1

Sub-20 fs All-Optical Switching in a Single Au-Clad

Si Nanodisk

Gustavo Grinblat1*, Rodrigo Berté1,2, Michael P. Nielsen1,3, Yi Li1, Rupert F. Oulton1, Stefan

A. Maier1,4

1The Blackett Laboratory, Department of Physics, Imperial College London, London SW7 2AZ,

United Kingdom

2CAPES Foundation, Ministry of Education of Brazil, Brasília, DF 70040-020, Brazil

3School of Photovoltaic and Renewable Energy Engineering, University of New South Wales,

Sydney NSW 2052, Australia

4Chair in Hybrid Nanosystems, Nanoinstitut Munchen, Fakultät fur Physik, Ludwig-Maximilians-

Universität Munchen, 80539 Munchen, Germany

ABSTRACT. Dielectric nanoantennas have recently emerged as promising elements for nonlinear

and ultrafast nanophotonics due to their ability to concentrate light on the nanometer scale with

low losses, while exhibiting large nonlinear susceptibilities. In this work, we demonstrate that

single Si nanodisks covered with a thin 30-nm thick layer of Au can generate positive and negative

sub-20 fs reflectivity modulations of ⁓0.3% in the vicinity of the first-order anapole mode, when

excited around the second-order anapole mode. The experimental results, characterized in the

visible to near infrared spectral range, suggest that the nonlinear optical Kerr effect is the

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responsible mechanism for the observed all-optical switching phenomena. These findings

represent an important step toward nanoscale ultrafast all-optical signal processing.

KEYWORDS: Dielectric nanoantennas, pump-probe spectroscopy, ultrafast all-optical switching,

optical Kerr effect, anapole modes.

The realization of efficient and compact all-optical information processing devices at the

nanoscale has attracted great attention within the nanophotonics community in recent years, as

they are predicted to overcome the intrinsic speed and heat dissipation limitations of conventional

electronics.1-5 A variety of platforms have been proposed for the required all-optical processing

elements, such as photonic crystal6 and nanowire7 switches, graphene-clad microfiber8 and ring

resonator9 modulators, photonic crystal wavelength-addressable memories,10 and matched

nanoantenna interconnects.11 In essence, all-optical computing and communication require the

possibility of manipulating light with light itself through photon-photon interactions, which can be

mediated by optically modifying a material’s optical properties. In particular, nonlinear optical

effects are expected to be the basis for achieving the fastest performance, as they can reach

response times in the femtosecond range,12 often limited only by optical pulse duration. The third-

order optical Kerr effect (OKE), for example, is a well-known phenomenon that arises from the

nonlinear polarization generated in the material via the response of bound electrons to the

incoming electric field, which modifies the refractive index of the medium. Given that no direct

transfer of carriers into excited states takes place, no time limitation for the excitation or relaxation

processes exist, and hence the effect can occur in an instantaneous manner. However, nonlinear

phenomena are naturally weak and therefore cannot be easily exploited in an efficient way without

long interaction lengths, a significant impediment to nanoscale implementations. In addition,

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slower phenomena such as free-carrier (FC) relaxation, which can extend into the picosecond

range and beyond, can overlap with ultrafast signals hindering the performance of the device.13,14

In this scenario, nanostructured high refractive index dielectrics represent excellent

candidates for enhancing and isolating nonlinear effects within subwavelength volumes, as they

can strongly confine electromagnetic fields and tailor light dispersion,15-19 while presenting high

third-order susceptibilities as predicted by Miller’s rule.20 Indeed, Si and Ge nanoantennas and

metasurfaces have been recently investigated for third-order optical effects such as third harmonic

generation21-25 and four-wave mixing,26 demonstrating enhancement factors of up to five orders of

magnitude with respect to their unstructured counterparts. Moreover, Si metasurfaces have been

studied for ultrafast all-optical switching, showing dips in the transmittance signal of the order of

10-3 with a technique-limited response time of 65 fs.27 When the system is optically pumped and

probed at the magnetic dipole mode, FC contributions are found to be negligible, enabling the

effective use of the ultrafast nonlinear processes. However, this has not yet been attempted with

single dielectric-based nanostructures nor has the technique been extended to shorter, and thus

more broadband, pulses.

In this Letter, we investigate individual Au-covered Si nanodisks through non-degenerate

ultrafast pump-probe spectroscopy measurements in the visible to near infrared range using ~7 fs

FWHM (full width at half maximum) pulses. We find conditions that give rise to reflectivity

modulation values of ±0.3% depending on the wavelength, with sub-20 fs time response and no

appreciable FC background. By changing the disk size, we demonstrate the wavelength tunability

of the ultrafast optical modulation effect. We model the results by considering the OKE and find

very good agreement with the experimental findings.

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Si nanodisks of 180 nm height and diameters (D) ranging from 400 nm to 800 nm were

sputtered on borosilicate glass and patterned through electron beam lithography (refer to

Supporting Information, section 1, for fabrication details). In a second step, a thin 30-nm thick Au

film was evaporated on top of the sample to enhance reflectivity and thermal dissipation, while

still allowing access to the optical response of the inner dielectric component (see sample

schematic in Figure 1a). We note that smaller thicknesses (20 nm and less) of the metallic layer

were found to suffer optical damage under high pump excitation. A center-to-center pitch of 3 m

was chosen to avoid optical coupling between neighboring structures. Subsequently, the linear

optical properties of the nanoantennas were studied. To characterize the scattering cross section,

experimental measurements were carried out via single-particle dark-field spectroscopy, while

numerical simulations were performed using the finite-difference time-domain method for linearly

polarized illumination at normal incidence. For simplicity, we considered no Au coverage at Si

side walls, in consistency with EDS (energy-dispersive X-ray spectroscopy) analysis showing only

small traces of Au there (see Supplementary Information, section 1). (More details about linear

optical measurements and simulations can be found in the Supporting Information, section 2).

Figure 1. (a) Schematic representation of the fabricated Si/Au sample designed for the pump-

probe studies. (b,c) Simulated (b) and experimental (c) scattering cross section spectra for disk

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diameters in the D = 470-710 nm range. (d) Simulated electric field distributions for the Au-

covered Si nanodisk with D = 630 nm at two modes, identified by the highlighted minima in the

scattering spectra in (d). Scale bar, 200 nm. The obtained patterns reveal a second order anapole

mode (SOAM; top image) and first order anapole mode (FOAM; bottom image) character. (e)

Spectral dependence of the electric energy stored inside the dielectric nanodisk for D = 630 nm.

Figure 1b,c shows, respectively, the simulated and experimental scattering cross sections

of the designed nanodisks in the 500-1000 nm wavelength range, demonstrating good

correspondence. The agreement, however, deviates at large nanodisk sizes (630 nm diameter and

greater), probably due to prominent spectral features shifting toward wavelengths where the

measurement has reduced sensitivity (>900 nm), and because the size of the nanoantenna becomes

larger than the collection area in the experiment. Indeed, even though the structures were fully

illuminated using a condenser lens, the collection was diffraction limited, with a collection area of

diameter ⁓ 2λ/(πNA), which equals 637 nm when considering λ = 800 nm (central wavelength in

the experiment) and NA = 0.8 (numerical aperture of the objective used). We note that for the

pump-probe experiments shown next, such an issue was not present, since an objective of lower

numerical aperture (NA = 0.5) was used instead. In particular, in Figure 1b, we notice two relative

minima in the spectra which red shift with increasing diameter size, highlighted with dashed lines

in the graph. We find that they present strong second- and first-order anapole mode character,

respectively from left to right, as evidenced by the corresponding electric field distributions shown

in Figure 1d, computed for D = 630 nm as a representative example.24,28 Consistent with this, the

wavelength dependence of the electric energy stored inside the Si nanodisk ( 𝑊𝐸 =

1

2×∭𝜀(𝑟)|𝐸(𝑟)|

2𝑑𝑉), shows that 𝑊𝐸 is maximum at the anapole modes (see Figure 1e). The

acronyms FOAM and SOAM are used to denote the first and second order anapole modes,

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respectively. It should be mentioned that these modes have been recently reported for Si and Ge

all-dielectric nanodisks and have been exploited for enhanced third-harmonic generation on the

nanoscale.24,28 Therefore, they are predicted to provide strong ultrafast third-order nonlinear

signals.

To evaluate the ultrafast dynamics of the optical response of the fabricated nanoantennas,

a pump-probe spectroscopy technique was set up, as schematized in Figure 2a. Pulses of 180 fs

FWHM at 1120 nm wavelength were used to pump a sapphire plate, producing supercontinuum

light in the 400-1100 nm wavelength range, from which the 610-980 nm spectral components were

selected (see spectrum in Figure 2b). The generated white-light beam was coupled to a MIIPS

(Multiphoton Intrapulse Interference Phase Scan) device, able to compress the wide-spectrum

pulses in time down to bandwidth-limited 4.1 fs pulses, as demonstrated by the interferometric-

FROG (Frequency-Resolved Optical Gating) autocorrelation curve in Figure 2c, measured at the

position of the sample. To perform pump-probe studies, the supercontinuum beam was split into

610-745 nm (pump) and 760-980 nm (probe) components using dichroic beam splitters, giving

rise to ~7 fs non-degenerate pump and probe pulses after re-compression, stretched in time due to

the spectral division, as verified through interferometric-FROG (see Supporting Information,

section S3, for corresponding autocorrelation curves). The pump-probe measurements were

performed using lock-in detection, modulating the pump beam at ~1 kHz with an optical chopper,

and utilizing a delay-line to introduce controlled time differences between pump and probe pulses

with <1 fs accuracy. To characterize the nanoantenna’s response at the various wavelengths

composing the probe spectrum, a monochromator and a Si photodiode were used to analyze the

signal reflected by the sample, which was mounted on a XYZ piezo stage. Since the optical

information was dispersed with a grating only after interaction with the nanoantenna, such a

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process allowed registering the contribution from specific wavelengths without altering the pulse

duration at the position of the sample. The chosen set of light frequencies enabled us to probe the

Si/Au nanoantenna in the first-order anapole mode spectral region, while pumping in the vicinity

of the second-order anapole mode (see Figure 1e and Figure 2b).

Figure 2. (a) Schematic of the experimental setup employed for the pump-probe spectroscopy

measurements. M: Mirror; D-M: D-shape mirror; BS: Beam splitter; D-BS: Dichroic beam

splitter; SLM: Spatial light modulator; L: lens (focal length, 50 mm); R-R: Retroreflector; PD:

Photodiode. (b) Spectrum of the supercontinuum pulses used for the experiment. To perform non-

degenerate pump-probe characterization of the samples, the spectrum was split into two parts as

highlighted in the figure. (c) Interferometric-FROG (i-FROG) trace measured for the full-

spectrum supercontinuum pulses, revealing a ~4-fs pulse width.

Figure 3a-c presents differential reflectivity results measured on single Si/Au nanodisks of

diameters 630 nm (a), 670 nm (b) and 710 nm (c), within the first 80 fs time-period after pump

pulses arrived. In all cases, positive and negative contributions can be observed, which red shift

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with increasing disk size, indicating that they would originate from a nanoantenna’s tunable

resonance. Indeed, it is found that the strongest optical signals, reaching values around 0.5%, occur

in the region of the probed first-order anapole mode. Since this mode highly confines the electric

field inside the nanoantenna, it is particularly sensitive to changes in the sample’s optical properties

produced by the pump. Regarding the nanoantenna’s response in the time domain, the presence of

slow and rapid components can be identified, with changes in sample reflectivity occurring either

within 30 fs or persisting for much longer (experimental data in the picosecond range can be found

in the Supporting Information, section 4). In this context, due to its nearly instantaneous nature

and silicon’s high third-order nonlinearity, the OKE is thought to be responsible for the fastest

contributions, while FC effects would produce the slower response features.27 It should be noted

that measurements performed on a bare Au film showed negligible signal compared to that of the

Au-covered Si nanodisks, indicating that the main response would originate from the dielectric

element. Furthermore, we found that the single Si nanodisk reveals a similar behavior to that of

the Si/Au nanoantenna, but with a lower signal-to-noise ratio and damage threshold due to the

absence of the metal layer (see Supporting Information, section 5, for experimental data on bare

Si disks and Au-film samples). It is important to remark that no plasmonic effect is expected to

have contributed to the observed signal, as these are restricted to surfaces, and the OKE is mainly

a bulk phenomenon. Moreover, no particular signature of plasmonic enhancement is found in the

electric field diagrams in Figure 1d.

To exploit such nanophotonic structures for ultrafast light modulation, a convenient

situation would involve eliminating FC contributions while isolating the OKE response. Due to

the nanoantenna’s capability of tailoring light dispersion, we find that such conditions can be

achieved in specific spectral regions, highlighted with dashed lines in Figure 3a-c, where only fast

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components of either positive or negative sign are present. To numerically reproduce these

contributions, we investigated possible variations in silicon’s refractive index due to the OKE. In

a Kerr medium, the refractive index can be written as n = n0 + n2I, when n = n2I << n0, where n0

is the low-intensity refractive index, I the intensity of the light beam, and n2 the nonlinear

refractive index. Since the value of n2 for the chosen set of wavelengths is unknown, we analyze

possible positive n values that would lead to the measured differential reflectivity signals. Figure

3d-f shows the simulated differential scattering cross section (n+n -n)/n for the 630, 670, and

710 nm diameter Si/Au disks, respectively, considering an arbitrary time axis, and assuming n =

0.005, which implies a reasonable value of n2 = 1.25 × 10-18 m2/W at a pump fluence of 28 J/m2.29-

31 We find that small red shifts of 1.2 nm in the perturbed scattering cross sections around the first-

order anapole mode due to the modified refractive index (see amplified representation in Figure

4a), lead to the behavior measured experimentally with reasonable agreement. The ~60 nm

difference in wavelength position between experiment and calculations are thought to be the

consequence of small imperfections in the fabricated nanostructures as well as the normal

incidence illumination considered in the numerical simulations.

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Figure 3. (a-c) Differential reflectivity spectra as a function of pump-probe delay time for single

Au-covered Si nanodisks of 630 (a), 670 (b), and 710 (c) nm diameters. The dashed lines highlight

regions where only ultrafast sub-30 fs contributions are present. (d-f) Corresponding simulations

of the differential scattering cross section, considering n = 0.005 for the dielectric component

due to OKE, and an arbitrary time axis.

Figure 4. (a) Simulated OKE’s influence on the scattering cross section of a Si/Au nanoantenna

with D = 670 nm near the first-order anapole mode. (b,c) Cross-sections of the data plotted in

Figure 3b along the dashed lines. Solid red lines in the graphs correspond to fits considering the

convolution between the IRF and a Lorentzian function.

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Figure 4b,c shows, as representative examples, the results obtained for the Si/Au nanodisk

of 670 nm diameter at the two selected wavelengths, 820 nm and 875 nm, highlighted in Figure

3b (dashed lines), at which FC contributions are negligible. To fit the experimental data, we

consider the convolution between the instrument response function (IRF) and a Lorentzian profile.

The IRF was modelled as a 11 fs FWHM Gaussian function, based on the obtained convolution

between the pump and probe temporal responses. We find that the positive differential reflectivity

signal exhibits a shorter response time of 8 fs FWHM, compared to the 17-fs negative contribution,

which can be understood from the reduced spectral range of the latter (blue region in Figure 3b),

which broadens its length in time due to Heisenberg’s uncertainty principle. In contrast to the

reported magnetic dipole mode in Si metasurfaces, which shows the capability of ≤65 fs negative

modulations in sample’s transmission,27 this work demonstrates sub-20 fs modulations of

controllable sign at high-order anapole modes of a single nanostructure. It should be noted that the

magnitude of the response could be enhanced significantly by working at wavelengths above 1100

nm, where Si presents higher nonlinear index and lower absorption, allowing higher excitation

powers. A larger quality factor of the resonances, which can be achieved by using metasurfaces,25

would also increase the strength of the signal. However, it is important to mention that increasing

this factor would limit the response time that can be attained, and hence it should be carefully

chosen based on the intended application.

In summary, we have implemented a novel non-degenerate pump-probe technique with

~10 fs resolution to study the dynamics of individual Au-covered Si nanoantennas. Differential

reflectivity measurements showed that the nanosystems exhibit specific spectral regions, around

the first-order anapole mode, at which positive and negative sub-20 fs reflectivity modulations of

⁓0.3% in magnitude can be found with nearly no undesired FC background. Given the high third-

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order susceptibility of Si, we propose the OKE as the mechanism behind the observed ultrafast

phenomena, with the help of numerical simulations. To the best of our knowledge, this

nanostructure represents the fastest all-optical switch that can operate on the nanometer scale.

AUTHOR INFORMATION

Corresponding Author

*Email: g.grinblat@imperial.ac.uk

ASSOCIATED CONTENT

The authors declare no competing financial interest.

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI:

Fabrication of Au-covered Si nanodisks, Linear optical characterization of nanoantennas,

Autocorrelation of pump and probe pulses, Pump-probe spectroscopy in the picosecond range,

Measurements on bare Si nanodisks and Au-film samples (PDF)

ACKNOWLEDGMENTS

The authors acknowledge funding provided by the EPSRC Reactive Plasmonics Programme

(EP/M013812/1), the EPSRC Mathematical Fundamentals of Metamaterials Programme

(EP/L024926/1), ONR Global, and the Lee-Lucas Chair in Physics. G. G. further acknowledges a

Marie Skłodowska-Curie Fellowship. R.B. acknowledges the Capes Foundation for a Science

Without Borders fellowship (Bolsista da Capes - Proc. no BEX 13.298/13-5).

13

REFERENCES

1. Caulfield, H. J.; Dolev, S. Nature Photonics 2010, 4, 261-263.

2. Koenderink, A. F.; Alu, A.; Polman, A. Science 2015, 348, 516-521.

3. Pop, E. Nano Research 2010, 3, 47-169.

4. Engheta, N. Science 2007, 317, 1698-1702.

5. Touch, J.; Cao, Y. W.; Ziyadi, M.; Almaiman, A.; Mohajerin-Ariaei, A.; Willner, A. E.

Nanophotonics 2017, 6, 507-530.

6. Nozaki, K.; Tanabe, T.; Shinya, A.; Matsuo, S.; Sato, T.; Taniyama, H.; Notomi, M. Nature

Photonics 2010, 4, 477-483.

7. Piccione, B.; Cho, C. H.; van Vugt, L. K.; Agarwal, R. Nature Nanotechnology 2012, 7, 640-

645.

8. Li, W.; Chen, B. G.; Meng, C.; Fang, W.; Xiao, Y.; Li, X. Y.; Hu, Z. F.; Xu, Y. X.; Tong, L.

M.; Wang, H. Q.; Liu, W. T.; Bao, J. M.; Shen, Y. R. Nano Letters 2014, 14, 955-959.

9. Almeida, V. R.; Barrios, C. A.; Panepucci, R. R.; Lipson, M. Nature 2004, 431, 1081-1084.

10. Kuramochi, E.; Nozaki, K.; Shinya, A.; Takeda, K.; Sato, T.; Matsuo, S.; Taniyama, H.;

Sumikura, H.; Notomi, M. Nature Photonics 2014, 8, 474-481.

11. Alu, A.; Engheta, N. Physical Review Letters 2010, 104, 213902.

12. Makarov, S. V.; Zalogina, A. S.; Tajik, M.; Zuev, D. A.; Rybin, M. V.; Kuchmizhak, A. A.;

Juodkazis, S.; Kivshar, Y. Laser & Photonics Reviews 2017, 11, 1700108.

13. Doany, F. E.; Grischkowsky, D.; Chi, C. C. Applied Physics Letters 1987, 50, 460-462.

14. Esser, A.; Seibert, K.; Kurz, H.; Parsons, G. N.; Wang, C.; Davidson, B. N.; Lucovsky, G.;

Nemanich, R. J. Physical Review B 1990, 41, 2879-2884.

15. Caldarola, M.; Albella, P.; Cortes, E.; Rahmani, M.; Roschuk, T.; Grinblat, G.; Oulton, R. F.;

Bragas, A. V.; Maier, S. A. Nature Communications 2015, 6, 7915.

14

16. Miroshnichenko, A. E.; Evlyukhin, A. B.; Yu, Y. F.; Bakker, R. M.; Chipouline, A.;

Kuznetsov, A. I.; Luk'yanchuk, B.; Chichkov, B. N.; Kivshar, Y. S. Nature Communications

2015, 6, 8069.

17. Staude, I.; Schilling, J. Nature Photonics 2017, 11, 274-284.

18. Albella, P.; Ameen Poyli, M.; Schmidt, M. K.; Maier, S. A.; Moreno, F.; Jose Saenz, J.;

Aizpurua, J. Journal of Physical Chemistry C 2013, 117, 13573-13584.

19. Cambiasso, J.; Grinblat, G.; Li, Y.; Rakovich, A.; Cortes, E.; Maier, S. A. Nano Letters 2017,

17, 1219-1225.

20. Boyd, R. W., Nonlinear optics. Elsevier: New York, 2003.

21. Shcherbakov, M. R.; Neshev, D. N.; Hopkins, B.; Shorokhov, A. S.; Staude, I.; Melik-

Gaykazyan, E. V.; Decker, M.; Ezhov, A. A.; Miroshnichenko, A. E.; Brener, I.; Fedyanin, A.

A.; Kivshar, Y. S. Nano Letters 2014, 14, 6488-6492.

22. Grinblat, G.; Li, Y.; Nielsen, M. P.; Oulton, R. F.; Maier, S. A. Nano Letters 2016, 16, 4635-

4640.

23. Shibanuma, T.; Grinblat, G.; Albella, P.; Maier, S. A. Nano Letters 2017, 17, 2647-2651.

24. Grinblat, G.; Li, Y.; Nielsen, M. P.; Oulton, R. F.; Maier, S. A. Acs Nano 2017, 11, 953-960.

25. Yang, Y.; Wang, W.; Boulesbaa, A; Kravchenko, I. I.; Briggs, D. P.; Puretzky, A.; Geohegan,

D.; Valentine, J. Nano Lett., 2015, 15, 7388–7393.

26. Grinblat, G.; Li, Y.; Nielsen, M. P.; Oulton, R. F.; Maier, S. A. Acs Photonics 2017, 4, 2144-

2149.

27. Shcherbakov, M. R.; Vabishchevich, P. P.; Shorokhov, A. S.; Chong, K. E.; Choi, D. Y.;

Staude, I.; Miroshnichenko, A. E.; Neshev, D. N.; Fedyanin, A. A.; Kivshar, Y. S. Nano

Letters 2015, 15, 6985-6990.

15

28. Zenin, V. A.; Evlyukhin, A. B.; Novikov, S. M.; Yang, Y.; Malureanu, R.; Lavrinenko, A. V.;

Chichkov, B. N.; Bozhevolnyi, S. I. Nano Letters 2017, 17, 7152-7159.

29. Zhang, L.; Agarwal, A. M.; Kimerling, L. C.; Michel, J. Nanophotonics 2014, 3, 247-268.

30. Shoji, Y.; Ogasawara, T.; Kamei, T.; Sakakibara, Y.; Suda, S.; Kintaka, K.; Kawashima, H.;

Okano, M.; Hasama, T.; Ishikawa, H.; Mori, M. Optics Express 2010, 18, 5668-5673.

31. Narayanan, K.; Preble, S. F. Optics Express 2010, 18, 8998-9005.

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