pubs.acs.org/journal/apchd5 Letter Near-Field Imaging of Magnetic Complex Mode Volume Niccolò Caselli,* Tong Wu, Guillermo Arregui, Nicoletta Granchi, Francesca Intonti, Philippe Lalanne, and Massimo Gurioli Cite This: ACS Photonics 2021, 8, 1258−1263 Read Online ACCESS Metrics & More Article Recommendations See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. Downloaded via UNIV AUTONOMA DE BARCELONA on August 16, 2021 at 08:32:41 (UTC). ABSTRACT: The non-Hermitian nature of confined photonic modes is described by the electric complex modal volume, VE, which represents a key parameter that leads to counterintuitive effects, such as negative modal contribution to the local density of states and non-Lorentzian lineshapes. Here, we address the magnetic counterpart of VE by means of near-field perturbation experiments in a photonic crystal slab cavity. We study the relevant role played by the imaginary part of the magnetic modal volume, VH, which can increase the quality factor of the confined modes by means of a local external magnetic perturbation. We show how a mapping of the spatial distribution of both the real and imaginary parts of VH can be inferred by near-field experiments employing Al-covered near-field tips. Our findings deepen the role of the magnetic component of light and could open a new route in employing metamaterials, magnetic quantum emitters, and topological photonics. KEYWORDS: electromagnetic resonance, magnetic light, photonic microcavity, cavity perturbation theory, mode volume R ecently, important progresses have been achieved on the description of photonics as a non-Hermitian open system, and within quasinormal mode (QNM) theory, any optical Q and that the electric complex mode is directly observable and carries true physical significance.7 On the other hand, the imaginary part of the electric modal volume imposes a non- resonator can be described by a set of n modes with Lorentzian local density of states and therefore modifies the normalized complex electric fields Ẽ ̃ n(r) and complex Purcell effect in the spontaneous emission of a quantum frequencies ω̃ n = ωn − iΓn, with ωn the resonant frequency emitter with an allowed dipole electric transition.2 It has been and Γn the coherence damping rate.1−4 The phase of each evidenced by several experiments, even in systems with very mode is a well-defined quantity that can be measured, and high Q, that the imaginary part of the electric modal volume ultimately, it leads to deep modifications of the common fully defines the asymmetry parameter of the Fano local density picture of the Purcell5 effect and perturbation theory.6−8 Most of states (LDOS) profile.5 Recent results on hybrid systems of these phenomena can be described by introducing the reported a way to engineer arbitrary Fano lineshapes in the concept of complex modal volume. The complex-valued local density of optical states.9 electric modal volume, for the nth QNM of a given optical The growing interest of magnetic light−matter interaction in resonator, probed by an electric dipole p = pu and at the metamaterials and topological photonics10−12 advocates for the position r is defined as:1 introduction of an equivalent mode volume for the magnetic E fields H̃ n(r) of the nth resonant mode, probed by a magnetic Vñ (r) = [2εoε(r)(Ẽ n(r) ·u)2 ]−1 (1) dipole m = mu, where ε(r) is the relative dielectric constant. When an electric H Vñ (r) = −[2μ0 μ(r)(H̃ n·u)2 ]−1 = −[2μ0 (H̃ n·u)2 ]−1 (2) dipolar perturber is placed in the vicinity of the cavity, the complex frequency change Δω̃ n is proportional to where the last expression holds for μ(r) = 1, that is, the usual Δωñ α ω̃ = − ̃ E with α being the polarizability of the perturber. photonic cavity made by dielectric (and nonmagnetic) n 2Vn (r) The imaginary part of the electric modal volume is related to non-Hermitian effects, for example, the change of the Q factor Received: December 23, 2020 of the mode by constructive or destructive interference Published: April 14, 2021 between the scattered fields of the cavity and the scatterer. The powerfulness of Im(Ṽ En ) in predicting the Q change has recently been confirmed with near-field experiments, showing that the map of Im(Ṽ En ) fully explains the tip-induced change of © 2021 American Chemical Society https://doi.org/10.1021/acsphotonics.0c01943 1258 ACS Photonics 2021, 8, 1258−1263 ACS Photonics pubs.acs.org/journal/apchd5 Letter Figure 1. Computation of the spatial distributions of the real and imaginary parts of the relevant electric (a, b) and magnetic (c, d) inverse modal volume of a D2 cavity with holes of diameter 206 nm (black empty circles) and a lattice constant of 331 nm; the units are in μm−3. The black scale bars in the figures are 300 nm. The maps are computed in air on a plane placed 20 nm above the membrane surface. The yellow circles in (b) and (d) highlight the regions where the SNOM data of Figure 2 are acquired. materials. Note that the minus sign in the definition arises from This Letter addresses the topic of measurement and the normalization condition of the QNM, which is a tricky mapping of the magnetic modal volume in a photonic crystal aspect long debated.1,13 Here we use the following:2 cavity on slab. We provide experimental evidence that the magnetic perturbation theory should rely on non-Hermitian ∫ ∫ ∫ (εoε(r)Ẽ n(r)2 − μ0H̃ n(r)2 )d3r = 1 (3) physics. In particular, we show that a coated metallic tip in a scanning near-field experiment acts as an anisotropic magnetic perturbation able to give access to the spatial distribution of where the integral extends to the whole volume, including the the complex mode volume. This is an important result since perfect matching layer (PML) regions whenever FDTD Ṽ Hn (r) is deeply involved in light−matter interactions whenever simulations are used. In order to grasp the need of the the magnetic side of a photon plays a role, especially in the minus in eq 2 as well as in the normalization integral in eq 3, field of metamaterials and topological photonics.10−12 let us remember that, for a high Q and spectrally isolated We analyze eq 5 in the case of a photonic crystal in a mode, the normalized electric field Ẽ n(r) is almost real and the hexagonal array of holes on a dielectric slab. The cavity normalized magnetic field H̃ n(r) is almost imaginary.1 consists of four missing holes in a diamond geometry and was Therefore, in eq 2 we add the minus sign to require that the named as D2.14,15 We numerically solve Maxwell’s equations to real part of the magnetic volume is positive, as intuitively find the QNMs, which are normalized using the QNM solver expected. QNMEig16 of the freely available package MAN (Modal We stress that, in analogy to its electric counterpart, Ṽ Hn (r) Analysis of Nanoresonators). Therefore, we obtain the three defines the Purcell effect of an optical magnetic dipole components of the electric Ẽ n(r) and three components of the transition via the nth mode of an optical resonator, by the magnetic H̃ n(r) fields for any QNM of the D2 cavity. following formula: ÄÅ É ÅÅ Q ÑÑÑ ω Hereafter, we focus on the fundamental mode and further Å Ñ |m|2 ReÅÅÅÅ H n ÑÑÑÑ neglect to report the suffix n indicating the QNM index. ÅÅ Vñ (r) ÑÑ ωn (ω − ωn)2 + Γ n2 2μ0 Γ n2 ÅÇ ÑÖ γn(r, ω) = We also focus on hyperspectral scanning near-field optical ℏ ij Im[Vñ (r)] ω − ωn yzz microscopy (SNOM) experiments,17 where the tip can be j × jjj1 + zz j z Re[Vñ (r)] Γn z{ H exploited both as a perturber at the nanoscale and as a probe of k H (4) the complex eigenvalues.7,14,15 As shown in refs 7 and 14, a chemically etched uncoated near-field fiber probe is a good Here we consider a quantum emitter with magnetic dipole approximation of a point-like nonabsorbing scatterer, moment m = mu embedded in a photonic cavity at position r described by an isotropic electric dipole polarizability α. In and the quality factor of the mode is Qn = ωn/(2Γn). refs 15 and 18 it has been shown that a commercial Al-coated The introduction of a magnetic mode volume also allows for aperture near-field probe on a cavity in slab photonic crystal the prediction of the complex frequency shift of the mode acts as a perturber, exhibiting both in-plane isotropic electric when the cavity is perturbed by a point-like object with both dipolar and anisotropic diamagnetic responses. Note also that electric and magnetic responses: in a photonic crystal on slab the component normal to the slab plane, Ẽ 2z (r), is small with respect to Ẽ 2x(r) + Ẽ 2y (r), and it will Δωñ α β be neglected hereafter. The electric and magnetic polar- =− E − ωñ ̃ 2Vn (r) ̃ H 2Vn (r) (5) izabilities of the Al-coated probe can, thus, be defined as α̅ ij = αδi,j (Re(α) > 0) and β̅ij = −βδi,zδj,z (Re(β) > 0). It was also Note that the electric and magnetic polarizabilities α and β of reported that Re(β) > Re(α), which means that the Al-coated the perturber have the units of a volume, implying that the probe acts as an effective diamagnetic perturber by inducing a induced electric and magnetic dipole moments of the perturber blue-shift of the mode resonant wavelength.15,18 The electric are given by pind = αε0 Ẽ n(r) and mind = βH̃ n(r)/μ0, where and magnetic polarizabilities of the probe can be defined n(r) is the refractive index. Equation 5 indicates that within this picture, as for typical SNOM experiments we expect perturbation experiments may benchmark the magnetic to be able to address the two complex quantities either Ẽ 2(r) = interaction between light and matter as mediated by the Ẽ 2x(r) + Ẽ 2y (r), or H̃ 2z (r) via the following: complex magnetic modal volume and that the phase of the Δωñ 2 2 magnetic field of a QNM can be deduced with the knowledge = −αεo(Ex̃ (r) + Eỹ (r)) − βμo H̃ z2(r) of the polarizabilities. ωñ (6) 1259 https://doi.org/10.1021/acsphotonics.0c01943 ACS Photonics 2021, 8, 1258−1263 ACS Photonics pubs.acs.org/journal/apchd5 Letter Figure 2. (a) Scanning electron microscope (SEM) image of a D2 cavity in which the red and blue symbols correspond to the symmetric positions where the SNOM spectra shown in (c) and (d) were taken. (b) Schemes of the PL and RS setups. (c) SNOM-PL spectra taken at the red (upper panels) and blue (lower panels) positions in (a) are shown as circles and triangles with the same color code; the magenta curves show the best Lorentzian fits. (d) SNOM-RS spectra recorder at the red (upper panels) and blue (lower panels) positions in (a); the magenta curves show the fitted Fano line shapes. In each spectrum, the Q evaluated from the fit is reported. Note that the unperturbed quality factor was around 2500 for both cavities. In Figure 1a,b we report the results for the spatial distribution map of the QNM spectral blue shift was compared to |H̃ z(r)|2, in an air plane at 20 nm above the slab of a D2 cavity of the as predicted by Hermitian perturbation theory; however, real and imaginary parts of Ẽ 2x(r) + Ẽ 2y (r), and in Figure 1c,d we considering that H̃ z is nearly a purely imaginary number, the report the results for the spatial distribution of the real and approximation −Re(H̃ z2(r)) ≈ |H̃ z(r)|2 holds, hence, the imaginary parts of H̃ 2z (r). In all maps the empty circles define Hermitian theory predictions for the blue shifts due to the position of the air holes of the underlying photonic diamagnetic scatterers are quantitatively correct. structures. With the knowledge of these field maps and the The novelty of the non-Hermitian perturbation theory in polarizabilities, the complex resonance frequency variations high Q photonic cavities with spectrally isolated QNMs are induced by the pointlike perturber given by a metallic SNOM associated with the loss modulations, that is, the presence of tip at any position can be readily predicted by using eq 6. spatial regions on top of the cavity with both positive and Many general remarks can be done by inspecting these negative imaginary parts of the mode volume. In analyzing the maps. The utmost relevant aspect in our discussion is that the experimental results, we aim to assess the nature of the induced imaginary parts of both fields show large regions with either loss modulation due to the scanning in the near-field of a positive or negative values of almost the same intensity. This metallic-coated SNOM tip. Therefore, as a first step, we select means that, for a nonabsorbing scatterer, the real part of both two points of the D2 photonic crystal cavity where the effect of polarizabilities α and β gives a variation of mode losses, which a dielectric vs diamagnetic are expected to be opposite. These can be either positive or negative, thus inducing a change of Q. points are highlighted as yellow circles in Figure 1b,d. This evidence lies at the heart of the non-Hermitian Electron beam lithography followed by reactive ion etching perturbation theory and bears the modal volumes as complex was used to fabricate the perforated air-membrane.14,15 InAs quantities.1,7 We notice that the real parts of both Ẽ 2(r) and quantum dots were embedded in the GaAs membrane. Two H̃ 2z (r) are 3 orders of magnitude larger than their imaginary different near field experiments were performed: photo- parts and that they do not change sign over space. In addition, luminescence (PL) and resonant scattering (RS) by using a they have the opposite sign, that is Re(Ẽ 2) > 0 and Re(H̃ 2z ) < 0. All these features are common to any given spectrally isolated Al-coated aperture near-field probe (LovaLite, Besancon, photonic mode with a relatively high Q and according to the France),15,19 which both collected the near-field light and original idea in ref 2 and following eq 4 and ref 5 in such a acted as a local perturbation. The two setups are sketched in case, the Lorentzian line shape in the electric and magnetic Figure 2b. In the PL experiments, we used illumination/ LDOS is a very good approximation. Furthermore, Re(H̃ 2z ) < 0 collection configuration and the quantum dots were excited at is consistent with the definition of the complex magnetic 780 nm, and we detected the near-field photoluminescence volume possessing a negative sign (i.e., H̃ z(r) is almost purely under moderate state filling condition in order to have a large imaginary), and it gives the expected blue spectral shift of the emission band around 1300 nm. The RS experiments were diamagnetic polarizability when Re(β) > 0.15,18 performed in transmission geometry where light coming from a Another noteworthy feature is that the antinodes of Re(Ẽ 2) supercontinuum laser (ranging from 1100−1500 nm) was and Re(H̃ 2z ) are found at the positions of the nodes of Re(H̃ 2z ) focused on the sample surface on a spot of approximately 2 μm and Re(Ẽ 2), respectively. This helps to disentangle the role of diameter size to ensure a homogeneous excitation on the entire the dielectric and diamagnetic perturbation in near-field cavity. The transmitted light was collected by the Al-coated experiments. In refs 15 and 18, the experimental maps of the probe that allowed us to filter out and reduce the contribution blue shift having a maximum at the antinode of the magnetic of nonresonant scattering channels, which is mandatory for field map was indeed one key aspect to assess that a SNOM good signal/noise RS experiments. In both PL and RS metallic tip mainly acts as an anisotropic diamagnetic experiments, the tip remained fixed while the sample was perturber. It is worth stressing that in ref 15 the near-field raster scanned at a constant tip−sample distance of around 20 1260 https://doi.org/10.1021/acsphotonics.0c01943 ACS Photonics 2021, 8, 1258−1263 ACS Photonics pubs.acs.org/journal/apchd5 Letter nm, while detecting the optical signal collected by the same positioning of the slab holes (white circles), which are found probe. misaligned with respect to the designed honeycomb lattice. As In Figure 2c (Figure 2d) we report PL (RS) spectra for the already mentioned, the PL and RS experiments were lower-energy D2 cavity mode obtained in the blue and red performed on two different cavities and by different tips, points highlighted in Figure 2a and corresponding to the therefore it is not surprising that the absolute Q values were yellow spots in Figure 1b,d and to their symmetric positions in slightly different. Nevertheless, the Q spatial modulations are the lower part of the cavity. It is worth stressing that here the very similar, denoting the robustness of the near-field LDOS line shape is almost Lorentzian for the selected QNM, perturbation method for getting insight on the spatial as given by the PL spectrum; while the Fano profile of the RS distribution of a confined photonic mode. Note that the spectrum arises from the interference forming the driving and black regions in all the maps refer to points were the signal was the scattered fields.19 By fitting the two recorded line shapes too small for performing a reliable line shape fit. The data for with Lorentzian (for PL) and Fano (for RS) profiles, we the spectral shift were found fully in agreement with previous inferred the central resonance wavelength λ and the quality PL results15 and we avoid reporting them in order to better factor Q. Both these parameters change along the SNOM emphasize the novelty the Q map analysis. scanning due to the tip perturbation. However, in symmetric Following the existing literature on the diamagnetic nature positions with respect to the center of the cavity, the Q value of the perturbation of an Al-coated tip,18 that is, by assuming presents slight variations, as highlighted in Figure 2c,d, where Re(β) > Re(α), we expect that the Q maps contain insights the color and shape of the experimental data reproduce the onto the imaginary part of the magnetic modal volume. This is code used to label the two investigated points on the cavity indeed reflected in the two experimental Q modulations surface image in Figure 2a. reported in Figure 3, where the main spatial features associated The PL and RS data refer to two independent experiments with the map of Im(H̃ 2z ) can be recognized: two lobes performed with two different SNOM tips as well as slightly exhibiting low Q positioned on the larger diagonal of the D2 different photonic cavities, as can be inferred from the almost cavity symmetrically to the center, which are surrounded 50 nm difference in the central wavelengths of the two externally by a region of higher Q. resonances. Nevertheless, the QNM main features are very A quantitative fit of these data is quite complex, since Al- similar. The spectra taken in the blue points show a blue shift coated SNOM tips are challenging objects to be modeled. In of the QNM resonance and a much smaller quality factor (Q ∼ particular, the assumption that they induce an isotropic and 750); note also that the unperturbed quality factor was around homogeneous perturbation is questionable due to the 2500 for both cavities. The emergence of a blue shift agrees heterogeneous nature of these tips, which exhibit a dielectric with the previously discussed diamagnetic effect associated core and a metallic cover, without well-known thicknesses also with the metal-coated tip perturbation.15 The striking feature due to tip damaging during a few scans. Moreover, the tips are of these data is the large variation of Q between the two points not point-like dipoles in the plane since the dielectric aperture with different colors that are only about 200 nm apart. The red is about 100 nm and the extension of the metal coat thickness points correspond, in both experiments, to a Q twice time is almost 100 nm. The morphology in the vertical direction is larger; which compared with the predictions of Figure 1 even more complex and bulky, so we expect that the field confirms the dominance of the diamagnetic perturbation gradients should play a relevant role. Since α and β are induced by a metal-coated tip. complex numbers, a quantitative analysis must take into The maps of the quality factor Q obtained from RS and PL account also the contribution of their imaginary parts, which data are given in Figure 3a and b, respectively. On top of the give rise to Ohmic and scattering losses,20 as demonstrated by map we report the geometry of the D2 cavity with thin circles the fact that the unperturbed Q values of the two cavities describing the air holes, as obtained from the morphological (measured by far-field experiments) is around Q = 2500. This map measured during the SNOM scan. The distortion means that, in general, the local damping Γ(r) differs from the observed between the two main blue regions in the quality unperturbed value Γo by factor map of Figure 3a are ascribed to piezoelectric stage drift 2 2 during the long scan (more than 1 h) highlighted by the Γ(r) − Γo = ω(r)[Im(α)ε0 Re(E ̃ (r)) − Re(α)ε0 Im(E ̃ (r)) 2 2 − Im(β)μ0 Re(H̃ z (r)) + Re(β)μ0 Im(H̃ z (r))] (7) It is important to note that the terms in which Im(α) and Im(β) appear are both positive in all the points of the cavity, meaning that the Ohmic and scattering losses can only decrease the cavity Q. In order to reproduce the experimental data by eq 7, the parameters α and β should be estimated, which requires a detailed model of the perturbing probe. This would imply a demanding knowledge of the geometry of the heterogeneous SNOM tip. To overcome this issue, we employed a Figure 3. (a, b) Experimental map of the variation of Q for the RS phenomenological picture, including the minimum number and PL experiments, respectively. In both cases, the values of each Q were obtained by line shape fitting, as the examples reported in Figure of parameters, so neglecting Re(α) with respect to Re(β) and 2c,d. Black pixels refer to points where the signal was too low for Im(α), according to the literature.18 We chose to describe fitting the data. (c) Calculated map from eq 7 setting Re(β) ≅ 20, Ohmic and radiation losses by a single parameter, that is Im(α) = 1.6 × 10−2 μm+3, Γo = 2.5 × 10−4ωo, and neglecting the Im(α). Then we evaluated the predictions of eq 7 by terms in which Re(α) and Im(β) appear. The scale bar is 300 nm. calculating the QNM map of the resulting quality factor 1261 https://doi.org/10.1021/acsphotonics.0c01943 ACS Photonics 2021, 8, 1258−1263 ACS Photonics ■ pubs.acs.org/journal/apchd5 Letter ωo Q (r ) ≅ , where we neglected the small spectral shift using ACKNOWLEDGMENTS 2Γ(r ) the unperturbed QNM frequency ωo (i.e., ω(r) = ωo). We are thankful to Silvia Vignolini for contributing to the PL To reproduce the experimental maps, we chose the experiments. We acknowledge the sample nanofabrication by parameters of eq 7 to be Re(β) ≅ 20 Im(α) = 1.6 × 10−2 Laurent Balet and Andrea Fiore, who are also thanked for μm+3 and Γo = 2.5 × 10−4ωo (note, this is 20% larger than the many fruitful and interesting discussions. P.L. acknowledges experimental unperturbed value). In Figure 3c we reported the NOMOS (ANR-18CE24-0026) and I-SQUAD (ANR- convolution of the calculated quality factor map with a two- 18CE47-0006) Projects for financial support. M.G. acknowl- edges funding from CdR Firenze (2018/24257). ■ dimensional Gaussian point-spread function with a full width at half-maximum of 100 nm in order to encompass the real size of our SNOM tip. In addition, to be consistent with the REFERENCES experimental data, we colored as black the pixels where the (1) Lalanne, P.; Yan, W.; Vynck, K.; Sauvan, C.; Hugonin, J. P. Light calculated intensity of the electric field was below a given Interaction with Photonic and Plasmonic Resonances. Laser Photonics threshold (10−3 of the maximum), so that near-field signal Rev. 2018, 12 (5), 1−38. (2) Sauvan, C.; Hugonin, J. P.; Maksymov, I. S.; Lalanne, P. Theory would be too weak to detect. The comparison shows that our of the Spontaneous Optical Emission of Nanosize Photonic and calculations can reproduce the main features of the Plasmon Resonators. Phys. Rev. Lett. 2013, 110 (23), 1−5. experimental maps. Despite the very rough modeling, we (3) Muljarov, E. A.; Langbein, W. Exact Mode Volume and Purcell believe that our findings provide a qualitative method for Factor of Open Optical Systems. Phys. Rev. B: Condens. Matter Mater. imaging the imaginary part of the magnetic mode volume, a Phys. 2016, 94 (23), 1−19. noteworthy result opening the way for a better understanding (4) Lassalle, E.; Bonod, N.; Durt, T.; Stout, B. Interplay between of the light−matter interaction mediated by the magnetic field. Spontaneous Decay Rates and Lamb Shifts in Open Photonic In summary, we have shown that the QNM approach for Systems. Opt. Lett. 2018, 43 (9), 1950−1953. describing photonics resonant states requires the use of (5) Pellegrino, D.; Balestri, D.; Granchi, N.; Ciardi, M.; Intonti, F.; complex mode volumes also for the magnetic side of the Pagliano, F.; Silov, A. Y.; Otten, F. W.; Wu, T.; Vynck, K.; Lalanne, P.; Fiore, A.; Gurioli, M. Non-Lorentzian Local Density of States in modes. Our results prove that even a commercial SNOM tip Coupled Photonic Crystal Cavities Probed by Near- and Far-Field with Al-coating can induce a local perturbation on the mode Emission. Phys. Rev. Lett. 2020, 124 (12), 123902. quality factor that allows to retrieve the main spatial features of (6) Yang, J.; Giessen, H.; Lalanne, P. Simple Analytical Expression the QNM magnetic field. We expect that a carefully designed for the Peak-Frequency Shifts of Plasmonic Resonances for Sensing. SNOM probe could give a more quantitative mapping of the Nano Lett. 2015, 15 (5), 3439−3444. magnetic modal volume, paving the way for a better (7) Cognée, K. G.; Yan, W.; La China, F.; Balestri, D.; Intonti, F.; understanding of the magnetic light−matter interaction, Gurioli, M.; Koenderink, A. F.; Lalanne, P. Mapping Complex Mode which we expect to be crucial especially in developing new Volumes with Cavity Perturbation Theory. Optica 2019, 6 (3), 269− metamaterials devices and for magnetic quantum emitters. 273. ■ (8) Yan, W.; Lalanne, P.; Qiu, M. Shape Deformation of Nanoresonator: A Quasinormal-Mode Perturbation Theory. Phys. AUTHOR INFORMATION Rev. Lett. 2020, 125 (1), 13901. Corresponding Author (9) Doeleman, H. M.; Dieleman, C. D.; Mennes, C.; Ehrler, B.; Niccolò Caselli − Department of Physical Chemistry, Koenderink, A. F. Observation of Cooperative Purcell Enhancements Universidad Complutense de Madrid, E28040 Madrid, in Antenna-Cavity Hybrids. ACS Nano 2020, 14 (9), 12027−12036. Spain; orcid.org/0000-0003-2609-3834; (10) Baranov, D. G.; Savelev, R. S.; Li, S. V.; Krasnok, A. E.; Alù, A. Modifying Magnetic Dipole Spontaneous Emission with Nano- Email: ncaselli@ucm.es photonic Structures. Laser Photonics Rev. 2017, 11 (3), 1600268. Authors (11) Yen, T. J.; Padilla, W. J.; Fang, N.; Vier, D. C.; Smith, D. R.; Pendry, J. B.; Basov, D. N.; Zhang, X. Terahertz Magnetic Response Tong Wu − LP2N, Institut d’Optique, CNRS, Université de from Artificial Materials. Science (Washington, DC, U. S.) 2004, 303 Bordeaux, Talence 33400, France (5663), 1494−1496. Guillermo Arregui − Catalan Institute of Nanoscience and (12) Lu, L.; Joannopoulos, J. D.; Soljačić, M. Topological Photonics. Nanotechnology (ICN2), CSIC and BIST, 08193 Bellaterra, Nat. Photonics 2014, 8 (11), 821−829. Spain; Departamento de Física, Universitat Autònoma de (13) Lalanne, P. Mode Volume of Electromagnetic Resonators: Let Barcelona, 08193 Bellaterra, Spain Us Try Giving Credit Where It Is Due. arXiv:2011.00218 Nicoletta Granchi − LENS, University of Florence, Sesto [physics.optics] 2020, na. Fiorentino 50019, Italy (14) Intonti, F.; Vignolini, S.; Riboli, F.; Vinattieri, A.; Wiersma, D. Francesca Intonti − LENS, University of Florence, Sesto S.; Colocci, M.; Balet, L.; Monat, C.; Zinoni, C.; Li, L. H.; Houdré, R.; Fiorentino 50019, Italy Francardi, M.; Gerardino, A.; Fiore, A.; Gurioli, M. Spectral Tuning and Near-Field Imaging of Photonic Crystal Microcavities. Phys. Rev. Philippe Lalanne − LP2N, Institut d’Optique, CNRS, B: Condens. Matter Mater. Phys. 2008, 78 (4), 2−5. Université de Bordeaux, Talence 33400, France; (15) Vignolini, S.; Intonti, F.; Riboli, F.; Balet, L.; Li, L. H.; orcid.org/0000-0003-1979-2290 Francardi, M.; Gerardino, A.; Fiore, A.; Wiersma, D. S.; Gurioli, M. Massimo Gurioli − LENS, University of Florence, Sesto Magnetic Imaging in Photonic Crystal Microcavities. Phys. Rev. Lett. Fiorentino 50019, Italy; orcid.org/0000-0002-6779- 2010, 105 (12), 1−4. 1041 (16) Yan, W.; Faggiani, R.; Lalanne, P. Rigorous Modal Analysis of Plasmonic Nanoresonators. Phys. Rev. B: Condens. Matter Mater. Phys. Complete contact information is available at: 2018, 97 (20), 1−10. https://pubs.acs.org/10.1021/acsphotonics.0c01943 (17) Novotny, L.; Hecht, B. Principles of Nano-Optics: Cap 15; Cambridge University Press: Cambridge, 2006. Notes (18) Burresi, M.; Kampfrath, T.; Van Oosten, D.; Prangsma, J. C.; The authors declare no competing financial interest. Song, B. S.; Noda, S.; Kuipers, L. Magnetic Light-Matter Interactions 1262 https://doi.org/10.1021/acsphotonics.0c01943 ACS Photonics 2021, 8, 1258−1263 ACS Photonics pubs.acs.org/journal/apchd5 Letter in a Photonic Crystal Nanocavity. Phys. Rev. Lett. 2010, 105 (12), 1− 4. (19) Caselli, N.; Intonti, F.; La China, F.; Riboli, F.; Gerardino, A.; Bao, W.; Bargioni, A. W.; Li, L.; Linfield, E. H.; Pagliano, F.; Fiore, A.; Gurioli, M. Ultra-Subwavelength Phase-Sensitive Fano-Imaging of Localized Photonic Modes. Light: Sci. Appl. 2015, 4, e326. (20) Sersic, I.; Tuambilangana, C.; Kampfrath, T.; Koenderink, A. F. Magnetoelectric Point Scattering Theory for Metamaterial Scatterers. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 83, 1−12. 1263 https://doi.org/10.1021/acsphotonics.0c01943 ACS Photonics 2021, 8, 1258−1263