Enhanced Forward Scattering of Ellipsoidal Dielectric Nanoparticles
© The Author(s). 2017
Received: 12 November 2016
Accepted: 14 December 2016
Published: 19 January 2017
Dielectric nanoparticles can demonstrate a strong forward scattering at visible and near-infrared wavelengths due to the interaction of optically induced electric and magnetic dipolar resonances. For a spherical nanoparticle, the first Kerker’s condition within dipole approximation can be realized, where backward scattering can reach zero. However, for this type of dielectric sphere, maximum forward scattering without backward scattering cannot be realized by modulating the refractive index and particle size of this nanoparticle. In this paper, we have demonstrated that a larger directional forward scattering than the traditional spherical nanoparticle can be obtained by using the ellipsoidal nanoparticle, due to the overlapping electric and magnetic dipolar modes. For the oblate ellipsoid with a determined refractive index, there is an optimum shape for generating the suppressed backward scattering along with the enhanced forward scattering at the resonant wavelength, where the electric and magnetic dipolar modes overlap with each other. For the prolate ellipsoid, there also exist the overlapping electric and magnetic dipolar modes at the resonant wavelength of total scattering, which have much higher forward scattering than those for both oblate ellipsoid and sphere, due to the existence of the higher multipolar modes. Furthermore, we have also demonstrated the realization of the dimensional tailoring in order to make the strong forward scattering shift to the desired wavelength.
Electromagnetic waves scattered by nanoparticles has gained great attention because of its immense applications, including optical communications [1, 2], optical manipulations [3, 4], material science [5, 6], and so on. In general, scattering ordinarily relies on shape, size, and composition of nanoparticles. Due to its remarkable electric and magnetic resonances at optical frequencies, the scattering of dielectric nanoparticles has attracted lots of renewed interest in the last few years. The interactions between the electric and magnetic modes allow to fulfill certain conditions, which can generate directional scattering [7–14]. Such certain condition was called Kerker’s condition which was first proposed with small magnetodielectric spheres in 1983 , including the first Kerker’s condition for zero backward scattering (BS) and the second Kerker’s condition for minimum forward scattering (FS). In the middle of these two particular scattering properties, suppressed backward scattering and enhanced directional forward scattering are typically of more practical application, such as in optical antennas [15–17], plasmon-enhanced photovoltaics [18, 19], and other devices based on optically induced “negative forces” .
The proposed interactions between the electric and magnetic modes caused by dielectric nanoparticles could manipulate angular distributions of the scattering more flexibly than the pure electric-response-based method, which is usually driven by complex structures [21, 22]. Nevertheless, the zero backward scattering condition for spherical dielectric particles can only be fulfilled in the longer wavelength region than the magnetic dipole resonant wavelength. Moreover, such spherical nanoparticles are governed by only one geometrical parameter and thus do not allow for the spectral-shift of the resonant-position for the electric and magnetic dipoles. Recently, it was shown that in silicon nanodisks with the aspect ratio about 1:2, electric and magnetic dipolar resonances can be overlapped to utilize the spectral-shift of the resonant-position , providing a strong FS and near zero BS at the scattering resonance wavelength.
In this paper, we give a general discussion on the light scattering by the spherical and ellipsoidal dielectric nanoparticles. Firstly, with the method of Mie theory, it is shown that the scattered field for a plane wave illuminating the dielectric sphere can be decomposed into a series of electric and magnetic multipolar modes in free space. From the Mie decompositions of the scattered field, we can obtain the condition of the zero backward scattering. However, maximum forward scattering without backward scattering occurs away from the resonant wavelength of total scattering. Then, we present numerical parametric researches for the oblate ellipsoid and prolate ellipsoid by using finite element method and multipole decomposition based on electromagnetic multipole theory, which particularly demonstrate the possibility of suppressed backward scattering and enhanced directional forward scattering. For oblate ellipsoid, we can find an optimum aspect ratio usually, with near zero backward scattering and enhanced forward scattering at the resonant wavelength of total scattering, due to the overlapping of the electric and magnetic dipole resonances. For prolate ellipsoid, we can also find the overlapping of the electric and magnetic dipole resonances similar to that of oblate ellipsoid, where the forward scattering can be enhanced more strongly while the backward scattering is not zero due to the existence of the higher-order multipolar modes. Finally, we also provide an easy way to tune the strong forward scattering to the desired wavelength.
Results and discussions
To achieve a relatively strong forward scattering, one of the possibilities is to use metallic-dielectric core-shell nanoparticles [14, 26–28]. In the following, we will demonstrate that it can also be realized by changing the particle’s shape, e.g., using oblate ellipsoid or prolate ellipsoid instead of the sphere. As exhibited in Ref. , by using a nanodisk instead of sphere with an aspect ratio near 1:2, they could make the electric and magnetic dipole resonances overlap and make the minimized backward scattering approach to the wavelength of scattering resonance. As an effective way to reach a strong forward scattering, we will talk about it for both oblate ellipsoid and prolate ellipsoid.
In this paper, the scattering characteristics of the spherical and ellipsoidal dielectric nanoparticles have been investigated, in order to obtain enhanced total and forward scattering together with suppressed backward scattering. Ellipsoidal nanoparticles with different aspect ratios provide an effective method for obtaining the overlapped electric and magnetic dipole resonances. For both oblate ellipsoid and prolate ellipsoid, we could obtain strong asymmetric scattering of suppressed backward scattering and enhanced forward scattering at the resonance wavelength of total scattering, with the given value of refractive index n = 2.5. Moreover, we could obtain larger total and forward scattering in the situation of prolate ellipsoid than those for both oblate ellipsoid and sphere, at which the electric and magnetic dipolar modes are overlapped at the resonance wavelength of total scattering. Finally, we have performed the size parameter study of light scattering for ellipsoidal structures, which can move the suppressed backward scattering and enhanced forward scattering to the desired wavelength. Overall, we provide a flexible mean to gain enhanced total and forward scattering together with suppressed backward scattering. The above mentioned properties make the ellipsoidal dielectric nanoparticles have great potential applications in manipulating light at nanoscale, such as solar cell application, efficient directional optical nanoantennas, sensing, and so on.
The authors gratefully acknowledge the financial supports for this work from the National Natural Science Foundation of China under Grant No. 61575060, 61501159, and 11505043, State Key Laboratory of Millimeter Waves (K201711), and the Fundamental Research Funds for the Central Universities (2015HGCH0010).
ZHW and NA carried out the simulation works and drafted the manuscript. FS, HPZ, YXS, ZNJ, YHH, and YL were involved in the discussions and the evaluations of the simulated results. ZYG supervised the simulation works and revision of the article. All authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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