Toroidal metamaterials: Transition from 3D concept to 2D flatland

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Toroidal metamaterials: Transition from 3D concept to 2D flatland Manoj Gupta , Ranjan Singh PII: DOI: Reference:

S2405-4283(20)30003-4 https://doi.org/10.1016/j.revip.2020.100040 REVIP 100040

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Please cite this article as: Manoj Gupta , Ranjan Singh , Toroidal metamaterials: Transition from 3D concept to 2D flatland, Reviews in Physics (2020), doi: https://doi.org/10.1016/j.revip.2020.100040

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Toroidal metamaterials: Transition from 3D concept to 2D flatland

Manoj Gupta1,2, and Ranjan Singh1,2, * 1

Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore 2 Center for Disruptive Photonic Technologies, The Photonics Institute, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore *E-mail: [email protected] Abstract Radiative loss engineering in metamaterials is one of the most fundamental requirements to gauge the suitability of a metaphotonic device for a specific on-demand application. Conventional electric and magnetic electromagnetic (EM) excitations only partially fulfill this requirement as we scale from lower to higher frequency of the electromagnetic spectrum. Toroidal dipole, which is described as poloidal currents flowing on the surface of torus, belongs to a new class of electromagnetic excitation different from electric and magnetic dipoles. Toroidal dipole has opened a new route to control radiative losses via near field coupling mechanism or radiation cancellation approach in the unit cell of metasurface. Here, we discuss strategies that have been devised to excite toroidal dipolar modes in a planar metasurface. We further discuss the destructive interference between electric and toroidal dipoles to realize nonradiating modes in form of anapole excitation that fulfills the requirement for the excitation of extremely large quality factor resonances. 2D planar toroidal metasurfaces are conceptual simplification of 3D toroid configurations, which pose fabrication challenges at micronanoscales. Overall, the intriguing features of a toroidal dipole could have significant implications on the design of resonant metamaterials that are important for the development of low-loss sensors, modulators, filters, and efficient cavities for strong light matter interactions.

1. Introduction Electromagnetic excitation is one of the most important phenomena to study the basic characteristics of the material medium.[1-6] Particularly, such characterizations help to bifurcate 1

among the properties of material in terms of permittivity,[7, 8] permeability,[9] conductivity,[10, 11] nonlinearity[12, 13] that significantly affects the process or device dependent efficiency of material medium.[14,

15]

Considering the spatial extent of medium to be very small compared to

wavelength of light, the electromagnetic excitations could be further characterized in terms of elementary charge and current distribution.[16] Elementary charge and current distributions corresponds to distinct family of electric, magnetic and toroidal multipoles. Toroidal multipoles are missing from the standard multipole expansion, which primarily contains terms of electric and magnetic multipoles.[17, 18] First breakthrough study about toroidal excitation was made by Y. Zel’dovich in year 1957, when he theoretically studied the behavior of Dirac particles under weak interaction and termed these elementary particles as ‘anapole’.[19] Later, in 1970’s, Dubovik et al. extended the explanation of ‘anapole’, in the field of classical electrodynamics by establishing the term ‘polar toroidal moments’.[20] Figure 1 shows the fundamental difference among electric, magnetic and toroidal dipoles depicted in terms of charge and current distribution. Two separated opposite charges of equal magnitude constitute electric dipole, whose dipole moment is given by 𝑝⃗ (figure 1a), while closed loop circulating current density 𝑗⃗ constitutes a magnetic dipole with moment 𝑚 ⃗⃗⃗ (Figure 1b). Figure 1c shows closed loop circulating current density on the surface of torus (poloidal currents), known as polar toroidal dipole with moment 𝑡⃗. Similarly, closed loop head to tail arrangement of electric dipoles forms axial toroidal dipole moment (𝑔⃗ in figure 1d).[21, 22] The static nature of toroidal dipole moments and their interaction with optical waves have been previously explored in various materials.[4, 23] This article mainly discusses about dynamic polar (magnetic) toroidal excitation in metasurfaces and their role in radiative loss engineering, as they could be easily realized through electric charge current distribution. The moment of magnetic toroidal dipole is given by following formula: [24, 25]

𝑻=

1 10𝑐

∫[(𝒓. 𝑱)𝑟 − 2𝒓2 𝑱]𝑑3 𝒓

where ‘r’ is coordinate vector with its origin placed at the center of torus, ‘c’ is the speed of light and ‘J’ is the current density on the surface of torus (Figure 1c). The spatial feature of toroidal dipole straightforwardly relates to 3D metasurface composed of circular arrangements of subwavelength structures. As we approach towards higher frequencies, realization of 3D metasurface becomes cost-inefficient. Further, the practice of micro-nano 2

fabrication is not scale variant and is vastly more difficult than fabrication of millimeter scale subwavelength structures.[26] Therefore, there is a need to develop 2D platform with highly optimized subwavelength structures supporting toroidal excitation. This review article mainly focuses on the practically favorable approaches of radiative loss engineering through realization of toroidal dipole excitation as we move from 3D to 2D metamaterial platform. Additionally, this article discusses about extremely high-quality factor resonances through the excitation of anapole modes in 2D metasurface.[27-29]

Figure 1: Elementary charge-current distribution of a) electric, b) magnetic, c) polar toroidal, and d) axial toroidal moments. Adapted with permission from ref. [21], Springer Spektrum, Wiesbaden.

2. Toroidal modes for loss engineering Electric field localization using array of subwavelength structures (metamaterials) have enormously contributed in the field of photonics that has led to the implementation of electromagnetic devices in the areas of sensing,[30,

31]

energy confinement,[32,

33]

lasing,[34]

biosensing,[35-37] imaging,[38] and optical modulation.[39, 40] The loss channels in these devices are mainly from conductivity dependent non-radiative losses and structure/excitation dependent radiative losses.[41, 42] Methods to deal with radiative losses is of great interest as they are crucial for device efficiency. Structures with characteristic length R compared to free space wavelength

3

𝑅 3

λ, the electromagnetic scattering due to toroidal, magnetic and electric dipole scales as ~ (𝜆 ) , 𝑅 2

𝑅 1

~ ( 𝜆 ) and ~( 𝜆 ) , respectively.[43-45] The scattering dependency on length scales provides an alternate approach to tailor radiative losses through the excitation of charge and current distribution that supports toroidal modes in metamaterials composed of subwavelength (R<< λ) resonators. For long time toroidal modes have been overlooked because their radiation pattern is identical to that of an electric dipole.[24] Mathematical approach of multipole decomposition provides a solution in this regard to numerically analyze the contribution due to toroidal and other multipoles.[44,

45]

Toroidal modes are always accompanied by electric and magnetic

multipoles, so geometry of subwavelength structures needs to be optimized to experimentally observe the electromagnetic response dominated by toroidal multipole contribution.[46,

47]

Consideration of dynamic toroidal modes as an independent family member of multipole, like electric and magnetic multipoles, is still a matter of debate.[48] 3. 3D metasurface for toroidal excitation In 2010, first localized excitation of toroidal dipole has been experimentally demonstrated at microwave frequency, where a set of four rectangular bended metallic wires strips were arranged along mutually orthogonal planes to compose the 3D unit cell of metamaterial (as shown in Figure 2a).[49] The dimensional features (a, h, r, w, g) of subwavelength wire loops were in millimetre scale, which eased the fabrication of 3D metasurface. In this work, the front and rear pair of wire loops interact with in-phase and out-of-phase of magnetic component of incident electromagnetic wave to generate different alignment of magnetic dipoles (m), resulting in magnetic resonance (My in Figure 2b) and toroidal dipole resonance (Tz in Figure 2c), respectively. Transmission and reflection spectra (Figure 2d, 2e) showed magnetic (I) and toroidal (II) resonance resulting from in-phase and out-of-phase interaction, respectively. Multipole computation (Figure 2f) further revealed that at the IInd resonance scattering contribution is dominated by toroidal dipole (Tz), while magnetic dipole (My) response dominated at Ist resonance. High quality factor of toroidal resonance compared to magnetic resonance indicated weak coupling to free space, which establishes the fact of lower radiative loss due to toroidal excitation.

4

Figure 2: a) Schematic of 3D spatial orientation of four wire loops inside unit cell with respect to incoming EM waves. Induced magnetic moments (m) of wire loops during in phase (b) and out of phase interaction (c). Transmission (d), reflection (e) spectra of the metamaterial sample, where simulated and experimental results are depicted by black and red curves, respectively. f) Scattered power from five different multipoles (electric (Pz), magnetic (My) and toroidal (Tz) dipoles, electric and magnetic quadrupole). Adapted with permission from ref. [49], The American Association for the Advancement of Science.

Initial investigations on toroidal dipole quickly captured attention that lead to many works demonstrating many exotic electromagnetic phenomena’s, such as phase shifter,[50] electromagnetic transparency, [51,

52]

perfect absorber,[53,

54]

sensing,[55-57] and polarization

twister,[58] assisted by toroidal excitations in metamaterials. Figure 3 represents the work on 3D toroidal metasurface, which emphasized that more closely the unit cell design approaches to torus topology (4-fold and 8-fold symmetry in Figure 3a, 3b), the strength of toroidal dipole (T) enhances as one move for 4-fold (Figure 3c) to 8-fold (Figure 3d) toroidal topology.[59] In addition to field confinement, artificial chiral media could be designed for polarization sensitive response dominated by toroidal dipole.[60-62]

Figure 3: a, b) Schematic of unit cell of 3D metamaterial having close resemblance to torus topology with 4-fold and 8-fold symmetry. c, d) Numerically computed scattered power for different multipoles (electric

5

(P), magnetic (M), toroidal (T) dipole and electric quadrupole (Qe)) in 3D metamaterial with 4-fold (c) and 8-fold (d) symmetry. Adapted with permission from ref. [59], Springer Nature.

Moving ahead to higher frequency band of electromagnetic spectrum, 3D metasurface with toroidal excitation has been demonstrated at mid-infrared frequencies, which is an extension to the first work reported at microwave frequency.[63] In this work, U-shaped metallic patterns were fabricated on silicon nitride (SiNx) films and then folded to give 3D unit cell configuration as depicted in Figure 4. The dimensional features for this design (l, w, t) are on micron and submicron scales which involves multistep fabrication process. Photoresist patterning by electron beam lithography (EBL) and focused ion beam (FIB) cutting through the SiNx films are the crucial steps involved,[64, 65] which adds challenges in fabrication of 3D metasurface. Fabrication process involving EBL and FIB are very slow, complex and expensive compared to optical lithography.[66]

Figure 4: Schematic of fabrication steps involved in realization of 3D metasurface at mid-infrared frequency. Adapted with permission from ref. [63], John Wiley and Sons.

Owing to complexity involved in fabrication of 3D large area devices, these is a need to develop planar metamaterial platform for toroidal excitation, which bring ease in terms of simple fabrication and scalability. The localized toroidal excitation in planar metasurface confines electromagnetic energy by reducing the scattering loss to free space, which is of prime concern in designing low loss metasurface. Next section emphasizes on approach in harnessing the lowloss feature of toroidal dipole for enhancing the efficiency of well-established 2D metamaterial platform.[67, 68] 6

4. Planar metallic metasurface for toroidal excitation Besides 3D spatial orientation, in-plane spatial arrangement of U-shaped resonator in square unit cell displayed different transmittance characteristics, when excited separately with diagonal incident electric field polarization (top part of Figure 5a).[69] These directions dependent orientation of resonant magnetic modes of resonators in unit cell (at frequencies represented by dotted line in transmittance spectra) resemble to ferromagnetic (parallel) and antiferromagnetic (antiparallel) order of magnetic dipoles (bottom part of Figure 5a). Such different orders of magnetic dipoles have been probed to study the mode retardation effects in planar metasurface array.[70] Even hybrid metasurface composed of metallic and dielectric resonators (as shown in Figure 5b) have been demonstrated to give antiferromagnetic ordering of magnetic dipoles. [71, 72] The antiferromagnetic (antiparallel) ordering of magnetic dipoles involves scattering contribution from toroidal dipole due to anti parallel arrangement of magnetic dipoles between neighboring resonator. However, the resultant toroidal contribution from the unit cell is zero for antiferromagnetic order of magnetic dipoles in Figure 5a, because the toroidal dipole moment arising from the left half (top half) and the right half (bottom half) cancels each other. Therefore, specific arrangement of magnetic dipoles in planar is important for introducing nonzero toroidal contributions in planar metasurface. Following subsections discusses the adopted schemes to realize toroidal excitation in planar metasurface, which are well suited at higher electromagnetic frequencies.

Figure 5: a) Microscopic image (top left) and transmittance (top right) through sample for diagonal incident electric field polarization w.r.t unit cell enclosed by dotted line, whereas bottom images represents the ordering of magnetic dipoles in unit cell at frequencies represented by dotted line in transmittance spectra. b) Schematic of metasurface (top) consisting of dielectric spheres and metallic split ring resonators in XZ plane, whereas bottom image represents normalized magnetization (along Z direction) of hybrid structure at electromagnetic resonance. (a) Adapted with permission from ref. [69],

7

Optical Society of America. (b) Adapted with permission from ref. [71], Copyright 2012, American Chemical Society.

4.1 Magnetic dipole induced toroidal modes Radiative loss engineering at higher frequencies are usually accomplished through array of asymmetric double gap split ring resonators (SRRs) instead of U-shaped resonator. Resonant excitation of these asymmetric structures gives rise to narrow line width asymmetric and broad line shaped symmetric resonance features.[73, 74] The narrow line width asymmetric resonance has Fano line shape form and arises because of the interference phenomenon between “bright mode” electric dipole, and the “dark mode” magnetic dipole.[75,

76]

At asymmetric resonance current

density in asymmetric SRR is circulating in nature, which gives rise to strong magnetic dipole excitation. Figure 6a shows the first adopted passive scheme with microscopic image of 2D metasurface, where square shaped asymmetric SRRs were alternatively flipped along one direction to introduce toroidal dipole excitation (Configuration II), as compared to non-flipped configuration (Configuration I).[77] Figure 6b shows the schematic view of neighboring resonators excitation in both configurations, where at asymmetric resonance spatial orientation of induced magnetic dipole in neighboring SRR resonator is depicted. It could be seen that mirroring results in anti-aligned set of magnetic dipoles confines dynamic magnetic field in circular region between mirrored SRRs, which introduces toroidal dipole excitation. Figure 6c shows experimentally measured transmittance spectra for both metasurface sample where significant line narrowing has been observed in mirrored configuration of asymmetric SRRs. The asymmetric resonance in mirrored SRR configuration has again Fano line shape form, but now it is arising as a result of interference between the electric dipole (bright mode) and the toroidal dipole (dark mode).[78] The same has been verified my multipole computation where enhancement in the strength toroidal dipole has been clearly observed for mirrored configuration in Figure 6d.

8

Figure 6: a) Microscopic image of asymmetric resonators sample arranged in “I” and “II” configuration, where one configuration could be changed to another by flipping nearby resonator. b) Schematic image representing spatial orientation of induced magnetic dipoles at asymmetric resonance of SRRs in ‘I’ and ‘II’ arrangements. c) Measured transmitted intensity spectra of samples with ‘I’ and ‘II’ configurations. d) Strength of toroidal dipole excitation in both configurations computed via multipole analysis. Adapted with permission from ref. [77], John Wiley and Sons.

4.2 Electric dipole induced toroidal modes In metallic metasurface, electric dipole featuring current distribution of resonators in proximity could introduce toroidal scattering contributions. In one such demonstration, two layers of Ushaped metallic resonator patterned on both sides of flexible substrate, as shown by schematic and sample image in Figure 7a, 7b, to obtain dual toroidal dipole resonances metamaterial.[79] Obtained transmission spectra for this metasurface, with different gap ‘g’ between resonators, showed first low Q factor toroidal dipole resonance mode at lower frequency (Figure 7c) and second high Q factor toroidal dipole resonance mode at higher frequency (Figure 7d). Here, the low frequency toroidal excitation is a result of magnetic dipole interaction, while high frequency toroidal excitation originates due to electric dipole interaction between neighboring resonators. At these two resonances, surface currents distribution (in XY plane), confines magnetic field in circular region (in XZ plane) have been indicated for magnetic dipole (Figure 7e), and electric dipole (Figure 7f) induced toroidal excitation.

9

Figure 7: a) Schematic representation of U-shaped resonator above and below flexible substrate, where lx, ly, w, g, and t represent dimensional parameters of resonator and 𝑎 × 𝑏 represents unit cell dimension. b) Microscopic image of fabricated sample. Experimentally measured transmission spectra at lower (c) and higher (d) frequency. Surface currents (left) along resonator strips and magnetic field distribution (right) in XZ plane at lower (e) and higher frequency (f) of electromagnetic resonance. Adapted with permission from ref. [79], MDPI AG.

Initial investigations on tailoring radiative losses in metallic metasurface through toroidal excitation were targeted successfully, which is based on transferring fraction of electromagnetic energy to low scattering toroidal dipoles. Since intrinsic resistive loss in metals contribute significantly at higher frequencies, role of all-dielectric metasurface becomes important as they exhibit extremely low intrinsic loss.[80] 5. All-Dielectric planar metasurface for toroidal excitations At microwave frequencies, extremely low nonradiative loss in metals make them suitable for designing customized torus topology resonator to tailor spatial charge and current distribution, which has limited the scope of dielectric metasurface. [81,

82]

However, as we approach to

higher frequencies low loss dielectric plays a significant role in designing toroidal metasurfaces because of increasing resistive loss in metals and limitation in fabricating complicated metallic design with torus topology. Low loss subwavelength dielectric structure supports electric and magnetic Mie resonance modes, which are associated with displacement 10

currents.[83-86] These resonances modes are excited in bulk of resonating structure with simple geometry, hence offer simpler route for the fabrication of all-dielectric planar metasurfaces. Near-field mutual coupling between neighboring dielectric structures could be used for the resonant excitation of toroidal modes. The first all-dielectric metasurface exhibiting toroidal response had been proposed at terahertz frequencies, where unit cell contained closely placed four identical cylindrical shaped high index dielectric particles as shown in Figure 8a.[87] Here, for some specific frequencies Mie-type magnetic resonance modes excited in each cylindrical structure are coupled to form head to tail alignment of magnetic dipoles resulting in polar (magnetic) toroidal excitation (Ez component plot and circulating arrow representing |H| plot of unit cell cross-section along XY plane in Figure 8a). This scheme has been experimentally implemented at microwave frequency to observe toroidal dipolar response through water filled cylindrical glass tubes,[82] which led to several investigations for all-dielectric toroidal metasurface.[39,

88-91] [22]

dipole excitations,

Furthermore, dielectric metasurface is capable of exciting axial toroidal which is not possible through metallic metasurface. Figure 8b shows the

proposed scheme for the excitation of axial toroidal response at infrared wavelengths through metasurface unit cell containing asymmetric cluster of two pair of dielectric disks.[92] In this arrangement, the asymmetric nature of interaction leads to closed loop circulating displacement current among disks in unit cell, which is depicted by the bottom left image in Figure 8b. The axial nature of toroidal dipole excitation has been further verified through numerically obtained contour plot of magnetic field in the perpendicular direction of unit cell plane, which shows magnetic field (bottom right image in Figure 8b) confinement in central region encapsulating the portion of dielectric disks. Apart from structural asymmetry in metasurface unit cell, perturbed dielectric resonators have been studied to realize different orders of resonant magnetic dipoles. Perturbed dielectric resonators facilitates the coupling between incident wave and trapped resonances to excite toroidal dipole mode,[93] as well as ferromagnetic/antiferromagnetic orders of resonant magnetic mode in all-dielectric metasurface.[94]

11

Figure 8: a) Cylindrical structures (radius R with center-to-center separation a and one directional unit cell periodicity d) constituting all-dielectric metasurface unit cell indicated by dashed box, with resonant electric (Ez) and magnetic(|H|) field confinements. b) Schematic of metamolecule array at the top consisting of two pair of dielectric nanodisks of different radius (a1, a2) with center-to-center separation of dr in unit cell, whereas resonant displacement currents (along XY plane) and magnetic field (along Z direction) confinements are represented at the bottom. (a) Adapted with permission from ref. [87], American Physical Society. (b) Adapted with permission from ref.[92], Copyright 2018, American Chemical Society.

6. Toroidal excitations for stimulating anapole modes in 2D metasurface Primary investigation on toroidal dipole modes in metamaterials further triggered detailed study of their radiation scheme. Radiation cancellation through anapole excitation could be used as another approach to substantially reduce radiative losses. Far-field radiation pattern of toroidal dipole matches with electric dipoles, so their radiation pattern could be combined to interfere destructively. The complete destructive interference between electric and toroidal dipoles could lead to possible existence of non-radiating electromagnetic sources, known as anapoles,[29,

46]

which might lead to Aharonov–Bohm like phenomena.[95] The condition for non-radiating ⃗⃗, where 𝑃⃗⃗ and 𝑇 ⃗⃗ corresponds to anapole mode excitation is governed by the equation 𝑃⃗⃗ = 𝑖𝑘𝑇 electric and toroidal dipole moments, respectively, k is wavevector of electromagnetic wave.[96, 97]

Experimental realization of non-radiating anapole through toroidal and electric dipole modes

is challenging, as it difficult to simultaneously excite out of phase equal magnitude moments of both modes. The characteristic feature of toroidal dipole is its ability to radiate at similar angular momentum as electric dipole, which brings anapole modes into consideration to reduce radiative losses. In 12

2013, anapole mode was first experimentally realized in 3D microwave metamaterial for producing narrow transparency window,[59] which opened the pathway for exploiting toroidal modes for exciting narrow linewidth resonances in metamaterial cavity with high field confinements. In planar metasurface configuration unit cell composed of two semicircular symmetric SRRs as shown in Figure 9a, have been used to demonstrate near anapole modes in planar metasurface at microwave frequency.[98] The opposite circulating current density j (red) in each half of resonator confines magnetic field (green circle) in circular region, which induces toroidal excitation (T). Figure 9a showed the extremely sharp resonance dip in transmission spectra with Q factor on the order of ~104 due to excitation of anapole modes. For this design scattered power from five dominant multipoles plotted in Figure 9b showed nearly equal magnitude of electric dipole (P) and toroidal dipole (T). The phase difference (ϕP- ϕT) plot between electric and toroidal dipole in figure 9c showed that at the instance of high Q resonance the value of ϕP- ϕT is 90o (indicated by arrow), which satisfied the required condition to be fulfilled for anapole excitation. It is also important to pay attention towards contribution of magnetic quadrupole (red curve indicating Qm in Figure 9b has higher contribution compared to magnetic dipole (M) and electric quadrupole (Qe)), which competes with toroidal dipole. In planar metasurface, shape and design parameters of unit cell need to be optimized to suppress the contribution due to magnetic quadrupole.

Figure 9: a) Transmission spectra (theory and experiment) of metasurface with unit cell design shown in inset, where red arrow shows current density (j), green arrow shows circular magnetic moment (m) while blue arrow shows toroidal moment (T). b) Numerically computed scattering contribution from five dominant multipoles (P, M, T, Qe, Qm), which together contribute at resonance shown by dotted line. c) Numerical obtained phase plot of electric dipole (P), toroidal dipole (T) and phase difference (ϕP- ϕT) between them depicted by dotted line. Adapted with permission from ref. [98], American Physical Society.

13

Anapole excitation could also contribute significantly to the emerging field of nanophotonics by squeezing light into low less states, for implementing next generation application through photonic devices.[99] The planar profile of dielectric metasurface are promising for the development of on-chip nanophotonic devices owning to their simplified fabrication. The first experimental realization of resonant anapole mode in dielectric nanoparticle at visible frequency, where geometric tailoring of standalone Si nanodisk resulted in destructive interference of toroidal and electric dipoles. At infrared frequencies, the concept of anapole has been extended to the field of nanophotnoincs to pitch the idea of nanolaser.[100] In lasers, an optical amplification is achieved by stimulated illumination of electromagnetic radiation from the excited state to ground state. Figure 10a illustrates the idea of nanolaser with all-dielectric nanodisk metasurface, where the stimulated emission wavelength of light, which is governed by semiconducting properties of nanodisk material, matches with the wavelength of resonant excitation of anapole mode in nanodisk. The transition of free carriers from excited state to initial level through scattering free or radiation less state (anapole mode) could give enhanced optical amplification. The merging of nanophotonics with the arena of material science has incorporated new development in the physics of resonant dielectric structures to facilitate new practical applications. Figure 10b shows theoretical investigation of strong coupling behavior between anapole modes and molecular excitons.[101] The resonance dip in scattering spectra of Si nanodisk (black curve) corresponds to excitation of anapole mode. Heterostructure composed of Si nanodisk and molecular J-aggregate ring, which is modelled as classical Lorentzian oscillator with absorption peak close to anapole mode frequency, showed splitting of anapole mode (red curve) into a pair of eigenmodes (denoted green and red arrow). The electric field profile at these split modes are indicated at the top of Figure 10b. An additional dip (denoted by black arrow) corresponds to weak cavity resonance of J-aggregate structure, where field is concentrated along the periphery of ring (field profile indicated at the bottom left in Figure 10b). In another study, strong coupling between anapole modes and dark plasmon has been studied to enhance the strength and bandwidth of localized field confinement in a hybrid metal-dielectric nanostructure.[102] Although excitation of fundamental anapole modes reduces radiative loss, the loss due to scattering contribution of higher order electric multipoles need to suppressed for enhancing performance of all-dielectric metasurface. In this regard, the role of higher order 14

toroidal multipoles becomes important for realizing nonradiating anapole states of higher order, which is highly advantageous for strong light matter interaction.[103]

Figure 10: a) Scattering spectra of semiconducting dielectric disk (black color) represented by blue curve, where vertical red line represents stimulated emission wavelength of semiconducting material in presence of optical pump. b) Scattering spectra of Si nanodisk (black curve) and J-aggregate Si nanodisk (red curve), where |E| and |H| field profiles of hybrid structure are represented at respective resonance dips (red arrow corresponds to top right, green arrow corresponds to top left, black arrow corresponds to bottom left field profile). (a) Adapted with permission from ref. [100], Springer Nature. (b) Adapted with permission from ref.[101], Copyright 2018, American Chemical Society.

7. Conclusion Intriguing features of toroidal dipole allows an alternate approach to address radiative losses in metallic and dielectric photonic devices. Toroidal excitations, which were initially realized through 3D metasurface platform, also exhibits exceptional functionalities in 2D metasurface for tailoring electromagnetic radiation. The reduced dimensionality of 2D metasurface allows compatibility with large area fabrication and low-cost manufacturing, as compared to their 3D counterparts. The extraordinary ability of toroidal dipole is to excite low-loss non-radiating anapole modes, which could be extremely useful for the development of miniaturized on-chip planar photonic devices for lasing, 2D sensing, light-matter coupling and slow light applications.

Acknowledgement The authors acknowledge the funding support from the Ministry of Education Academic Research Fund Tier 1, Grant RG191/17. No new data were created as part of this review. 15

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Declaration of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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