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Register a new userTwo tractable models of dynamic resonances and their application to Fano resonances at light scattering
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Added by
Andrey Miroshnichenko
Publication date
2021
fields
Physics
and research's language is
English
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We study numerically and analytically effects of resonant light scattering by subwavelength high-index particles with weak dissipation in the vicinity of the destructive interference at Fano resonances. We show that sharp variations in the envelope of the incident pulse may initiate unusual, counterintuitive dynamics of the scattering associated with interference of modes with fast and slow relaxation. In particular, we observe and explain intensive sharp spikes in scattering cross section just behind the leading and trailing edges of the incident pulse. The latter occurs when the incident pulse is over and is explained by the release of the electromagnetic energy accumulated in the particle at the previous stages of the scattering. To mimic the numerical results, we develop two tractable analytical models. Both reproduce with high accuracy all the dynamic effects of the numerics. The models allow us to reveal the physical grounds for the spikes explained by the violation of balance between the resonant and background partitions during the transient. Besides, we compare the models with each other and reveal their mutual advantages and disadvantages.
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If the duration of the input pulse resonantly interacting with a system is comparable or smaller than the time required for the system to achieve the steady state, transient effects become important. For complex systems, a quantitative description of these effects may be a very difficult problem. We suggest a simple tractable model to describe these phenomena. The model is based on approximation of the actual Fourier spectrum of the system by that composed of the superposition of the spectra of uncoupled harmonic oscillators (normal modes). The physical nature of the underlying system is employed to select the proper approximation. This reduces the dynamics of the system to tractable dynamics of just a few driven oscillators. The method is simple and may be applied to many types of resonances. As an illustration, the approach is employed to describe the sharp intensive spikes observed in the recent numerical simulation of short light pulses scattered by a cylinder in the proximity of destructive Fano interference [Phys. Rev. A., vol. 100, 053824 (2019)] and exhibits excellent agreement with the numerics.
Based on the substantial difference in the response time for the resonant and background partitions at stepwise variations of the exiting signal, a simple exactly integrable model describing the dynamic Fano resonance (DFRs) is proposed. The model does not have any fitting parameters, may include any number of resonant partitions and exhibits high accuracy. It is shown that at the point of the destructive interference any sharp variation of the amplitude of the excitation (no matter an increase or a decrease) gives rise to pronounced flashes in the intensity of the output signal. In particular, the flash should appear behind the trailing edge of the exciting pulse, when the excitation is already over. The model is applied to explain the DFRs at the light scattering by a dielectric cylinder with two resonant modes excited simultaneously and exhibits the excellent agreement with the results of the direct numerical integration of the Maxwell equations.
It is shown that elastic resonance scattering of light by a finite-size obstacle with weak dissipation is analogous to quantum scattering by a potential with quasi-discrete levels and exhibits Fano resonances. Localized plasmons (polaritons), exited in the obstacle by the incident light, are equivalent to the quasi-discrete levels, while the radiative decay of these excitations plays exactly the same role as tunnelling from the quasi-discrete levels for the quantum problem. Mie scattering of light by a spherical particle and an exactly solvable discrete model with nonlocal coupling simulating wave scattering in systems with reduced spatial dimensionality are discussed as examples.
In this research, we report the experimental evidence of the directional Fano resonances at the scattering of a plane, linearly polarized electromagnetic wave by a homogeneous dielectric sphere with high refractive index and low losses. We observe a typical asymmetric Fano profile for the intensity scattered in, practically, any given direction, while the overall extinction cross section remains Lorentzian. The phenomenon is originated in the interference of the selectively excited electric dipolar and quadrupolar modes. The selectivity of the excitation is achieved by the proper choice of the frequency of the incident wave. Thanks to the scaling invariance of the Maxwell equations, in these experiments we mimic the scattering of the visible and near IR radiation by a nanoparticle made of common superconductor materials (Si, Ge, GaAs, GaP) by the equivalent scattering of a spherical particle of 18 mm in diameter in the microwave range. The theory developed to explain the experiments extends the conventional Fano approach to the case when both interfering partitions are resonant. The perfect agreement between the experiment and the theory is demonstrated.
A detailed analytical inspection of light scattering by a particle with high refractive index m+ikappa and small dissipative constant kappa is presented. We have shown that there is a dramatic difference in the behavior of the electromagnetic field within the particle (inner problem) and the scattered field outside it (outer problem). With an increase in m at fix values of the other parameters, the field within the particle asymptotically converges to a periodic function of m. The electric and magnetic type Mie resonances of different orders overlap substantially. It may lead to a giant concentration of the electromagnetic energy within the particle. At the same time, we demonstrate that identical transformations of the solution for the outer problem allow to present each partial scattered wave as a sum of two partitions. One of them corresponds to the m-independent wave, scattered by a perfectly reflecting particle and plays the role of a background, while the other is associated with the excitation of a sharply-m-dependent resonant Mie mode. The interference of the partitions brings about a typical asymmetric Fano profile. The explicit expressions for the parameters of the Fano profile have been obtained from the first principles without any additional assumptions and/or fitting. In contrast to the inner problem, at an increase in m the resonant modes of the outer problem die out, and the scattered field converges to the universal, m-independent profile of the perfectly reflecting sphere. Numerical estimates of the discussed effects for a gallium phosphide particle are presented.
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