Limits...
Universal lineshapes at the crossover between weak and strong critical coupling in Fano-resonant coupled oscillators.

Zanotto S, Tredicucci A - Sci Rep (2016)

Bottom Line: In this article we discuss a model describing key features concerning the lineshapes and the coherent absorption conditions in Fano-resonant dissipative coupled oscillators.The model treats on the same footing the weak and strong coupling regimes, and includes the critical coupling concept, which is of great relevance in numerous applications; in addition, the role of asymmetry is thoroughly analyzed.Due to the wide generality of the model, which can be adapted to various frameworks like nanophotonics, plasmonics, and optomechanics, we envisage that the analytical formulas presented here will be crucial to effectively design devices and to interpret experimental results.

View Article: PubMed Central - PubMed

Affiliation: Istituto Nazionale di Ottica - CNR, Via Nello Carrara 1, 50019 Sesto Fiorentino (FI), Italy.

ABSTRACT
In this article we discuss a model describing key features concerning the lineshapes and the coherent absorption conditions in Fano-resonant dissipative coupled oscillators. The model treats on the same footing the weak and strong coupling regimes, and includes the critical coupling concept, which is of great relevance in numerous applications; in addition, the role of asymmetry is thoroughly analyzed. Due to the wide generality of the model, which can be adapted to various frameworks like nanophotonics, plasmonics, and optomechanics, we envisage that the analytical formulas presented here will be crucial to effectively design devices and to interpret experimental results.

No MeSH data available.


Related in: MedlinePlus

Panel (a), schematic of a resonant metasurface embedding quantum wells, which implement a prototype of strongly and critically coupled oscillators with asymmetry. Panels (b,c), resonant field and spectral transmittance of two structures which differ by the value of t1. These resonators are described by different asymmetry parameters, resulting in differently contrasted lineshapes. The calculations from a rigorous electromagnetic solver (dots) are faithfully reproduced by the coupled-mode model (red and blue lines).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4836300&req=5

f3: Panel (a), schematic of a resonant metasurface embedding quantum wells, which implement a prototype of strongly and critically coupled oscillators with asymmetry. Panels (b,c), resonant field and spectral transmittance of two structures which differ by the value of t1. These resonators are described by different asymmetry parameters, resulting in differently contrasted lineshapes. The calculations from a rigorous electromagnetic solver (dots) are faithfully reproduced by the coupled-mode model (red and blue lines).

Mentions: A schematic of the structure is sketched in Fig. 3(a). It consists of a heterostructure of 60 equispaced GaAs/Al0.33Ga0.67As MQW, with well/barrier thicknesses 6.8/20 nm resulting in an intersubband transition frequency 28. The membrane has thickness t2 = 1.3 μm, and is periodically patterned with thin (50 nm) gold stripes, whose spacing is a and filling fraction is f. A high-index coating (ε = 10) coating with thickness t1 completes the layer stack. A fully vectorial electromagnetic modeling of the structure is performed through rigorous coupled wave analysis (RCWA). The permittivity of gold is assumed to be εAu = 4000 + 300i, that of GaAs εGaAs = 10, while the MQW response follows a Lorentz oscillator model (see refs 25,30 for details; the key parameters in this model are the resonance frequency ω12, the damping rate γ12 and the subband surface charge difference Δn, which is eventually proportional to the oscillator strength). Suppose, at first, that the response of the MQW is turned off (Δn = 0). The device exhibits an isolated photonic resonance at ωc ≃ 150 meV, depending on the specific values of a, f, and t1. An analysis of the transmittance lineshape, following Eq. 2, revealed that the device acts as a symmetric resonator (i.e., ξ = 0), unless t1 ≠ 0. Indeed, if t1 = 0, the transmission lineshape is a fully-contrasted Lorentzian, which can only be reproduced with the coupled-mode model by setting ξ = 0. If instead a finite value of t1 is chosen, the transmission lineshape has a contrast smaller than one, which can be only reproduced by setting ξ ≠ 0. For the present structure the lineshapes turned out to be almost pure upward Lorentzians, hence the non-resonant scattering parameter r is expected to be very close to unity.


Universal lineshapes at the crossover between weak and strong critical coupling in Fano-resonant coupled oscillators.

Zanotto S, Tredicucci A - Sci Rep (2016)

Panel (a), schematic of a resonant metasurface embedding quantum wells, which implement a prototype of strongly and critically coupled oscillators with asymmetry. Panels (b,c), resonant field and spectral transmittance of two structures which differ by the value of t1. These resonators are described by different asymmetry parameters, resulting in differently contrasted lineshapes. The calculations from a rigorous electromagnetic solver (dots) are faithfully reproduced by the coupled-mode model (red and blue lines).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4836300&req=5

f3: Panel (a), schematic of a resonant metasurface embedding quantum wells, which implement a prototype of strongly and critically coupled oscillators with asymmetry. Panels (b,c), resonant field and spectral transmittance of two structures which differ by the value of t1. These resonators are described by different asymmetry parameters, resulting in differently contrasted lineshapes. The calculations from a rigorous electromagnetic solver (dots) are faithfully reproduced by the coupled-mode model (red and blue lines).
Mentions: A schematic of the structure is sketched in Fig. 3(a). It consists of a heterostructure of 60 equispaced GaAs/Al0.33Ga0.67As MQW, with well/barrier thicknesses 6.8/20 nm resulting in an intersubband transition frequency 28. The membrane has thickness t2 = 1.3 μm, and is periodically patterned with thin (50 nm) gold stripes, whose spacing is a and filling fraction is f. A high-index coating (ε = 10) coating with thickness t1 completes the layer stack. A fully vectorial electromagnetic modeling of the structure is performed through rigorous coupled wave analysis (RCWA). The permittivity of gold is assumed to be εAu = 4000 + 300i, that of GaAs εGaAs = 10, while the MQW response follows a Lorentz oscillator model (see refs 25,30 for details; the key parameters in this model are the resonance frequency ω12, the damping rate γ12 and the subband surface charge difference Δn, which is eventually proportional to the oscillator strength). Suppose, at first, that the response of the MQW is turned off (Δn = 0). The device exhibits an isolated photonic resonance at ωc ≃ 150 meV, depending on the specific values of a, f, and t1. An analysis of the transmittance lineshape, following Eq. 2, revealed that the device acts as a symmetric resonator (i.e., ξ = 0), unless t1 ≠ 0. Indeed, if t1 = 0, the transmission lineshape is a fully-contrasted Lorentzian, which can only be reproduced with the coupled-mode model by setting ξ = 0. If instead a finite value of t1 is chosen, the transmission lineshape has a contrast smaller than one, which can be only reproduced by setting ξ ≠ 0. For the present structure the lineshapes turned out to be almost pure upward Lorentzians, hence the non-resonant scattering parameter r is expected to be very close to unity.

Bottom Line: In this article we discuss a model describing key features concerning the lineshapes and the coherent absorption conditions in Fano-resonant dissipative coupled oscillators.The model treats on the same footing the weak and strong coupling regimes, and includes the critical coupling concept, which is of great relevance in numerous applications; in addition, the role of asymmetry is thoroughly analyzed.Due to the wide generality of the model, which can be adapted to various frameworks like nanophotonics, plasmonics, and optomechanics, we envisage that the analytical formulas presented here will be crucial to effectively design devices and to interpret experimental results.

View Article: PubMed Central - PubMed

Affiliation: Istituto Nazionale di Ottica - CNR, Via Nello Carrara 1, 50019 Sesto Fiorentino (FI), Italy.

ABSTRACT
In this article we discuss a model describing key features concerning the lineshapes and the coherent absorption conditions in Fano-resonant dissipative coupled oscillators. The model treats on the same footing the weak and strong coupling regimes, and includes the critical coupling concept, which is of great relevance in numerous applications; in addition, the role of asymmetry is thoroughly analyzed. Due to the wide generality of the model, which can be adapted to various frameworks like nanophotonics, plasmonics, and optomechanics, we envisage that the analytical formulas presented here will be crucial to effectively design devices and to interpret experimental results.

No MeSH data available.


Related in: MedlinePlus