September 15, 2008 / Vol. 33, No. 18 / OPTICS LETTERS 2137

Ultrafast control of grating-assisted light couplingto surface plasmons

Nir Rotenberg,1,* Markus Betz,1,2 and Henry M. van Driel1

1Department of Physics and Institute for Optical Sciences, University of Toronto, 60 St. George Street,Toronto, Ontario, M5S 1A7, Canada

2Current address: Physik-Department E11, Technische Universität, München, 85748 Garching, Germany*Corresponding author: nrotenbe@physics.utoronto.ca

Received June 6, 2008; revised August 11, 2008; accepted August 13, 2008;posted August 18, 2008 (Doc. ID 97022); published September 12, 2008

We demonstrate subpicosecond control over the coupling of free-space radiation to surface-plasmon polari-tons using 830 and 500 nm period gold gratings. Thermal changes to the electron distribution following ir-radiation by 100 fs, 810 nm pulses produce a shift of the 570 nm plasmon resonance by �0.75 nm with re-flectivity change up to 6% and decay time of �1 ps. © 2008 Optical Society of America

OCIS codes: 240.6680, 320.0320.

The controlled coupling of free-space radiation tosurface-plasmon polaritons (SPPs) utilizing texturedmetal films is a key part of nanoplasmonics [1–3].Much attention has been devoted to 2-D texturing,e.g., through subwavelength hole arrays, and signifi-cant changes of the transmission of periodically per-forated metal films at least in the THz domain, havebeen induced by optically pumping a silicon substrate[4]. In this approach the response time is limited bycarrier recombination and thus is incompatible withmodern multi-GHz electronics. 1-D gratings repre-sent the most straightforward implementation of ef-ficient and broadband coupling of light into surface-bound electromagnetic modes [5,6]. Since theperformance of grating couplers is intimately linkedto the geometry of the grating and the incident radia-tion, active control of such couplers, as required formany applications, is intrinsically difficult.

In this Letter we demonstrate a method that couldserve as the basis to actively alter grating-mediatedplasmonic coupling on ultrashort timescales. This ap-proach uses transient changes to the electron distri-bution function induced by 100 fs, 810 nm pumppulses [7–9]. Wood’s anomalies [10] related to lightcoupling into SPP modes are identified for two goldgratings with different periods. Subpicosecond, all-optical switching is observed for probe pulse wave-lengths ranging from 530 to 640 nm, taking advan-tage of the resonant enhancement of the transientdielectric response close to the 530 nm d-band tran-sitions in gold [11]. Observed peak reflectivitychanges of 6% are indicative of a spectral shift of theWood’s anomaly of ���0.75 nm.

The dispersion relation of a SPP mode bound to ametal-dielectric interface is [12]

kSPP = k0� �d�m

�d + �m, �1�

where k0=2� /� is the light wave vector for vacuumwavelength � and �d�m� is the complex dielectric func-tion of the dielectric (metal). The SPP wave vector,kSPP, differs from that of free-space radiation and is

very sensitive to the frequency-dependent dielectric

0146-9592/08/182137-3/$15.00 ©

properties of both the metal and the dielectric. Grat-ings are widely used to overcome this momentummismatch according to

kSPP = k0 sin � + mKG, �2�

where k0 sin � is the in-plane wave vector of incidentTM polarized light with an off-normal angle of inci-dence of �, KG=2� /� is the wave vector associatedwith a grating of period �, and m is an integer. Con-sequently, changes of �m through ultrafast carrierheating modify kSPP along with the conditions neededto induce grating coupling into a SPP mode.

The two gratings (A,B) used in the experimentshave �A�B�=830�500� nm, with grating A having asawtooth profile with blaze angle 29.9°, while gratingB is holographic; both gratings are of �1.2-�m-thickunprotected Au. Time- and spectrally resolved reflec-tivities are measured with 100 fs (FWHM), 810 nmpulses from a 250 kHz Ti:sapphire regenerative am-plifier. A portion of this beam’s power is focused atnear normal incidence to a 200 �m (FWHM) spot ona grating with a peak intensity of 20 GW/cm2. Theremaining portion of the beam is incident on a sap-phire plate to generate a continuum from480 to 700 nm. This is passed through a prism-based4f-pulse shaper [13] to yield �400 fs (FWHM) probepulses with a �5 nm bandwidth. The polarizationstate of the probe light is adjusted with a half-waveplate.

Figure 1 shows the probe differential reflectivity��R /R� for TE- and TM-polarized probe pulses with�=−18° for various probe wavelengths and delaytimes from the pump pulse. The inset to Fig. 1(b)shows unnormalized probe TE and TM reflectivity inzero order in the absence of the pump beam and givesevidence for a SPP resonance near 570 nm character-ized by low reflectivity of TM radiation (Wood’sanomaly). Rotation of the grating yields a shift in theresonance wavelength as expected, while the choiceof the present geometry is mainly related to the spec-tral proximity to the d-band resonance of gold at530 nm [11]. Using the dielectric function of gold [14],

we find the resonance wavelength to correspond to

2008 Optical Society of America

2138 OPTICS LETTERS / Vol. 33, No. 18 / September 15, 2008

m=2 in Eq. (2). The dropping intensity of the reflec-tion spectra around 500 nm arises from two effects:(i) The probe continuum of our experiment has arather sharp cutoff around 480 nm, and (ii) the nor-malized reflectivity of the gold grating slowly de-creases toward shorter wavelengths as expected fromthe dielectric properties of bulk gold. The reflectivityminima for TE and TM light at 650 nm are associ-ated with a Woods–Rayleigh anomaly. The inset toFig. 1(a) illustrates the temporal evolution of �R /Rat �=568 nm for TM and TE polarizations.

For TE polarization [cf. Fig. 1(b)], we identify anondispersive, negative temporal peak of �R /R of�1% consistent with previous findings in untexturedgold films. In contrast, for TM polarization, Fig. 1(a)shows strong dispersive behavior near the 570 nmSPP resonance. A �R /R as large as �6% is observedat 200 fs probe delay. The �R /R associated with cou-pling of TM radiation into SPP modes is opposite insign as compared with the nonresonant TE polariza-tion behavior. The 1 ps decay time observed in the in-set of Fig. 1(a) is consistent with both theoreticalmodeling [7] and experimental observations [9] of thecooling of the electron distribution, while the small,nonzero residual in differential reflectivity at long de-lay times is due to the heating of the lattice by sev-eral degrees.

As seen in Fig. 1(a), the reflectivity changes of the

Fig. 1. (Color online) Differential reflectivity spectra atseveral delay times for ��−18° for grating A for (a) TM po-larization and (b) TE polarization. Inset to (a), differentialreflectivity traces for TE and TM polarizations as a func-tion of time for �=568 nm. Inset to (b), zero-order reflectiv-ity spectra for TE and TM polarizations with the plasmonresonance identified by the arrow.

low (high) wavelength part of the SPP resonance are

positive (negative). This pattern suggests that a reso-nance spectral shift (Fig. 2) dominates the responseowing to the time-dependent changes of the opticalproperties of the grating. To quantify this shift, we fitthe shifted, excited TM reflectivity spectra to theroom-temperature spectra [cf. inset of Fig. 1(b)]; wecheck this by comparing the observed �R /R to spec-tral derivatives of the TM reflectivity spectrum. Anexample of such a fit obtained for 200 fs delay isshown in the inset of Fig. 2 and reproduces the mainexperimental feature. As displayed in the mainpanel, we extract a resonance shift of ���0.75 nm,corresponding to several percent of the resonancewidth. Consistently with �R /R kinetics, the shift isfound to decay in �1 ps.

The basic features discussed above have also beenobserved for grating B. For an angle of �=10° weidentify a SPP resonance at 595 nm. The �R /Rtraces (not shown) are similar to those of grating A(Fig. 1), with a time-dependent dispersive behavior inthe vicinity of the resonance for the TM spectra thatis not present in the TE spectra. However, in contrastto the 570 nm resonance, �R /R is dominated by abroadening, not a shift. Further, the magnitude ofthe peak �R /R is smaller than for grating A, i.e., only�1%. We attribute these differences to the greaterseparation of this plasmonic resonance from thed-band resonance at 530 nm: At 600 nm the ther-mally induced changes to the dielectric function aresmaller by �40% than at 570 nm, and the same spec-tral shift requires stronger optical pumping. To en-sure that this is not a grating-dependent phenomenawe probed a resonance at 600 nm on grating A andobserved the same trends.

Qualitatively, the observations are readily under-stood from the dielectric response of gold upon elec-tron heating. With increasing electron temperature�Te�, the real part of �m��� increases in the spectralrange considered here, which, e.g., leads to the de-

Fig. 2. (Color online) Time-dependent shift of the centralwavelength of the 570 nm resonance. The inset shows thedifferential reflectivity spectra at tD=200 fs (curve withdiamonds) as well as the normalized changes to the zero-order reflectivity spectra [inset of Fig. 1(b)] for the corre-

sponding central wavelength shift of ��=0.75 nm.

September 15, 2008 / Vol. 33, No. 18 / OPTICS LETTERS 2139

creasing reflectivity of the TE polarized light. As a re-sult, kSPP in Eq. (1) is altered and, for the couplingcondition to be maintained, the resonance wave-length shifts. Any spectral broadening is caused bychanges to the lifetime of the SPP mode related to theimaginary part of kSPP [12]. For a quantitative analy-sis we first compute the transient temperaturechanges using the two-temperature model [7] and re-late them to the changes of �m��� of gold using Roseiet al.’s model [11]. Further, the spectral range that weconsider is sufficiently close to the d-band resonancethat the contribution from the thermal electronsdominates over that of the nonthermal electrons [8].For the excitation conditions used above, we expect aTe=600 K in the probed layer, while the lattice re-mains near room temperature [7]. Figure 3 illus-trates the coupling of radiation with frequency � intoSPP modes for the unperturbed as well as thepumped grating. We emphasize that kSPP representsthe momentum of the SPP mode and that negativek0c sin � values arise from coupling conditions thatrequire that the SPP propagate in the counterdirec-tion to the in-plane component of the incident lightfor a resonance with m=2 in Eq. (2). The light disper-sion, shifted 2KG, is found to intersect the room tem-perature SPP dispersion relation at a frequency of3.311015 s−1 �570 nm�, i.e., close to the observedanomaly in Fig. 1. The close-up of this crossing alsocontains the modified SPP dispersion relation forelectron-heated films. For Te=600 K the intersectionof the dispersion relations is shifted by ��=0.90 nm,which is in reasonable agreement with the experi-mental value of 0.75 nm.

Fig. 3. (Color online) Dispersion relation for a thick goldfilm at room temperature (dashed–dotted line) as well asthat for the in-plane component, k0 sin �, of free-space ra-diation needed to couple into a SPP mode at 570 nm forgrating A ��=−18° �. The inset reproduces the regionaround 570 nm as well as the dispersion relation for a goldfilm at the following electron temperatures: 300 K, 600 K,and 1000 K. The calculated wavelength shift of the reso-

nance of �0.90 nm is shown.

Finally, we address possible enhancements andlimitations of the present approach. Femtosecond la-ser pulses can induce transient Te the lattice melt-ing temperature. As seen in Fig. 3 a transient Te=1000 K more than triples the spectral shift of theresonance, and as has been previously shown, Te�10,000 K is achievable [15]. In addition, a SPP at adifferent wavelength might exhibit larger shifts. Thepresent wavelength of �570 nm is associated withlarge positive changes of the real part of �m��� uponheating. In contrast, the low-wavelength side of thed-band resonance in gold exhibits even larger butnegative changes to the dielectric response [11], al-though also the imaginary part of kSPP is large, andthus any resonance broadens. Engineering of thegrating’s surface profile is expected to yield sharperSPP resonances and associated switching effectswhich in comparison with the resonance width arelarger than the present results.

In conclusion, we demonstrate subpicosecond con-trol over SPP coupling at visible wavelengths by op-tically modulating the dielectric function of a goldgrating. At 570 nm peak reflectivity changes of up to6% are observed, corresponding to a 0.75 nm shift ofthe SPP resonance, and are shown to arise from ther-mal effects near the d-band resonance. This type ofultrafast control could play a part in future nanoplas-monic applications.

We gratefully acknowledge financial support fromthe National Sciences and Engineering ResearchCouncil of Canada (NSERC).

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