Optical scattering of a nanopaticle under the excitation of a plane wave is usually determined by its predominant electromagnetic multipole moment¹. Such predominant multipole moment can even decide the electric or magnetic nature of the scattering in all-dielectric photonics². Therefore, tailoring such a predominant electromagnetic multipole moment becomes an effective and unified way to manipulate optical scattering³. Many abnormal optical scattering phenomena have been proposed to enable new possibility and functionality in photonics³. The nonscattering electromagnetic state is one of the typical examples^4-20 [see these elaborated reviews in refs.^21-24 for details]. In contrast to the embedded eigenstates or bound state in the continuum which cannot be accessed by the excitation in the continuum²⁵, the so-called electromagnetic anapole condition provides a nonscattering condition sustained under the excitation of external field^{5, 26}, which resembles a promising physical mechanism for tailoring light-matter interaction in a nonscattering manner^{21-24, 27}. It is generally perceived that such an anapole condition requires that all of the induced electromagnetic multipole moments are suppressed at the same wavelength, resembling the canonical way of realizing the radiationless anapole condition^4-20. In particular, the optical anapole condition corresponds to a pronounced minimum in the far-field scattering associated with highly confined electromagnetic near-field^{6, 28}. Such condition is quite challenge to meet since the degree of freedom for tailoring the induced electromagnetic multipolar moments of a nanoparticle is quite limited. Such a condition can also be readily fulfilled through structured light illumination¹⁶ which generally extends the scopes of light-matter interaction from both fundamental science and application prospective, such as high numerical aperture (NA) focusing^29-31, optical computation³² , optical data storage³³, customized excitation of electromagnetic multipole resonances^{17, 33-40} and radiationless anapole condition^{9, 16, 17}, enhancement of optical nonlinearity^{41, 42}, optical tweezers^43-45 and advanced metrology^{46, 47}.

According to Mie theory, the total scattering power of a spherical nanoparticle excited by a plane wave is determined by both contributions of electric and magnetic multipole moments of different order n¹.

1Ptotal=π|Ei|2kωμ0∑n=1∞(2n+1)(|an|2+|bn|2),

where E_i, k and ω are the amplitude, k-vector and angular frequency of the incident plane wave, respectively. There are numerous zeros of Mie scattering coefficients an and bn, which are corresponding to zero contribution to the total scattering from the electromagnetic multipole moments of different orders⁴⁸. It was suggested that the electromagnetic anapole condition could be interpreted as the destructive interference between toroidal moments and Cartesian electromagnetic multipole moments^{4-7, 14, 21, 49-51}. In general, the zero amplitude conditions of an and bn are usually accompanied with other spectral overlapping electromagnetic multipole moments. As a result, such zero conditions of Mie scattering coefficients could be physically hidden in far-field scattering response. For example, zero | a1| can even coexist with the resonant magnetic dipole (MD) condition at the same frequency⁴⁸.

In this paper, we show that sophisticated tailoring of electromagnetic multipolar moments in nanoparticles is not essential for the realization of the anapole condition, which is different from previous efforts in realizing the anapole condition^4-19. In particular, we experimentally demonstrate that the combination of tightly focused cylindrical vector beam (CVB) and structured Mie resonances can reveal the radiationless anapole condition which is overlapped in spectrum with a resonant state. More importantly, it subsequently enables reconfigurable optical scattering of a silicon nanoparticle with simple morphology, where the optical scattering of the nanoparticle at a specified wavelength can be switched from the radiationless anapole condition to the magnetic resonant scattering condition and vice versa, as shown in Fig. 1.

The electric field of a focused CVB can be expressed in terms of the electric and magnetic multipole fields⁵²:

2Ef(r)=∑l=1∞∑−ll[pEl0Nl0(r)+pMl0Ml0(r)],

where pEl0 and pMl0 are the strength of the electric and magnetic multipole components, Nl0 and Ml0 are the vector spherical harmonics related to the electric and magnetic multipole components, respectively. For a RP beam without orbital angular momentum, the magnetic component pMl0 is zero while the electric component pEl0 is zero for a AP beam⁵². As a result, the focused RP beam can be used to excite the electric and toroidal dipole moments because of their similarity of far-field radiation^{9, 16, 39} while the focused AP beam can be used to excite the magnetic multipole modes^{17, 34-38}. As the excited strength of an electromagnetic multipolar mode depends on both the vectorial properties of the excitation source and the eigenmodes supported by the spherical nanoparticle, therefore, the key enablers for realizing high contrast reconfigurable optical scattering include two points: 1) a nanoparticle supports a pure electromagnetic multipole mode at a specified frequency, which is spectrally overlap with an anapole condition; 2) the spatial overlapping between the electromagnetic field of the nanoparticle’s eigenmode and that of the tightly focused CVBs. High permittivity dielectric nanoparticles resemble a promising platform that fulfills both conditions. For a spherical Au core/Si shell nanoparticle (SN), the contributions of the spherical electric dipole (ED) can be designed to be totally suppressed at the resonant condition of MD⁴⁸. One of the typical solution under plane wave excitation is shown in Fig. 2(a). If the scattering of a tightly focused AP beam is considered, it can be seen from Fig. 2(b) that all electric multipole moments have zero contribution to the total scattering, resembling the ideal MD scattering. On the contrary, the total scattering is zero at the same frequency of the MD resonance if the excitation of a tightly focused RP beam is applied, realizing the optical anapole condition, as shown in Fig. 2(c). Such a sharp contrast in optical scattering power of a nanoparticle at the same wavelength enables the realization of reconfigurable optical scattering.

In order to show the generality of this mechanism, we further consider a simple dielectric nanostructure where its magnetic quadrupole resonance overlaps with the anapole condition. Such dielectric nanostructure is much easier to fabricate in experiment than the core-shell nanoparticle. The Si nanodisk is optimized to fulfill the aforementioned enablers to realize high contrast reconfigurable optical scattering in the visible spectrum. According to the Cartesian electromagnetic multipole decomposition results under the excitation of a focused RP beam shown in Fig. 3(a), the destructive interference between the Cartesian ED and toroidal dipole moments results in the anapole condition where the contributions of high order electromagnetic multipole moments are negligible. The schematic of current geometry (red) and the corresponding magnetic field (blue) are shown in the inset of Fig. 3(a). The calculated electromagnetic near-field distributions at different cross sections of the Si nanodisk are shown in Fig. 3(b) and 3(c) which manifest themselves as typical signatures of near-field excitation under the anapole condition⁶. If the excitation source is switched to a tightly focused AP beam, the Si nanodisk is turned into the resonant scattering condition, where the dominant Cartesian electromagnetic multipole is the electric quadrupole (EQ) moment. The corresponding electromagnetic near-field distributions are shown in Fig. 3(e) and 3(f), which validates qualitatively the dominant excitation of an MQ resonance. It should be pointed out that there is still a residual induced MD moment accessed by the focused AP beam. More importantly, such high contrast reconfigurable optical scattering is tunable by simply changing the radius of the Si nanodisk, as shown in Fig. 4(a) and 4(b). As can be seen from this figure, the MQ resonance overlaps with the anapole condition quite well when the radius of the Si disk is changed. According to the calculated results of the Si nanodisk with different radius under the excitation of AP and RP beams, the wavelength of reconfigurable optical scattering can be effectively tuned about 50 nm, indicating sufficient tolerance for experimental demonstration.

The Si nanodisk shown in Fig. 3 can be readily fabricated on a glass substrate (see Supplementary information Section 1). The substrate effect only has minor effect on the results of Fig. 3, as will be addressed in the following. The geometry parameters of the Si nanodisk are outlined in Fig. 5(a), where the radius r of the Si nanodisk is 150 nm while the height h is 160 nm. The top and side views of scanning electron microscopy (SEM) images of the fabricated Si nanodisk are shown in Fig. 5(b) and 5(c), respectively. The side view is taken by tilting the sample stage of SEM by 30 degrees. As can be seen in Fig. 5(e), the back-scattering spectra measured by the home-built optical setup shown in Fig. 5(d) features a resonant scattering at around 735 nm under the excitation of tightly focused AP beam. The resonance wavelength is red-shifted compared with the result of Fig. 3(d) because of the substrate effect. However, the scattering intensity at the same wavelength is one order of magnitude smaller than the AP case when a tightly focused RP beam is used. This results quantitatively agree with the theoretical results of Fig. 3. The reason for small scattering signal collected at the anapole condition might be attributed to the morphology deformation (size difference and surface roughness) in the fabricated sample utilizing mask based inductively coupled plasma reactive ion etching (see Supplementary information Section 1), as shown in the inset of Fig. 5(b) and 5(c). In order to further access the scatteringless anapole condition, the preparation of Si nanodisks with well-defined morphology is subject to further optimization by e-beam lithography technology⁶ and colloidal synthesis technology¹⁶. Furthermore, we can confirm from the dark-field back scattering images that the radiationless anapole condition is approached under the RP excitation [see Fig. 5(g)] while clear resonant scattering can be visualized in Fig. 5(f). These experimental results validate that the anapole condition can be realized without sophisticated tailoring of electromagnetic multipole moments of nanoparticle. More importantly, one can simply turn on or turn off the optical scattering of a fixed nanoparticle at the same wavelength utilizing tightly focused AP and RP beams, validating the concept of reconfigurable optical scattering for meta-optics. It is also expected that such a mechanism can be applied in the nonlinear scattering region, where distinct harmonic generation, stimulated Raman scattering and saturated scattering can be manipulated by different CVBs.

In summary, we propose a new mechanism to excite the radiationless anapole condition without sophisticated manipulation of electromagnetic multipolar moments of all orders to realize superpositions of suppressed moment strengths at the same wavelength. As a result, high contrast reconfigurable optical scattering utilizing the unique combination of structured light and structured Mie resonances can be realized. It means that a Si nanoparticle whose anapole condition is hidden in an electromagnetic multipolar resonance can be selectively accessed as the radiationless condition or resonant scattering state by utilizing different tightly focused CVBs. More importantly, experimental validation based on a simple Si nanodisk in the visible spectrum is provided to further consolidate the proposed reconfigurable optical scattering. Our results might provide a basic idea to realize a reconfigurable electromagnetic atom for meta-optics. By combining both degrees of freedom in structured light and structured Mie resonances, one might anticipate the possibility to realize ultrafast manipulation of optical signal without applying optical nonlinear and optomechanic effects.