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

Abstract

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 = d 2 + d 3 connected to a stub of length d 4 . The whole cavity is attached vertically to two semi-infinite waveguides by a wire of length d 1 . We demonstrate that the BICs can be induced either by the loop-stub system or by the two arms of lengths d 2 and d 3 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.

Quasi-Trapped Guided Mode in a Metasurface Waveguide for Independent Control of Multiple Nonlocal Modes

“…where |s + ⟩, |s − ⟩, K, C, and D denote the matrices that represent incident wave, outgoing wave, in-coupling coefficient, direct scattering, and out-coupling coefficient, respectively. Equation 9a represents an eigenequation in the absence of |s + ⟩, and under this condition, the Hamiltonian can be expressed as 32,71,72…”

“…Utilizing the notations a L and a Q for the amplitudes of LGM TM and QTGM, and | a false⟩ = ( lefttrue0.25ex a normalL a normalQ ) for their corresponding state, the following equations hold normald | a false⟩ normald t = prefix− i scriptH | a false⟩ + K | s + false⟩ | s − false⟩ = C | s + false⟩ + D | a false⟩ where | s + ⟩, | s – ⟩, K , C , and D denote the matrices that represent incident wave, outgoing wave, in-coupling coefficient, direct scattering, and out-coupling coefficient, respectively. Equation represents an eigenequation in the absence of | s + ⟩, and under this condition, the Hamiltonian scriptH can be expressed as ,, scriptH = [ lefttrue ω normalL κ κ ω normalQ ] − normali [ lefttrue γ normalL ...…”

“…The intersection results in a strong coupling between the two modes, leading to an anticrossing behavior and a subsequent band splitting. 32,71,72 In this context, one of the resultant bands becomes nonradiative, constituting the F−W BIC, whereas the other assumes a highly radiative nature.…”

“…A focused view, specifically in the range where fa/c ranges from 0.695 to 0.711 and k y / k 0 spans from 0.018 to 0.033 in Figure a, confirms this intersection between LGM TM and QTGM. The intersection results in a strong coupling between the two modes, leading to an anticrossing behavior and a subsequent band splitting. ,, In this context, one of the resultant bands becomes nonradiative, constituting the F–W BIC, whereas the other assumes a highly radiative nature.…”

“…Utilizing the notations a L and a Q for the amplitudes of LGM TM and QTGM, and for their corresponding state, the following equations hold where | s + ⟩, | s – ⟩, K , C , and D denote the matrices that represent incident wave, outgoing wave, in-coupling coefficient, direct scattering, and out-coupling coefficient, respectively. Equation represents an eigenequation in the absence of | s + ⟩, and under this condition, the Hamiltonian can be expressed as ,, where ω L and ω Q denote the resonant frequencies of LGM TM and QTGM, γ L and γ Q represent the decay rates of LGM TM and QTGM, k indicates the coupling coefficient, and ψ denotes the phase difference between two modes. In the case ψ equals zero, the corresponding eigenvalues of eq can be described as below. …”