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Ultrafast dephasing time of localized surface plasmon polariton resonance and the involved damping mechanisms in colloidal gold nanoparticles
Progress in Surface Science 82 (2007) 378–387 www.elsevier.com/locate/progsurf
Review
Ultrafast dephasing time of localized surface plasmon polariton resonance and the involved damping mechanisms in colloidal gold nanoparticles Frank Hubenthal
*
Universita¨t Kassel, Institut fu¨r Physik and Center for Interdisciplinary Science and Technology – CINSaT, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
Abstract In this contribution, for the first time precise in situ measurements of the ultrafast dephasing time T2 of localized surface plasmon polariton resonances in colloidal gold nanoparticles with the objective to identify the involved damping mechanisms are presented. T2 is an essential parameter that does not only allow one to determine the field enhancement factor that is of great importance for many applications of nanoparticles, but also reflects the role of different dephasing mechanisms. The most essential result is the observation of a chemical interface damping which causes a dramatic shortening of the dephasing time. While T21 = 9.4 fs can be obtained from the bulk dielectric function, the value shrinks to 3.7 fs if the nanoparticles are in aqueous solution. Ó 2007 Elsevier Ltd. All rights reserved. PACS: 78.67.Bf; 61.46.+w; 71.75.Gm; 68.43.h Keywords: Dephasing time; Surface plasmons; Gold; Nanoparticles
Contents 1. 2.
*
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
Tel.: +49 561 804 4501. E-mail address: [email protected]
0079-6816/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.progsurf.2007.03.005
F. Hubenthal / Progress in Surface Science 82 (2007) 378–387
3. 4. 5.
2.1. Preparation of colloidal gold nanoparticles . . . . . . . . . . . . . . . . . . . . . . 2.2. Persistent spectral hole burning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
379
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380 382 383 384 385 386 386
1. Introduction The optical properties of noble and alkali metal nanoparticles are dominated by localized surface plasmon polariton (LSPP) resonances. Contrary to bulk materials LSPP resonances can be excited in nanoparticles by an electromagnetic light field and distinct resonances in the optical spectra appear. In recent years, the dephasing time of the LSPP resonance T2, i.e. the time during which the excited electrons loose their phase coherence, has gained a lot of interest [1–16]. One reason is that T2 is directly connected to the local field enhancement which results in a drastic increase of the electric field in the vicinity of the nanoparticle surface as compared to the incoming electric field [17,18]. The field enhancement can be exploited in a lot of applications, such as surface enhanced Raman spectroscopy [19–22], surface enhanced fluorescence [23–25], confocal microscopy [26], or all-optical switching devices [27–29]. Most importantly, T2 connected to the homogeh neous line width Chom of the LSPP resonances via T 2 ¼ C2 is interesting by itself, because hom the damping mechanisms of the collective excitation are still an open question. To clarify the role of the different damping mechanisms in small colloidal gold nanoparticles, systematic measurements of T2 are urgently needed. As known [30,31], only surface scattering of electrons or Landau-damping,1 chemical interface damping, and electron–electron scattering play a role for such nanoparticles with reduced dimensions. However, electron–electron scattering can be ruled out, because this happens only for very small metal nanoparticles excited with intense femtosecond pulsed laser light [34,35] which has been not used in the experiments presented here. The main obstacle for measurements of T2 is the inhomogeneous broadening of the LSPP resonances that is due to broad size and shape distributions of the nanoparticle ensembles. Although some in situ measurements of the dephasing time of colloidal gold nanoparticles have been presented in the literature [36–39], T2 was always determined from an inhomogeneously broadened ensemble of nanoparticles. Due to the broadening which results from a shape distribution and different crystalline structures, the homogeneous line width cannot be obtained and thus, the presented dephasing times are not exact, i.e. they are to short. There are several methods to overcome the inhomogeneous broadening, e.g. spectroscopy of single particles [5,9,40–42] or generation of nanoparticles with
1
In quantum mechanical calculations surface scattering is included in the Landau-damping [32], while in semiclassical calculations the surface scattering is inserted as an additional factor in the theory and an increased Landau-damping is not taken into account [33]. In general, both damping mechanisms cannot be treated independently.
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extremely narrow size and shape distributions by electron beam lithography [7,8,11,43]. While the latter method is limited at present to particles larger than about 20 nm [10], the first method, spectroscopy of single nanoparticles, suffers from the fact that during the ex situ measurements the nanoparticles are exposed to different chemical environments [5,44,45] which may influence the measurements. Thus, different damping mechanisms cannot be distinguished. Hence, in the size range from 1 nm to 20 nm, where one expects a pronounced influence of shape, size, and chemical surrounding, information on the dephasing time and the involved damping mechanisms is still lacking. In this article I present for the first time precise in situ measurements of the dephasing time of the localized surface plasmon polariton excitation in colloidal gold nanoparticles in solution. For this purpose, the well established method of persistent spectral hole burning [1,46,47] has been applied using a photon energy of 2.05 eV. The main scope of this paper is to investigate which damping mechanisms play a role in colloidal gold nanoparticles with reduced dimensions. 2. Experimental 2.1. Preparation of colloidal gold nanoparticles The colloidal gold nanoparticles were produced using the method of Turkevich [48]. Briefly, 10 mg of HAuCl4 Æ 3H2O was dissolved in 95 ml bi-distilled water and heated to the boiling point. In the boiling solution, 5 ml aqueous solution of tri-sodium citrate (10 g/l) were added under permanent mechanical agitation. No additional stabilizers have been added to the solution. After about 15 s the clear solution suddenly turned to winered-color, indicating the formation of Au-nanoparticles. Subsequently, the solution was allowed to cool down to room temperature. The concentration of the nanoparticle solution was chosen so that no electromagnetic coupling is expected and agglomeration has been not observed within two weeks. The colloidal nanoparticles were mainly characterized by transmission electron microscope (TEM) measurements (Zeiss/LEO, EM 109 T). Additional in situ optical spectroscopy, recorded with the light of a Xe-arc lamp (Osram, XBO 450 W/1) in combination with a monochromator (Amko, 1200 lines/mm, blaze: 220 nm), combined with theoretical modelling using the T-Matrix method [49] and the bulk dielectric function of gold [50], have been applied to characterize the nanoparticles in solution. The experimental set up allows to obtain optical spectra in transmission. Thus, the extinction, i.e. the sum of absorption and scattering, of the nanoparticle ensemble was measured with respect to a reference spectrum without nanoparticles. Fig. 1 depicts a typical TEM image of the prepared colloidal gold nanoparticles. The image shows that mainly elongated polycrystalline polyheadrons which can be roughly approximated as rotational ellipsoids, with different shapes and sizes have been synthesized. Each particle is characterized by its equivalent radius Req, i.e. the radius of a sphere with the same volume as the actual non-spherical particle and by the axial ratio a/b, a being the short and b being the long axis of the rotational ellipsoid. The mean equivalent radius of the nanoparticles was determined by analyzing a set of TEM images to hReqi = (17 ± 2) nm. It is worth to note that the nanoparticles in solution are not agglomerated. The agglomeration which can be seen in Fig. 1 is caused by the drying process.
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Fig. 1. Typical TEM image of colloidal gold nanoparticles. Most of the particles exhibit shapes that can be roughly approximated as rotational ellipsoids with different axial ratios which cause an inhomogeneous broadening of the optical spectrum and deliver the precondition for persistent spectral hole burning. The mean radius of the particles has been determined to hReqi = (17 ± 2) nm.
Fig. 2. An extinction spectrum of the prepared colloidal gold nanoparticles and a calculated spectrum is displayed. A clear inhomogeneous broadening of the measured spectrum is observed.
Fig. 2 depicts the corresponding optical spectrum of the colloidal gold nanoparticles and, for comparison, a spectrum2 calculated with the T-Matrix method for spherical nanoparticles (a/b = 1), using the bulk dielectric function of gold [50], a dielectric surrounding
2
The kinks in the calculated spectrum result from discontinuities in the bulk dielectric function of gold, given in [50].
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with a refractive index of nsol = 1.33, and a particle radius of R = 17 nm. As a result of the different axial ratios, an inhomogeneous broadening of the LSPP resonance is observed with a relatively large extinction at photon energies below 2.1 eV and, in particular, a shoulder at around 1.95 eV. Although, a small broadening of the modeled spectrum is expected due to electron surface scattering/increased Landau-damping [5,30,44], a clear inhomogeneous broadening, caused mainly by the non-spherical nanoparticles with different a/b, exists and persistent spectral hole burning can be applied to the colloidal nanoparticles. 2.2. Persistent spectral hole burning For in situ persistent spectral hole burning, the colloidal nanoparticles were irradiated in solution at room temperature with nanosecond pulsed laser light, generated by a BBOOPO (beta-barium borate optical parametrical oscillator, GWU, OPO-ST355-15), pumped by the third harmonic (k = 355 nm, hm = 3,49 eV) of a Nd:YAG laser (Spectra Physics, GCR-170). The laser pulse duration was approximately 5 ns with a repetition rate of 10 Hz. For each hole burning experiment, approximately 6000 laser pulses with a photon energy of 2.05 eV that addresses nanoparticles with an axial ratio of a/b = 0.49, have been applied, while different fluences which were gradually increased from 7.6 mJ/cm2 to 20.4 mJ/cm2 have been used to create different holes. The spectral width of the laser pulses is much narrower than the homogeneous line width of the nanoparticles. Thus, only nanoparticles with LSPP resonances in the immediate vicinity of the laser frequency are excited, heat is generated, and diffusion and evaporation of atoms are activated. As a result, a spectral hole is burned into the optical spectrum due to the altered size and/or shape of the nanoparticles. Subsequently, the width of the hole is determined. For this purpose, the difference of the extinction spectra before and after irradiation has been calculated. Under certain simplifications which are fulfilled in the experiments described in Section 3, a analytical expression of the difference spectrum can be given [46]: dSðxÞ ¼ A
ðx
C 2 2h 2 X0 Þ þ
2 þ B
C 2 h
ðx X0 Þ 2
ðx X0 Þ þ
C 3 2 h
2 C 2 2 h
:
ð1Þ
A and B are the amplitudes of the even and odd contributions, representing the size and shape modifications of the irradiated nanoparticles, respectively. X0 is the center frequency of the spectral hole which nearly coincides with the laser frequency. C is the line width of the burned hole which is, in fact, power broadened and increases linearly with increasing laser fluence F by [46]: C ¼ Chom ð1 þ CF Þ;
ð2Þ
where C is a constant. Using Eqs. (1) and (2), the homogeneous line width Chom can be calculated by fitting spectral holes burned with different laser fluences, and extrapolating the determined hole widths C to zero fluence. Thus, persistent spectral hole burning overcomes the problem of inhomogeneous broadening, resulting from shape and size distributions or, eventually, from different crystalline structures of the nanoparticles. Details of the processing and evaluation of the persistent spectral hole burning are published elsewhere [1,46,47,51].
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3. Results Fig. 3 depicts the optical spectra of the colloidal gold nanoparticles before and after persistent spectral hole burning with different fluences and an increasing hole depth and width for higher fluences are observed. To demonstrate this more clearly extinction difference spectra were calculated and the hole widths determined by fitting Eq. (1) to the experimental data. Fig. 4 displays exemplarily two extinction difference spectra after laser irradiation with a fluence of 12.2 mJ/cm2 (a) and 20.4 mJ/cm2 (b). In addition, the theoretical curves corresponding to Eq. (1) (solid lines) are also displayed and a good agreement between the experiment and the modelling is found. The hole widths C have been determined for these experiments to be (445 ± 5) meV and (471 ± 5) meV, respectively. The broadening of the hole width is due to the former mentioned power-broadening, since more energy is deposited for higher fluences in nanoparticles that possess similar LSPP resonances as those that are exactly in resonance with the laser photon energy. Hence, those nanoparticles contribute more and more to the hole width. Fig. 5 shows the relationship between the hole width and the fluence. A clear broadening of C as a function of fluence is observed. Using Eq. (2) and extrapolating to zero fluence, a homogeneous line width of Chom = (360 ± 32) meV which corresponds to a dephasing time of T2 = (3.7 ± 0.4) fs, is obtained. This value is about 2.5 times shorter than the expected value of T21 = 9.4 fs, obtained from the bulk dielectric function. A comparison to already published dephasing times of gold nanoparticles [5,30,44] yields that all of these experimentally determined T2 values are significant longer than the value of T2 determined for the colloidal gold nanoparticles under examination here. This can be explained by the fact that the chemical environment in my experiments is significant different compared to the experiments and the theory, already presented in the literature [5,30,32,33,44]. Obviously the aqueous solution surrounding the nanoparticles causes a strong chemical interface damping which may not play a predominant role in the other experiments [5,30,44] and has not been taken into account in the theory [32,33].
Fig. 3. Optical spectra of colloidal nanoparticles before and after irradiation with different fluences. The spectral hole width and depth increase for higher fluences.
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Fig. 4. Difference spectra (squares) after laser irradiation with a fluence of 12.2 mJ/cm2 (a) and 20.4 mJ/cm2 (b) and the theoretical curves corresponding to Eq. (1) (solid lines). A good agreement between the experimental data and the theoretical curves is obtained. The hole widths C have been determined to be (445 ± 5) meV and (471 ± 5) meV, respectively, demonstrating the power-broadening. The dashed lines indicate the photon energy of the laser light for the persistent spectral hole burning. Note the different Y-scales in the diagrams.
I emphasize that the exact size of the Au-nanoparticles whose T2 has been determined is not known due to the size distribution of the colloidal nanoparticles. Nevertheless, this does not influence the results in general, since the dephasing time is only weakly depending on the size for nanoparticles with radii around 17 nm, discussed here [5,30,44]. 4. Discussion Persistent spectral hole burning, performed at a photon energy of 2.05 eV with Au-nanoparticles in solution, yields a dramatically shorter dephasing time compared to the expected value calculated from the bulk dielectric function. Although it is known that
F. Hubenthal / Progress in Surface Science 82 (2007) 378–387
385
Fig. 5. Width of the spectral holes as a function of laser fluence. By linear extrapolation to zero fluence, a homogeneous line width of Chom = (360 ± 32) meV which corresponds to a dephasing time of T2 = (3.7 ± 0.4) fs is obtained. The dotted line is the dephasing time which can be calculated using the bulk dielectric function of gold bulk.
surface scattering/increased Landau-damping should have a pronounced influence [5,30,32,33,44], the measured dephasing time of T2 = 3.7 fs is significant shorter than experimental values presented in [5,30,44] which are among each other in good agreement and are dominated by surface scattering/increased Landau-damping. Consequently, the extremely short dephasing time can be attributed to an additional chemical interface damping that causes ultrafast dephasing of the coherent oscillating electrons. The experimentally determined short dephasing time for colloidal gold nanoparticles of T2 = (3.7 ± 0.4) fs is directly supported by recent experimental findings of Vogel et al. [52]. They found that shape tailoring of small colloidal nanoparticles, similar to those used in this study, leads to completely spherical nanoparticles which should exhibit only a homogeneous broadened LSPP resonance. Nevertheless, the measured line width of the LSPP resonance after laser tailoring is much broader than the line width, obtained from the bulk dielectric function, even if a broadening due to surface scattering/increased Landau-damping is taken into account. Including the chemical interface damping and thus, a dephasing time of T2 = (3.7 ± 0.4) fs, determined in the present study, a modeled spectrum for the colloidal gold nanoparticles can be calculated that is in good agreement with the experimental spectrum after laser tailoring. 5. Conclusion For the first time, the well established method of persistent spectral hole burning has been applied to colloidal Au-nanoparticles in solution with a LSPP resonance at 2.05 eV such that nanoparticles with an axial ratio of a/b = 0.49 have been addressed. The measured dephasing time of only (3.7 ± 0.4) fs is in good agreement to the experimental findings of Vogel et al. [52], but approximately 2.5 times shorter than the value of T200 = 9.4 fs which can be obtained from the bulk dielectric function. This shortening
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can be clearly attributed to a predominating strong chemical interface damping, i.e. the main damping mechanism acting in colloidal gold nanoparticles with hReqi = (17 ± 2) nm is chemical interface damping, while the contribution of the surface scattering increased Landau-damping is negligible for the investigated nanoparticles. Acknowledgement The financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]
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Review
Ultrafast dephasing time of localized surface plasmon polariton resonance and the involved damping mechanisms in colloidal gold nanoparticles Frank Hubenthal
*
Universita¨t Kassel, Institut fu¨r Physik and Center for Interdisciplinary Science and Technology – CINSaT, Heinrich-Plett-Str. 40, 34132 Kassel, Germany
Abstract In this contribution, for the first time precise in situ measurements of the ultrafast dephasing time T2 of localized surface plasmon polariton resonances in colloidal gold nanoparticles with the objective to identify the involved damping mechanisms are presented. T2 is an essential parameter that does not only allow one to determine the field enhancement factor that is of great importance for many applications of nanoparticles, but also reflects the role of different dephasing mechanisms. The most essential result is the observation of a chemical interface damping which causes a dramatic shortening of the dephasing time. While T21 = 9.4 fs can be obtained from the bulk dielectric function, the value shrinks to 3.7 fs if the nanoparticles are in aqueous solution. Ó 2007 Elsevier Ltd. All rights reserved. PACS: 78.67.Bf; 61.46.+w; 71.75.Gm; 68.43.h Keywords: Dephasing time; Surface plasmons; Gold; Nanoparticles
Contents 1. 2.
*
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
Tel.: +49 561 804 4501. E-mail address: [email protected]
0079-6816/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.progsurf.2007.03.005
F. Hubenthal / Progress in Surface Science 82 (2007) 378–387
3. 4. 5.
2.1. Preparation of colloidal gold nanoparticles . . . . . . . . . . . . . . . . . . . . . . 2.2. Persistent spectral hole burning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
379
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1. Introduction The optical properties of noble and alkali metal nanoparticles are dominated by localized surface plasmon polariton (LSPP) resonances. Contrary to bulk materials LSPP resonances can be excited in nanoparticles by an electromagnetic light field and distinct resonances in the optical spectra appear. In recent years, the dephasing time of the LSPP resonance T2, i.e. the time during which the excited electrons loose their phase coherence, has gained a lot of interest [1–16]. One reason is that T2 is directly connected to the local field enhancement which results in a drastic increase of the electric field in the vicinity of the nanoparticle surface as compared to the incoming electric field [17,18]. The field enhancement can be exploited in a lot of applications, such as surface enhanced Raman spectroscopy [19–22], surface enhanced fluorescence [23–25], confocal microscopy [26], or all-optical switching devices [27–29]. Most importantly, T2 connected to the homogeh neous line width Chom of the LSPP resonances via T 2 ¼ C2 is interesting by itself, because hom the damping mechanisms of the collective excitation are still an open question. To clarify the role of the different damping mechanisms in small colloidal gold nanoparticles, systematic measurements of T2 are urgently needed. As known [30,31], only surface scattering of electrons or Landau-damping,1 chemical interface damping, and electron–electron scattering play a role for such nanoparticles with reduced dimensions. However, electron–electron scattering can be ruled out, because this happens only for very small metal nanoparticles excited with intense femtosecond pulsed laser light [34,35] which has been not used in the experiments presented here. The main obstacle for measurements of T2 is the inhomogeneous broadening of the LSPP resonances that is due to broad size and shape distributions of the nanoparticle ensembles. Although some in situ measurements of the dephasing time of colloidal gold nanoparticles have been presented in the literature [36–39], T2 was always determined from an inhomogeneously broadened ensemble of nanoparticles. Due to the broadening which results from a shape distribution and different crystalline structures, the homogeneous line width cannot be obtained and thus, the presented dephasing times are not exact, i.e. they are to short. There are several methods to overcome the inhomogeneous broadening, e.g. spectroscopy of single particles [5,9,40–42] or generation of nanoparticles with
1
In quantum mechanical calculations surface scattering is included in the Landau-damping [32], while in semiclassical calculations the surface scattering is inserted as an additional factor in the theory and an increased Landau-damping is not taken into account [33]. In general, both damping mechanisms cannot be treated independently.
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extremely narrow size and shape distributions by electron beam lithography [7,8,11,43]. While the latter method is limited at present to particles larger than about 20 nm [10], the first method, spectroscopy of single nanoparticles, suffers from the fact that during the ex situ measurements the nanoparticles are exposed to different chemical environments [5,44,45] which may influence the measurements. Thus, different damping mechanisms cannot be distinguished. Hence, in the size range from 1 nm to 20 nm, where one expects a pronounced influence of shape, size, and chemical surrounding, information on the dephasing time and the involved damping mechanisms is still lacking. In this article I present for the first time precise in situ measurements of the dephasing time of the localized surface plasmon polariton excitation in colloidal gold nanoparticles in solution. For this purpose, the well established method of persistent spectral hole burning [1,46,47] has been applied using a photon energy of 2.05 eV. The main scope of this paper is to investigate which damping mechanisms play a role in colloidal gold nanoparticles with reduced dimensions. 2. Experimental 2.1. Preparation of colloidal gold nanoparticles The colloidal gold nanoparticles were produced using the method of Turkevich [48]. Briefly, 10 mg of HAuCl4 Æ 3H2O was dissolved in 95 ml bi-distilled water and heated to the boiling point. In the boiling solution, 5 ml aqueous solution of tri-sodium citrate (10 g/l) were added under permanent mechanical agitation. No additional stabilizers have been added to the solution. After about 15 s the clear solution suddenly turned to winered-color, indicating the formation of Au-nanoparticles. Subsequently, the solution was allowed to cool down to room temperature. The concentration of the nanoparticle solution was chosen so that no electromagnetic coupling is expected and agglomeration has been not observed within two weeks. The colloidal nanoparticles were mainly characterized by transmission electron microscope (TEM) measurements (Zeiss/LEO, EM 109 T). Additional in situ optical spectroscopy, recorded with the light of a Xe-arc lamp (Osram, XBO 450 W/1) in combination with a monochromator (Amko, 1200 lines/mm, blaze: 220 nm), combined with theoretical modelling using the T-Matrix method [49] and the bulk dielectric function of gold [50], have been applied to characterize the nanoparticles in solution. The experimental set up allows to obtain optical spectra in transmission. Thus, the extinction, i.e. the sum of absorption and scattering, of the nanoparticle ensemble was measured with respect to a reference spectrum without nanoparticles. Fig. 1 depicts a typical TEM image of the prepared colloidal gold nanoparticles. The image shows that mainly elongated polycrystalline polyheadrons which can be roughly approximated as rotational ellipsoids, with different shapes and sizes have been synthesized. Each particle is characterized by its equivalent radius Req, i.e. the radius of a sphere with the same volume as the actual non-spherical particle and by the axial ratio a/b, a being the short and b being the long axis of the rotational ellipsoid. The mean equivalent radius of the nanoparticles was determined by analyzing a set of TEM images to hReqi = (17 ± 2) nm. It is worth to note that the nanoparticles in solution are not agglomerated. The agglomeration which can be seen in Fig. 1 is caused by the drying process.
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Fig. 1. Typical TEM image of colloidal gold nanoparticles. Most of the particles exhibit shapes that can be roughly approximated as rotational ellipsoids with different axial ratios which cause an inhomogeneous broadening of the optical spectrum and deliver the precondition for persistent spectral hole burning. The mean radius of the particles has been determined to hReqi = (17 ± 2) nm.
Fig. 2. An extinction spectrum of the prepared colloidal gold nanoparticles and a calculated spectrum is displayed. A clear inhomogeneous broadening of the measured spectrum is observed.
Fig. 2 depicts the corresponding optical spectrum of the colloidal gold nanoparticles and, for comparison, a spectrum2 calculated with the T-Matrix method for spherical nanoparticles (a/b = 1), using the bulk dielectric function of gold [50], a dielectric surrounding
2
The kinks in the calculated spectrum result from discontinuities in the bulk dielectric function of gold, given in [50].
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with a refractive index of nsol = 1.33, and a particle radius of R = 17 nm. As a result of the different axial ratios, an inhomogeneous broadening of the LSPP resonance is observed with a relatively large extinction at photon energies below 2.1 eV and, in particular, a shoulder at around 1.95 eV. Although, a small broadening of the modeled spectrum is expected due to electron surface scattering/increased Landau-damping [5,30,44], a clear inhomogeneous broadening, caused mainly by the non-spherical nanoparticles with different a/b, exists and persistent spectral hole burning can be applied to the colloidal nanoparticles. 2.2. Persistent spectral hole burning For in situ persistent spectral hole burning, the colloidal nanoparticles were irradiated in solution at room temperature with nanosecond pulsed laser light, generated by a BBOOPO (beta-barium borate optical parametrical oscillator, GWU, OPO-ST355-15), pumped by the third harmonic (k = 355 nm, hm = 3,49 eV) of a Nd:YAG laser (Spectra Physics, GCR-170). The laser pulse duration was approximately 5 ns with a repetition rate of 10 Hz. For each hole burning experiment, approximately 6000 laser pulses with a photon energy of 2.05 eV that addresses nanoparticles with an axial ratio of a/b = 0.49, have been applied, while different fluences which were gradually increased from 7.6 mJ/cm2 to 20.4 mJ/cm2 have been used to create different holes. The spectral width of the laser pulses is much narrower than the homogeneous line width of the nanoparticles. Thus, only nanoparticles with LSPP resonances in the immediate vicinity of the laser frequency are excited, heat is generated, and diffusion and evaporation of atoms are activated. As a result, a spectral hole is burned into the optical spectrum due to the altered size and/or shape of the nanoparticles. Subsequently, the width of the hole is determined. For this purpose, the difference of the extinction spectra before and after irradiation has been calculated. Under certain simplifications which are fulfilled in the experiments described in Section 3, a analytical expression of the difference spectrum can be given [46]: dSðxÞ ¼ A
ðx
C 2 2h 2 X0 Þ þ
2 þ B
C 2 h
ðx X0 Þ 2
ðx X0 Þ þ
C 3 2 h
2 C 2 2 h
:
ð1Þ
A and B are the amplitudes of the even and odd contributions, representing the size and shape modifications of the irradiated nanoparticles, respectively. X0 is the center frequency of the spectral hole which nearly coincides with the laser frequency. C is the line width of the burned hole which is, in fact, power broadened and increases linearly with increasing laser fluence F by [46]: C ¼ Chom ð1 þ CF Þ;
ð2Þ
where C is a constant. Using Eqs. (1) and (2), the homogeneous line width Chom can be calculated by fitting spectral holes burned with different laser fluences, and extrapolating the determined hole widths C to zero fluence. Thus, persistent spectral hole burning overcomes the problem of inhomogeneous broadening, resulting from shape and size distributions or, eventually, from different crystalline structures of the nanoparticles. Details of the processing and evaluation of the persistent spectral hole burning are published elsewhere [1,46,47,51].
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3. Results Fig. 3 depicts the optical spectra of the colloidal gold nanoparticles before and after persistent spectral hole burning with different fluences and an increasing hole depth and width for higher fluences are observed. To demonstrate this more clearly extinction difference spectra were calculated and the hole widths determined by fitting Eq. (1) to the experimental data. Fig. 4 displays exemplarily two extinction difference spectra after laser irradiation with a fluence of 12.2 mJ/cm2 (a) and 20.4 mJ/cm2 (b). In addition, the theoretical curves corresponding to Eq. (1) (solid lines) are also displayed and a good agreement between the experiment and the modelling is found. The hole widths C have been determined for these experiments to be (445 ± 5) meV and (471 ± 5) meV, respectively. The broadening of the hole width is due to the former mentioned power-broadening, since more energy is deposited for higher fluences in nanoparticles that possess similar LSPP resonances as those that are exactly in resonance with the laser photon energy. Hence, those nanoparticles contribute more and more to the hole width. Fig. 5 shows the relationship between the hole width and the fluence. A clear broadening of C as a function of fluence is observed. Using Eq. (2) and extrapolating to zero fluence, a homogeneous line width of Chom = (360 ± 32) meV which corresponds to a dephasing time of T2 = (3.7 ± 0.4) fs, is obtained. This value is about 2.5 times shorter than the expected value of T21 = 9.4 fs, obtained from the bulk dielectric function. A comparison to already published dephasing times of gold nanoparticles [5,30,44] yields that all of these experimentally determined T2 values are significant longer than the value of T2 determined for the colloidal gold nanoparticles under examination here. This can be explained by the fact that the chemical environment in my experiments is significant different compared to the experiments and the theory, already presented in the literature [5,30,32,33,44]. Obviously the aqueous solution surrounding the nanoparticles causes a strong chemical interface damping which may not play a predominant role in the other experiments [5,30,44] and has not been taken into account in the theory [32,33].
Fig. 3. Optical spectra of colloidal nanoparticles before and after irradiation with different fluences. The spectral hole width and depth increase for higher fluences.
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Fig. 4. Difference spectra (squares) after laser irradiation with a fluence of 12.2 mJ/cm2 (a) and 20.4 mJ/cm2 (b) and the theoretical curves corresponding to Eq. (1) (solid lines). A good agreement between the experimental data and the theoretical curves is obtained. The hole widths C have been determined to be (445 ± 5) meV and (471 ± 5) meV, respectively, demonstrating the power-broadening. The dashed lines indicate the photon energy of the laser light for the persistent spectral hole burning. Note the different Y-scales in the diagrams.
I emphasize that the exact size of the Au-nanoparticles whose T2 has been determined is not known due to the size distribution of the colloidal nanoparticles. Nevertheless, this does not influence the results in general, since the dephasing time is only weakly depending on the size for nanoparticles with radii around 17 nm, discussed here [5,30,44]. 4. Discussion Persistent spectral hole burning, performed at a photon energy of 2.05 eV with Au-nanoparticles in solution, yields a dramatically shorter dephasing time compared to the expected value calculated from the bulk dielectric function. Although it is known that
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Fig. 5. Width of the spectral holes as a function of laser fluence. By linear extrapolation to zero fluence, a homogeneous line width of Chom = (360 ± 32) meV which corresponds to a dephasing time of T2 = (3.7 ± 0.4) fs is obtained. The dotted line is the dephasing time which can be calculated using the bulk dielectric function of gold bulk.
surface scattering/increased Landau-damping should have a pronounced influence [5,30,32,33,44], the measured dephasing time of T2 = 3.7 fs is significant shorter than experimental values presented in [5,30,44] which are among each other in good agreement and are dominated by surface scattering/increased Landau-damping. Consequently, the extremely short dephasing time can be attributed to an additional chemical interface damping that causes ultrafast dephasing of the coherent oscillating electrons. The experimentally determined short dephasing time for colloidal gold nanoparticles of T2 = (3.7 ± 0.4) fs is directly supported by recent experimental findings of Vogel et al. [52]. They found that shape tailoring of small colloidal nanoparticles, similar to those used in this study, leads to completely spherical nanoparticles which should exhibit only a homogeneous broadened LSPP resonance. Nevertheless, the measured line width of the LSPP resonance after laser tailoring is much broader than the line width, obtained from the bulk dielectric function, even if a broadening due to surface scattering/increased Landau-damping is taken into account. Including the chemical interface damping and thus, a dephasing time of T2 = (3.7 ± 0.4) fs, determined in the present study, a modeled spectrum for the colloidal gold nanoparticles can be calculated that is in good agreement with the experimental spectrum after laser tailoring. 5. Conclusion For the first time, the well established method of persistent spectral hole burning has been applied to colloidal Au-nanoparticles in solution with a LSPP resonance at 2.05 eV such that nanoparticles with an axial ratio of a/b = 0.49 have been addressed. The measured dephasing time of only (3.7 ± 0.4) fs is in good agreement to the experimental findings of Vogel et al. [52], but approximately 2.5 times shorter than the value of T200 = 9.4 fs which can be obtained from the bulk dielectric function. This shortening
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can be clearly attributed to a predominating strong chemical interface damping, i.e. the main damping mechanism acting in colloidal gold nanoparticles with hReqi = (17 ± 2) nm is chemical interface damping, while the contribution of the surface scattering increased Landau-damping is negligible for the investigated nanoparticles. Acknowledgement The financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]
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