Optical magnetic field enhancement at nanoscale:a nanoantenna comparative studyMAHSA DARVISHZADEH-VARCHEIE, MOHAMMAD KAMANDI, MOHAMMAD ALBOOYEH, AND FILIPPO CAPOLINO*Department of Electrical Engineering and Computer Science, University of California, Irvine, California 92697, USA*Corresponding author: f.capolino@uci.edu

Received 26 July 2019; accepted 22 August 2019; posted 5 September 2019 (Doc. ID 373411); published 8 October 2019

We show and compare various metallic and dielectric nano-structures for local magnetic field enhancement at opticalfrequency. We elaborate on the origin of the magnetic fieldenhancement in each structure and define figures of meritto compare the ability of the structures to enhance the mag-netic field. We show that dielectric structures can be a goodalternative to their plasmonic counterpart due to their lowloss. The magnetic field enhancement of these structurescan be utilized in studying magnetic dipole transitions,magnetic imaging, chirality, and enhanced spectroscopyapplications. © 2019 Optical Society of America

https://doi.org/10.1364/OL.44.004957

Various rare-Earth ions such as Er3�, Ho3�, Nd3�, and Eu3�have magnetic dipole transition at near-infrared, especiallyaround 800 nm [1]. These lanthanide are famous not only be-cause some of their electronic transitions are forbidden by elec-tric dipole selection rules [2–5] but also because of theirapplications in optical technology like lasers, LEDs, and fiber-based telecommunications [5,6–8]. Promoting magnetic dipoletransitions of these trivalent lanthanides to investigate their pos-sible applications in optical process, by placing them close to anengineered nanostructure to enhance the magnetic field, is thescope of many recent researches [4,5,9–12].

During the last decade, various nanostructures for electricfield enhancement using metamaterials have been realized[13–15]; however, a few structures have been proposed to en-hance the magnetic counterpart. Conventionally, ferromagneticmaterials are exploited to enhance local magnetic fields, but atmuch lower frequencies. Indeed, in the optical regime magneticproperties of materials are rather weak, and we must resort toother means to enhance the magnetic near-field. The overallmagnetism of a metamaterial can be engineered by tailoringthe artificial magnetic resonance in “meta-atoms.” Thesemeta-atoms are responsible to create magnetic dipoles forwhich the ratio of the magnetic-to-electric near-field is en-hanced compared to that pertinent to plane waves. Differentstructures such as a metallic split ring or U-shaped resonatorsand nanostructured dielectric surfaces have been used to createmagnetic dipoles to exclusively enhance the magneticfield [16–19].

The ability of circular nanostructures to develop magneticmoments offers the possibility to locally enhance the magneticnear-fields [20–24]. This was shown, for example, in [23], forwhich clusters of nanospheres are used to create a magneticdipole moment, which in turn enhances the magnetic field lo-cally. These types of structures are made of plasmonic particles.However, plasmonic structures are known to be affected byunavoidable losses in metals in optical frequencies. This inher-ent problem of metals can be avoided by using subwavelengthdielectric particles with high permittivity, which are providing anew paradigm to constitute building blocks of novel nanostruc-tures for magnetic field enhancement [25–30]. Unlikeplasmonic antennas where oscillations of the free-electronplasma and collective lattice vibrations dictate the local re-sponse of the light–matter interaction, dielectric antennas relyon the fields and displacement currents induced in the antennastructure.

In this Letter, we discuss the choice of material, structure,shapes, and arrangements that can create a highly enhancedmagnetic field in the optical regime. Specifically, we study dif-ferent metallic and dielectric structures to enhance the localmagnetic field and compare their performance under similarcondition. Moreover, we employ a structured beam as an ex-citation to achieve maximum magnetic-to-electric field en-hancement. Specifically, we turn our attention to vectorbeams with cylindrical symmetry, or so-called vortex beams,which are experimentally functional in the selective excitationof Mie resonances in dense dielectric particles [30,31]. A par-ticular cylindrically symmetric vector beam category useful forselective excitation of the magnetic dipolar moment is theazimuthally electric-polarized vector beam (APB), which hostsa strong longitudinal magnetic field along the beam axis whereelectric field vanishes [32,33], and it has been used to excitemagnetic dipoles [21,34,35].

In order to compare the capabilities of various magneticnanoantennas in enhancing quantum magnetic transitions inmatter that are overshadowed by electrical ones, we use thetwo figures of merits defined in [21,23]: the magnetic field en-hancement FH � jHt�r�j∕jHi�r�j and the magnetic-to-electricfield ratio, i.e., the normalized local field admittanceFY � ηjHt�r�j∕jEt�r�j, in which jHt�r�j and jEt�r�j are themagnitude of total magnetic and electric fields at location r,and jHi�r�j is the magnitude of incident magnetic field at

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0146-9592/19/204957-04 Journal © 2019 Optical Society of America

the same location, respectively. The magnetic field enhance-ment (FH ) represents the ability of a magnetic nanoantennato enhance the magnetic field with respect to the incidentone. The normalized magnetic-to-electric field ratio, i.e., thenormalized local field admittance (FY ), shows the ability ofa magnetic nanoantenna to enhance the magnetic field whilesuppressing the electric field, normalized to the field impedanceη �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiμ0∕�ε0εh�

pof a plane wave in the same host medium.

Large local field admittance in a region shows the magnetic na-naoantenna succeeds in generating a magnetic dominant re-gion, and FY > 1 means that the magnetic-to-electric fieldratio is larger than that of a plane wave.

The structures we study include a cluster of gold nano-spheres, a cluster of gold nanopillars, gold triabolo, and a siliconshell, all placed over a glass substrate with permittivity 2.25,while being excited by APB with the half-beam waist [36]as w0 � 0.7λ at the corresponding excitation frequency. Wedesign the parameters for each structure such that all of themhave magnetic resonance in the near-infrared region aroundλ � 800 nm to be suitable for investigating magnetic dipoletransition of trivalent lanthanides.

The first structure that we investigate is a cluster of six goldnanospheres (hexamer) as shown in Fig. 1(a). The diameter ofeach nanosphere is 120 nm, and the gap between the twoadjacent ones in the cluster is 10 nm. The gold nanosphereis described with its relative permittivity εm given by theDrude model [37]. When excited by an APB, due to cylindricalpolarization of the electric field, each sphere forms an azimu-thally directed electric dipole, and the collection of dipolesmakes a circular electric current in the azimuthal direction,which is equivalent to a magnetic dipole along the z direction(normal to the cluster plane) [21,23]. In the near-field of a

magnetic dipole, the magnetic field is much stronger thanthe electric field, and this used in a variety of recent researchdirections. In Fig. 1(b), we have illustrated the magnetic fieldenhancement at the center of the cluster varying the excitationwavelength. Full-wave simulations are performed by thefrequency-domain finite-element method implemented inCOMSOL Multiphysics. As one can infer, this magnetic nano-antenna is able to enhance the magnetic field more than 3.5-fold at 780 nm. Figures 1(c) and 1(d) demonstrate the profile ofFH and FY , in the x − y plane passing through the middle ofcluster, at the magnetic resonance wavelength of the cluster,respectively (780 nm). The strongest normalized field admit-tance FY occurs on the center of the cluster, thanks to the van-ishing electric field component of the APB and the rotationalsymmetry of the nanocluster. As it is shown in [23], if we in-crease the number of nanospheres in the cluster, the area withthe strong magnetic field becomes wider; however, it results inthe reduction of the magnetic field enhancement at the clustercenter.

The next structure is a cluster of six gold nanopillars, asshown in Fig. 2(a). For each circular pillar, the diameter andheight are 95 nm and 90 nm, respectively, and the gap betweentwo adjacent pillars is 15 nm, so the cluster resonates at780 nm. Under APB excitation, the pillars form an azimuthalelectric current, which is equivalent to a magnetic dipole placedat the center of the cluster. The magnetic field enhancement atthe cluster center versus excitation wavelength and the profileof FH and FY at the resonance wavelength in the x − y planepassing through the middle of cluster are shown in Figs. 2(b),2(c), and 2(d), respectively. By comparing this structure withthe cluster of nanospheres, one can observe that they resonate atthe same wavelength, the gap spacing is larger in the cluster of

Fig. 1. (a) Cluster of gold nanospheres on top of a glass substrate,excited with an APB illuminated from the glass side. (b) Magnetic fieldenhancement at the center of cluster versus excitation wavelength.(c) Magnetic field enhancement (FH ) profile and (d) local normalizedfield admittance FY , both at the resonance wavelength at the x − yplane crossing the middle of cluster. In (d), FY is shown in the log-arithmic scale, and the color legend is saturated for the values higherthan 2. In (c) and (d), white circles show the nanosphere cross sectionat the observation plane.

Fig. 2. (a) Cluster of gold nanopillars on top of a glass substrate,excited with an APB illuminated from the glass side. (b) Magnetic fieldenhancement at the center of cluster versus excitation wavelength.(c) Magnetic field enhancement (FH ) profile and (d) local field admit-tance FY at the resonance wavelength at the x − y plane crossing themiddle of cluster. In (d), FY is shown in logarithmic scale, and thecolor legend is saturated for the values higher than 2. In (c) and(d), white circles show the nanopillar cross section with the observa-tion plane.

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nanopillars, and the magnetic field enhancement is slightlyhigher. Moreover, in terms of design of clusters, pillars haveone more degree of freedom than spheres to tune the resonancewavelength. However, their fabrication is challenging and lim-ited to the resolution of electron beam lithography or focusedion beam methods.

The last plasmonic structure that we investigate here is a goldtriabolo. The ability of a plasmonic diabolo structure to en-hance the magnetic field at visible and infrared wavelengthshas been explored recently [10,17,19,38,39]. Here, by modi-fying the diabolo structure, we add some circular symmetry toit. As a result, when excited with an APB, the symmetry ofstructure helps to generate additional circular electric currentand therefore provides stronger longitudinal magnetic dipole.A triabolo consists of three planar metal triangles attached to-gether through their facing tips. The side of each equilateraltriangle [shown with s in Fig. 3(a)] is 150 nm, and the sideof joint face (small equilateral triangle in the middle, shownwith g) is 50 nm, whereas the thickness of this structure is100 nm. This structure is placed over a glass substrate andis illuminated with an APB from the bottom, as shown inFig. 3(a). The magnetic field enhancement versus wavelengthevaluated 5 nm above the center of triabolo and the profile ofFH and FY in the x − y plane 5 nm above the triabolo structureat 810 nm are given in Figs. 3(b), 3(c), and 3(d), respectively.As one can predict, the magnetic field is enhanced between themain triangles and around the joint of triangles since the elec-tric current is strong on the joint. However, the field admit-tance is maximum at the center of the structure mainlybecause of the APB characteristics. Although this structure issuccessful in providing magnetic field enhancement in thenear-infrared region, its enhancement is weaker compared toother proposed structures in this Letter. This kind structurecan be easily used also at lower frequencies.

Before turning our attention to the last magnetic nanoan-tenna, it is worth mentioning that, as is well-known, all of theaforementioned metallic nanostructures provide giant electricfield in the gaps between adjacent nanoparticles. Based onBabinet’s principle (with some approximation, since thisstructure has finite thickness), complementary structures tothe investigated ones should provide a strong magnetic fieldin the gap between adjacent nanoparticles.

Next, we show that high-index dielectric nanoantennas are agreat alternative to their plasmonic counterpart as a way to en-hance the magnetic response at optical regime. Indeed, when ahigh-refractive-index dielectric is excited at its resonance, astrong electric displacement current is generated inside it.This displacement current can be used to form a magneticdipole for magnetic field enhancement [30,40–43]. In [30],we previously analytically and experimentally investigatedthe ability of a silicon disk illuminated by an APB to enhancethe magnetic field at optical frequencies. However, in order tomake a strong magnetic field “inside” the disk accessible formagnetic dipole emitters, it may be useful to make a hollownanodisk [5,22,44]. The geometry of a silicon hollow disk isshown in Fig. 4. The outer and inner diameters of the hollowdisk are 250 and 100 nm, respectively, whereas the height is175 nm, and it is placed over a glass substrate. Under APBillumination, the circulating displacement current, which isformed in the hollow disk azimuthally, makes a magnetic dipolealong the axis of the disk, which enhances the magnetic re-sponse in the near-field. In Fig. 4(b), we demonstrate the mag-netic field enhancement versus wavelength at the center of thehollow disk. As one can observe, the maximum magnetic fieldenhancement is 5.3, which is higher than all the plasmonicstructures that we have studied at this wavelength range.This is probably related to the larger volume hosting field

Fig. 3. (a) Gold triabolo on top of a glass substrate, excited with anAPB illuminated from the glass side. (b) Magnetic field enhancementversus excitation wavelength at 5 nm above the center of triabolo.(c) Magnetic field enhancement (FH ) profile and (d) local field admit-tance FY at the resonance wavelength at the x − y plane 5 nm abovethe triabolo structure. In (d), FY is shown in the logarithmic scale, andthe color legend is saturated for the values higher than 1.5.

Fig. 4. (a) Silicon hollow disk on a glass substrate excited with anAPB illuminated from the glass side. (b) Magnetic field enhancementversus excitation wavelength at the center of hollow disk. (c) Magneticfield enhancement (FH ) profile and (d) normalized field admittance(FY ) profile in the x − y plane passing through the center of hollowdisk at the resonance wavelength of disk (810 nm). In (d), FY is shownin logarithmic scale, and the color legend is saturated for the valueshigher than 2. In (c) and (d), the white area indicates the hollow disk.

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displacement currents and not necessarily to lower losses in thesilicon structure compared to its plasmonic counterparts, sincethe linewidth is comparable to the previous examples.Moreover, we have shown the profile of FH and FY in thex − y plane crossing the center of the hollow disk inFigs. 4(b) and 4(c). As expected, the admittance is maximumon the axis of the hollow disk for symmetry reasons, of both thenanoantenna and the illumination.

In conclusion, we have demonstrated the ability of variousplasmonic and dielectric nanoengineered structures to enhancethe magnetic field under a vortex beam illumination in thenear-infrared region. Because of rotational symmetry, the mag-netic field at the center area of these nanoantennas is 10–100times stronger than the electric field there, which illustrates theefficacy of these nanoantennas to enhance the magnetic fieldwhen illuminated with the APB. In all cases, we have utilizedthe azimuthally polarized beam as excitation because its rota-tional symmetry facilitates the excitement of azimuthal electriccurrent in rotationally symmetric antennas that leads to a dom-inant magnetic field region at the center of the nanoantennas.These antennas act as magnetic nanoprobes and are useful todetect magnetic dipole transitions in molecules and in lantha-nides, and to enhance the magnetic part of light in chiralitydetection.

Funding. W. M. Keck Foundation.

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