Ultracompact all-dielectric superdirective antennas:theory and experiment

A.E. Krasnok∗, P.A. Belov∗, D.S. Filonov∗, C.R. Simovski†, A.P. Slobozhanyuk∗,and Yu.S. Kivshar‡

∗National Research University of Information Technologies, Mechanics and Optics, 197101, St. Petersburg, RussiaEmail: krasnokfiz@mail.ru

†Aalto University, School of Electric and Electronic Engineering, Aalto FI76000, Finland‡Nonlinear Physics Centre, Research School of Physics and Engineering,

Australian National University, Canberra ACT 0200, Australia

Abstract—We demonstrate a simple way to achieve superdi-rectivity of electrically small antennas based on a sphericaldielectric particle with a notch. We predict this effect theoreticallyfor nanoantennas excited by a point-like emitter located in thenotch, and then confirm it experimentally at microwaves for aceramic sphere excited by a small wire dipole. We explain theeffect of superdirectivity by the resonant excitation of high-ordermultipole modes of electric and magnetic fields which are usuallynegligible for small perfect spherical particles.

Electrically small radiating systems whose directivity ex-ceeds significantly that of a dipole are usually called su-perdirective [1]. Superdirectivity is an important property ofradio-frequency antennas employed for space communicationsand radioastronomy, and it can be achieved in antenna arraysin a narrow frequency range and for a sophisticated systemof phase shifters [1]. Achieving high radiation directivity isalso important for actively studied optical nanoantennas [2],[3]. Usually, small plasmonic nanoantennas possess weakdirectivity close to that of a point dipole. Despite its im-portance, antenna’s superdirectivity in the optical frequencyrange was not discussed or demonstrated so far. Recently, itwas suggested to use different dielectric and semiconductormaterials for the development of antennas at the nanoscale [4],[5], [6]. Such all-dielectric nanoantennas consist of high-permittivity nanoparticles having both resonant electric andmagnetic optical responses [4], [5], [6]. This approach allowsto study an optical analogue of the so-called Huygens source,an elementary emitting system with properly balanced electric

(a) (b)

Fig. 1. (a) Geometry of the notched all-dielectric nanoantenna. (b) Maximumof directivity depending on the position of the dipole (λ = 455 nm) in thecase of a sphere with and without notch, respectively.

and magnetic dipoles oscillating with the same phase [1], [4],[5], [6]. As a result, nearly twice higher directivity than thatof a single electric dipole has been reported. However, thisdirectivity is still insufficient for nanophotonics applications.

Here we reveal a way for achieving superdirectivity ofantennas with a subwavelength (maximum size 0.4-0.5 λ)radiating system without using complex antenna arrays, and itis valid for a wide range of frequencies.

First, we demonstrate possibility to create a superdirectiveoptically small nanoantenna that does not require metama-terial. We consider one semiconductor nanoparticle with thepermittivity Reε = 15 − 16 radiated by light at wavelengthλ (for λ =440-460 nm this corresponds to a nanoparticlemade of crystalline silicon [7]) and the radius Rs = 90nm being almost five times smaller than λ. For a perfectsphere, lower-order multipoles for both electric and magneticfields are excited while the contribution of higher-order modesis negligible [4], [5], [6]. However, making a small notchin the spherical particle breaks the symmetry allowing theexcitation of higher-order multipole moments of the sphere.This is achieved by placing a nanoemitter (e.g. a quantumdot) within a small notch created on the sphere surface, asshown in Fig. 1a. The notch in our example has the shapeof a hemisphere with a radius Rn ≪ Rs. The emitter can bemodeled as a point-like dipole and it is shown in the figureby a red arrow. It turns out that such a small modification ofthe sphere would allow the efficient excitation of higher-orderspherical multipole modes.

To study the problem numerically, we employ the softwarepackage CST Microwave Studio. Figure 1b shows the depen-dence of the maximum directivity Dmav on the position of theemitting dipole in the case of a sphere Rs = 90 nm withouta notch, at the wavelength λ = 455 nm (blue curve withcrosses). This dependence has the maximum (Dmax = 7.1)when the emitter is placed inside the particle at the distance20 nm from its surface. The analysis shows that in this casethe electric field distribution inside a particle corresponds tothe noticeable excitation of higher-order multipole modes. Thisbecomes possible due to strong inhomogeneity of the externalfield produced by the nanoemitter. Furthermore, the excitationof higher-order multipoles can be significantly improved by

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making a small notch in the silicon spherical nanoparticle andplacing the emitter inside that notch, as shown in Fig. 1. Thismodification of the nanoparticle transforms it into a resonatorfor high-order multipole moments.

In our problem, the notch has the form of a hemisphere withthe center it the dielectric nanoparticle’s surface. The optimalradius of the notch is Rn = 40 nm, that we find by means ofnumerical optimization. Red curve with circles in the Fig. 1bshows maximum of directivity corresponding to this geometry.Maximal directivity at wavelength 455 nm is Dmax = 10.

Expansion of the field into multipoles offers an illustrativedescription of the internal field composition for the sphericalparticle. This is given by a series of spherical harmonics withthe coefficients aE(l,m) and aM (l,m), which characterize theelectrical and magnetic multipole moments [8].

Fig. 2. Absolute values of (a) electric and (b) magnetic multipole momentsthat provide the main contribution to the radiation of antenna at the wavelength455 nm. Particle and notch radii are equal to Rs = 90 nm and Rn = 40 nm,respectively.

In general, the multipole coefficients determine not onlythe mode structure of the internal field but also the angulardistribution of the radiation. Internal field was calculatednumerically with the expansion into the multipole series.The values of high-order multipole moments for this elec-tric field distribution are calculated, and they are shownin Figs. 2(a,b), where we observe strong high-order multi-poles excited together with the electric and magnetic dipolesaE(1, 1), aE(1, 0), aM (1, 1), and aM (1, 0). We notice that theabsolute values of all magnetic moments are larger than thoseof the electric moments in the corresponding multipole orders.

We have confirmed the generality of the predicted effectby studying the similar problem in the microwave range. Todo this, we scale up the nanoantenna discussed above to themicrowave frequencies. As a high-permittivity all-dielectricantenna in this frequency range, we employ MgO-TiO2 ce-ramic [5] characterized at microwaves by dielectric constantof 16 and dielectric loss factor of (1.12-1.17)10−4. We use theparticle with the radius of Rs = 5 mm and apply a small vi-brator [1] excited by a coaxial cable [see Figs. 3(a,b)]. The sizeof the hemispherical notch is approximately equal to Rn = 2mm. Styrofoam material with the dielectric permittivity closeto 1 is used to fix the antenna in the azimuthal-rotation unit, asshown in Figs. 3(a,b). First, we perform numerical simulationsof this antenna in CST Microwave Studio, and observe highdirectivity of this dielectric antenna at the frequency 16.8GHz. Next, we study experimentally the radiation pattern

Fig. 3. Photographs of (a) top view and (b) perspective view of a notchedall-dielectric microwave antenna. Experimental (c) and numerical (d) radiationpatterns of the antenna in both E- and H-planes at the frequency 16.8 GHz.

of the antenna in the anechoic chamber. The results of theexperimental measurements and numerical simulation of theradiation pattern in both E- and H-planes are summarized inFigs. 3(c),(d). Radiation patterns in both the planes are narrowbeams with a lobe angle about 35◦. Experimental coefficientsof the directivity in both E- and H-planes are equal to 5.9 and8.4, respectively. The numerical values of these quantities areequal to 6.8 and 8.1. Our experimental data is in a very goodagreement with the numerical results. The small differencebetween the experimental and numerical results in the E plane,can be explained by the asymmetry of the dipole.

Note, that the observed directivity is the same as one of all-dielectric Yagi-Uda antenna with size about 2 wavelength [5].However, the total size of our antenna with notch is ∼ λ/2.5.Thus, our experiment is clearly demonstrating superdirectivityperformance.

ACKNOWLEDGEMENT

This work was supported by the Ministry of Educationand Science of the Russian Federation, Dynasty Foundation(Russia), and the Australian Research Council.

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