Enhancing Magnetic Dipole Emission by a Nano-Doughnut-Shaped

Jul 31, 2017 - In this paper, we design a nano-doughnut-shaped silicon disk, i.e., a disk with an open hole through its center. This way, the maximum ...
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Letter pubs.acs.org/journal/apchd5

Enhancing Magnetic Dipole Emission by a Nano-Doughnut-Shaped Silicon Disk Jiaqi Li,*,†,‡ Niels Verellen,† and Pol Van Dorpe†,‡ †

IMEC, Kapeldreef 75, B-3001 Leuven, Belgium Department of Physics and Astronomy, KULeuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium

‡

S Supporting Information *

ABSTRACT: High-index dielectric nanostructures support inherently strong magnetic dipole (MD) resonances at optical frequencies with minimal dissipative absorptions. They are promising candidates for MD radiation enhancement. Previous investigations, however, show that the maximum magnetic field enhancement is confined inside the nanostructure and therefore inaccessible to nearby MD emitters, limiting the achievable emission enhancement. In this paper, we design a nano-doughnut-shaped silicon disk, i.e., a disk with an open hole through its center. This way, the maximum magnetic field intensity is exposed and can be leveraged to fully enhance MD radiations. On the basis of numerical calculations, a record high enhancement factor of the radiative decay rate up to 350 has been achieved with minimal nonradiative losses. We further demonstrate the importance of spectral and spatial overlap of the MD emitter with the MD resonance in the silicon nanodisk in order to maximize the MD radiations. Our study opens new possibilities for MD emission enhancement and paves the road toward novel magnetic light−matter interactions. KEYWORDS: all-dielectric nanoparticles, magnetic dipole, radiative decay rate, nonradiative decay rate, quantum efficiency

A

Recently, high-index dielectric nanoparticles have arisen as favorable candidates for the optical manipulation of local emitters. All-dielectric nanostructures, made from, for example, Si, possess strong Mie-type electromagnetic multipole resonances with low absorption losses in the visible spectrum.21−24 As a result, they have been shown to find promising applications in surface-enhanced spectroscopy to amplify Raman scattering,25−27 fluorescence,27−29 and mid-infrared absorption spectroscopy.30 In addition, because of the inherently strong magnetic resonance at optical frequencies, MD emission can be tuned and enhanced.31−33 Recent studies have shown that strong fluorescence enhancement using dielectric nanoparticles can be achieved in silicon dimers in order to leverage the electromagnetic hotspots in their small gap regions.27,29,33,34 However, such a configuration highly depends on the polarization of the excitation light in optical measurements. More importantly, as indicated by previous reports,24,33 in contrast to the electric field enhancement results, the strongest magnetic field enhancement is not located in the open gap regions of the dimer but inside the dielectric nanoparticles, which is unfortunately inaccessible to the nearby MD emitters. Therefore, it seriously restricts the potential for further MD emission enhancement. In this work, to fully take advantage of the enhanced magnetic field in dielectric particles, a silicon nanocylinder with a small hole through the center is designed. This nano-

magnetic dipole (MD) specifically couples to the magnetic component of light and reveals useful information on the, often overlooked, magnetic dimension in the electromagnetic interactions with matter. For example, strong interactions with MD emitters have been used to map the local magnetic field distributions of a laser beam,1 they provide access to spatial and/or spectral magnetic field properties at the nanoscale,2−4 and they quantitatively uncover the magnetic local density of optical states.5−7 Nevertheless, coupling to MD transitions is inherently weak in nature compared to electric dipole (ED) transitions. Magnetic interactions become significant in materials only where the ED transitions are forbidden to the first order, e.g., in some transition metals such as Cr3+ 8 and lanthanide series ions such as Eu3+1,4,5,7,9−11 and Er3+.12 Therefore, it is of fundamental interest to enhance MD emission in a controllable way, especially for nanostructured systems. To this purpose, various plasmonic nanoparticles are commonly exploited in order to take advantage of their specially designed magnetic hotspots. 13−17 It has been abundantly demonstrated in theory6,18−20 and in experimental studies7,10−12 that carefully engineered plasmonic structures can strongly modify MD emission. An enhancement factor of the radiative decay rate up to ∼200 has been theoretically predicted recently.6 However, due to the high intrinsic ohmic losses in metals, especially in the visible range, the nonradiative decay channels start to dominate in close proximity to the surface of plasmonic systems, resulting in considerable quenching of MD emission. This will strongly limit their further applicability. © XXXX American Chemical Society

Received: May 22, 2017 Published: July 31, 2017 A

DOI: 10.1021/acsphotonics.7b00509 ACS Photonics XXXX, XXX, XXX−XXX

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Figure 1. (a) Scattering and absorption cross sections of a nano-doughnut-shaped silicon disk. The inset shows the plane-wave excitation and the shape of the silicon nanoparticle. The height of the nanodisk is 150 nm, the diameter is 200 nm, and the size of the central hole is 10 nm. (b) The black curve is the normalized magnetic field intensity at the center of the nanodisk. The inset displays the magnetic field intensity profile at the MD resonance in the middle plane of the nanodisk (marked as the light gray plane in the inset of panel a). The blue dot indicates the spectral position of the MD resonance. The black dashed lines indicate the silicon boundary. The white arrow indicates the position where the magnetic field intensity is monitored (and also where the MD emitter will be placed in Figure 2).

Figure 2. (a) Radiative and nonradiative decay rate enhancement for an in-plane-polarized MD emitter. The MD emitter source is positioned in the center of the nano-doughnut-shaped nanodisk, as shown in the inset. (b) Quantum efficiency (QE) enhancement for MD emitters with intrinsic QE of 100%, 50%, and 10%. The geometry of the nanodisk is the same as in Figure 1.

interactions with an MD emitter. As a starting point, we take a nanodisk with a height of 150 nm and diameter of 200 nm. To expose the maximum magnetic field strength, a circular hole with a diameter of 10 nm penetrates through the center of the nanodisk (inset of Figure 1a). In Figure 1a, the calculated scattering and absorption cross sections are shown. In the scattering spectrum, a strong Mie-type MD resonance at ∼750 nm and a weaker ED resonance at ∼650 nm are observed. These are the modes typically expected for a high-index dielectric nanoparticle.22,23 At the MD resonance, the nanodisk shows strong enhancement of the magnetic near field, as can be seen in the inset of Figure 1b, which shows the normalized magnetic field intensity in the middle plane of the nanodisk. Unlike the electric field enhancement, which can be concentrated on the nanodisk’s outer surface33 (see also Supporting Information Figure S4e, red dot), the magnetic near-field is mostly confined to the inner volume. The white arrow in the inset of Figure 1b indicates the position of the highest magnetic field enhancement, which coincides with the center of the nanodisk. The spectral response of the normalized intensity at this position in Figure 1b (black curve) shows a pronounced resonance, which coincides with the MD resonance in the scattering cross section in panel a. We see that a magnetic field intensity enhancement factor of up to

doughnut-shaped particle is shown in the inset of Figure 1a. By opening up the center of the resonator, the strongest magnetic field in the silicon particle is exposed and becomes accessible to MD emitters. Similarly shaped nanoparticles have been proposed to control the ED and MD resonance modes35 and enhance MD emission.36 Here, based on numerical calculations, we further systematically study the outstanding enhancement of MD emission and the polarization dependence of this specially designed silicon nanoparticle. The MD resonator interaction is independent of the in-plane excitation polarization and outperforms the enhancement of similar sized solid dimers. Moreover, we demonstrate the importance of the spatial and spectral overlap of the MD emitter with the maximum magnetic field. This study opens new possibilities to maximize MD emission enhancement using dielectric nanoparticles and paves the way toward novel magnetic light− matter manipulations.

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RESULTS AND DISCUSSION Plane-Wave Excitation. We first examine the scattering and absorption properties of the nano-doughnut-shaped silicon disk upon plane-wave excitation. This will reveal its electromagnetic resonances and provide information on its B

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Figure 3. Geometry dependence of the radiative decay rate enhancement. (a) Dependence on the size of the central hole g (fixed diameter D = 200 nm). (b) Dependence on the nanodisk diameter D (fixed hole size g = 10 nm). The height is kept constant at 150 nm. The nanodisk is excited by an in-plane-polarized MD emitter that is positioned at its center.

range. Especially around the MD resonance at ∼750 nm, an extrinsic QE approaching 100% becomes attainable even for an emitter with a low intrinsic QE (e.g., QE enhancement up to a factor of 10 for an emitter with an intrinsic QE of 10%). This can be difficult for plasmonic nanoparticles considering their inevitable high absorption losses and the resulting large nonradiative rate enhancement.6,18,19 In Supporting Information Figure S2 we provide a comparison of the emission properties shown in Figure 2 to two other silicon nanodisk topologies, namely, a solid single nanodisk and a nanodisk dimer. Compared to the nanodoughnut-shaped disk, the solid single nanodisk presents a radiative decay rate enhancement of almost 1 order of magnitude smaller (red curve in Figure S2a). The nanodisk dimer enhancement factor is higher than that for the solid single disk, but still weaker than that of the nano-doughnutshaped disk by a factor of ∼4 (blue curve in Figure S2a). Additionally, the optical response of the nano-doughnut-shaped disk is independent from the in-plane dipolar polarization by virtue of its rotational symmetry. In contrast, for the nanodisk dimer, the MD emission enhancement is highly polarization sensitive, and a decrease of radiation rate enhancement by 1 order of magnitude is possible for the perpendicular dipole orientation.33 To complete the analysis, the interaction with the out-of-plane polarization has been studied as shown in Supporting Information Figure S3. For a plane-wave excited from the side with the incident magnetic field polarized along the z-axis (Figure S3a), the MD resonance is red-shifted to ∼795 nm. Interestingly, the z-polarized MD emitter demonstrates an even larger enhancement of the radiative decay rate up to a factor of ∼355 at the corresponding MD resonance at 795 nm (Figure S3c). Consequently, an orientation-averaged radiative decay rate enhancement of ∼255 is obtained at 750 nm. Compared to a carefully designed plasmonic structure,6 this corresponds to an improvement by a factor of ∼4. Moreover, it could be possible to further optimize the orientation-averaged enhancement factor by engineering the geometry of the nanoparticle, e.g., by making it an ellipsoid and adjusting the aspect ratio. The enhancement of an ED emitter has been investigated as well. The results are shown in Supporting Information Figure S4. For the nano-doughnut-shaped nanodisk, the radiative decay rate enhancement of an ED emitter is lower than 30 (Figure S4a, black curve), more than 1 order of magnitude

∼320 can be supported by the high refractive index silicon resonator. In addition, despite the strong MD resonance, the absorption of the nanodisk remains low for wavelengths above 700 nm (red curve in Figure 1a) due to the vanishing imaginary part of the refractive index of silicon (see Methods). This implies minimal dissipative loss in the interactions with a dipolar emitter. We have also compared the extinction cross sections of the nano-doughnut-shaped disk and a solid nanodisk of the same size (Supporting Information Figure S1a, black and red curves). Due to the high refractive index of silicon, introducing the small hole in the nanodisk results in only a marginal blue shift in the extinction spectrum. The spatial magnetic field distribution also remains mostly unchanged (Figure S1c, black and red dots). However, and most importantly, for the nano-doughnut-shaped disk the maximum magnetic field region has now become accessible to an MD emitter in the open hole region. In contrast, for the solid nanodisk, the maximum accessible enhancement is located at the disk surface and is almost 1 order of magnitude lower (Figure S1b, black and red curves). Dipolar Excitation. Having characterized the magnetic field enhancement upon plane-wave excitation, we are ready to explore the interaction with an MD emitter. We first place an in-plane-polarized MD emitter in the center of the nanodoughnut-shaped disk as indicated in the inset of Figure 2. At this location, the magnetic field intensity reaches its maximum. Figure 2a presents the magnetic dipole’s radiative and nonradiative decay rate enhancement. The radiative decay rate peaks at ∼750 nm with an enhancement factor up to ∼335. This is among the highest reported in the literature.6,33 The spectrum of the radiative rate enhancement perfectly agrees with that of the magnetic field enhancement shown in Figure 1b, evidencing the important role of the MD resonance in the emission enhancement. In other words, this means that in order to maximize the MD emission, it is required that the MD emitter spectrally overlaps with the magnetic resonance of the dielectric nanoparticle. In addition, due to the minimal absorption loss, the nonradiative decay rate approaches zero for wavelengths above 700 nm. Hence, in this spectral range we obtain a strongly enhanced radiative decay rate with minimal nonradiative losses. Furthermore, we calculate the quantum efficiency (QE) enhancement for MD emitters with intrinsic QE of 100%, 50%, and 10%,37 respectively, as shown in Figure 2b. The QE can be strongly enhanced over a broad spectral C

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Figure 4. (a) Radiative decay rate enhancement spectra as a function of the z position of the MD emitter. The geometry of the nanodisk is the same as in Figures 1 and 2. The center of the nanodisk is set as z = 0 nm. Horizontal black dashed line and red dot indicate the MD resonance. (b) Enhancement factor of normalized magnetic field intensity (black squares) and radiative decay rate (red dots). The black curve and black square symbols simulated results using a plane-wave source, while the red curve and red dot symbols are the results simulated using a point MD source. Inset shows the vertical profile of magnetic field intensity at the MD resonance. White dashed line indicates the silicon boundary.

decay rate enhancement on the z position of the MD emitter matches well that of the normalized magnetic field intensity. This again indicates the importance of adapting to the spatial profile of the MD resonance in order to maximize the MD radiations. In Supporting Information Figure S5, we show similar results for an ED emitter, likewise indicating the importance of spatial overlap with the electric field enhancement in order to optimize ED emission. The nano-doughnut-shaped silicon disk constitutes a new platform to strongly enhance MD transitions in natural-iondoped particles such as Eu3+ and Er3+.7,10−12 This dielectric resonator can also be coupled with artificially made metamolecules such as metallic split-ring resonators for novel magnetic field dominated light−matter interactions. Especially with its low-loss resonant behavior in the visible spectral range, it provides exciting possibilities for unprecedented magnetic light control compared to its plasmonic counterparts. In addition, combined with the ability of directional scattering by dielectric antennas,21,38 magnetic signals can efficiently be extracted and detected. It is a promising route to use this type of rationally designed dielectric nanoparticle as a building block for engineering meta-materials to further enhance the coupling to the magnetic field component of light. The unique magnetic responses in these disks can lead to more interesting physical effects and photonic functionalities.

weaker than the MD radiation enhancement. The doughnutshaped disk is therefore better suited to enhance MD emission. Geometric and Spatial Dependence. The size and shape of a dielectric nanoparticle determine the spectral position of its MD resonance, which will further determine its interaction with nearby MD emitters. Next, we demonstrate how the radiation of a local MD emitter can be effectively tuned by engineering the geometry of the nano-doughnut-shaped silicon disk. In Figure 3, the dependence of radiative decay rate enhancement on the central hole size g and the diameter D of the nanodisk is shown. Figure 3a exhibits a spectral blue shift and decrease of the radiative decay rate enhancement with increasing hole size g. The peaks of radiative decay rate enhancement agree well with the MD resonance positions in the scattering spectra (data not shown). It is shown that a relatively small hole size in the nanodisk center does not dramatically change the radiative decay rate enhancement. For example, for the nanodisk diameter of 200 nm and height of 150 nm, a hole size of 20 nm can still offer an enhancement factor of ∼290 (Figure 3a). Such a size has been realized experimentally using electron beam lithography in proof-of-concept studies,27,29,35 and the resulting enhancement factor is still among the highest in the literature.6,33 An even larger hole size of 40 nm produces a reasonable enhancement factor of ∼200. Next, adjusting the diameter D of the disk, while keeping the hole size constant at 10 nm, results in effective tuning of the radiative decay rate enhancement over a very broad spectral range, as shown in Figure 3b. A high enhancement factor larger than ∼200 is maintained, and an even larger enhancement factor of ∼370 is obtained at a diameter of 160 nm. These results indicate an effective method to engineer MD radiation in a controllable manner. Leveraging magnetic resonances to enhance MD radiation also entails the spatial overlap of the MD emitter with the maximum magnetic field. In Figure 4, we demonstrate the radiative decay rate enhancement as a function of MD emitter position in the vertical z-axis. The center of the nanodisk (z = 0 nm) supports the largest magnetic field enhancement (inset of Figure 4b). Consequently, an MD emitter closer to the nanodisk center provides a higher radiative decay rate enhancement (Figure 4a). An enhancement larger than ∼200 requires a position within ∼30 nm from the center. Moreover, as demonstrated in Figure 4b, the dependence of the radiative

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CONCLUSIONS In order to maximize the magnetic dipole emission in alldielectric nanostructures, it is essential to fulfill spectral and spatial overlap of the nanostructure’s MD resonance with the magnetic dipolar emitter. To this end, we have investigated a silicon nanodisk structure that contains an open hole through the center in order to rationally engineer the MD emission. In this way, the region of maximum magnetic field is exposed and becomes available for MD radiation enhancement. A record high radiative decay rate enhancement up to ∼350 times is obtained for an in-plane-polarized MD emitter. When including the out-of-plane polarization, an average enhancement factor of ∼255 is reached. This is a significant improvement over the results obtained for silicon dimers, which are additionally highly dependent on the emitter’s polarization. The radiative decay rate enhancement is only mildly sensitive to the hole size in the nanodisk, which can be practical for experimental realizations. D

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(5) Aigouy, L.; Cazé, A.; Gredin, P.; Mortier, M.; Carminati, R. Mapping and Quantifying Electric and Magnetic Dipole Luminescence at the Nanoscale. Phys. Rev. Lett. 2014, 113, 76101. (6) Mivelle, M.; Grosjean, T.; Burr, G. W.; Fischer, U. C.; GarciaParajo, M. F. Strong Modification of Magnetic Dipole Emission through Diabolo Nanoantennas. ACS Photonics 2015, 2, 1071−1076. (7) Karaveli, S.; Weinstein, A. J.; Zia, R. Direct Modulation of Lanthanide Emission at Sub-Lifetime Scales. Nano Lett. 2013, 13, 2264−2269. (8) Karaveli, S.; Wang, S.; Xiao, G.; Zia, R. Time-Resolved EnergyMomentum Spectroscopy of Electric and Magnetic Dipole Transitions in Cr 3+:MgO. ACS Nano 2013, 7, 7165−7172. (9) Rabouw, F. T.; Prins, P. T.; Norris, D. J. Europium-Doped NaYF 4 Nanocrystals as Probes for the Electric and Magnetic Local Density of Optical States throughout the Visible Spectral Range. Nano Lett. 2016, 16, 7254−7260. (10) Hussain, R.; Kruk, S. S.; Bonner, C. E.; Noginov, M. A.; Staude, I.; Kivshar, Y. S.; Noginova, N.; Neshev, D. N. Enhancing Eû3+ Magnetic Dipole Emission by Resonant Plasmonic Nanostructures. Opt. Lett. 2015, 40, 1659. (11) Karaveli, S.; Zia, R. Spectral Tuning by Selective Enhancement of Electric and Magnetic Dipole Emission. Phys. Rev. Lett. 2011, 106, 193004. (12) Choi, B.; Iwanaga, M.; Sugimoto, Y.; Sakoda, K.; Miyazaki, H. T. Selective Plasmonic Enhancement of Electric- and Magnetic-Dipole Radiations of Er Ions. Nano Lett. 2016, 16, 5191−5196. (13) Lorente-Crespo, M.; Wang, L.; Ortuño, R.; García-Meca, C.; Ekinci, Y.; Martínez, A. Magnetic Hot Spots in Closely Spaced Thick Gold Nanorings. Nano Lett. 2013, 13, 2654−2661. (14) Nazir, A.; Panaro, S.; Proietti Zaccaria, R.; Liberale, C.; De Angelis, F.; Toma, A. Fano Coil-Type Resonance for Magnetic HotSpot Generation. Nano Lett. 2014, 14, 3166−3171. (15) Panaro, S.; Nazir, A.; Proietti Zaccaria, R.; Razzari, L.; Liberale, C.; De Angelis, F.; Toma, A. Plasmonic Moon: A Fano-Like Approach for Squeezing the Magnetic Field in the Infrared. Nano Lett. 2015, 15, 6128−6134. (16) Shafiei, F.; Monticone, F.; Le, K. Q.; Liu, X.-X.; Hartsfield, T.; Alù, A.; Li, X. A Subwavelength Plasmonic Metamolecule Exhibiting Magnetic-Based Optical Fano Resonance. Nat. Nanotechnol. 2013, 8, 95−99. (17) Chen, W. T.; Chen, C. J.; Wu, P. C.; Sun, S.; Zhou, L.; Guo, G.Y.; Hsiao, C. T.; Yang, K.-Y.; Zheludev, N. I.; Tsai, D. P. Optical Magnetic Response in Three-Dimensional Metamaterial of Upright Plasmonic Meta-Molecules. Opt. Express 2011, 19, 12837−12842. (18) Chigrin, D. N.; Kumar, D.; Cuma, D.; Von Plessen, G. Emission Quenching of Magnetic Dipole Transitions near a Metal Nanoparticle. ACS Photonics 2016, 3, 27−34. (19) Feng, T.; Zhou, Y.; Liu, D.; Li, J. Controlling Magnetic Dipole Transition with Magnetic Plasmonic Structures. Opt. Lett. 2011, 36, 2369. (20) Hein, S. M.; Giessen, H. Tailoring Magnetic Dipole Emission with Plasmonic Split-Ring Resonators. Phys. Rev. Lett. 2013, 111, 26803. (21) Li, J.; Verellen, N.; Vercruysse, D.; Bearda, T.; Lagae, L.; Van Dorpe, P. All-Dielectric Antenna Wavelength Router with Bidirectional Scattering of Visible Light. Nano Lett. 2016, 16, 4396−4403. (22) Evlyukhin, A. B.; Novikov, S. M.; Zywietz, U.; Eriksen, R. L.; Reinhardt, C.; Bozhevolnyi, S. I.; Chichkov, B. N. Demonstration of Magnetic Dipole Resonances of Dielectric Nanospheres in the Visible Region. Nano Lett. 2012, 12, 3749−3755. (23) Kuznetsov, A. I.; Miroshnichenko, A. E.; Fu, Y. H.; Zhang, J.; Luk’yanchuk, B. Magnetic Light. Sci. Rep. 2012, 2, 1−6. (24) Bakker, R. M.; Permyakov, D.; Yu, Y. F.; Markovich, D.; Paniagua-Domínguez, R.; Gonzaga, L.; Samusev, A.; Kivshar, Y.; Luk’yanchuk, B.; Kuznetsov, A. I. Magnetic and Electric Hotspots with Silicon Nanodimers. Nano Lett. 2015, 15, 2137−2142. (25) Dhakal, A.; Wuytens, P. C.; Peyskens, F.; Jans, K.; Thomas, N. Le; Baets, R. Nanophotonic Waveguide Enhanced Raman Spectroscopy of Biological Submonolayers. ACS Photonics 2016, 3, 2141−2149.

The MD emission enhancement can also be effectively tuned over a broad spectral range while maintaining a high enhancement factor. Our results open new possibilities for enhancing the radiation of MD emitters and pave the way to innovative magnetic light manipulations.

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METHODS This study is based on the finite-difference time-domain (FDTD) method using the commercial Lumerical FDTD Solutions solver. A nano-doughnut-shaped disk (inset of Figure 1a) made of amorphous silicon is placed in a vacuum. The refractive index of the disk (n and k), shown in Supporting Information Figure S6, is determined from ellipsometry measurements of an amorphous silicon film deposited using plasma-enhanced chemical vapor deposition.21 The particle is excited either with a total-field scattering-field source to calculate the scattering and absorption cross sections upon plane-wave illumination or with a dipole source to calculate the radiative and nonradiative decay rates. Perfectly matched layer absorbing boundary conditions are taken for all six boundaries. A mesh override region with a minimum mesh size of 1 nm is employed in the central disk opening.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.7b00509. Extinction and MD emission comparison between nanodoughnut-shaped nanodisk, solid single nanodisk, and nanodisk dimer; enhancement of out-of-plane-polarized MD emitter; ED emission enhancement; spectral and spatial dependence of ED emission; refractive index of amorphous silicon (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail (J. Li): [email protected]. ORCID

Jiaqi Li: 0000-0003-2021-2310 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.L. gratefully acknowledges the financial support from FWO (Flanders).

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