Third-Order Nonlinear Optical Properties of Colloidal Gold Nanorods

Article pubs.acs.org/JPCC

Third-Order Nonlinear Optical Properties of Colloidal Gold Nanorods Joanna Olesiak-Banska,*,† Marta Gordel,† Radoslaw Kolkowski,†,‡ Katarzyna Matczyszyn,† and Marek Samoc† †

Wroclaw University of Technology, Institute of Physical and Theoretical Chemistry, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland ‡ Laboratoire de Photonique Quantique et Moléculaire, École Normale Supérieure de Cachan, 61, avenue du Président Wilson, 94235 Cachan, France S Supporting Information *

ABSTRACT: We have evaluated the third-order nonlinear optical properties of gold nanorods in water solution in a broad range of wavelengths including both the longitudinal and transverse surface plasmon resonance (SPR) bands. On the basis of the analysis of Z-scan measurements performed with femtosecond laser pulses, we conclude that the optical nonlinearity in the longitudinal-SPR absorption range originates mainly from the saturation of the one-photon absorption, whereas a resonant two-photon absorption process is dominant in the transverse-SPR range of wavelengths. The discrepancies in the values of twophoton absorption coefficients reported by various researchers and the methods of reliable comparison of the results are discussed.

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phenomena as well as nonlinear optical coefficients varying by several orders of magnitude. Photons absorbed in the SPR range excite plasmons, which, after approximately 20 fs, transfer their energy into electron− hole excitations or into photons.5 The nonradiative plasmon decay may result in:20,21 (a) intraband transitions of free electrons within the s−p conduction band, (b) interband transitions between the states of the d valence band and the s− p band, and (c) two-photon absorption at high incident laser intensities. In approximately 450 fs after the absorption, excited electrons equilibrate via electron−electron and electron− surface scattering, and hot Fermi distribution is created. Then, the energy is transferred to the lattice via electron− phonon interactions. After 1 ps, phonon−phonon interactions are dominant, and energy is dissipated to the surroundings. Additional effects take place when NRs are illuminated in the SPR range of wavelengths, with a beam of very high fluence (∼1 mJ/cm2). Strong heating of the sample is observed, and spectral hole burning takes place in the l-SPR band. Illumination with pulses of higher energy transforms the shape of all NRs into spherical and reduces the l-SPR band.14 The ambiguities in determination of NLO parameters of metal nanoparticles originate mostly from differences in the time scales, wavelengths, and ranges of intensities employed, as it is discussed in this article. We concentrate here on quantification of the third-order nonlinear optical properties of NRs illuminated with 130 fs pulses, employing open- and closed-aperture Z-scan technique. The dispersion of the two-

mong all different shapes of gold nanoparticles described in the literature, nanorods (NRs) have gained particular interest due to the characteristic features of their surface plasmon resonances.1,2 In comparison with nanospheres and nanoshells, NRs provide better tunability of surface plasmon resonance (SPR) bands in a wide range of optical frequencies, while the small overall size of the nanoparticle is kept.3,4 The existence of two modes of SPR oscillation, longitudinal (l-SPR) and transverse (t-SPR), introduces additional light polarization and frequency dependences. Moreover, NRs exhibit reduced damping of surface plasmons5 and significant enhancement of the electric field in the vicinity of NR tips. NRs find applications in a variety of fields, from biosensors6 to information recording.7 They are also becoming an increasingly important alternative to molecular labels in linear and nonlinear optical (NLO) microscopy8 and medical therapies.9 The high resolution of NLO microscopy and strong third-order nonlinearities of gold nanoparticles are instrumental for reliable probing and imaging of gold nanoantennas10 and plasmon modes in gold nanostructures.11−13 To control the optical properties and design NRs with specific functionality, a systematic and quantitative description of NR interactions with light is required. Optical properties of gold NRs at low intensity illumination have already been widely investigated, and the dependences of light scattering and absorption of a NR on aspect ratio, size, and end-cap shape have been evaluated.3,14−16 On the other hand, the behavior of NRs under high intensity, short-pulse laser illumination has not been well determined yet. Under such conditions NRs may behave either as saturable absorbers or reverse saturable absorbers, depending on the intensity of excitation.17−19 Researchers have reported various threshold intensity values and provided different interpretations of the observed © XXXX American Chemical Society

Received: February 23, 2012 Revised: May 28, 2012

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dx.doi.org/10.1021/jp301821p | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 1. Stability of NR-756 (a) and NR-845 (b) in Z-scan measurements. Absorption curves of NR-845 before and without Z-scan overlap.

parameters assuming the rod shape and bulk crystal structure of gold, fcc, with a unit cell of a dimension a = 0.408 nm. These calculations were based on the information provided by Sau et al.22 and recent findings of E. Carbó-Argibay et al.24 and Katzboon et al.25 about the crystal structure of NRs synthesized in the seed-mediated procedure, as applied by us. Moreover, according to the work of Zweifel et al., surface modification with Na2S does not influence the crystal structure of a NR.23 The same concentrations were obtained when the density of bulk gold equal to 19 300 mg/mL was applied in calculations. The absorption spectra of solutions were collected with a Perkin-Elmer Lambda 20 spectrophotometer. The concentration of each sample was determined from calibration curves prepared by drying and weighing a series of NR solution volumes (see Supporting Information, Figure S1). Z-Scan Measurements. The Z-scan measurements were performed as described previously, with some modifications.26,27 A Quantronix Integra-C regenerative amplifier operating as a 800 nm pump and a Quantronix-Palitra-FS BIBO crystal-based optical parametric amplifier were used to deliver wavelength tunable pulses of 60 fJ28). The stability of the NRs was investigated before and after the Z-scan B



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Figure 2. Representative Z-scan traces of NR-845: (a) closed-aperture (CA) (red dots); (b, c, d, e, f) open-aperture (OA) (blue dots). Fitting of OA traces (black curves) is performed assuming a negative value of α2 (c, e) or a combination of 2PA and saturation of 1PA (b, d, f).

the solute sum up and the Lorentz local field approximation is valid.31 Measurement on a glass cuvette filled with the solvent (water) needed to be performed to provide the background for the measurements for identical cuvettes with NR solutions.32 Real and imaginary parts of the second hyperpolarizability (γ) of the NRs, Re[γ] and Im[γ], obtained in this way provide a measure of the nonlinear refraction and nonlinear absorption contribution of a single nanoparticle, respectively. Finally, σ2 of a single nanorod was calculated as

experiments. Stabilization of NR-833 and NR-845 by Na2S helped to conserve their shape upon the laser illumination in Zscan and when stored in the dark for the time equivalent to the time of Z-scan experiment (see Figure 1 and Supporting Information Figure S2). As the shape and the concentration of nanorods in NR-756 were changing during the experiment, this sample was excluded from the further analysis. Representative CA and OA Z-scan traces of NR-845 are depicted in Figure 2a,b. The CA traces were similar for all wavelengths, the beam exhibiting defocusing before and focusing after the focal plane, which is characteristic behavior for positive (self-focusing) refractive nonlinearity. For wavelengths in the t-SPR absorption range, a dip in the OA trace at the focus is seen, indicating two-photon absorption (2PA) (Figure 2b). However, for the incident wavelength in the l-SPR band, an increase of transmittance is observed, with a maximum at the focal plane, z = 0 (Figure 2c,d). At higher intensity, a more complicated pattern with a decrease of the transmittance at the focus of the beam superimposed on the broader increase is observed (Figure 2e,f). To quantitatively interpret the collected data, we first analyzed them using the equations derived by Sheik-Bahae et al.29,30 Macroscopic NLO parameters, n2 and α2, of the solutions were obtained from the nonlinear phase shift and the transmittance reduction of light passing through the sample. To extract information about the NLO parameters of the solute, we assumed that the nonlinear contributions of the solvent and

σ2 =

ℏωα2 N

(1)

where N stands for the number of nanoparticles in a unit volume. Proper estimation of N is crucial for the quantitative analysis of the nonlinear optical response. Molar concentration of NR-845 and NR-833 equaled c845 = 0.010 μM and c833 = 0.013 μM, respectively. Full characteristics of our NR solutions together with the analysis of available methods of determination of nanorod concentration in a solution are given in the Supporting Information. The numerical fitting of the experimental curves using equations of Sheik-Bahae et al. provided reasonable results in the case of CA Z-scan traces which were made “absorptionfree” by dividing them by the corresponding OA traces and in the case of OA traces showing well-defined minima, thus likely to be caused by the dominating presence of 2PA. In OA traces at wavelengths within the l-SPR band an increase in OA C



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forbidden due to symmetry reasons and the fact that the initial and final states differ in their momentum. However, in metal nanoparticles this limitation is no longer valid. Due to local field enhancement introduced by plasmon oscillations as well as nonradiative plasmon decay, the electron−hole (e−h) pairs are efficiently created in the sp band. The process corresponds to the 1PA in the l-SPR range of wavelengths, described by σ1 in Figure 3. Under the illumination with the high photon flux, the hole is created below the Fermi level EF by the first photon (denoted with (1) in Figure 3). This empty electron state can be immediately filled by the d band electron excited by the second photon ((2) in Figure 3). Imura et al.12,13 were the first to propose such a sequential 2PA in gold NRs. The whole process is described by σ2 which is related to α2 according to eq 1. Simultaneously, under high-intensity illumination saturation effects can be observed in this system since the intraband 1PA successfully competes with 2PA about the availability of electrons below the Fermi level. As a result of the saturation process, the observed value of α0 is decreased, and we introduce αSA to account for this change. The incorporation of various plausible absorption saturation laws in interpretation of Z-scan results was discussed by Samoc et al.36 In the Supporting Information a simple kinetic rate approach and its modifications are considered. On that basis, we determined the formula describing the one-photon saturable absorption coefficient as

transmittance is seen (Figure 2c−f), which requires the application of negative values of the nonlinear absorption coefficients in the fitting procedure. Negative values of Im[γ], α2, or σ2 were reported in multiple articles concerning the resonantly excited NLO properties of gold nanorods, nanoparticles, or nanoshells17−19,33,34 (Figure 2c,e); however, the physical meaning of those parameters is not obvious. For the sake of comparison with literature data, we nevertheless determined the spectral characteristics of Re[γ], Im[γ], and σ2 using the negative nonlinear absorption coefficients (Supporting Information, Figure S3). The limitations of fitting with negative 2PA coefficients are clearly visible when one attempts to reproduce broad peaks in OA transmittance and curves which show a broad positive peak, with some drop of the transmittance at z = 0. These effects can be attributed to the competition of the saturable absorption (SA) with processes causing additional absorption, including 2PA. In the low-intensity regime, SA in the l-SPR band overwhelms 2PA (Figure 2c,d), whereas under high-intensity illumination reverse saturable absorption (RSA) behavior is observed with the clearly visible dip caused by 2PA (Figure 2e,f). Saturation effects follow different intensity dependence than 2PA, thus they do not cancel each other; however, the broad peak of saturated absorption is decorated with a narrower 2PA-induced drop at the focal point, z = 0. In the literature, there have been suggestions of several models of SA in metal nanoparticles, where 1PA, 2PA, or both of them exhibit saturation under high intensity laser illumination.19,33,35 To provide a consistent quantitative description of the NLO effects in the nanorods investigated by us, we need to take into account at least two of the possible effects: the two-photon absorption and saturation of 1PA. Thus, the one-photon absorption coefficient α0 describing linear absorption in Zscan29 needs to be substituted with saturable 1PA coefficient αSA. The equation concerning the change of the transmitted light intensity with the distance of propagation of the beam in the sample (z) takes the form dI = −αSAI − α2I 2 dz

αSA =

α0 + Δα 1+

I Isat

(3)

−1

τ1−1

where Isat = hνσ1 is the saturation intensity; hν is the photon energy; and τ1 is the lifetime of the excited sp electrons. Following the derivations of αSA presented in the Supporting Information, the Δα = Nd‑spσ1 term is introduced, where Nd‑sp is a concentration of d electrons transferred to the sp band. It reflects the contribution of d band electrons to the one-photon absorption, and it was found necessary to provide fully quantitative agreement of the experimental Z-scans with calculated ones. We estimated the values of Δα from the transmittance in the low-intensity range of each Z-scan measurement. They take the highest value of 7 cm−1 at 700 nm and drop down to zero for λ < 600 nm and λ > 1000 nm. For photon energies higher than E′ (Figure 3) (λ < ∼600 nm), the d band electrons are efficiently excited to the sp band above EF, and thus Δα reduces to 0. This results from the fact that the energy E′ depends on the symmetry point in the first Brillouin zone of gold NRs and corresponds to 650 and 550 nm for the X and L symmetry points, respectively.12 Δα equals 0 also for λ > 1000 nm, due to an insufficient number of holes available for d band electrons below the Fermi level. Note that in many considerations in the literature there is no differentiation between the two interband transitions: d → sp′ and d → sp. In our model the former transition is present for energies higher than E′ and is included in the linear α0, whereas the latter is observed as the additional term Δα induced in NRs under high intensity illumination. Substitution of eq 3 into eq 2 provides the final function, which we applied to fit the Z-scan data. We found that it gave superior numerical fits to the Z-scan data obtained for Au NRs. The obtained values of α2 were recast into values of σ2 presented in Figure 4, along with the contribution from the SA, expressed as the reciprocal of Isat (it should be noted that in the rate equation approach 1/Isat should scale with the one-

(2)

The meaning of the αSA and α2 parameters can be visualized in terms of a simplified band scheme of gold nanorods (Figure 3). Photons which excite longitudinal SPR modes have too low energy to induce interband electron excitation and thus are absorbed in a process of intraband electron excitation within the sp band. Intraband optical transitions are normally

Figure 3. Simplified band scheme of gold NRs. EF is the Fermi level, and E′ is an energy of transition from the top of the d band to EF. σ1 and σ2 are the 1PA and 2PA cross sections for transitions depicted here, respectively. τ1 is the characteristic time for the excited electron thermalization. Nsp′ and Nsp are concentrations of sp-band electrons above and below EF, respectively, and Nd is a concentration of electrons in the d band. D



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Figure 4. 2PA cross sections (empty circles) and the reciprocals of saturation intensities (black squares) of NR-833 (a) and NR-845 (b) calculated with application of eq 3. Black solid and dashed lines are added to guide the eyes. Green areas represent the 1PA spectra of the NRs.

Table 1. Summary of NLO Properties of Gold NRsa reference Measurement method Experimental details Wavelengths [nm] Intensity, I [GW/cm2] Energy per pulse, E [μJ/pulse] Sample morphology Aspect ratio Concentration/ transmittance, T λAbsmax [nm] α2 [cm/GW] (wavelength)

Elim et al.18

De Boni et al.17

Z-scan

Z-scan

220 fs, 1 kHz

15 ps, white light supercontinuum 450−750

800−850

Zijlstra et al.7 luminescence excitation fs, tunable

I = 1 × 1023 photons/s/cm2

ISA = 0.5−7, IRSA > 7

Li et al.19 Z-scan

NR in water

NR in PVA film

3.85 T = 70%

2.2, 2.4

4 single NR

800 −1.5 (800 nm) −1.25 (830 nm) −1.1 (850 nm) Imχ(3) [esu] (at l- −1.2 × 10−12 SPR) ησ2 [GM] σ2 [GM] (at lSPR)

645 −0.7 (520 nm) −2.4 (645 nm)

this work Z-scan

3 ns, 10 Hz

luminescence excitation 200 fs, 77 MHz

800

830

550−1550

I = 0.03 − 0.2

ERSA > 9 NR in water

Wang et al.35

NR in PVA, stretched films 4 v/v conc. = 0.04%

I = 60 − 150 E = 0.001, 15 fJ/NR NR on a glass plate 3

820 −27 (800 nm)isotropic −72.3 (800 nm)|| −3.7 (800 nm)⊥ 3 × 104 3 × 108

130 fs, 1 kHz

E = 0.1 − 0.5 NR in water 3.4 T = ∼70% 833 −0.072 (850 nm)c 0.012 (850 nm)cb

845 −0.023 (850 nm)d 0.005 (850 nm)db

−2.2 × 10−14c

−6.8 × 10−15d

−2.2 × 108 2.1 × 107b (for Isat = 8 GW/cm2) 0.61 × 108b (for Isat = 8 GW/cm2)

−0.9 × 108 0.75 × 107b (for Isat = 8 GW/cm2) 2.65 × 108b (for Isat = 8 GW/cm2)

2320

σ2 [GM] (at tSPR)

ησ2: a two-photon excitation cross-section (luminescence quantum yield multiplied by two-photon absorption cross-section), 1 GM = 10−50 cm4s/ photon. || and ⊥: values measured in the film parallel and perpendicular to the stretching direction, respectively. bValues determined with combination of 2PA and saturation of 1PA, eqs 2 and 3. cValues at the NR concentration 3.79 × 10−4 (w/w). dValues at the NR concentration 3.36 × 10−4 (w/w). a

experiments with nanosecond pulsed lasers as well as absorption measurements conducted with femtosecond pulses at high repetition rates (∼MHz) have to be excluded from the comparison, as their results concern mostly cumulative thermal effects and nonlinear scattering. In the case of pulse duration below 1 ps, the nonthermal regime preceding Fermi−Dirac distribution of electrons contributes strongly to third-order NLO properties, but after 1−5 ps it is negligible.37 Hence, comparison between third-order NLO parameters measured with pulses shorter and those longer than a few picoseconds cannot be reliable. Elimination of contributions from slow processes and thermal effects is vitally important for

photon absorption coefficient; see Supporting Information). The major impact on changes of transmission in the l-SPR band (at ∼850 nm) is found to come from the saturation of 1PA. In this spectral range the SA dominates, but the 2PA absorption cross sections at 850 nm could still be estimated to be equal to σ2 = 2.1 × 107 GM and 7.5 × 106 GM for NR-833 and NR-845, respectively (1 GM = 10−50 cm4 s/photon). The maximum of 2PA is observed in the wavelength range of the tSPR band where σ2 is much higher than at the l-SPR maximum. The differences between NR-833 and NR-845 spectra can be attributed to the differences of the size of the NRs. Table 1 compares the NLO coefficients for Au NRs reported in the literature with those from our investigations. Most of the E



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ACKNOWLEDGMENTS The authors gratefully acknowledge Mateusz Banski for fruitful discussions and comments. This work was supported by the Foundation for Polish Science, Program “Welcome”, the National Science Centre grant no. 352538/I.30, and by a statutory activity subsidy from the Polish Ministry of Science and Higher Education for the Faculty of Chemistry of WUT.

comparisons between the optical nonlinearities of NRs reported in the literature. It should be noted that none of the reports mentioned in the table provide the full, wide wavelength range spectral characterization of the NLO properties of NRs. Such a spectral dependence of NLO properties is essential to recognize the physical phenomena occurring in the NRs. Our 2PA coefficients determined without the implicit consideration of the mechanism of SA are 2 orders of magnitude lower than the ones reported by Elim et al.18 (compare with Supporting Information, Figure S3). However, laser light intensities in their experiments also do not correspond to intensities evaluated in our experiments for similar frequency and laser pulse duration. It needs to be noted that to avoid ambiguities the reliable comparison of macroscopic NLO coefficients should be performed between concentration-independent quantities, such as σ2. We note that the value estimated by Zijlstra et al.7 is in good agreement with our results. One more important issue is the determination of figures of merit, which enable comparison between various disparate NLO materials. Lately, we proposed that scaling of σ2 by the object volume is the most useful for comparison of such different materials like organometallic compounds and nanocrystals.38 The value of this merit factor determined for the tSPR range of gold NR-845 is 92, which is several hundred times higher than those for two-photon absorbing dyes, CdSe quantum dots, and upconverting NaYF4 nanocrystals.27,39 Extremely strong 2PA together with two-photon excited luminescence makes gold NRs important markers in NLO microscopy.

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CONCLUSIONS In conclusion, we determined the first complete spectrum of the 2PA cross-section of colloidal gold NRs (aspect ratio ∼3.4) in the visible and NIR region. The model of 1PA saturation was proposed, and 1PA, 2PA, and saturation effects were evaluated. The saturation of 1PA was found to dominate the changes in the transmittance in the SPR band. α2 and σ2 were calculated, and their highest values were observed at ∼550 nm, within tSPR bands. Results strongly depend on the size of NRs, with larger nonlinearities for bigger NRs (maximum σ2,NR‑833 = 6.1 × 107 GM, σ2,NR‑845 = 2.65 × 108 GM). To further understand the 1PA and 2PA mechanisms and saturation effects in metal NRs, the intensity-dependent changes determined with Z-scan have to be combined with temporal changes of absorption coefficients. Femtosecond pump−probe experiments on gold NR solutions are currently in progress. ASSOCIATED CONTENT

S Supporting Information *

Additional figures, table with sample characteristics, Z-scan interpretation, and kinetic rate equation derivations. 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. F



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Third-Order Nonlinear Optical Properties of Colloidal Gold Nanorods

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