Capturing the Optical Phase Response of Nanoantennas by Coherent

Letter pubs.acs.org/NanoLett

Capturing the Optical Phase Response of Nanoantennas by Coherent Second-Harmonic Microscopy Nicolò Accanto,† Lukasz Piatkowski,† Jan Renger,† and Niek F. van Hulst*,†,‡ †

ICFO−Institut de Ciences Fotoniques, Mediterranean Technology Park, 08860 Castelldefels Barcelona, Spain ICREAInstitució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain

‡

S Supporting Information *

ABSTRACT: The ultrafast coherent control of light localization in resonant plasmonic nanostructures is intricately related to the phase response of the involved plasmon resonances. In this work, we exploit the second harmonic signal generated by single optical nanoantennas subject to broadband phase-controlled femtosecond pulses to study and tailor the coherent resonance response. Our results reveal that both the spectral phase and the amplitude components associated with the plasmon resonance of arbitrary individual nanoantennas can be accurately determined. KEYWORDS: Nanoantenna, phase control, second harmonic generation, nonlinear microscopy, MIIPS

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therefore the intrinsic plasmon resonance of the nanoantennas could not be measured. In the following, we present a novel, background free, noninvasive and direct determination of the intrinsic phase and amplitude response of single resonant optical nanoantennas that can readily be extended to arbitrary plasmonic structures. The experiment is based on the detection of the second harmonic (SH) spectrum generated by the investigated nanoantennas and builds on a method we have recently developed for controlling ultrafast laser pulses on the nanoscale.29 SH from metal nanoparticles has been detected despite the centrosymmetric nature of these materials4,6,29,30 and mainly attributed to the symmetry breaking occurring at the interfaces of the nanoparticles as well as to volume contributions arising from intensity gradients in particles that are no longer small compared to the SH wavelengths.31,32 In the experiment, we used a broadband titanium sapphire laser (Octavius 85M, Menlo Systems) tuned to a central wavelength of ∼830 nm with a bandwidth of ∼100 nm combined with a liquid crystal-based spatial light modulator (SLM) pulse shaper arranged in a 4f-configuration. The shaped laser pulse was then focused to a diffraction-limited spot with a high numerical aperture objective onto a microscope coverslip containing the plasmonic nanostructures. The excitation polarization was always linear and parallel to the long axis of the nanoantennas, while the total collected SH signal was integrated over all polarization directions. The nanoantennas were typically excited with ∼40 μW laser power. The SH from the sample was collected in reflection through the same

ocalized plasmon resonances in metallic nanostructures, such as optical nanoantennas, provide a means to efficiently confine propagating electromagnetic waves in nanometric volumes.1 Such plasmon resonances are composed of a phase and an amplitude response, both affecting the incident electromagnetic field at resonant wavelengths.2,3 The amplitude component is responsible for the enhancement of the localized electromagnetic field at the nanoantenna, which is of fundamental importance for a broad range of applications such as nonlinear optics,4−7 super resolution imaging,8,9 photovoltaics,10 and so forth. However, it is the phase component that is the crucial parameter for nanoscale coherent control.11−14 Combining plasmonic nanostructures with tailored ultrafast excitation is thus very promising for simultaneously accessing the nanometer and femtosecond regimes, as demonstrated by various experiments.15−26 Ultrafast coherent control of plasmonic nanostructures, however, requires precise knowledge of the intrinsic phase responses associated with the plasmon resonances over the full spectral bandwidth of the excitation pulse. Even though various experimental approaches have been proposed in order to measure such phase responses,17,22,26−28 the experimental determination of the intrinsic spectral phase in arbitrary plasmonic nanostructures remains challenging. Complete resonance response from the nanometer apex of microscopic resonant gold tips was measured.22 Such approach however is limited to the study of microscopic structures and cannot be extended to arbitrary nanostructures. Also, a near-field optical microscope combined with a femtosecond laser pulse was used to measure the plasmon resonances in single nanoantennas.28 In that experiment, the response of the nanoantennas was modified by the proximity of a metallic near-field probe and © XXXX American Chemical Society

Received: April 29, 2014 Revised: June 10, 2014

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Figure 1. (a) Ensemble extinction spectra for different nanoantenna arrays of the indicated length L, and excitation laser spectrum (gray-shaded curve). (For the 450 nm array (blue curve), as a result of a slightly different design resulting in a different geometrical cross section, the extinction curve peaks at shorter wavelengths than the 425 nm array.) (b) SH image of the A1 array obtained by scanning the sample and collecting the spectrally integrated SH signal. The inset shows an SEM image of a single nanoantenna. (c) SH spectra of single nanoantennas from the A1, A2, and A3 arrays together with reference SH spectrum from ITO layer (gray-shaded curve).

dimensional MIIPS traces as those shown in Figure 2a,b. In the experiment, we first measured a reference MIIPS trace on ITO (Figure 2a). A subsequent MIIPS scan on a resonant nanoantenna (Figure 2b) allows us to directly measure the phase and amplitude components of the associated plasmon resonance. The SH spectrum at the frequency 2ω for every δ in a MIIPS can be written as33

objective and sent either to a spectrometer equipped with an electron-multiplying charge-coupled device (CCD) camera or to an avalanche photodiode (APD) that allowed confocal optical imaging of the sample. The nanoantennas were made of silver (Ag) using electron beam lithography on a glass coverslip coated with a 10 nm thin layer of indium tin oxide (ITO). The antenna resonance was tuned to overlap with different parts of the excitation laser spectrum by changing the dimensions of the nanoantennas, as confirmed by ensemble extinction measurements at nanoantenna arrays (see Figure 1a). In the following, we will show results on single nanoantennas of increasing resonant wavelength, belonging to the antenna arrays labeled A1, A2, and A3 in Figure 1a. Figure 1b shows an SH image acquired from the A1 array. SH emitted by individual optical nanoantennas is resolved. Increasing the incident power from 40 μW to 10 mW, allows detecting SH emission from the thin ITO layer on which the nanoantennas were deposited. We have used SH from ITO as a reference signal. In Figure 1c, we show SH spectra from single nanoantennas belonging to A1, A2, and A3 arrays excited with Fourier limited pulses, along with the reference SH spectrum of ITO (gray-shaded curve). The SH spectra from single nanoantennas exhibit a spectral shift from shorter (blue) to longer wavelengths (red) going from the A1 to the A3 array, closely following the trend observed in the ensemble extinction spectra. Next, to unveil the phase information in our experiments, we consider the coherent SH response in detail. Let the incident electric field be EL(ω) = E0(ω)eiφ0(ω). For an optimized Fourier limited pulse, as the one used in the experiment, the phase φ0(ω) is close to zero across the full laser spectral range. When this field is focused on a resonant nanoantenna, the effect of the phase φA(ω) and amplitude A(ω) response of the plasmon resonance leads to a new effective field EA(ω) = E0(ω)A(ω)ei[φ0(ω) + φA(ω)]. In order to measure the intrinsic resonance response of the nanoantennas, we performed multiphoton intrapulse interference phase scan (MIIPS) experiments28−31 using the SH emitted by the nanoantennas. During a MIIPS scan a set of known sinusoidal phases φSLM(ω,δ) = α sin(γω − δ) is imposed onto to the laser field by the SLM as a function of the phase offset δ varying from 0 to 2π, and the corresponding SH spectra are measured for every δ phase offset. This allows constructing two-

SH(2ω , δ) ∝|

∫ |F0(ω + Ω)||F0(ω − Ω)|*e{i[φ(ω+Ω,δ)+φ(ω−Ω,δ)]}dΩ|2 (1)

where F0(ω) = E0(ω)A(ω) and φ(ω,δ) = φ0(ω) + φSLM(ω,δ) + φA(ω) for a resonant nanoantenna, while F0(ω) = E0(ω) and φ(ω,δ) = φ0(ω) + φSLM(ω,δ) in the case of the reference ITO. The integral ∫ dΩ runs over the excitation laser frequency band. Equation 1 does not include possible resonances in the SH range, as no major contribution is expected there. First, the nanoantennas were designed to be resonant at the fundamental frequency range of the excitation laser, and no major resonance occurs in the SH range. Second, the SH frequencies are still low enough not to overlap with the region of interband transitions in silver that arise at wavelengths below 350 nm.34 As for ITO, no resonance occurs either in the SH or in the fundamental range,35 which allows one to neglect the intrinsic response of the material in eq 1. The points of maximum SH intensity in a MIIPS trace of a Fourier limited pulse lie in the ω,δ plane on two straight parallel lines separated by π-radians.33,36,37 Moreover, for Fourier limited pulses the first [0 < δ < π] and the second [π < δ < 2π] phase interval of a MIIPS trace are fully equivalent to each other. The reference MIIPS trace from the ITO shown in Figure 2a illustrates this behavior. The minor differences between the first and the second phase interval in the MIIPS trace result from small deviation from a perfectly Fourier limited pulse, that is, from a residual nonzero φ0(ω). The MIIPS trace measured subsequently on the A3 nanoantenna (Figure 2b) differs significantly from the reference trace, and the difference stems from the antenna resonance response. First, the trace is spectrally shifted toward longer wavelengths (vertically upshifted), which is consistent with the spectral shift of the SH spectra shown in Figure 1c. Second, the first and the second period of the trace differ from each other with the two B

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Figure 2. SH-spectrum as a function of phase offset (MIIPS trace) measured (a) on the reference ITO (average laser power 10 mW) and (b) on a single nanoantenna from the A3 array (average laser power 40 μW). (c) Difference of the experimental MIIPS traces shown in (b) and (a). (d) Difference of the fitted MIIPS traces for the A3 nanoantenna and ITO.

unknown plasmon resonance. In Figure 2d, we report the difference between the fitted MIIPS traces of the nanoantenna and the reference using the polynomial model. A very good agreement with the experimental data of Figure 2c is found. The spectral amplitude and phase resulting from the polynomial fit are presented in Figure 3a. The black solid line represents the effective spectrum that includes the amplitude component of the resonance, that is, SAntenna(ω) = |E0(ω)A(ω)|2, whereas the black-dashed line corresponds to the excitation laser spectrum SLaser(ω) = |E0(ω)|2. A comparison between SLaser and SAntenna clearly indicates how the amplitude component of the plasmon resonance (in this case belonging to the A3 antenna) enhances the red part of the excitation spectrum. Here we note that SAntenna(ω) does not represent the emission spectrum from the nanoantenna but rather how the amplitude response of the nanoantenna has modified the excitation laser spectrum SLaser(ω), as retrieved from an analysis of the SH generated at the nanoantenna. The retrieved antenna phase φA(ω) is plotted with a solid red line, whereas the dashed red line represents the reference phase φ0(ω). Interestingly, the phase of the antenna follows the reference phase in the short wavelength side of the spectrum (λ < 820 nm), while it deviates significantly toward longer wavelengths (λ > 820 nm). It is thus evident that the nanoantenna introduces a nontrivial phase in the spectral region of the plasmon resonance. The measured phase response has a simple interpretation in the time domain if one takes into account that a phase slope in the frequency domain corresponds to a delay in the time domain. The initial Fourier limited pulse (φ0(ω) ≅ 0) gets dispersed when interacting with a plasmon resonance, that is, it becomes longer than the Fourier limit. In particular, the long wavelength side of the incident field experiences a time delay with respect to the

lines of the maximum SH intensity lying closer to each other, and a considerable amount of the SH intensity being localized in between these two trails (horizontal asymmetry). These distinct differences are highlighted in Figure 2c where the difference between the nanoantenna and the reference ITO MIIPS traces is plotted. The red features indicate a spectral region where the SH signal from the nanoantenna signal is stronger than the SH signal from ITO (longer wavelengths), while the blue features indicate spectral range where the signal from ITO is higher. The difference between the first and the second periods is clearly visible as a tilt of the red features with respect to the blue ones, that is, the red features point toward the inside, while the blue ones point toward the outside of the trace as indicated by the dashed (red and blue) lines in Figure 2c. As eq 1 describes the MIIPS traces, by performing a twodimensional fit of the two MIIPS traces for reference and antennas, we can determine the phase φ0(ω) for the reference, which represents the small deviations from Fourier limited pulses, and the spectral phase φA(ω) and amplitude response A(ω) for the antenna. For the reference, the term F0(ω) = E0(ω) is known from the measurement of the excitation spectrum SLaser(ω) = |E0(ω)|2, while the small residual laser phase φ0(ω) was fitted with a sixth order polynomial function. The retrieved residual spectral phase φ0(ω) was then used in the fit of the nanoantenna trace, where sixth order polynomial functions were assumed for both the amplitude response A(ω) and the intrinsic antenna phase φ0(ω); we will therefore refer to this model as polynomial model. The choice of polynomial functions is particularly convenient in this context, as it does not need any assumption on the specific shape of the antenna resonance, that is, it could be used as a starting model to fit any C

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analyze the response of a single nanoantenna with such analytical model, verify whether our antenna response is compatible with a Lorentzian approximation, and thus deduce the linear terms in the phase expansion. We performed a twodimensional fit of the nanoantenna MIIPS trace of Figure 2b, this time based on a Lorentzian model, that is, assuming for the effective field localized at the nanoantenna the form EA(ω) = E0(ω)L(ω)ei[φ0(ω) + φL(ω)] where L(ω) ∝ [1/((ω − ω0)2 + Δ2)]1/2 and φL(ω) = tan−1 [(ω − ω0)/Δ] with ω0 = 2πc/λ0 central position of the resonance and Δ half width at halfmaximum (hwhm). The amplitude and phase terms in eq 1 therefore become F0(ω) = E0(ω)L(ω) and φ(ω,δ) = φ0(ω) + φSLM(ω,δ) + φL(ω). The results of the Lorentzian fit are displayed in Figure 3b, where the effective antenna spectrum | E0(ω)L(ω)|2 and the spectral phase φL(ω) are plotted. From the fit, we find the central position λ0 = 852 nm and hwhm = 28 nm for the plasmon resonance. It is apparent from Figure 3b that the amplitude response in the case of the polynomial model and the Lorentzian model yields very similar results. However, in the Lorentzian model, φ(0) and φ(1) in the Taylor expansion for the phase response around ω̃ are in general nonvanishing. The observed difference between the phases retrieved with the polynomial and the Lorentzian fit result from the linear phase components φ(0) and φ(1), which play no role in the description of the antenna effect on the electric field. We verify this by adding a nonzero φ(0) and φ(1) to the phase previously retrieved using the polynomial fit. The resulting phase is plotted with a red-dashed line in Figure 3b. Indeed, the antenna spectral phases obtained from both models are in very good agreement. This demonstrates that the two models are completely equivalent to each other and further justifies the use of the polynomial model as a general fit model that could be used to analyze any unknown response from arbitrary resonant nanostructures. The robustness and versatility of the method is confirmed by the measurements we performed on nanoantennas of different lengths belonging to the arrays A1, A2, and A3. In Figure 4, we report differential MIIPS traces (a−c) along with the fit results (d) for these antennas using the Lorentzian model, as our antennas can be well described with this model. As expected, the resonances shift from the blue to the red side of the laser spectrum going from the A1 to the A3 array, following the trend of the extinction measurements shown in Figure 1a. Moreover, the asymmetry between the first and second period of the MIIPS traces, which is evidence of the phase response, is apparent for all three antennas, as highlighted by the dashed arrows. It should be noticed that the tilt of the blue features

Figure 3. (a) Spectral phase and effective spectrum for the antenna φA(ω), SAntenna(ω), and reference φ0(ω) resulting from a fit of the MIIPS traces (Figure 2a,b) using a polynomial model. (b) Fit results of the MIIPS trace in Figure 2b using a Lorentzian model. The blue solid line is the phase obtained from a Lorentzian fit of the data, while the red-dashed line represents the phase obtained from the polynomial fit including the terms φ(0) and φ(1) (see text).

short wavelength side, which is due to the presence of the plasmon resonance. In order to understand the nature of the measured intrinsic antenna phase φA(ω) we expand the phase function in a Taylor series around the frequency ω̃ , representing the center of gravity of the laser spectrum: φA(ω) = φ(0) + φ(1)(ω − ω̃ ) + φ(2)(ω − ω̃ )2 + .... It is important to note that the first two terms in the expansion, that is φ(0) and φ(1), play no role in describing the effect of the nanoantenna on the measured MIIPS traces. The zero order term φ(0) represents a shift of the relative position of the carrier wave in the pulse with respect to the pulse envelope. This term for a multicycle pulse, as the one used in the experiment, has negligible importance. The first order term φ(1) on the other hand, sets the absolute time at which the pulse arrives, which plays no role in the detection of SH. Thus, the linear phase terms have no effect on the MIIPS method, as on most pulse diagnostic methods. In contrast, MIIPS is exclusively sensitive, as our experiment demonstrates, to the nonlinear phase terms, which carry all the physical information. Our experimental results, together with the totally unconstrained model we used for the fits, demonstrate our ability to measure nonlinear phases and amplitude responses of arbitrary resonant plasmonic structures. Localized surface plasmons excited by an electric field are often approximated as damped harmonic oscillators.2,3,38 In this approximation, plasmon resonances assume the form of complex Lorentzian functions that can be decomposed in amplitude and phase components.17,22 We can therefore

Figure 4. (a−c) Differences of the antenna MIIPS traces with the reference measured for three different single nanoantennas belonging to the A1, A2, and A3 antenna arrays, respectively (average laser power 60, 20, and 40 μW). (d) Intensity |L(ω)|2 and phase response φL(ω) for the three nanoantennas. D

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(12) Brixner, T.; Garcia de Abajo, F. J.; Schneider, J.; Pfeiffer, W. Phys. Rev. Lett. 2005, 95, 093901. (13) Huang, J. S.; Voronine, D. V.; Tuchscherer, P.; Brixner, T.; Hecht, B. Phys. Rev. B 2009, 79, 195441. (14) Leveque, G.; Martin, O. J. Phys. Rev. Lett. 2008, 100, 117402. (15) Aeschlimann, M.; Bauer, M.; Bayer, D.; Brixner, T.; García de Abajo, F. J.; Pfeiffer, W.; Rohmer, M.; Spindler, C.; Steeb, F. Nature 2007, 446, 301−4. (16) Aeschlimann, M.; Bauer, M.; Bayer, D.; Brixner, T.; Cunovic, S.; Dimler, F.; Fischer, A.; Pfeiffer, W.; Rohmer, M.; Schneider, C.; Steeb, F.; Struber, C.; Voronine, D. V. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 5329−33. (17) Brinks, D.; Castro-Lopez, M.; Hildner, R.; van Hulst, N. F. Proc. Natl. Acad. Sci. U.S.A. 2013, 110, 18386−90. (18) Hanke, T.; Krauss, G.; Trautlein, D.; Wild, B.; Bratschitsch, R.; Leitenstorfer, A. Phys. Rev. Lett. 2009, 103, 257404. (19) Hanke, T.; Cesar, J.; Knittel, V.; Trugler, A.; Hohenester, U.; Leitenstorfer, A.; Bratschitsch, R. Nano Lett. 2012, 12, 992−6. (20) Aeschlimann, M.; Brixner, T.; Fischer, A.; Kramer, C.; Melchior, P.; Pfeiffer, W.; Schneider, C.; Strüber, C.; Tuchscherer, P.; Voronine, D. V. Science 2011, 333, 1723−26. (21) Kubo, A.; Onda, K.; Petek, H.; Sun, Z.; Jung, Y. S.; Kim, H. K. Nano Lett. 2005, 5, 1123−7. (22) Anderson, A.; Deryckx, K. S.; Xu, X. G.; Steinmeyer, G. n.; Raschke, M. B. Nano Lett. 2010, 10, 2519−24. (23) Schmidt, S.; Piglosiewicz, B.; Sadiq, D.; Shirdel, J.; Lee, J. S.; Vasa, P.; Park, N.; Kim, D. S.; Lienau, C. ACS Nano 2012, 6, 6040−8. (24) Berweger, S.; Atkin, J. M.; Xu, X. G.; Olmon, R. L.; Raschke, M. B. Nano Lett. 2011, 11, 4309−13. (25) Gunn, J. M.; Ewald, M.; Dantus, M. Nano Lett. 2006, 6, 2804−9. (26) Gunn, J. M.; High, S. H.; Lozovoy, V. V.; Dantus, M. J. Phys. Chem. C 2010, 114, 12375−81. (27) Schnell, M.; Garcia-Etxarri, A.; Huber, A. J.; Crozier, K. B.; Borisov, A.; Aizpurua, J.; Hillenbrand, R. J. Phys. Chem. C 2010, 114, 7341−5. (28) Onishi, S.; Matsuishi, K.; Oi, J.; Harada, T.; Kusaba, M.; Hirosawa, K.; Kannari, F. Opt. Express 2013, 21, 26631−41. (29) Accanto, N.; Nieder, J. B.; Piatkowski, L.; Castro-Lopez, M.; Pastorelli, F.; Brinks, D.; van Hulst, N. F. Light Sci. Appl. 2014, 3, e143. (30) Jin, R.; Jureller, J. E.; Kim, H. Y.; Scherer, N. F. J. Am. Chem. Soc. 2005, 127, 12482−3. (31) Bachelier, G.; Butet, J. R. M.; Russier-Antoine, I.; Jonin, C.; Benichou, E.; Brevet, P. F. Phys. Rev. B 2010, 82, 235403. (32) Reichenbach, P.; Eng, L. M.; Georgi, U.; Voit, B. J. Laser Appl. 2012, 24, 042005. (33) Xu, B.; Gunn, J. M.; Cruz, J. M. D.; Lozovoy, V. V.; Dantus, M. J. Opt. Soc. Am. B 2006, 23, 750−9. (34) Johnson, P. B.; Christy, R. W. Phys. Rev. B 1972, 6, 4370−9. (35) Kim, H.; Gilmore, C. M.; Piqué, A.; Horwitz, J. S.; Mattoussi, H.; Murata, H.; Kafafi, Z. H.; Chrisey, D. B. J. Appl. Phys. 1999, 86, 6451−61. (36) Coello, Y.; Lozovoy, V. V.; Gunaratne, T. C.; Xu, B. W.; Borukhovich, I.; Tseng, C. H.; Weinacht, T.; Dantus, M. J. Opt. Soc. Am. B 2008, 25, A140−50. (37) Lozovoy, V. V.; Pastirk, I.; Dantus, M. Opt. Lett. 2004, 29, 775− 7. (38) Zuloaga, J.; Nordlander, P. Nano Lett. 2011, 11, 1280−3.

with respect to the red ones, changes sign as the resonance position changes from the lower (A1 antenna) to the higher wavelength side (A2 and A3 antennas). In summary, we have shown that by detecting the SH generated by single plasmonic nanoantennas subject to phasecontrolled broadband pulses it is possible to retrieve the intrinsic phase and amplitude responses of the nanoantennas. The generality of the method described here will allow the study of any arbitrarily shaped, more complex plasmonic nanostructures, as the amplitude and phase responses are directly encoded in the SH signals. Moreover, the results we have presented clearly demonstrate that a single nanoantenna intrinsically acts as a nanometer-sized pulse shaper for both the amplitude and the phase of the incident electric field. This, together with the versatility of the fabrication processes, could be exploited to design specific nanostructures that can shape incident laser pulses in the desired way and in a nanometersized area, therewith facilitating coherent control by plasmonic nanostructures.

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ASSOCIATED CONTENT

S Supporting Information *

Details on the nanoantennas invesigated, SEM images of the samples, and MIIPS scans on different nanoantennas. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was funded by the European Union (ERC Advanced Grant 247330 - NanoAntennas) and the MICINN (program Consolider Ingenio-2010: CSD2007-046-NanoLight.es). L.P. acknowledges financial support from the Marie-Curie International Fellowship COFUND and ICFOnest program. We thank Dmitry Pestov (Biophotonics Solutions) for helpful discussions on the MIIPS technique.

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REFERENCES

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