Theoretical and experimental evidence of Fano-like resonances in simple monomode photonic circuits

Mouadili, A.; Boudouti, El Houssaine El; Soltani, A.; Talbi, Abdelkrim; Akjouj, Abdellatif; Djafari‐Rouhani, Bahram

doi:10.1063/1.4802695

Cited by 42 publications

(38 citation statements)

References 80 publications

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“…However, the shape of these resonances still remains visible for low-absorbing media. The shapes of the resonances (see Appendix) are similar to those we have obtained recently in photonic crystals based on lossy coaxial cables [36,37].…”

Section: Discussionsupporting

confidence: 81%

“…Although all these resonances were first proposed in quantum mechanics, it was demonstrated that such phenomena can be extended to classical systems such as plasmonic materials and planar metamaterials [18][19][20][21][22][23][24], photonic crystal waveguides coupled to cavities [25][26][27][28][29], coupled microresonators [30][31][32][33][34][35], photonic crystal slabs [14,15], and photonic circuits [36,37]. However, little work has been devoted to acoustic counterpart systems [38][39][40][41][42][43][44][45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

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Trapped-mode-induced Fano resonance and acoustical transparency in a one-dimensional solid-fluid phononic crystal

Quotane¹,

Boudouti²,

Djafari‐Rouhani

2018

Phys. Rev. B

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We investigate theoretically and numerically the possibility of existence of Fano and acoustic-induced transparency (AIT) resonances in a simple though realistic one-dimensional acoustic structure made of solid-fluid layers inserted between two fluids. These resonances are obtained by combining appropriately the zeros of transmission (antiresonance) induced by the solid layers and the local resonances induced by the solid or combined solid-fluid layers with surface free boundary conditions. In particular, we show the possibility of trapped modes, also called bound states in continuum, which have recently found a high renewal interest. These modes appear as resonances with zero width in the transmission spectra as well as in the density of states (DOS). We consider three different structures: (i) a single solid layer inserted between two fluids. This simple structure shows the possibility of existence of trapped modes, which are discrete modes of the solid layer that lie in the continuum modes of the surrounding fluids. We give explicit analytical expressions of the dispersion relation of these eigenmodes of the solid layer which are found independent of the nature of the surrounding fluids. By slightly detuning the angle of incidence from that associated to the trapped mode, we get a well-defined Fano resonance characterized by an asymmetric Fano profile in the transmission spectra. (ii) The second structure consists of a solid-fluid-solid triple layer embedded between two fluids. This structure is found more appropriate to show both Fano and acoustic-induced transparency resonances. We provide detailed analytical expressions for the transmission and reflection coefficients that enable us to deduce a closed-form expression of the dispersion relation giving the trapped modes. Two situations can be distinguished in the triple-layer system: in the case of a symmetric structure (i.e., the same solid layers) we show, by detuning the incidence angle θ, the possibility of existence of Fano resonances that can be fitted following a Fano-type expression. The variation of the Fano parameter that describes the asymmetry of such resonances as well as their width versus θ is studied in detail. In the case of an asymmetric structure (i.e., different solid layers), we show the existence of an incidence angle that enables to squeeze a resonance between two transmission zeros induced by the two solid layers. This resonance behaves like an AIT resonance, its position and width depend on the nature of the fluid and solid layers as well as on the difference between the thicknesses of the solid layers. (iii) In the case of a periodic structure (phononic crystal), we show that trapped modes and Fano resonances give rise, respectively, to dispersionless flat bands with zero group velocity and nearly flat bands with negative or positive group velocities. The analytical results presented here are obtained by means of the Green's function method which enables to deduce in closed form: dispersion curves, transmission and reflection coeffic...

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Section: Discussionsupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Trapped-mode-induced Fano resonance and acoustical transparency in a one-dimensional solid-fluid phononic crystal

Quotane¹,

Boudouti²,

Djafari‐Rouhani

2018

Phys. Rev. B

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“…Once we now know the recurrence formulas for the scattering coefficients of a linear quantum graph, we can return to the Green's function in Eq. (86). But first we shall recall that G(x f , x i ; k) can be generally interpreted as the transition probability amplitude for a particle (of fixed energy E = 2 k 2 /(2µ)) initially in x i to get to x f [181].…”

Section: Green's Function As a Transition Probability Amplitude And Tmentioning

confidence: 99%

Green’s function approach for quantum graphs: An overview

et al. 2016

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Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function (G) framework. This approach is particularly interesting because G can be written as a sum over classical-like paths, where local quantum effects are taking into account through the scattering matrix amplitudes (basically, transmission and reflection amplitudes) defined on each one of the graph vertices. Hence, the exact G has the functional form of a generalized semiclassical formula, which through different calculation techniques (addressed in details here) always can be cast into a closed analytic expression. It allows to solve exactly arbitrary large (although finite) graphs in a recursive and fast way. Using the Green's function method, we survey many properties for open and closed quantum graphs as scattering solutions for the former and eigenspectrum and eigenstates for the latter, also considering quasi-bound states. Concrete examples, like cube, binary trees and Sierpiński-like topologies are presented. Along the work, possible distinct applications using the Green's function methods for quantum graphs are outlined.

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“…Recent studies have demonstrated that the analog of EIT can be also realized in classical systems due to similar interference effects. Different systems have been proposed for this purpose such as: photonic crystal waveguides coupled to cavities [7][8][9], coupled-microresonator systems [10,11], nonlinear materials [12,13], plasmonic nanostructures and metamaterials [14,15], acoustic waveguides [16][17][18], multilayers [19] and photonic circuits [20,21]. In addition to the EIT resonances, the electromagnetically induced reflection (EIR) refers to the formation of a reflection window inside a transparency band of an atomic system.…”

Section: Introductionmentioning

confidence: 99%

Aharonov-Bohm-effect induced transparency and reflection in mesoscopic rings side coupled to a quantum wire

Mrabti

Labdouti

Mouadili

et al. 2020

Physica E: Low-dimensional Systems and Nanostructures

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We demonstrate analytically and numerically the possibility of existence of the analogues of electromagnetic induced transparency (EIT) and electromagnetic induced reflection (EIR) in a simple mesoscopic structure. The latter consists of a ring of length 2d attached vertically to two semi-infinite leads (waveguide) by a wire of length d 1 . The ring is threaded by a magnetic flux Φ, the so-called Aharonov-Bohm effect. The number of dangling wire-ring resonators attached at the same point can be increased to N. First, we demonstrate analytically that in the absence of the magnetic flux (Φ ¼ 0) and for particular values of d 1 , the structure may present some states that are confined in the ring and do not interact with the waveguide states. These trapped states fall in the continuum states of the two leads and therefore represent bound in continuum (BIC) states. These states are characterized by a zero width resonance (i.e., infinite life-time) in the transmission and reflection spectra. In presence of a weak magnetic flux (Φ 6 ¼ 0), the BIC states transform to EIT or EIR resonances for specific values of the lengths d 1 and d of the wire and the ring respectively. In addition to the numerical results, we have developed Taylor expansion calculations of the transmission and reflection coefficients around EIT and EIR resonances to show that the latter can be written following a Fano shape. In particular, we have deduced the Fano parameter q and the quality factor Q of these resonances as function of N and the flux Φ. We have found that Q decreases as function of Φ for both EIT and EIR resonances, whereas it increases (decreases) as function of N for EIT (EIR) resonances. These results show the possibility of tuning EIT and EIR resonances by means of the magnetic flux Φ and the number of dangling resonators N. The effect of temperature on EIT and EIR resonances is also considered through an analysis of the Landauer-Buttiker conductance formula obtained from transmission. The theoretical results are obtained within the framework of the Green's function method which enables us to deduce analytically the dispersion relation, transmission and reflection coefficients. These results may have important applications for electronic transport in mesoscopic systems such as filters and demultiplexers.

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Theoretical and experimental evidence of Fano-like resonances in simple monomode photonic circuits

Cited by 42 publications

References 80 publications

Trapped-mode-induced Fano resonance and acoustical transparency in a one-dimensional solid-fluid phononic crystal

Trapped-mode-induced Fano resonance and acoustical transparency in a one-dimensional solid-fluid phononic crystal

Green’s function approach for quantum graphs: An overview

Aharonov-Bohm-effect induced transparency and reflection in mesoscopic rings side coupled to a quantum wire

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