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1. Bound States in the Continuum and Induced Resonances in a Simple Plasmonic Waveguide with Sensing Application

Author

Yamina Rezzouk, Soufyane Khattou, Madiha Amrani, Adnane Noual, El Houssaine El Boudouti, Abdelkrim Talbi, and Bahram Djafari-Rouhani

Subjects
Friedrich–Wintgen bound states in the continuum, plasmon-induced transparency resonance, metal–insulator–metal waveguide, sensor, Applied optics. Photonics, TA1501-1820
Abstract

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.

Published
2023
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2. Contribution of Ribbon-Structured SiO2 Films to AlN-Based and AlN/Diamond-Based Lamb Wave Resonators

Author

Mohammed Moutaouekkil, Jérémy Streque, Othmane Marbouh, El Houssaine El Boudouti, Omar Elmazria, Philippe Pernod, Olivier Bou Matar, and Abdelkrim Talbi

Subjects
S0 Lamb-wave mode, K2, AlN/SiO2 bi-layer, SiO2 ribbons, TCF, Chemical technology, TP1-1185
Abstract

New designs based on S0 Lamb modes in AlN thin layer resonating structures coupled with the implementation of structural elements in SiO2, are theoretically analyzed by the Finite Element Method (FEM). This study compares the typical characteristics of different interdigital transducer (IDTs) configurations, involving either a continuous SiO2 cap layer, or structured SiO2 elements, showing their performance in the usual terms of electromechanical coupling coefficient (K2), phase velocity, and temperature coefficient of frequency (TCF), by varying structural parameters and boundary conditions. This paper shows how to reach temperature-compensated, high-performance resonator structures based on ribbon-structured SiO2 capping. The addition of a thin diamond layer can also improve the velocity and electromechanical coupling coefficient, while keeping zero TCF and increasing the solidity of the membranes. Beyond the increase in performance allowed by such resonator configurations, their inherent structure shows additional benefits in terms of passivation, which makes them particularly relevant for sensing applications in stern environments.

Published
2023
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3. Tunable Topological Acoustic Tamm States in Comblike Structures Based on Band Inversion around Flat Bands

Author

Soufyane Khattou, Yamina Rezzouk, Madiha Amrani, Mohamed El Ghafiani, El Houssaine El Boudouti, Abdelkrim Talbi, and Bahram Djafari-Rouhani

Subjects
topological interface states, phononic crystals, comblike structure, Zak phase, Crystallography, QD901-999
Abstract

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.

Published
2022
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4. A Biosensor Based on Bound States in the Continuum and Fano Resonances in a Solid–Liquid–Solid Triple Layer

Author

Ilyasse Quotane, Madiha Amrani, Cecile Ghouila-Houri, El Houssaine El Boudouti, Leonid Krutyansky, Bogdan Piwakowski, Philippe Pernod, Abdelkrim Talbi, and Bahram Djafari-Rouhani

Subjects
bound states in continuum (BIC), fano resonance, phononic crystal, biosensor, Crystallography, QD901-999
Abstract

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.

Published
2022
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5. Y-Shaped Demultiplexer Photonic Circuits Based on Detuned Stubs: Application to Radiofrequency Domain

Author

Abdelkader Mouadili, Soufyane Khattou, Madiha Amrani, El Houssaine El Boudouti, Noureddine Fettouhi, Abdelkrim Talbi, Abdellatif Akjouj, and Bahram Djafari-Rouhani

Subjects
demultiplexer, EIT resonance, Fano resonance, BIC, photonic circuit, Applied optics. Photonics, TA1501-1820
Abstract

We present a theoretical and experimental study of photonic demultiplexers based on detuned stubs. The demultiplexers consist of Y-shaped structures with one input line and two output lines. Two different types of structures are proposed to achieve a selective transfer of a single mode in one output line without disturbing the second one. (i) In the first platform each output contains two different stubs attached at two different sites (U-shaped resonators). We derive in closed form the geometrical parameters of the stubs to achieve a selected frequency in each line while keeping the other line unaffected. The frequency selection can be made on the basis of two different mechanisms, namely a Fano or an electromagnetic induced transparency (EIT) resonance. Consequently, different demultiplexing schemes can be designed by a combination of the two mechanisms, such as Fano-Fano, Fano-EIT or EIT-EIT. In particular, the width of the Fano or EIT resonances can become zero for an appropriate choice of the stubs’ lengths, giving rise to trapped modes also called bound in continuum states (BICs) with infinite quality factors. We also show that the crosstalk between the two outputs can reach minimum values around −45 dB. (ii) In the second platform, each output line contains a photonic comb with a defect stub. The latter is appropriately designed to filter one or a few frequencies in the bandgap of the photonic comb. The analytical calculations are performed with the help of the Green’s function method which enables us to derive the transmission and reflection coefficients as well as the density of states (DOS). These results are confirmed by experimental measurements using coaxial cables in the radio frequency domain.

Published
2021
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6. Miniaturized Coplanar Waveguide for Nanostructured Magnetostrictive Multilayer Characterization

Author

Abdelhatif El Fellahi, Aurélien Mazzamurro, Jean Claude Gerbedoen, Yannick Dusch, Olivier Bou Matar, Phillippe Pernod, Abdelkrim Talbi, and Nicolas Tiercelin

Subjects
nanostructured thin film, magnetostrictive thin film, RF characterization, General Works
Abstract

A miniaturized coplanar waveguide (CPW) on a Y-cut LiNbO3 substrate operating in Radio Frequency region (RF) is proposed for studying of magnetostrictive multi-layered structure. The structure is composed of a 14 × [TbCo2 (3.7 nm)/FeCo (4 nm)] nanostructured multi-layer. Using microtechnology process, the miniaturized CPW has been designed with a 50 µm wide signal line in the frequency range from 6 MHz to 6 GHz. Electromagnetic simulations based on ®Ansys/HFSS demonstrate insertion losses less than 2 dB and show that the magnetic field is more confined in the nanostructured multi-layer placed on top of the micro-sized CPW. By using Vectorial Network Analyzer (VNA) the Ferromagnetic Resonance (FMR) is investigated from the reflection (Sii) or transmission (Sij) coefficients of scattering parameters. An inversion model is finally used to extract the complex permeability spectrum of the thin-film in a large frequency range.

Published
2019
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7. Highly Confined Love Waves Modes by Defects States in a Phononic Crystal Based on Holey-SiO2/ST-Cut Quartz Structure

Author

Yu-Xin Liu, Abdelkrim Talbi, Philippe Pernod, and Olivier Bou Matar

Subjects
phononic crystal, love waves, band gap, defect, General Works
Abstract

We investigate the properties of highly confined Love modes in a phononic crystal based on an array of holes made in SiO2 deposited on ST-cut Quartz substrate. An optimal choice of the geometrical parameters of the holes enables us to obtain wide stop-bands frequency for shear wave’s modes. The introduction of defect by removing lines of holes leads to nearly flat modes within the band gap and consequently paves the way to implement advanced design of electroacoustic filters and high-performance cavity resonators based on shear wave modes. The calculations are performed using finite element method based on the commercial software (COMSOL-Multiphysics). For transmission spectra, piezoelectric excitations are applied by considering the interdigital transducers, with results corroborating well the band structure predictions and the position of defects modes within the band gap.

Published
2018
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8. Highly Sensitive Surface Acoustic Wave Magnetic Field Sensor Using Multilayered TbCo2/FeCo Thin Film

Author

Aurelien Mazzamurro, Abdelkrim Talbi, Yannick Dusch, Omar Elmazria, Philippe Pernod, Olivier Bou Matar, and Nicolas Tiercelin

Subjects
SAW sensor, magnetostriction, ∆E-effect, multilayered thin film, General Works
Abstract

Over the last decades, the use of Surface Acoustic Waves (SAW) has emerged as a promising technology in many applications such as filters, signal processing but also sensors. We report the fabrication and the characterization of a SAW delay line magnetic field sensor using uniaxial multi-layered 14×[TbCo2(3.7nm)/FeCo(4nm)] nanostructured thin film deposited on Y36° Lithium Niobate (Figure 1a). The sensor shows an interesting dependency to a tunable bias magnetic field with different orientations relative to the easy axis. The obtained results are well explained using an equivalent piezo-magnetic model described in a previous work.

Published
2018
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9. Robust Calorimetric Micro-Sensor for Aerodynamic Applications

Author

Cécile Ghouila-Houri, Célestin Ott, Romain Viard, Quentin Gallas, Eric Garnier, Abdelkrim Talbi, and Philippe Pernod

Subjects
MEMS sensor, thermal sensor, calorimetric sensor, wall shear stress sensor, active flow control, General Works
Abstract

This paper reports a calorimetric micro-sensor designed for aerodynamic applications. Measuring both the amplitude and the sign of the wall shear stress at small length-scale and high frequencies, the micro-sensor is particularly suited for flow separation detection and flow control. The micro-sensor was calibrated in static and dynamic in a turbulent boundary layer wind tunnel. Several micro-sensors were embedded in various configurations for measuring the shear stress and detecting flow separation. Specially, one was embedded inside an actuator slot for in situ measurements and twelve, associated with miniaturized electronics, were implemented on a flap model for active flow control experiments.

Published
2018
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10. Nanogap Pirani Sensor Operating in Constant Temperature Mode for Near Atmospheric Pressure Measurements

Author

Cécile Ghouila-Houri, Ralph Sindjui, Mohammed Moutaouekkil, Omar Elmazria, Quentin Gallas, Eric Garnier, Alain Merlen, Romain Viard, Abdelkrim Talbi, and Philippe Pernod

Subjects
MEMS sensors, pressure sensors, pirani sensors, flow control, General Works
Abstract

This paper presents a high sensitive micro-sensor designed for pressure measurements in a wide range around atmospheric pressure, for application in aerodynamics. The sensor is a temperature-resistance transducer operating with the Pirani effect, which states that below a certain pressure limit, the thermal conductivity of a gas is pressure-dependent. The sensor presents a wide measurement range between 10 kPa and about 800 kPa, in both constant current and constant temperature mode. The last mode enables high-sensitive measurements with a maximum of sensitivity around atmospheric pressure, enabling the use of the sensor for applications in aerodynamics and fluid dynamics, such as active flow control.

Published
2017
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11. Wall Shear Stress Calorimetric Micro-Sensor Designed for Flow Separation Detection and Active Flow Control

Author

Cécile Ghouila-Houri, Quentin Gallas, Eric Garnier, Alain Merlen, Romain Viard, Abdelkrim Talbi, and Philippe Pernod

Subjects
MEMS sensors, wall shear stress sensors, calorimetric sensors, flow control, separation detection, General Works
Abstract

This paper presents an efficient and high-sensitive micro-sensor designed for wall shear stress measurement. The main technical application targeted is flow separation detection for closed-loop active flow control. The sensor is a temperature-resistance transducer operating on heat transfer. The device is micro-structured with three substrate-free wires presenting a high aspect ratio, and periodic perpendicular micro-bridges ensuring mechanical toughness and thermal insulation. This design achieves a homogeneous temperature distribution along the wires. Welded on a flexible printed circuit, the sensor is wall-mounted on a wind tunnel. The experiments, conducted in both attached and separated flow configurations, demonstrate the sensor sensitivity to wall shear stress up to 2.4 Pa and the ability of the 3-wires based design to perform flow direction sensing for back-flow detection.

Published
2017
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26. Flat band induced topological photonic Tamm states in stubbed structures:Theory and experiment

Author

Soufyane Khattou, Yamina Rezzouk, Mohamed El Ghafiani, Madiha Amrani, Mohammed Elaouni, El Houssaine El Boudouti, Abdelkrim Talbi, Abdellatif Akjouj, Bahram Djafari-Rouhani, Université Mohammed Premier [Oujda], University of Mohammed I - Université Mohammed Premier, Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN [AIMAN-FILMS - IEMN], Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 [IEMN], Physique - IEMN [PHYSIQUE - IEMN], Laboratoire International associé sur les phénomènes Critiques et Supercritiques en électronique fonctionnelle, acoustique et fluidique (LIA LICS/LEMAC), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Physique - IEMN (PHYSIQUE - IEMN), and no information found

Subjects
[PHYS]Physics [physics], [SPI]Engineering Sciences [physics]
Abstract

International audience; 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.

Published
2023

27. Friedrich-Wintgen bound states in the continuum and induced resonances in a loop laterally coupled to a waveguide

Author

El Houssaine El Boudouti, Leonard Dobrzynski, Bahram Djafari Rouhani, Soufyane Khattou, Madiha Amrani, Abdellatif Akjouj, Abdelkrim Talbi, Université Mohammed Premier [Oujda], Laboratoire International associé sur les phénomènes Critiques et Supercritiques en électronique fonctionnelle, acoustique et fluidique (LIA LICS/LEMAC), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Physique - IEMN (PHYSIQUE - IEMN), and Université Lille Nord (France)

Subjects
[PHYS]Physics [physics], [SPI]Engineering Sciences [physics]
Abstract

International audience; 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.

Published
2022

28. Bound states in the continuum and Fano resonances in photonic and plasmonic loop structures

Author

Madiha Amrani, Soufyane Khattou, Housni Al-Wahsh, Yamina Rezzouk, El Houssaine El Boudouti, Cecile Ghouila-Houri, Abdelkrim Talbi, Abdellatif Akjouj, Leonard Dobrzynski, Bahram Djafari-Rouhani, Université Mohammed Premier [Oujda], Benha University (BU), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Physique - IEMN (PHYSIQUE - IEMN), This study was funded by the National Center of Scientific and Technical Research (CNRST), Morocco, University of Mohammed I - Université Mohammed Premier, Université Moulay Ismail (UMI), and Université Lille Nord (France)

Subjects
[PHYS]Physics [physics], [SPI]Engineering Sciences [physics], Electrical and Electronic Engineering, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, [SPI.TRON]Engineering Sciences [physics]/Electronics
Abstract

International audience; 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 d1 and d2 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 (d1 and d2) 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.

Published
2022

30. Electrolyte ohmic heating during electrodeposition: The role of coupled kinetic-transport phenomena that lead to morphological and microstructural changes

Author

Pınar Eribol, Sarathy K. Gopalakrishnan, S.V. Diwakar, Abdelkrim Talbi, Ranga Narayanan, Farzam Zoueshtiagh, Kirk J. Ziegler, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Institut supérieur de l'électronique et du numérique (ISEN)-Université de Valenciennes et du Hainaut-Cambrésis (UVHC)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Laboratoire International associé sur les phénomènes Critiques et Supercritiques en électronique fonctionnelle, acoustique et fluidique (LIA LICS/LEMAC), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), and This work was partially supported by grants from the National Science Foundation, United States NSF-DMR-2004527, the University of Florida Space Research Initiative, United States, and the French Space Agency (CNES). PE acknowledges the financial support of The Scientific and Technological Research Council of Turkey (TUBITAK) 2219 - International Postdoctoral Research Fellowship. SKG acknowledges the travel support from Research Abroad for Doctoral Students (RAD) award, United States, Botic Family Scholars Professional Pathways Program award, France, Graduate Student Council travel award, United States, and University of Florida Office of Research travel fund, United States. RN acknowledges financial support from the William P. and Tracy Cirioli Professorship, United States. KJZ acknowledges financial support from the Dow Chemical Company Foundation Professorship, United States, the Charles A. Stokes Professorship, United States, and a Visiting Professorship from Université de Lille/IEMN, France .

Subjects
Morphology, Concentration, [SPI]Engineering Sciences [physics], Electrodeposition, General Chemical Engineering, Electrochemistry, Instability, Copper sulfate, Convection, Copper
Abstract

International audience; Understanding the morphological changes to the electrodes during electrochemical processes is important to many fields. These morphological changes often lead to dendrite formation and significant heat generation that can be detrimental to the process, especially the performance and lifetime of batteries. In situ infrared thermometry and microscopy are used to study the evolution of temperature profiles during the microscale electrodeposition of copper from copper sulfate. Under certain conditions, the growth front of the deposit receded and the fastest growing dendrites would suddenly stop growing. Analysis of physicochemical, temperature, and current changes show that many dynamic phenomena are correlated and associated with localized pH changes that change the chemistry of electrodeposition and potential drops occurring across the electrodes that alter the transport around dendrites.

Published
2023

32. A New Approach to Improve the Control of the Sensitive Layer of Surface Acoustic Wave Gas Sensors Using the Electropolymerization

Author

Zakariae Oumekloul, Sebastien Pecqueur, Arnaud de Maistre, Philippe Pernod, Kamal Lmimouni, Abdelkrim Talbi, Bilel Hafsi, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Transduction, Propagation et Imagerie Acoustique - IEMN (TPIA - IEMN), INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Nanostructures, nanoComponents & Molecules - IEMN (NCM - IEMN), Institut Catholique d'Arts et Métiers (ICAM), Laboratoire International associé sur les phénomènes Critiques et Supercritiques en électronique fonctionnelle, acoustique et fluidique (LIA LICS/LEMAC), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), and The authors thank the support of an internal project ‘IOT Make Sense’

Subjects
Surface Acoustic Wave (SAW), [SPI]Engineering Sciences [physics], Radio Frequency (RF), Electropolymerization, Organic Electrochemical Sensors
Abstract

International audience; Surface acoustic waves (SAWs) have a broad spectrum of applications, especially in sensing. However, deposition methods of sensitive layers can be controlled locally through electrodeposition unlike other conventional methods, such as drop-casting and atmospheric-pressure plasma. Employing this method, we experimentally demonstrate the local electrodeposition of PEDOT: PSS on a structured active gold surface. We investigate the response of a piezoelectric transducer at 215MHz, by exploiting shear-horizontal (SH) surface waves of the ST-cut quartz substrate. The sensor responses were then tested under acetone, methanol, isopropanol and water vapor gases. Phase changes were more observed under water vapors gases. These changes depended on the surface conductivity of PEDOT: PSS deposited on the sensor. The double-port SAW gas sensors modified with the PEDOT: PSS presented the highest sensitivity in the case of water vapor, with a maximum phase shift of 0.8° and an insertion loss of about 0.5 dB at room temperature. The obtained results could pave the way to implement advanced designs of high-performance and wireless electroacoustic gas sensors based on electropolymerization.

Published
2022

33. High temperature gradient Pirani micro-sensor designed and tested for aerodynamic wall pressure measurement

Author

Cécile Ghouila-Houri, Q. Gallas, M. Kazar-Mendes, Romain Viard, T. Arnoult, A. Merlen, Philippe Pernod, A. Mazzamurro, Eric Garnier, Abdelkrim Talbi, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Fluiditech (Thurmelec), ISEN Yncréa Ouest, Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet - UMR 9014 (LMFL), Centrale Lille-ONERA-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), DAAA, ONERA, Université Paris Saclay [Meudon], ONERA-Université Paris-Saclay, This work is funded by the French National Research Agency (ANR) in the framework of the ANR ASTRID 'CAMELOTT' project, grant number ANR-14-ASTR-0023-01. It is supported by the regional platform CONTRAERO in the framework of the CPER ELSAT 2020 project. The authors also thank RENATECH, the French national nanofabrication network, and FEDER., Renatech Network, ANR-14-ASTR-0023,CAMELOTT,Capteurs et Actionneurs MEMS pour Le ConTrôle réactif de décollement sur voleT(2014), and European Project

Subjects
Materials science, Aerodynamic wall pressure micro-sensor, Mechanics, Aerodynamics, Pirani sensor, law.invention, Boundary layer, Temperature gradient, MEMS, [SPI]Engineering Sciences [physics], Pressure measurement, Flow velocity, law, Thermal, Perpendicular, pressure sensor, Electrical and Electronic Engineering, Instrumentation, Wind tunnel
Abstract

An earlier version of this paper was presented at the IEEE Sensors 2020 conference and was published in its Proceedings with the title “Aerodynamic wall pressure measurement using a high temperature gradient Pirani micro-sensor” (DOI: 10.1109/SENSORS47125.2020.9278842); International audience; This paper presents and discusses the first demonstration of aerodynamic wall pressure measurement using a thermal Pirani effect based micro-sensor. The thermal micro-sensor is designed as a suspended micro-hot-wire separated from the substrate by a nanoscale gap, and mechanically supported by perpendicular micro-bridges. The micro-sensor was calibrated for pressure measurement from 10 kPa to 800 kPa. It was then used as aerodynamic wall pressure sensor in a turbulent boundary layer wind tunnel and successfully measured the 1.1 kPa depression occurring in the wind tunnel when the flow velocity goes up to 40 m/s.

Published
2022

35. Y-shaped demultiplexer photonic circuits based on detuned stubs: application to radiofrequency domain

Author

Abdelkrim Talbi, E. H. El Boudouti, Madiha Amrani, Abdellatif Akjouj, A. Mouadili, Noureddine Fettouhi, Bahram Djafari-Rouhani, Soufyane Khattou, LPMR, Department de Physique, Faculty of science, University Mohammed I, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Physique - IEMN (PHYSIQUE - IEMN), This study was funded by the National Center of Scientific and Technical Research (CNRST), Morocco., and Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA)

Subjects
demultiplexer, Demultiplexer, Electromagnetically induced transparency, Physics::Optics, 02 engineering and technology, Topology, 01 natural sciences, 010309 optics, Resonator, [SPI]Engineering Sciences [physics], 0103 physical sciences, BIC, Applied optics. Photonics, Radiology, Nuclear Medicine and imaging, Instrumentation, Physics, Single-mode optical fiber, EIT resonance, Fano resonance, Filter (signal processing), 021001 nanoscience & nanotechnology, Atomic and Molecular Physics, and Optics, photonic circuit, TA1501-1820, Stub (electronics), Radio frequency, 0210 nano-technology
Abstract

International audience; We present a theoretical and experimental study of photonic demultiplexers based on detuned stubs. The demultiplexers consist of Y-shaped structures with one input line and two output lines. Two different types of structures are proposed to achieve a selective transfer of a single mode in one output line without disturbing the second one. (i) In the first platform each output contains two different stubs attached at two different sites (U-shaped resonators). We derive in closed form the geometrical parameters of the stubs to achieve a selected frequency in each line while keeping the other line unaffected. The frequency selection can be made on the basis of two different mechanisms, namely a Fano or an electromagnetic induced transparency (EIT) resonance. Consequently, different demultiplexing schemes can be designed by a combination of the two mechanisms, such as Fano-Fano, Fano-EIT or EIT-EIT. In particular, the width of the Fano or EIT resonances can become zero for an appropriate choice of the stubs’ lengths, giving rise to trapped modes also called bound in continuum states (BICs) with infinite quality factors. We also show that the crosstalk between the two outputs can reach minimum values around −45 dB. (ii) In the second platform, each output line contains a photonic comb with a defect stub. The latter is appropriately designed to filter one or a few frequencies in the bandgap of the photonic comb. The analytical calculations are performed with the help of the Green’s function method which enables us to derive the transmission and reflection coefficients as well as the density of states (DOS). These results are confirmed by experimental measurements using coaxial cables in the radio frequency domain.

Published
2021

36. Wind tunnel integration of Micro-Magneto-Mechanical Systems (MMMS) microvalves for flow control experiments

Author

Philippe Pernod, Denis Sipp, Eric Garnier, T. Arnoult, Cécile Ghouila-Houri, Abdelkrim Talbi, Colin Leclercq, Romain Viard, M. Benedito, A. Mazzamurro, Q. Gallas, DAAA, ONERA, Université Paris Saclay [Meudon], ONERA-Université Paris-Saclay, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), JMH Conception F- 68100 Mulhouse, France, Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet - UMR 9014 (LMFL), Centrale Lille-ONERA-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), Laboratoire International associé sur les phénomènes Critiques et Supercritiques en électronique fonctionnelle, acoustique et fluidique (LIA LICS/LEMAC), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), This work was funded by the French National Research Agency (ANR) in the framework of the ANR ASTRID MATURATION 'CAMELOTT-MATVAL' Project. It is supported by the regional platform CONTRAERO in the framework of the CPER ELSAT 2020 Project. The Innovation Defense Agency (AID) has also financially sustained this work. The authors also thank RENATECH, the French national nanofabrication network, and FEDER., Renatech Network, ANR-18-ASMA-0008,CAMELOTT-MATVAL,Maturation & Valorisation de Capteurs et Actionneurs MEMS pour Le cOnTrôle réacTif d'écoulements(2018), and European Project

Subjects
Flow control (data), quasi-steady jets, Materials science, Mechanical engineering, cavity, flow control, pulsed jets, Physics::Fluid Dynamics, Momentum, Mechanical system, [SPI]Engineering Sciences [physics], Flow (mathematics), Control system, Micro-Magneto-Mechanical Systems (MMMS), Actuator, Magneto, Computer Science::Databases, Wind tunnel
Abstract

International audience; Flow control techniques can be defined as methods changing a flow natural dynamics. The control of a flow can be achieved with actuators affecting the flow momentum. Therefore, a MMMS microvalve was designed and characterized. The micro-actuators have then been integrated to a wind tunnel on the upstream corner of a cavity. Open-loop flow control experiments have been performed.

Published
2021

37. Temperature Sensitivity of Surface Phononic Crystals modes (SPnC) based on Ni Pillars array deposited on LiNBO3

Author

Olivier Bou-Matar, Abdelkrim Talbi, Aurelien Mazzamurro, Philippe Pernod, Cecile Ghouila Houri, Ghizlaine Boussatour, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), This work was funded by the regional platform CONTRAERO in the framework of the CPER ELSAT 2020 Project. The authors also thank RENATECH, the French national nanofabrication network, and FEDER, Renatech Network, and European Project

Subjects
Work (thermodynamics), Materials science, Acoustic wave, Condensed matter physics, SAW, Lithium niobate, Surface acoustic wave, Resonance, Bandgap, Substrate (electronics), TCF, Brillouin zone, chemistry.chemical_compound, [SPI]Engineering Sciences [physics], chemistry, Phononic Crystals, Local resonance, Surface Phononic crystal, Temperature coefficient
Abstract

International audience; This work focuses on the theoretical and experimental investigation of acoustic waves sensors based on 2D Surface Phononic Crystals (PnC). We investigated the temperature coefficient of frequency (TCF) for surface localized modes in 2D PnCs composed of Ni pillars deposited on Y-cut LiNBO3 substrate. We demonstrated both theoretically and experimentally that near the first limit of the Brillouin zone, the surface acoustic wave's temperature sensitivity depends considerably on pillars stiffness temperature constants, theirs resonance modes and lattice symmetry of the PnC.

Published
2021

38. High temperature gradient micro-sensors for skin-friction measurement in flow control applications

Author

Abdelkrim Talbi, A. Mazzamurro, Eric Garnier, Romain Viard, Cécile Ghouila-Houri, T. Arnoult, A. Merlen, Philippe Pernod, Q. Gallas, M. Benedito, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), DAAA, ONERA [Lille], ONERA, JMH Conception F- 68100 Mulhouse, France, Université de Lille, ONERA, Université de Toulouse [Mauzac], ONERA-PRES Université de Toulouse, Agence Nationale de la Recherche, ANR, This work was funded by the French National ResearchAgency (ANR) in the framework of the ANR ASTRID'CAMELOTT' and the ANR ASTRID MATURATION'CAMELOTT-MATVAL' projects. It is also supported bythe regional platform CONTRAERO in the framework of theCPER ELSAT 2020 Project. The Innovation Defense Agency(AID) has also financially sustained this work. The authorsalso thank RENATECH, the French national nanofabricationnetwork, and FEDER., Renatech Network, ANR-18-ASMA-0008,CAMELOTT-MATVAL,Maturation & Valorisation de Capteurs et Actionneurs MEMS pour Le cOnTrôle réacTif d'écoulements(2018), ANR-14-ASTR-0023,CAMELOTT,Capteurs et Actionneurs MEMS pour Le ConTrôle réactif de décollement sur voleT(2014), and European Project

Subjects
Flow control (data), Jet (fluid), Work (thermodynamics), Materials science, Calorimetric sensors, Acoustics, Temperature measurement, Temperature gradient, Flow separation, Flow control, [SPI]Engineering Sciences [physics], Transducer, Thermal, Wind tunnel experiments, MEMS sensors, Thermal sensors
Abstract

International audience; Robust micro machined high temperature gradient calorimetric (HTGC) transducers were designed and developed for flow separation control. Based on thermal principle, the transducers measure the amplitude and the sign of skin friction, making them particularly useful for flow separation detection. A set of 12 calorimetric micro-sensors along with miniaturized electronics was implemented on a flap model also equipped with pulsed jets. Flow control experiments were successfully conducted as the natural separation occurring on the model was detected by the micro sensors network and controlled by pulsed jet actuation. Ongoing work concerns the realization of closed-loop flow control experiments using the micro-sensors for feedback. © 2021 IEEE.

Published
2021

39. Design of a solid-fluid acoustic sensor based on Fano resonances

Author

Abdelkrim Talbi, E. H. El Boudouti, Bahram Djafari-Rouhani, M. Amrani, Bogdan Piwakowski, L. Krutyanskiy, Philippe Pernod, Cécile Ghouila-Houri, Ilyasse Quotane, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Transduction, Propagation et Imagerie Acoustique - IEMN (TPIA - IEMN), INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Physique - IEMN (PHYSIQUE - IEMN), no information, Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Institut d’Électronique, de Microélectronique et de Nanotechnologie - Département Opto-Acousto-Électronique - UMR 8520 (IEMN-DOAE), INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France)-Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), and Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA)-INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France)-Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN)

Subjects
[PHYS]Physics [physics], Work (thermodynamics), Materials science, Physics::Medical Physics, Continuum (design consultancy), Acoustic sensor, Fano resonance, solid-liquid, biosensor, Molecular physics, Bound state, phononic crystal, Acoustic metamaterials, Detection performance, bound state in the continuum (BICs), Biosensor
Abstract

International audience; The achievement of an efficient acoustic biosensor based on one dimensional solid-liquid phononic crystals supporting bound states in the continuum (BICs) and Fano resonances is reported herein. The structure used in this work is made of solid-liquid-solid triple layer embedded in water. The main results in this paper consist to study the impact of: i) the effect of albumin concentration, ii) the effect of the albumin layer thickness and iii) the influence of the incidence angle θ on albumin detection performance.

Published
2021

40. Experimental Evidence of the Existence of Bound States in the Continuum and Fano Resonances in Solid-Liquid Layered Media

Author

Cécile Ghouila-Houri, E. H. El Boudouti, L. M. Krutyansky, Philippe Pernod, Abdelkrim Talbi, Bahram Djafari-Rouhani, Madiha Amrani, Ilyasse Quotane, Bogdan Piwakowski, LPMR, Department de Physique, Faculty of science, University Mohammed I, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Siberian Branch of the Russian Academy of Sciences (SB RAS), Transduction, Propagation et Imagerie Acoustique - IEMN (TPIA - IEMN), Institut d’Électronique, de Microélectronique et de Nanotechnologie - Département Opto-Acousto-Électronique - UMR 8520 (IEMN-DOAE), INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France)-Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA)-INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France)-Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille Institut (CLIL), Laboratoire International associé sur les phénomènes Critiques et Supercritiques en électronique fonctionnelle, acoustique et fluidique (LIA LICS/LEMAC), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Physique - IEMN (PHYSIQUE - IEMN), no information, Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Prokhorov General Physics Institute of the Russian Academy of Sciences, INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN)

Subjects
[PHYS]Physics [physics], Physics, Acoustic metamaterials, Superluminal motion, Condensed matter physics, Continuum (design consultancy), Bound states, General Physics and Astronomy, Fano resonance, Mechanical properties, 02 engineering and technology, Decoupling (cosmology), 021001 nanoscience & nanotechnology, 01 natural sciences, Spectral line, Elasticity, Transverse plane, [SPI]Engineering Sciences [physics], Transmission (telecommunications), 0103 physical sciences, Bound state, Acoustical properties, [INFO]Computer Science [cs], 010306 general physics, 0210 nano-technology
Abstract

International audience; 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.

Published
2021

41. Transmission line photonic crystals: a comparison of Green's formalism, lumped circuit element model, and finite element method

Author

Leonard Dobrzynski, Cécile Ghouila-Houri, Bahram Djafari-Rouhani, Abdelkrim Talbi, Abdellatif Akjouj, and El Houssaine El Boudouti

Subjects
Physics, business.industry, Multiphysics, Mechanical engineering, Electrical element, 01 natural sciences, 7. Clean energy, Electromagnetic radiation, Finite element method, 010305 fluids & plasmas, Transmission line, 0103 physical sciences, Photonics, 010306 general physics, business, Electronic circuit, Photonic crystal
Abstract

This chapter presents the modeling, using Advanced Design System (ADS) from Keysight Technologies and Finite Element Method (FEM) based on Comsol Multiphysics tools, of photonic circuits. We particularly report in this chapter a confirmation of the results reported in Chapters 9, 10, and 11 concerning Fano, electromagnetic induced transparency (EIT), electromagnetic induced absorption (EIA) resonances, demultiplexer design based on EIT resonance, and the properties of comb structures with or without a defect state. In this chapter, we focus on three models: (i) lumped circuit elements used by ADS, (ii) FEM analysis of telegrapher's equation using Comsol, and (iii) FEM analysis of electromagnetic waves equation using Comsol. A comparison of these model results with those obtained by the Green's formalism in Chapters 9, 10, and 11 shows a good agreement. The analytical Green's function formalism enables an in-depth understanding of the physics; whereas the use of software-aided design will enable making the design, optimization, and experimentation of new designs in the field of photonics and microwaves quicker.

Published
2021

42. Open loop

Author

Abdelkrim Talbi, Abdellatif Akjouj, Gaëtan Lévêque, Yabin Jin, Cécile Ghouila-Houri, Housni Al Wahsh, El Houssaine El Boudouti, Leonard Dobrzynski, Bahram Djafari-Rouhani, and Yan Pennec

Subjects
Physics, business.industry, Mathematical analysis, Open-loop controller, Function (mathematics), Radius, Wave equation, 01 natural sciences, 010305 fluids & plasmas, 0103 physical sciences, Boundary value problem, Electromagnetic propagation, Photonics, 010306 general physics, business, Eigenvalues and eigenvectors
Abstract

Networks can be constructed out of finite open loops. Open loops are guides such that their one-dimensional properties may be considered independent of the open loop shape and radius. Their response function is derived from that of infinite open loops. A general definition of eigenstates is also given. The difference between resonant and force responses is made precise. These open loops have free boundary conditions at their two ends when they are used in network construction. The case of open loops with fixed end conditions is considered also. The photonic analysis is done with the Maxwell electromagnetic propagation wave equation.

Published
2021

43. Introduction

Author

Leonard Dobrzyński, Abdellatif Akjouj, El Houssaine El Boudouti, Gaëtan Lévêque, Housni Al Wahsh, Yan Pennec, Cécile Ghouila-Houri, Abdelkrim Talbi, Bahram Djafari-Rouhani, and Yabin Jin

Published
2021

44. MEMS High Temperature Gradient Sensor for Skin-Friction Measurements in Highly Turbulent Flows

Author

Pascal Molton, Cécile Ghouila-Houri, Eric Garnier, Quentin Gallas, Romain Viard, Alain Merlen, Jerome Delva, Abdelkrim Talbi, Philippe Pernod, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Laboratoire International associé sur les phénomènes Critiques et Supercritiques en électronique fonctionnelle, acoustique et fluidique (LIA LICS/LEMAC), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), Laboratoire de Mécanique des Fluides de Lille – Kampé de Fériet - UMR 9014 (LMFL), Centrale Lille-ONERA-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), DAAA, ONERA, Université Paris Saclay [Meudon], ONERA-Université Paris-Saclay, +CPER ELSAT 2020 project, This work was supported in part by the French National Research Agency (ANR) in the framework of the ANR ASTRID 'CAMELOTT' Project under Grant ANR-14-ASTR-0023-01, in part by the regional platform CONTRAERO in the framework of the CPER ELSAT 2020 project. T, Renatech Network, ANR-14-ASTR-0023,CAMELOTT,Capteurs et Actionneurs MEMS pour Le ConTrôle réactif de décollement sur voleT(2014), European Project, Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), and HESAM Université (HESAM)-HESAM Université (HESAM)

Subjects
Materials science, Temperature measurement, 7. Clean energy, 01 natural sciences, MEMS SENSOR, 010305 fluids & plasmas, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Physics::Fluid Dynamics, symbols.namesake, SKIN-FRICTION MEASUREMENT, Parasitic drag, Wide dynamic range, 0103 physical sciences, Shear stress, [PHYS.PHYS.PHYS-INS-DET]Physics [physics]/Physics [physics]/Instrumentation and Detectors [physics.ins-det], Electrical and Electronic Engineering, Aerospace engineering, [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics, Instrumentation, Wind tunnel, Microelectromechanical systems, business.industry, Turbulence, 010401 analytical chemistry, Aerodynamics, Mechanics, 0104 chemical sciences, Temperature gradient, Mach number, Power consumption, symbols, business, Microfabrication
Abstract

This article was presented in part at the IEEE Sensors 2019 and in part at the Selected Papers from the IEEE SENSORS 2019 Conference.; International audience; This paper presents and discusses the results obtained with a MEMS (Micro-Electro-Mechanical System) high temperature gradient sensor for time-averaged and fluctuating skin-friction measurements in highly turbulent flows. Designed as a robust wall-mounted suspended hot-wire structure, the micro-sensor was made using conventional microfabrication techniques, compatible with microelectronics for designing integrated smart systems. Successfully implemented into two air wind tunnels, the sensor was tested in a large range of turbulent flows, with mainstream velocities going up to 270 m/s (Mach number of 0.79), which corresponds to the mean velocity of airliner cruise flights. The experiments demonstrated the wide dynamic range of the micro-sensor without reaching its limits. The micro-sensor thereby demonstrated its value for measuring turbulence in aerodynamic applications, being particularly suitable for aeronautics.

Published
2021

45. Electromagnetic induced transparency, induced absorption, and Fano resonances in photonic circuits

Author

Bahram Djafari-Rouhani, El Houssaine El Boudouti, Abdellatif Akjouj, Leonard Dobrzynski, and Abdelkrim Talbi

Subjects
Physics, Condensed matter physics, Electromagnetically induced transparency, Attenuation, Fano resonance, Resonance, 02 engineering and technology, 021001 nanoscience & nanotechnology, 01 natural sciences, law.invention, Resonator, Transmission (telecommunications), law, 0103 physical sciences, Transmission coefficient, 010306 general physics, 0210 nano-technology, Waveguide
Abstract

In this chapter, a simple photonic device consisting of two dangling side resonators grafted at two sites (U-shape) or at the same site (cross-shape) along a waveguide is designed in order to obtain sharp resonant states inside the transmission gaps without introducing any defects in the structure. This results from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or placed between two zeros of transmission, the so-called Fano resonances. A general analytic expression for the transmission coefficient is given for various systems of this kind. The amplitude of the transmission is obtained following the Fano form. The full width at half maximum of the resonances and the asymmetric Fano parameter are discussed explicitly as functions of the geometrical parameters of the system. In addition to the usual asymmetric Fano resonance, we show that this system may exhibit an electromagnetic induced transparency (EIT) resonance, as well as a particular case where such resonances collapse in the transmission coefficient, giving rise to the so-called bound in continuum (BIC) states. Also, we give a comparison between the phase of the determinant of the scattering matrix, the so-called Friedel phase, and the phase of the transmission amplitude. By taking into account the loss in the waveguides, we show that at the transmission resonance, the transmission (reflection) increases (decreases) as a function of the detuning δ between the lengths of the two stubs, whereas the absorption goes through a maximum around 0.5 for a threshold value δth, giving rise to electromagnetic induced absorption (EIA) resonance, which depends on the attenuation in the system and then falls to zero. The effect of the boundary conditions at the end of the resonators on the EIA resonance is also discussed. The analytical results are obtained by means of the Green's function method, whereas the experiments are carried out using coaxial cables in the radio-frequency regime. These results should have important consequences for designing integrated devices such as narrow-frequency optical or microwave filters and high-speed switches. This system is proposed as a simpler alternative to coupled microresonators.

Published
2021

46. Closed loop and stubs

Author

Abdellatif Akjouj, Housni Al Wahsh, El Houssaine El Boudouti, Cécile Ghouila-Houri, Gaëtan Lévêque, Leonard Dobrzynski, and Abdelkrim Talbi

Subjects
Physics, Reflection (mathematics), Line (geometry), Degenerate energy levels, Path (graph theory), Eigenfunction, Topology, Multiplexer, Eigenvalues and eigenvectors, Stub (electronics)
Abstract

Closed loops with finite open loops attached to the robust zeros of one of their two twin states are the systems investigated in this chapter. Such attached finite loops are called stubs. For simplicity, here only the cases where all the stubs have the same length are considered. This length is chosen to be commensurable with the closed loop length. So the interface points of such systems remain robust zeros for many eigenfunctions of the final systems. As a consequence, the corresponding eigenwavelengths are robust. All the states of such systems are obtained with particular attention to the path ones. An eigenfunction zero is robust because its eigenstate cannot be activated by any action applied on it. The path states are robust because they are confined within one-dimensional paths, and when they are degenerate they can turn around defects. Multiplexer and wide reflection band applications of such systems are presented. It is shown that some path states can be transferred from one infinite line to another without any perturbation. Such single wavelength transfers are of infinite quality. It is possible to transform them into finite-width resonances just by tuning the stub lengths.

Published
2021

47. Path states

Author

Bahram Djafari-Rouhani, Housni Al Wahsh, El Houssaine El Boudouti, Abdellatif Akjouj, Abdelkrim Talbi, Gaëtan Lévêque, Cécile Ghouila-Houri, and Leonard Dobrzynski

Subjects
Physics, Degenerate energy levels, State (functional analysis), Eigenfunction, Space (mathematics), 01 natural sciences, Action (physics), 010305 fluids & plasmas, Loop (topology), Classical mechanics, 0103 physical sciences, Path (graph theory), 010306 general physics, Eigenvalues and eigenvectors
Abstract

Any open and closed loop eigenfunction has zero motion space points, called here robust zeros. Any such zero is robust because its eigenstate cannot be activated by any action applied on it. Indeed, such zero space positions remain unaffected when the loop is interfaced with its outside world only through one or several such robust zeros. The corresponding eigenwavelengths and eigenfunctions remain also unaffected by such interfacing. When this interfacing introduces one or several new pathways whose lengths are commensurable with the unaffected eigenwavelength, the eigenstate becomes degenerate or more degenerate. Such states remain strictly confined within an ensemble of open or closed loop paths. A confined state is strictly confined in its space subdomain. So path states belong to a subset of confined states. They are confined within combinations of open and closed loops. In such an interfacing process, the other eigenvalues shift. They may have in general more complicated eigenfunctions. Similar considerations can be developed for any system state and lead to a confined state theorem. This enables also to propose a construction method of systems with confined states. This construction method is developed in what follows for path states. They are the simplest ones, as being confined along loop paths. When the path states are degenerate, their paths can go around defects. The path states are robust because they are confined within one-dimensional paths, and when they are degenerate they can turn around defects. This chapter presents also general eigenfunction rules. These rules are mainly eigenfunction continuities and outgoing source forces equal to zero, at each network point. The source forces are for electromagnetic waves, the outgoing derivatives of the wave electric and magnetic fields. For other types of waves, the source forces are, for example, the outgoing stresses, currents, etc. These new tutorial results are illustrated by simple examples. All this can lead to a construction procedure of robust transmission lines. The confined path states can pave the way for the future of information communication technology and contribute to many other sciences.

Published
2021

48. Optimization of Reactive-Ion Etching (RIE) parameters to maximize the lateral etch rate of silicon using SF6/N2 gas mixture: An alternative to etching Si in MEMS with Au components

Author

Abdelkrim Talbi, T. Arnoult, S. Hammami, Cécile Ghouila-Houri, Philippe Pernod, M. Kazar Mendes, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN (AIMAN-FILMS - IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Laboratoire International associé sur les phénomènes Critiques et Supercritiques en électronique fonctionnelle, acoustique et fluidique (LIA LICS/LEMAC), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF), The authors would like to thank SERB, India for Extra Mural Research Funding (EMR/2017/003117)., Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), and Renatech Network

Subjects
Materials science, Silicon, chemistry.chemical_element, Au Thin films, 02 engineering and technology, 010402 general chemistry, 01 natural sciences, [SPI.MAT]Engineering Sciences [physics]/Materials, Etching (microfabrication), DOE, General Materials Science, Isotropic Si RIE, Reactive-ion etching, [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics, Microstructure, Microelectromechanical systems, business.industry, Mechanical Engineering, Isotropy, SF6/N2 plasma, Plasma, 021001 nanoscience & nanotechnology, Condensed Matter Physics, 0104 chemical sciences, Volumetric flow rate, MEMS, chemistry, Mechanics of Materials, Torr, Optoelectronics, 0210 nano-technology, business
Abstract

International audience; In this work, the effects of the N2 addition to the SF6 plasma used in the isotropic silicon etching of Microelectromechanical systems (MEMS) with Au components are investigated. A four-variables Doehlert design was implemented for optimizing the etching parameters (power, pressure, gas flow rate, and N2 /SF6 ratio) to maximize the lateral etch rate of Si using SF6 /N2 gas mixture. The optimized etch condition founded for a lateral etch rate of 1.8 mm/min was: power = 143 W, chamber pressure = 86 mTorr, flow rate = 22 sccm, and N2 /SF6 ratio = 0.1. Furthermore, it was demonstrated that the established etching process avoids the structure damage of Au components.

Published
2021

49. Photonic demultiplexers based on Fano and induced transparency resonances

Author

Bahram Djafari-Rouhani, Abdellatif Akjouj, El Houssaine El Boudouti, Leonard Dobrzynski, and Abdelkrim Talbi

Subjects
Physics, Waveguide (electromagnetism), Demultiplexer, Electromagnetically induced transparency, business.industry, Physics::Optics, 02 engineering and technology, Fano plane, 021001 nanoscience & nanotechnology, 01 natural sciences, 010309 optics, Optics, Position (vector), 0103 physical sciences, Line (geometry), Coaxial, Photonics, 0210 nano-technology, business
Abstract

In this chapter, we give an analytical and experimental demonstration of the possibility to realize a simple photonic demultiplexer based on Fano and electromagnetically induced transparency resonances. The demultiplexer consists on a Y-shaped waveguide with an input line and two output lines. Each output line contains two grafted stubs at a given position far from the input line. We derive in closed form the expressions for a selective transfer of a single propagating mode through one line, keeping the other line unaffected. We illustrate the analytical and numerical results by a simple experiment carried out using coaxial cables in the radio-frequency domain.

Published
2021

50. Closed loop

Author

Abdelkrim Talbi, Housni Al Wahsh, Abdellatif Akjouj, Cécile Ghouila-Houri, Gaëtan Lévêque, Leonard Dobrzynski, El Houssaine El Boudouti, and Bahram Djafari-Rouhani

Subjects
010302 applied physics, Physics, Degenerate energy levels, Mathematical analysis, Open-loop controller, 02 engineering and technology, Function (mathematics), Eigenfunction, 021001 nanoscience & nanotechnology, 01 natural sciences, Superposition principle, 0103 physical sciences, 0210 nano-technology, Degeneracy (mathematics), Closed loop, Eigenvalues and eigenvectors
Abstract

A closed loop can be obtained by linear superposition of the two free ends of an open loop. Its main property is the double degeneracy of its states. The analytical expressions of its eigenvalues, eigenfunctions, and response function are presented. The case of two simultaneous identical measures at two different points of a closed loop is briefly addressed. The simultaneous activation of these two degenerate states is presented from the theoretical and experimental points of view.

Published
2021

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