting the other one. This is performed by implementing the Fano and PIT resonances which are characterized by a resonance placed near an antiresonance or placed between two antiresonances respectively. In particular, we show the possibility of trapped modes, also called bound in continuum (BIC) modes. These modes appear as resonances with zero width in the transmission spectra for appropriate lengths of the stubs. Then, by detuning slightly the stubs, BICs transform to PIT or Fano resonances. The existence of a full transmission besides a transmission zero, enables to filter a given wavelength on one output waveguide, by vanishing both the transmission on the second waveguide as well as the reflection in the input waveguide. The demultiplexer is capable to separate two fundamental optical windows (i.e. 1310 and 1550 nm). The performance of the demultiplexer platform is measured using the crosstalk of the two outputs and quality factor. The lowest value of the crosstalk −96.8 dB with an average of −84.7 dB is achieved and a maximum quality factor 45 is obtained. The maximum transmission reaches a high value of 85% despite the large metallic losses. These values are suitable for integrated photonic circuits in the optical communication. The analytical results are obtained by means of the Green’s function method which enables us to deduce the transmission and reflection coefficients, as well as the delay times and density of states. These results are confirmed by numerical simulations using a 2D finite element method. The analytical analysis developed in this work represent a predictive method to understand deeply different physical phenomena in more complex plasmonic devices.

We propose a simple solid–liquid–solid triple layer biosensor platform based on bound states in the continuum (BICs) and Fano resonances to detect the acoustic properties of liquids and apply the method to a mixture of water and albumin with various concentrations. The solid–liquid–solid triple layer is composed of an epoxy as a solid layer and an albumin–water mixture as a liquid layer, and the entire system is immersed in water. In this work, we show that the structure exhibits a high sensitivity (S), quality factor (Q), and figure of merit (FOM) with a better detection limit (DL) in the vicinity of the BICs where the transmission spectra exhibit Fano resonances. The Fano resonances shift towards high frequencies as the concentration increases. The detection limit can reach very small values for a small albumin concentration (4.7%). In addition, for a given concentration and layer thickness of the sensing material, we show the effect of the incidence angle on the efficiency of the sensor in terms of the sensitivity and quality factor. The proposed structure can be designed from low-cost material and can be used as a sensor to detect different types of liquids and gases as well.

The design and study of structures exhibiting bound states in the continuum (BICs) are the object of continuous works in wave physics. These long-lived states which are localized in some parts of the system without interacting with the background have found several potential applications due to their high sensitivities to weak perturbations, in particular in filtering and sensing. In this paper, we present a theoretical demonstration of BICs in an asymmetric loop composed of two arms of lengths $$d_1$$ and $$d_2$$ with both an experimental validation in the radio-frequency (RF) domain using coaxial cables and a numerical validation in the infrared (IR) domain using plasmonic metal-insulator-metal nanometric waveguides. The analytical study is performed by means of the Green's function method, whereas the numerical calculation is obtained using finite element method. The BICs correspond to localized resonances of infinite lifetime inside the loop, without any leakage into the surrounding waveguides. We demonstrate that the condition for the existence of the BICs is to make the lengths of the two arms ( $$d_1$$ and $$d_2$$ ) commensurate with each other. At the corresponding frequencies, one of the two degenerate modes of the isolated loop (associated with the clockwise and anti-clockwise propagations) couples to the waveguides while the other remains unaffected. When the lengths are slightly shifted from the BICs, the latter transform to Fano resonances exhibiting dips in the transmission spectra and sharp peaks in the density of states (DOS). As an application of our design, we show the efficiency of the Fano resonances in designing an efficient gaz-sensor with a high sensitivity and factor of merit in the IR domain. In addition, we derive an exact formula about the proportionality between DOS and the derivative of the argument of the determinant of the scattering matrix (Friedel phase) for a lossless structure; then, we discuss the validity and deviation from this rule when the loss is increased.

Bound states in continuum (BICs) are resonances with zero width (infinite lifetime) without any leakage into the surrounding media. Their fascinating properties and potential applications have attracted a great deal of interest. In this paper, we give an analytical, numerical, and experimental demonstration of BICs in simple acoustic structures based on either a single solid layer or a triple solid-liquid-solid layer inserted between two liquids. These modes are an intrinsic property of the inserted structure (solid layer or solid liquid-solid triple layer) with free surfaces and are independent of the surrounding media. Two kinds of BICs are discussed: (i) Fabry-Perot (FP) BICs exist as the consequence of the intersection of the local resonances induced by inserted structure intersect the transmission zeros induced by the solid layers. (ii) Symmetry-protected (SP) BICs occur when appear at normal incidence due to the decoupling of the transverse modes in the solid layer from the longitudinal modes that propagate in the solid and solid liquid multilayer media. When the incidence angle departs slightly from the BIC conditions, the latter transform into Fano resonances characterized by an asymmetric line shape in the transmission spectra. In addition, we show that the transmission zeros give rise to negative delay times and therefore acoustic superluminal effect. The theoretical results are obtained by means of the Green's function method, whereas the experimental measurements are carried out in ultrasonic domain using plexiglass plates in water. These results may have important applications to realize subsonic and acoustic superluminal phenomena as well as acoustic filters and sensors.