Open Access
Add to BibSonomyAbstract
Heavily doped Cu2-xS nanoparticles with hole densities of ~1021 cm−3 were chemically synthesized and their localized surface plasmon resonance (LSPR) in the near-infrared region was investigated by nonlinear optical spectroscopy. We found that their third-order susceptibility χ(3) exhibits resonant enhancement around LSPR, similar to that in plasmonic noble metal nanoparticles. It was found that the maximum χ(3) value of Cu2-xS nanoparticles was comparable to that of Au nanoparticles with the same dimensions and concentrations. Our results indicate that Cu2-xS nanoparticles can be used as nonlinear optical materials operating in the near-infrared region, even though their near-field enhancement effect is slightly weaker than that of Au nanoparticles.
© 2016 Optical Society of America
1. Introduction
Localized surface plasmon resonance (LSPR) is a collective oscillation of conduction electrons that have been directly excited by light, and it is a characteristic optical response of metal nanoparticles [1]. A coherent oscillation of these electrons inside a nanoparticle provides an electric field enhancement near the nanoparticle’s surface. LSPRs have attracted considerable attention, as a strong near-field effect can dramatically improve the efficiency of light-matter interaction [2]. It enables various photonic applications, including highly efficient photovoltaic devices, light emitting devices, photo-catalysts, highly sensitive bio-imaging, and spectroscopy [2, 3]. Until recently, studies of LSPRs and their related phenomena have mostly looked at noble metal nanoparticles (Au, Ag, and Cu)—however, the LSPRs of noble metal nanoparticles are usually limited to the visible region due to the high conduction carrier densities of metals. In contrast, frequency-tunable LSPR that covers a much wider frequency range, i.e., between mid- to near-infrared (NIR), can be achieved using doped semiconductor nanoparticles [4, 5]. In the past few years, the LSPRs of heavily doped semiconductor nanoparticles, such as copper chalcogenides [6–9], copper phosphate [10], indium-doped tin oxide (ITO) [11], aluminum-doped zinc oxide [12], germanium telluride [13], and tungsten oxide [14], have been observed and their plasmonic properties investigated. Most of these studies were conducted on copper chalcogenide nanoparticles, which are self-doped semiconductors, where vacancies in the copper result in p-type doping [4–6]. Their strong plasmonic response in the NIR region has promised biological applications, because there exists an optical window where a living body is transparent [15].
One of the characteristic plasmonic properties studied extensively since the 1980s with noble metal nanoparticles is third-order nonlinear optical responses [16]. Au, Ag, and Cu nanoparticles dispersed in dielectric media exhibit large and ultrafast nonlinear optical responses around LSPR, which results in an application potential in Kerr-type all-optical switching devices. A response time of less than 1 ps was ascribed to the relaxation of the non-equilibrium electron distribution created by photo-excitation [17]. Large third-order nonlinear susceptibilities, χ(3), of 10−7 esu were explained by the dielectric confinement effect enhancing the incident electric field [18]. According to the Maxwell–Garnett theory, the electric field inside a spherical nanoparticle surrounded by a dielectric, El, is related to the electric field of the incident light E0 by the following equation [16].
In Eq. (1), ε(ω) and εm are the dielectric functions of a nanoparticle and a surrounding medium, respectively. This expression indicates that El is enhanced around the frequency ω, where ε(ω) + 2εm (the denominator of fl) becomes minimum. This term can be an extremely small value in the metallic system, as the real part of ε(ω) is negative for metals below the bulk plasma frequency. At this frequency, therefore, fl becomes maximum, El is resonantly enhanced, and LSPR is excited. Hence, fl is called a local field enhancement factor. Resonant enhancement of El results in a huge nonlinear optical response, because the nonlinear polarization generated in the nanoparticle is proportional to the power of El. χ(3) of nanoparticle dispersions with a low volume fraction of nanoparticles p (<< 1) can be represented by the following equation.In Eq. (2), χNP(3) is the third-order susceptibility of the nanoparticle itself [16]. This expression means that χ(3) of nanoparticle dispersions is enhanced close to LSPR by the fourth power of fl. Semiconductor nanoparticles are more suitable than metal nanoparticles for nonlinear optical devices used for optical fiber communications, as the frequencies of their LSPRs are in the NIR region, which is used in telecoms as its loss in silica fiber is extremely low.Studies on the third-order nonlinear optical properties of LSPRs in doped-semiconductor nanoparticles have been conducted on copper chalcogenide nanoparticles by transient absorption spectroscopy [19, 20]. In these studies, absorption saturation and an ultrafast response of a few picoseconds were observed. The results revealed that the mechanisms of the nonlinear optical response of copper chalcogenide nanoparticles can be understood in the same context as the metal nanoparticle systems. Zolotovskaya [21] and Liu [10] demonstrated the Q-switch performance of an NIR laser using CuxSe and Cu3-xP nanoparticles as a saturable absorber. Scotgnella et al. [19] claimed that Cu2-xSe nanoparticles exhibit a one order of magnitude larger nonlinear transmission than that of noble metal nanoparticles. However, the difference in the number density of nanoparticles in both samples was not taken into account, while nonlinear transmission of nanoparticle dispersions depends upon the concentration of nanoparticles. Moreover, the magnitude of the nonlinearity, which usually expressed as χ(3), has not been investigated in these studies. It is known that χ(3) of nanoparticle dispersions depends on the pulse width and repetition rate of the laser used in the measurements, as well as on the size and shape of the nanoparticles [22]. Thus, in order to provide an exact comparison of χ(3) between the semiconductor and metal nanoparticles, it is necessary for an evaluation to be conducted using the same measurement system and method and that metallic nanoparticles with the same dimensions and concentrations are used.
Most of the current plasmonic applications that have been examined in the literature are based on near-field enhancement (NFE) effects—estimating the efficiency of NFE of heavily doped semiconductor nanoparticles is therefore necessary. Furube et al. [11] investigated the factor of NFE (ratio of the near-field to the incident field) from an ITO nanoparticle assembly by measuring the enhancement of the two-photon absorption of the attached dye molecules, and estimated its value to be ~5. Kriegel et al. [8] used discrete dipole approximation (DDA) to calculate the same factors for Cu2-xTe nanoparticles to be ~3, while the values for Au nanoparticles with the same shape and size were ~90. The lower free-carrier densities of these materials, as compared to the metal nanoparticles, were seen as being responsible for lower NFE values (although no decisive evidence is given). Another experimental result, this time using organic dyes mixed into a solution of CuTe and Au nanoparticles, was obtained through the use of surface-enhanced Raman scattering (SERS) spectroscopy [23]. Although NFE was determined through the detection of SERS signals, accurate quantitative estimation proved to be difficult because the intensities of the signals strongly depend on the dye species. As an SERS signal is enhanced by a chemical mechanism (charge transfer) as well as by NFE [1], we cannot be confident that SERS is a good indicator of the NFE factor. It has, therefore, not yet been determined whether the NFE of doped-semiconductor nanoparticles is comparative to that of metallic nanoparticles. According to Eq. (1), when LSPR is excited, a nanoparticle becomes strongly polarized due to the intense local field. Polarization inside the nanoparticle leads to a large near-field. Therefore, we can examine the magnitude of NFE by estimating the local field enhancement factor, fl. As χ(3) strongly depends on fl (Eq. (2)), χ(3) measured at the LSPR frequency can provide information about the characteristics of NFE, albeit indirectly.
In this study, we focused on the third-order nonlinear optical properties of self-doped copper sulfide (Cu2-xS) nanoparticles and their NFE effect. Our investigations of χ(3) around the LSPR of Cu2-xS and Au nanoparticles, which have the same dimensions and concentrations, indicate that Cu2-xS nanoparticles can compete with Au nanoparticles in third-order nonlinearities, even though their free carrier density is only one-tenth that of Au. We also examined the magnitude of NFE from Cu2-xS nanoparticles relative to that from Au nanoparticles through the analysis of χ(3) values.
2. Experimental
Cu2-xS nanoparticles were synthesized via a solution route developed from various copper-alkylamine complexes [24]. We mixed 0.4 mmol of copper acetate with alkylamines (sample A: oleylamine, B & D: octhylamine, C: di-octhylamine) in toluene. After the solutions were heated up to 363 K in an inert atmosphere, sulfur powders (A, B, C: 0.4 mmol, D: 0.8 mmol) dissolved in 1-dodecanethiol (DDT) were injected. The mixtures were then kept intact at 363 K for 30 min and purified by precipitation and re-dispersion using ethanol and hexane.
The size and shape of the nanoparticles were determined using a scanning transmission electron microscope (STEM, JEOL JEM-2100F). X-ray diffraction (XRD) patterns were measured by a powder diffractometer (MAC Science M18XCE) using a CuKα radiation. Elemental analysis of the nanoparticles was conducted by energy-dispersive X-ray spectroscopy (EDX, Horiba EMAX-7000). The linear absorption spectra of nanoparticle dispersions in a quartz cell (optical path length of 1 mm) were measured by a standard double-beam spectrophotometer (JASCO, V-570).
The χ(3) values were measured through nonlinear absorption spectroscopy. Laser pulses with a duration of 2 ps and repetition rate of 1 kHz from an optical parametric amplifier (Quantronix, TOPAS) pumped with an amplified Ti:sapphire laser (Spectra Physics, Millennia-Tsunami and Quantronix Titan) were used for the measurements. An NIR beam, which had been tuned to LSPR (900–1500 nm), was focused onto a 1 mm quartz cell containing Cu2-xS nanoparticles dispersed in hexane. The volume fraction of the nanoparticles was estimated to be p ~4 × 10−5 from a molar absorption coefficient of Cu2-xS nanoparticles [25]. The transmittance of the sample was calculated from intensity of the transmitted beam. Changing the intensities of the laser pulse allowed for a relation (Eq. (3)) between an absorption coefficient α and the incident laser intensity I to be obtained [22].
In Eq. (3), α0 and β represent a linear and a nonlinear absorption coefficient, respectively. We can estimate β by measuring the dependence of α on I. The imaginary part of χ(3), Imχ(3), was obtained from a following relation between β and Imχ(3) [22].where n and c are the refractive index of the sample and the velocity of light in vacuum, respectively. For a precise comparison of the LSPR-mediated optical nonlinearities with those of noble metal nanoparticles, we also measured Imχ(3) for an aqueous solution of citrate-stabilized Au nanoparticles with a diameter of 5 nm (purchased from Sigma-Aldrich) by using the same instruments in the visible region. The volume fraction of Au nanoparticles was p ~4 × 10−6. The incident laser intensity I was changed within the range between 106 and 1012 W/cm2.3. Results and discussions
The high angle annular dark field (HAADF) images of nanoparticles A–D and their size distribution histograms are shown in Fig. 1(a)–1(d) and Fig. 1(e)–1(h), respectively. The figure shows that the nanoparticles are spherical and have uniform diameters. The average diameters, Davr, of the nanoparticles A–D are estimated to be 4.6 ± 0.5, 5.1 ± 0.9, 3.7 ± 0.4, and 4.5 ± 0.7 nm, respectively.
Fig. 1 HAADF images and size distributions of Cu2-xS nanoparticles A ((a) and (e)). B ((b) and (f)), C ((c) and (g)), and D ((d) and (h)), respectively.
Figure 2 shows the XRD patterns of the nanoparticles. By referring to the Joint Committee for Powder Diffraction Standards (JCPDS) data of their bulk counterparts, we can see that all diffraction peaks of nanoparticles A–D can be ascribed to hexagonal or cubic Cu1.8-2S crystals, although accurate phase identification is difficult due to the significant broadening of the diffraction peaks due to the nanoscale crystallite sizes. EDX measurements of the composition ratios between copper and sulfur, Cu/S, in nanoparticles A–D are found to be 1.57, 1.20, 1.56, and 1.44, respectively. These values deviate from the composition ratios of Cu/S = 1.8–2 investigated from crystal structure by the XRD, and thus, the results suggest that Cu vacancies possibly form in copper (I) sulfides (Cu2S), which lead to hole doping. However, accurate analyses of the compositions of the nanoparticle cores are difficult because of the S atoms that are also contained in surfactant DDT molecules.
Fig. 2 XRD patterns of Cu2-xS nanoparticles with the standard diffraction lines of hexagonal Cu2S (JCPDS 046-1195), hexagonal Cu1.97S (JCPDS 020-0365), cubic Cu2S (JCPDS 053-0522), and cubic Cu1.8S (JCPDS 056-1256).
Figure 3(a) shows the absorption spectra of Cu2-xS nanoparticles. Absorption of solvent (hexane) was subtracted, although its absorbance was smaller, 1/10 of those of the nanoparticles. In all nanoparticles, strong LSPR peaks and continuous absorption bands due to interband transitions are observed in the NIR region and above 1.8–2.0 eV, respectively. Meanwhile, the peak position of LSPR varies for the four samples. The frequencies of LSPR depend on various parameters: free carrier density, nanoparticle size and shape, and the dielectric constant of the surrounding media [1]. However, the diameters of nanoparticles A–D are close in which their size distributions overlap each other. Moreover, as shown in Fig. 3(b), there is no systematic variation in the wavelength of LSPR due to the nanoparticle diameters. Therefore, we conclude that the difference in the free carrier densities of nanoparticles A–D is a primary factor of LSPR frequency variation, although the LSPR frequency is slightly affected by the small differences in the crystal structures between the nanoparticles. Carrier densities of each nanoparticle sample, N, are estimated by the procedure described in the Appendix using the peak frequency ω1 and FWHM γ of the LSPR band. The spectral profiles of the LSPR bands of nanoparticles A–D are successfully fitted with a Lorentzian function, and ω1 and γ are obtained. N is calculated from the plasma frequency ωp, which is obtained using the values of ω1 and γ. These parameters are summarized in Table 1. In this analysis, the effective mass of a hole of bulk Cu2-xS is used. We can find that the reported effective mass of a hole of hexagonal Cu2S is 1.65–1.82m0 and of cubic Cu1.8S is 1.8m0, where m0 is the free electron mass [26]. Therefore, an approximate value of 1.8m0 is adopted as the hole mass in this study. As a result, the carrier (hole) densities of N = (5.6–7.6) × 1021 cm−3 are estimated for nanoparticles A–D (Table 1). This result indicates that Cu-vacancy concentration increases in this order because a hole is created by the formation of a Cu-vacancy, thereby indicating the degenerate level of carrier doping. This suggests that both the concentrations of Cu-vacancy in Cu2-xS nanoparticles and hole densities can be controlled by alkylamine species and the initial contents of sulfur. Carrier densities are about one-tenth of the free electron density of typical metals; for example, the density is 5.9 × 1022 cm−3 for gold.
Fig. 3 (a) Absorption spectra of Cu2-xS nanoparticles and solvent (hexane), (b) the relation between the diameter and LSPR peak wavelength, and (c) absorption spectra in modified forms.
Table 1. Diameters, spectral parameters, and carrier densities of Cu2-xS nanoparticles
An absorption onset for the spectral component that originates in the interband transition exhibits an apparent blue-shift, which is large for a larger carrier (hole) density. Such blue-shifts have been already reported in Cu2-xS [4, 25] and GeTe [13] nanoparticles and explained as the Burstein–Moss effect which is a blue-shift of the absorption edge caused by the band filling of the near-bandgap states in heavily doped semiconductors. Absorption components due to the interband transition were extracted from Fig. 3(a) and shown in Fig. 3(c). Vertical axes of the spectra are modified for analysis of optical bandgap energies, Egopt [27]. The values of Egopt were estimated from the linear parts of these spectra and shown in Table 1. In Cu2-xS, the widening of the optical bandgap is induced by filling the top of the valence band with holes generated by doping with a degenerate level [28]. Variations in the Burstein–Moss shift also support differences in the carrier densities estimated for nanoparticles A–D.
The χ(3) values of Cu2-xS nanoparticle D, which has the highest carrier density of 7.6 × 1021 cm−3, are evaluated. In Fig. 4(a), we show the absorption coefficient α at the LSPR peak (1.03 eV, ~1200 nm) measured as a function of incident laser intensity I. While α remains constant for I < 1 GWcm−2, it decreases at higher intensities, thereby representing the absorption saturation that is a typical nonlinear optical response of LSPR. The saturable absorption behavior of the LSPR band has been observed in various copper chalcogenide nanoparticles as well as in noble metal nanoparticles [17, 19–22]. Such behavior, so-called the bleaching of LSPR absorption, has previously been explained in terms of both hot carrier creation and following modification into the dielectric functions of nanoparticles. Experimental data fit well with Eq. (3), with the least-square method giving the linear and nonlinear absorption coefficients α0 and β as the fitting parameters. Then, β is converted to Imχ(3). Imχ(3) = –(9.34 ± 0.48) × 10−12 esu is obtained for the LSPR peak. The Imχ(3) values around the LSPR peak are measured in the same way, namely by changing the wavelength of the laser. The results are plotted in Fig. 5 after being divided by α0 in order to compensate for the difference in the number density of nanoparticles; this is because both χ(3) and α0 are proportional to the volume fraction of nanoparticles. Saturable absorption of spherical Au nanoparticles with Davr = 5 nm, which is comparable diameter to the Cu2-xS nanoparticles, are also measured around the LSPR. The data measured at the LSPR peak (2.39 eV, ~520 nm) is shown in Fig. 4(b). Imχ(3)/α0 values around the LSPR are also shown in Fig. 5. Imχ(3) values of both nanoparticles are negative and exhibit similar resonant behavior as LSPR. The largest absolute value, |Imχ(3)|/α0, is obtained under the resonant condition, and is (3.02 ± 0.15) × 10−15 esu cm for Cu2-xS nanoparticles and (2.24 ± 0.25) × 10−15 esu cm for Au nanoparticles. These results indicate that heavily doped Cu2-xS nanoparticles possess strong third-order nonlinearity in the NIR region, being comparable to noble metal nanoparticles with the same dimensions. Frequency-tunable LSPR in the NIR region and large χ(3) of Cu2-xS nanoparticles have therefore shown their high potential ability as applications to photonic devices based on Kerr-type optical nonlinearities in fiber-optic communications. Additionally, Cu2-xS nanoparticles are much advantageous in terms of cost, when compared to noble metal nanoparticles.
Fig. 5 Absorption spectra (lines) and values of Imχ(3)/α0 (dots) measured for Cu2-xS and Au nanoparticles. Absorption spectrum of Au nanoparticles is enlarged by a factor of 10.
According to Eq. (2), χ(3) around LSPR strongly depends on the local field enhancement factor. Thus, we can estimate the degree of field enhancement inside the Cu2-xS nanoparticle by using the χ(3) values and make a comparison with Au nanoparticles. In the vicinity of the peak frequency of LSPR, the absorption coefficient of the nanoparticle dispersions is given by the following equation [16].
Here, ε2 is the imaginary part of the dielectric function of a nanoparticle. From Eqs. (2) and (5), χ(3)/α0 can be written as in Eq. (6)This equation indicates that we can compare the magnitude of plasmonic enhancement in the local field between Cu2-xS and Au nanoparticles by using χ(3)/α0. χ(3) around LSPR exhibits large frequency dispersions. Near the resonance, the real component of χ(3) changes its sign and is thus negligible, while Imχ(3) becomes the negative maximum [22]. |χ(3)| and |Imχ(3)| are, as such, comparable at the resonance frequency. The measured values of |Imχ(3)|/α0 for Cu2-xS and Au nanoparticles at their LSPR peaks are shown in Table 2 with the values of n (refractive indices of hexane and water), ω, and ε2. Although ε2 of Au nanoparticles with a diameter of 5 nm is already known [1], that of Cu2-xS nanoparticles has not yet been identified. Therefore, the ε2 values for bulk Cu2-xS are shown [29]. Based on these parameters, the values of |fl|2|χNP(3)| of Au and Cu2-xS nanoparticles can be derived. The result of this analysis reveals that |fl|2|χNP(3)| of Cu2-xS nanoparticles is 1/3–1/6 that of Au nanoparticles, which suggests that the local field enhancement effect is weaker (0.4–0.6) in Cu2-xS nanoparticles than that in Au nanoparticles. This means that the dipole generated in a Cu2-xS nanoparticle under LSPR excitation is relatively small, and thus, the near-field surrounding the nanoparticle is weaker than that of Au nanoparticles. Such characteristics in the LSPR-mediated NFE of doped-semiconductor nanoparticles qualitatively agree with earlier reports. In the theoretical investigations, a lower efficiency in NFE compared to noble metal nanoparticles is expected. The factor of NFE calculated for a Cu2-xTe nanorod is 1/30 of that obtained for an equivalently sized Au nanorod [8]. This difference is ascribed to Cu2-xTe’s lower carrier density. Using our analyses of the enhancement effect in third-order nonlinear susceptibilities induced by LSPR excitation, we can qualitatively confirm the theoretical expectation that NFE by the NIR-LSPR of Cu2-xS nanoparticles is relatively weak compared to that of Au nanoparticles.Table 2. Nonlinear optical parameters for Cu2-xS and Au nanoparticles
4. Conclusions
Spherical Cu2-xS colloidal nanoparticles, with average diameters of 4–5 nm and different hole densities on the order of 1021 cm−3, were synthesized by a wet-chemical method. Third-order optical nonlinearities were investigated for strong LSPR absorption bands in the NIR region. Nonlinear susceptibilities were negative and resonantly enhanced in the vicinity of the LSPR peak, similar to the case of noble metal nanoparticles, which indicates that LSPR is in the visible region. The maximum value of Cu2-xS nanoparticles is comparable to that of Au nanoparticles with the same dimensions and nanoparticle concentrations, indicating that they can be used as nonlinear optical materials operating in the NIR area. Slightly weaker local field enhancement was estimated for Cu2-xS nanoparticles, relative to Au nanoparticles, which corroborates earlier reports indicating a lower NFE.
Appendix
According to the Mie theory [1], the extinction cross section of a metal nanoparticle, σext(ω), with a volume V0 and a dielectric function of ε(ω) = ε1(ω) + iε2(ω) is given by equation (A1) in the quasi-static regime, where the nanoparticle diameter is much smaller than the wavelength of light.
Here, ω and c are the frequency and velocity of light in vacuum, respectively, and εm is the dielectric constant of a surrounding medium. The dielectric function of metal nanoparticles can be represented by the Drude model of free electrons asIn this equation, Γ and ωp represent the damping constant and plasma frequency, respectively. The plasma frequency definition is given by Eq. (9).In this equation, N, e, m, and ε0 indicate free-carrier density, elementary charge, effective mass of the carrier, and vacuum permittivity, respectively. Inserting Eq. (8) into Eq. (7) gives a line profile of the extinction spectrum.For a frequency range where ω is excessively larger than Γ, i.e., ω >> Γ, ε1(ω) and ε2(ω) can be approximated from Eq. (8) to Eqs. (10) and (11).
By inserting Eqs. (10) and (11) into Eq. (7), the spectral shape can be represented by the following Lorentzian function, with a peak on ω0 and FWHM of Γ.In this equation,Such an approach has been accepted for metallic nanoparticles that exhibit LSPR in the visible region (ω0 >> Γ). The free-carrier density of metal nanoparticles can thus be evaluated from the frequency of the LSPR peak, ω0, using Eqs. (9) and (13). An analysis such as this, however, is inapplicable for heavily doped semiconductor nanoparticles, because LSPR is in NIR and ω ≈Γ. In this case, the extinction spectrum should be calculated from the exact form of the dielectric function in Eq. (8), i.e., not using approximate expressions, and is given by the next equation.Here,In the frequency region near ω1, Eq. (14) can be approximated to a Lorentzian function with a peak at ω1.Here, the FWHM of a spectrum, γ, is given as the following form.Consequently, the spectral line shape of LSPR is also represented by a Lorentzian function, with an FWHM γ not coincidental with the damping constant Γ. Accurate carrier densities of heavily doped semiconductor nanoparticles can be derived from both the peak frequency ω1 and the FWHM γ of the LSPR band, followed by an analysis using Eqs. (9), (15), and (17).Funding
Nanotechnology Platform Program (Molecule and Material Synthesis) of the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT); JSPS KAKENHI (25420785 and 26400316).
Acknowledgments
We would like to acknowledge Mr. T. Ueda and the Institute for Molecular Science for their assistance in the use of the picosecond laser system.
References and links
1. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
2. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
3. M. Pelton and G. W. Bryant, Introduction to Metal-Nanoparticle Plasmonics (Wiley, 2013).
4. A. Comin and L. Manna, “New materials for tunable plasmonic colloidal nanocrystals,” Chem. Soc. Rev. 43(11), 3957–3975 (2014). [CrossRef] [PubMed]
5. J. A. Faucheaux, A. L. D. Stanton, and P. K. Jain, “Plasmon resonances of semiconductor nanocrystals: physical principles and new opportunities,” J. Phys. Chem. Lett. 5(6), 976–985 (2014). [CrossRef] [PubMed]
6. Y. Zhao, H. Pan, Y. Lou, X. Qiu, J. Zhu, and C. Burda, “Plasmonic Cu(2-x)S nanocrystals: optical and structural properties of copper-deficient copper(I) sulfides,” J. Am. Chem. Soc. 131(12), 4253–4261 (2009). [CrossRef] [PubMed]
7. D. Dorfs, T. Härtling, K. Miszta, N. C. Bigall, M. R. Kim, A. Genovese, A. Falqui, M. Povia, and L. Manna, “Reversible tunability of the near-infrared valence band plasmon resonance in Cu2-xSe nanocrystals,” J. Am. Chem. Soc. 133(29), 11175–11180 (2011). [CrossRef] [PubMed]
8. I. Kriegel, J. Rodríguez-Fernández, A. Wisnet, H. Zhang, C. Waurisch, A. Eychmüller, A. Dubavik, A. O. Govorov, and J. Feldmann, “Shedding light on vacancy-doped copper chalcogenides: shape-controlled synthesis, optical properties, and modeling of copper telluride nanocrystals with near-infrared plasmon resonances,” ACS Nano 7(5), 4367–4377 (2013). [CrossRef] [PubMed]
9. X. Liu, X. Wang, B. Zhou, W.-C. Law, A. N. Cartwright, and M. T. Swihart, “Size-controlled synthesis of Cu2-xE (E = S, Se) nanocrystals with strong tunable near-infrared localized surface plasmon resonance and high conductivity in thin films,” Adv. Funct. Mater. 23(10), 1256–1264 (2013). [CrossRef]
10. Z. Liu, H. Mu, S. Xiao, R. Wang, Z. Wang, W. Wang, Y. Wang, X. Zhu, K. Lu, H. Zhang, S.-T. Lee, Q. Bao, and W. Ma, “Pulsed laser employing solution-processed plasmonic Cu3-xP colloidal nanocrystals,” Adv. Mater. 28(18), 3535–3542 (2016). [CrossRef] [PubMed]
11. A. Furube, T. Yoshinaga, M. Kanehara, M. Eguchi, and T. Teranishi, “Electric-field enhancement inducing near-infrared two-photon absorption in an indium-tin oxide nanoparticle film,” Angew. Chem. Int. Ed. Engl. 51(11), 2640–2642 (2012). [CrossRef] [PubMed]
12. R. Buonsanti, A. Llordes, S. Aloni, B. A. Helms, and D. J. Milliron, “Tunable infrared absorption and visible transparency of colloidal aluminum-doped zinc oxide nanocrystals,” Nano Lett. 11(11), 4706–4710 (2011). [CrossRef] [PubMed]
13. M. J. Polking, P. K. Jain, Y. Bekenstein, U. Banin, O. Millo, R. Ramesh, and A. P. Alivisatos, “Controlling localized surface plasmon resonances in GeTe nanoparticles using an amorphous-to-crystalline phase transition,” Phys. Rev. Lett. 111(3), 037401 (2013). [CrossRef] [PubMed]
14. K. Manthiram and A. P. Alivisatos, “Tunable localized surface plasmon resonances in tungsten oxide nanocrystals,” J. Am. Chem. Soc. 134(9), 3995–3998 (2012). [CrossRef] [PubMed]
15. H. Nishi, K. Asami, and T. Tatsuma, “CuS nanoplates for LSPR sensing in the second biological optical window,” Opt. Mater. Express 6(4), 1043–1048 (2016). [CrossRef]
16. F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys., A Mater. Sci. Process. 47(4), 347–357 (1988).
17. Y. Hamanaka, J. Kuwabata, I. Tanahashi, S. Omi, and A. Nakamura, “Ultrafast electron relaxation via breathing vibration of gold nanocrystals embedded in a dielectric medium,” Phys. Rev. B 63(10), 104302 (2001). [CrossRef]
18. K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, and A. Nakamura, “Optical nonlinearities of a high concentration of small metal particles dispersed in glass: copper and silver particles,” J. Opt. Soc. Am. B 11(7), 1236–1243 (1994). [CrossRef]
19. F. Scotognella, G. Della Valle, A. R. Srimath Kandada, D. Dorfs, M. Zavelani-Rossi, M. Conforti, K. Miszta, A. Comin, K. Korobchevskaya, G. Lanzani, L. Manna, and F. Tassone, “Plasmon dynamics in colloidal Cu2-xSe nanocrystals,” Nano Lett. 11(11), 4711–4717 (2011). [CrossRef] [PubMed]
20. I. Kriegel, C. Jiang, J. Rodríguez-Fernández, R. D. Schaller, D. V. Talapin, E. da Como, and J. Feldmann, “Tuning the excitonic and plasmonic properties of copper chalcogenide nanocrystals,” J. Am. Chem. Soc. 134(3), 1583–1590 (2012). [CrossRef] [PubMed]
21. S. A. Zolotovskaya, V. G. Savitski, P. V. Prokoshin, K. V. Yumashev, V. S. Gurin, and A. A. Alexeenko, “Nonlinear optical properties and Q-switch performance of silica glasses doped with CuxSe nanoparticles,” J. Opt. Soc. Am. B 23(7), 1268–1275 (2006). [CrossRef]
22. B. Palpant, “Third-order nonlinear optical response of metal nanoparticles” in Non-Linear Optical Properties of Matter, M. G. Papadopoulos, A. I. Sadlej, and J. Leszczynski, eds. (Springer, 2006).
23. W. Li, R. Zamani, P. Rivera Gil, B. Pelaz, M. Ibáñez, D. Cadavid, A. Shavel, R. A. Alvarez-Puebla, W. J. Parak, J. Arbiol, and A. Cabot, “CuTe nanocrystals: shape and size control, plasmonic properties, and use as SERS probes and photothermal agents,” J. Am. Chem. Soc. 135(19), 7098–7101 (2013). [CrossRef] [PubMed]
24. T. Kuzuya, K. Itoh, and K. Sumiyama, “Low polydispersed copper-sulfide nanocrystals derived from various Cu-alkyl amine complexes,” J. Colloid Interface Sci. 319(2), 565–571 (2008). [CrossRef] [PubMed]
25. J. M. Luther, P. K. Jain, T. Ewers, and A. P. Alivisatos, “Localized surface plasmon resonances arising from free carriers in doped quantum dots,” Nat. Mater. 10(5), 361–366 (2011). [CrossRef] [PubMed]
26. O. Madelung, Semiconductor Data Handbook (Springer, 2004).
27. P. Y. Yu and M. Cardona, Fundamentals of Semiconductors: Physics and Materials Properties (Springer, 2010).
28. P. Lukashev, W. R. L. Lambrecht, T. Kotani, and M. van Schilfgaarde, “Electronic and crystal structures of Cu2-xS: full-potential electronic structure calculations,” Phys. Rev. B 76(19), 195202 (2007). [CrossRef]
29. B. J. Mulder, “Optical properties of crystals of cuprous sulphides (calcosite, djeurleite, Cu1.9S, and digenite),” Phys. Status Solidi 13(1), 79–88 (1972). [CrossRef]
