Quantum nonlocal effects on optical properties of spherical nanoparticles

Abstract

To study the scattering of electromagnetic radiation by a spherical metallic nanoparticle with quantum spatial dispersion, we develop the standard nonlocal Mie theory by allowing for the excitation of the quantum longitudinal plasmon modes. To describe the quantum nonlocal effects, we use the quantum longitudinal dielectric function of the system. As in the standard Mie theory, the electromagnetic fields are expanded in terms of spherical vector wavefunctions. Then, the usual Maxwell boundary conditions are imposed plus the appropriate additional boundary conditions. Examples of calculated extinction spectra are presented, and it is found that the frequencies of the subsidiary peaks, due to quantum bulk plasmon excitations exhibit strong dependence on the quantum spatial dispersion.

Plasmon modes of spherical nanoparticles: The effects of quantum nonlocality

“…2 [panels (al)-(a4)] for bulk modes, where we have presented the ω/ω p curves as a function of the η = aω p /α. For the other parameters appearing in the dispersion equation, the sodium values of ω p = 8.97 × 10 15 s −1 , and v F = 1.07 × 10 6 m/s have been employed [13,24]. The results for the SNL dispersion relation are shown by the dashed red curves.…”

“…The second term is regarded as the quantum statistical effect caused by the internal interactions in the electron species and the third term regarded as quantum diffraction effect comes from the quantum pressure. In particular, α ¼ ffiffiffiffiffiffiffiffi 3=5 p v F ; β = a B v B /2, with the Fermi speed v F = ℏ(3π 2 n 0 ) 1/3 /m e , the Bohr radius a B = ℏ 2 /e 2 m e , and the Bohr speed v B = e 2 /ℏ, respectively [22][23][24][25].…”

“…In order to carry out the calculations of the quantum effects on the surface and bulk plasmon modes of a spherical metal nanoparticle of radius a bounded by vacuum, we start with the linearized QHD theory of an electron gas [22][23][24]. The appropriate equations; where Φ(r, t), Ψ(r, t), and n(r, t) [with r = (r, θ, ϕ)] are perturbations in the electric potential, velocity potential, and electronic density, respectively, in the electron fluid.…”

“…In the present work, following our previous paper [23][24][25] and motivated by the recent works given in Refs. [19][20][21][22], we study the quantum nonlocal effects on the optical properties of spherical metal nanoparticles by means of the linearized QHD theory.…”

“…Fuchs and Claro [18], investigated the multipolar response of a small metallic sphere with use of a nonlocal dielectric function. However, it is well-known that the classical electronic pressure in the SHD model may not suffice for studying the nonlocal effects for electron excitations in nanometer sized structures [19][20][21][22][23][24][25]. Generally, the quantum effects should be considered in an electron fluid system when the de Broglie wavelength associated with the electrons is comparable to dimension of the system.…”