## Abstract

The nonlinear optical properties of thin ZnO film are studied using interferometric autocorrelation (IFRAC) microscopy. Ultrafast, below-bandgap excitation with 6-fs laser pulses at 800 nm focused to a spot size of 1 µm results in two emission bands in the blue and blue-green spectral region with distinctly different coherence properties. We show that an analysis of the wavelength-dependence of the interference fringes in the IFRAC signal allows for an unambiguous assignment of these bands as coherent second harmonic emission and incoherent, multiphoton-induced photoluminescence, respectively. More generally our analysis shows that IFRAC allows for a complete characterization of the coherence properties of the nonlinear optical emission from nanostructures in a single-beam experiment. Since this technique combines a very high temporal and spatial resolution we anticipate broad applications in nonlinear nano-optics.

© 2010 OSA

## 1. Introduction

When illuminating semiconducting or metallic solid state nanostructures with intense and broadband ultrashort optical pulses, a variety of nonlinear optical processes such as second or third harmonic generation (SHG, THG), multiphoton-induced luminescence (MPL), photoemission and others are induced. Quite often several of these phenomena occur simultaneously under the same experimental conditions, making it sometimes difficult to distinguish between them. Prominent examples having attracted considerable recent interest are the competition between SHG and multiphoton-induced visible photoluminescence in gold nanoparticles [1] or SHG, THG and MPL in wide bandgap semiconductors such as gallium nitride [2].

Particularly well-studied examples are ZnO films and nanostructures. The wide band gap energy of ZnO of 3.37 eV at room temperature and its large exciton binding energy of ~60meV makes it a highly interesting material for various optoelectronics applications [3,4]. Also, ZnO powders and nanorods present an interesting prototypical material for exploring random lasing [5,6]. Consequently, the nonlinear optical properties of a variety of different ZnO thin films [7–10] and nanostructures [11–15] have been studied extensively. Quite generally, it is found that nonlinear optical efficiencies in ZnO nanostructures can be significantly larger than those of ZnO thin films but that the relative intensities of the different harmonic generation and photoluminescence contributions depend critically on the structural and morphological characteristics of the nanostructures as well as on the nature and concentration of defects in these samples [16].

Being able to clearly distinguish between optical harmonic generation (OHG) and luminescence processes is therefore crucial for a further optimization of their device performance. In general, this requires a complete characterization of the coherence properties of the light being re-emitted from the nanostructures. Whereas OHG is a fully phase-coherent resonant scattering process, phase coherence to the driving laser is lost in incoherent MPL emission. Even though the coherence properties of the emitted radiation have been studied in great detail for linear light scattering from, e.g., semiconductor quantum wells [17–19], such analyses are scarce for nonlinear light scattering from nanostructures.

Here we show that interferometric frequency-resolved autocorrelation (IFRAC) spectroscopy, a technique recently introduced to characterize ultrashort laser pulses [20], can quantitatively discriminate between OHG and MPL from semiconducting nanostructures. By experimentally and theoretically analyzing IFRAC spectra from thin ZnO films, we show that IFRAC probes the most important difference between SHG and MPL, i.e., their phase correlation with the excitation pulse. Due to its high temporal (< 6 fs) and spatial (< 500 nm) resolution, we foresee a variety of applications of this technique in probing the optical nonlinearities of individual nanostructures.

## 2. Experimental setup

The experimental setup used in this work is schematically shown in Fig. 1(a)
. Few-cycle laser pulses with an energy of 2.5 nJ and a duration of 6 fs are generated in a commercial Ti:sapphire oscillator (Femtolasers Rainbow) operating at a repetition rate of 82 MHz. The pulse dispersion is controlled by a pair of chirped mirrors with a group delay dispersion (GDD) of −45 fs^{2}/bounce (Femtolasers GSM014). A pair of wedges (Femtolasers UA124, angle 2°48′, Suprasil 1) is used to fine-tune the dispersion. Appropriately pre-compensated pulses with a GDD of < −200fs^{2} enter a dispersion-balanced, unstabilized Michelson interferometer with low-dispersion broadband dielectric beamsplitters. In the interferometer, a collinearly propagating pair of pulses with variable time delay *τ* is generated. The pulse delay is controlled using a hardware-linearized single-axis piezo scanner (Physik Instrumente P-621.1CD PI-Hera). Fluctuations of *τ* due to mechanical vibrations of the interferometer and the finite precision of the piezo scanner are less than 30 as. The pulse pair is expanded to a beam size of 15 mm in an all-reflective Kepler telescope. The beam is then focused to its diffraction limit using an all-reflective, aluminum-coated 36x Cassegrain (Davin Optronics, 5004-000) microscope objective with a numerical aperture (NA) of 0.5. The spatial intensity profile of the focused spot is characterized by collecting the laser light through an aluminum coated near-field optical fiber (Veeco Instruments) with an aperture diameter of ~300nm, fabricated by focused-ion-beam milling. The tip is mounted on a hardware-linearized three-axis piezo stage (Physik Instrumente NanoCube) with a positioning accuracy of better than 10 nm. The intensity of the collected laser light is detected with a photomultiplier tube while scanning the tip through the focus. The spatial intensity distribution of the beam in the focus of the Cassegrain objective is shown in Fig. 1(b). The full width at half maximum of this distribution is 1.0 µm. The rather pronounced Airy fringes result from the obscuration of the central part of the beam by the inner mirror of the objective.

To record the time structure of the focused pulses, the tip is replaced with a 10 µm thick BBO crystal and interferometric autocorrelation (IAC) traces are recorded in the laser focus. In Fig. 1(c), a typical IAC trace of the laser pulses in the focus of the Cassegrain objective is shown. The spectrum of the incident laser pulses extending from 650 to 1050 nm is shown in the inset. A simulation of the IAC trace (Fig. 1(c), red dashed line) based on the measured pulse spectrum gives evidence that the focusing with the Cassegrain objective results in essentially bandwidth-limited pulses with a temporal duration of 6.0 fs (full width at half maximum of the pulse intensity) focused to a spot size of 1.0 µm.

Thin ZnO layers with a thickness of 430 nm are deposited on a sapphire substrate using a sputtering technique. The films are sputter-deposited for 50 min at a RF power of 200 W and an Ar flow rate of 16 sccm. A scanning electron microscope (SEM) image of the ZnO film recorded under a viewing angle of 30° in shown in the inset of Fig. 2
. The sputtering technique results in a slightly granular surface morphology with a typical grain size of about 50 nm, much smaller than the wavelength of light. For the optical measurements reported here, the ZnO thin film can therefore be considered as a spatially homogeneous layer. Photoluminescence spectra are recorded at room temperature by exciting the sample at 337 nm with a N_{2}-laser. For the nonlinear optical measurements, the film is illuminated with 6-fs Ti:sapphire pulses focused through the Cassegrain objective. The emission from the ZnO sample is collected in reflection geometry, spectrally dispersed in a monochromator (SpectraPro-2500i, Acton) and detected with a deep-depletion liquid-nitrogen cooled CCD camera (Spec-10, Princeton Instruments). Interferometric frequency-resolved autocorrelation (IFRAC) traces are recorded by illuminating the film with a pair of phase-locked 6-fs laser pulses and monitoring the nonlinear emission spectrum as a function of the delay *τ* between these pulses.

## 3. Experimental results

A room-temperature photoluminescence spectrum of the ZnO layer recorded for above bandgap excitation at 337 nm is displayed in Fig. 2. As known for such films [21], it shows a strong and spectrally narrow free-exciton emission centered at 392 nm and a spectrally broad, defect-related blue-green emission band extending from 400 to 550 nm. The origin of the blue-green emission has strongly been debated in the literature [21] and it is generally believed that this emission involves multiple defects and/or defect complexes.

Nonlinear optical spectra recorded for below-band gap excitation with 6-fs-laser pulses centered at around 800 nm are shown in Fig. 3(a)
. Two prominent emission bands are found. The first one is centered at around 400 nm, slightly below the free-exciton resonance. The second emission band is centered around 500 nm. The intensity of both bands depends very differently on the laser intensity. The intensity ${I}_{1}$ of the 400-nm-band (red circles in Fig. 3(b)) scales essentially as the second power of the laser power *P*, ${I}_{1}\propto {P}^{b1}$ with $b1=1.85\pm 0.1$ (solid line in Fig. 3(b)). This suggests that this emission arises predominantly from resonantly enhanced second harmonic generation (SHG) from the ZnO film. The drop in SHG intensity at $\lambda <380$ nm is then attributed to the reabsorption of SH radiation in the ZnO film. This assignment is in agreement with recent studies using more narrowband, spectrally tunable below-bandgap excitation [9]. The intensity ${I}_{2}$ of the blue-green emission band (red circles in Fig. 3(c)) depends much more strongly on the laser power, ${I}_{2}\propto {P}^{b2}$ with $b2=3.5\pm 0.3$ (solid line in Fig. 3(c)). A similarly pronounced power dependence has been observed before [9] and has led the authors to conclude that this emission band can be assigned to a multiphoton-induced luminescence band. Since the spectral shape in Fig. 3 is independent on the excitation power we conclude that stimulated emission processes, well known in ZnO nanostructures, can be neglected under excitation conditions chosen in our experiments.

To further characterize the two nonlinear optical emission bands, we induce this emission by a phase-locked pair of collinearly propagating 6-fs laser pulses and record the emission intensity ${I}_{IF}\left(\tau ,{\lambda}_{d}\right)$ as a function of the interpulse delay *τ* and the emission wavelength ${\lambda}_{d}$. Such interferometric frequency resolved autocorrelation (IFRAC) measurements have successfully been used to characterize ultrashort laser pulses [20, 22] and very recently also to probe the optical nonlinearity of a single metallic nanotip [23]. An IFRAC trace ${I}_{IF}\left(\tau ,{\lambda}_{d}\right)$ from the ZnO-layer recorded with pulses having an energy of 0.44 nJ (laser power 35 mW) is shown in Fig. 4(a)
. Here, the time delay *τ* between the two pulses is varied between −30 fs and + 30 fs and the spectral emission is detected between 370 nm and 520 nm. As in Fig. 3, two distinct emission bands, the blue emission around 400 nm and the blue-green band around 500 nm are discerned. The IFRAC signals of both bands show distinctly different dynamics and, most importantly, very different interference fringe patterns. In the blue emission band, the modulation period, i.e., the time difference between two fringe maxima, in a narrow region around $\tau =0$ is $T=2{\lambda}_{d}/c=4\pi /{\omega}_{d}$ (${\omega}_{d}$: detection frequency) and varies linearly with the detection wavelength. This is schematically illustrated by the dotted lines in Fig. 4(a). At $\lambda =400$ nm we find $T=2.69\pm 0.05$ fs, in good agreement with the expected value of 2.67 fs. For larger *τ*, the fringe spacing reduces to half this value. The wavelength-dependence of the fringes is more clearly seen when looking at the magnitude of the Fourier transforms ${\tilde{I}}_{IF}\left({\omega}_{\tau},{\lambda}_{d}\right)={\displaystyle \int {I}_{IF}\left(\tau ,{\lambda}_{d}\right)\mathrm{exp}\left(-i{\omega}_{\tau}\tau \right)d\tau}$ along the delay axis *τ* (Fig. 4(b)). This Fourier transform shows peaks around ${\omega}_{\tau}=0$ (the DC component), ${\omega}_{\tau}=\pm {\omega}_{d}/2$ (the fundamental sidebands) and ${\omega}_{\tau}=\pm {\omega}_{d}$ (the second order sidebands). It is important to note that in an off-resonant, coherent second harmonic experiment, the center frequencies of the fundamental and second order sidebands are proportional to the detection frequency [20].

Very different fringe patterns are observed in the IFRAC signal of the blue-green emission band (Fig. 4(a)). Here, pronounced fringes are only seen in a narrow region around $\tau =0$ due to the large ($b2=3.5$)nonlinear power dependence. Moreover, we observe, in the entire detection wavelength range between 460 and 520 nm, a fringe spacing $T=2.40\pm 0.05$fs which is independent of the detection wavelength. The detection-wavelength-independence of the fringe spacing is confirmed by looking at the Fourier transform ${\tilde{I}}_{IF}\left({\omega}_{\tau},{\lambda}_{d}\right)$. This signal is arguably much more complex than the corresponding signal in the blue emission band. In addition to the fundamental and second order sideband peaks it shows third order sideband peaks. Weak sidebands at the fourth and even fifth order (not shown) are also resolved when plotting ${\tilde{I}}_{IF}\left({\omega}_{\tau},{\lambda}_{d}\right)$ on a logarithmic scale. Most notably, however, the center frequency ${\omega}_{\tau}$ of all sidebands is independent of the detection frequency. Regular interferometric autocorrelation (IAC) traces ${I}_{IAC}\left(\tau \right)={\displaystyle \int {I}_{IF}\left(\tau ,{\lambda}_{d}\right)d{\lambda}_{d}}$are deduced from the data in Fig. 4a by spectral integration over the wavelength range from 380 to 460 nm (blue-emission band) and 460 to 520 nm (blue-green emission band). The IAC traces are shown in Fig. 4(c) and (d), respectively. Notable in the IAC trace of the blue emission is the enhancement factor $\eta ={I}_{IAC}(\tau =0)/{\mathrm{lim}}_{\tau \to \infty}{I}_{IAC}(\tau )$ of 6, which agrees well with $\eta ={2}^{2\xb71.85}/2=6.5$ expected for the observed nonlinear power dependence of 1.85. This IAC trace appears slightly broader than that recorded with a BBO crystal (Fig. 1(c)). The IAC trace of the blue-green emission (Fig. 4(d)) displays a much larger enhancement factor of $\eta =50$, close to the value of 64 resulting from the strong power dependence of the involved optical nonlinearity. Consequently, the IAC extends over essentially only three cycles of the light field in the time domain.

## 4. Discussion

Apart from their different dynamics, the most notable difference between the interferometric frequency-resolved autocorrelation functions recorded in the blue and blue-green emission is the different detection wavelength dependence of the fringe spacing *T*. While $T=2{\lambda}_{d}/c$ in the blue band, *T* is found to be independent of *λ* in the blue-green band. For a coherent, off-resonant second harmonic process, the wavelength scaling of *T* is readily explained. Here, the interferometric SH signals recorded when exciting the sample with a phase-locked pulse pair are ${I}_{IAC}\left(\tau \right)={{\displaystyle \int \left|{\left(E\left(t\right)+E\left(t-\tau \right)\right)}^{2}\right|}}^{2}dt$ and ${I}_{IF}\left(\tau ,{\omega}_{d}\right)={\left|{\displaystyle \int {\left(E\left(t\right)+E\left(t-\tau \right)\right)}^{2}\mathrm{exp}\left(-i{\omega}_{d}t\right)}dt\right|}^{2}$. For excitation with a spectrally narrow-band laser pulse $E=\epsilon \left(t\right)\mathrm{exp}\left(-i{\omega}_{L}t\right)$ one readily sees that $T=4\pi /{\omega}_{d}$. For excitation with spectrally broad-band few-cycle pulses the analysis is slightly more involved and has been given in [20]. Here, the fringes in the IFRAC signal at early delay times are governed by the fundamental sideband which oscillates as $\mathrm{cos}\left(\frac{{\omega}_{d}\tau}{2}\right)$ [20]. The fringe spacing is thus $T=4\pi /{\omega}_{d}$. At longer delay times, pronounced fringes with half the spacing are seen which reflect the second order sideband.

In case of an incoherent, spontaneous emission process (photoluminescence), the expected IFRAC signals are fundamentally different. Here the phase relation between the excitation laser and re-emitted electric field form the sample is lost and the emitted intensity is proportional to the incoherent carrier population ${n}_{e}$ in the light-emitting state. We emphasize that despite of the incoherent nature of the emission, coherences fringes can be observed in autocorrelation measurements. Such fringes necessarily result from interferences in the excitation process of the system. This is readily understood by considering a dipole-allowed one-photon transition of a simple two-level system impulsively excited with a short pulse ${n}_{e}\approx {\left|d\cdot \tilde{E}\left({\omega}_{r}\right)\right|}^{2}/{\hslash}^{2}$. Here, *d* is the transition dipole moment and $\tilde{E}\left({\omega}_{r}\right)$ is the amplitude of the Fourier component of the laser electric field $E\left(t\right)$ at the transition frequency ${\omega}_{r}$ between the ground and excited state of the system. The equality holds if the duration of the laser pulse is much shorter than the dephasing time of the two-level system. When impulsively exciting the system with a pair of pulses, a large population ${n}_{e}$ is therefore created if the field components at ${\omega}_{r}$ interfer contructively. The fringe spacing therefore is $T=2\pi /{\omega}_{r}$. It is thus defined only by the energetics of the optically excited system and independent of the detection frequeny. It is important to note that in case of an incoherent emission process the emission frequency ${\omega}_{d}$ may differ from the transition frequency ${\omega}_{r}$ since the optically excited state may be coupled to the emitting state by inelastic relaxation processes.

For multiphoton-excitation of a two-level system, the Rabi frequency ${\Omega}_{r}\left(t\right)=d\cdot E\left(t\right)/\hslash $ can be replaced by a generalized Rabi frequency ${\Omega}_{r}\left(t\right)=\alpha \cdot E{\left(t\right)}^{n}/\hslash $ [24]. Here, *α* is the transition matrix element for an *n*-photon transition between ground and excited state. The impulsively excited carrier density is ${n}_{e}\approx {\left|d\cdot \tilde{{E}^{n}}\left({\omega}_{r}\right)\right|}^{2}/{\hslash}^{2}$, where $\tilde{{E}^{n}}\left({\omega}_{r}\right)$ is the Fourier component of the *n*-th harmonic of the laser field at ${\omega}_{r}$. This results in a fringe-spacing $T=2n\pi /{\omega}_{r}$, which is – again – independent of the detection wavelength.

We therefore conclude very generally that coherent and incoherent emission processes result in fundamentally different IFRAC signals. Coherent emission processes such as Rayleigh scattering or optical harmonic generation result in a fringe spacing which is proportional to the detection wavelength. Incoherent spontaneous emission processes, however, are characterized by a detection-wavelength independent fringe spacing. This spacing is governed by the energy of the optically excited state which may differ from that of the light-emitting state. IFRAC measurements can therefore distinguish between coherent and incoherent emission and provide a full characterization of the coherence properties of the re-emitted light.

This leads us to conclude that in the case of the ZnO films studied in this work, the IFRAC signal in the blue emission region in Fig. 4(a) results predominantly from coherent second harmonic generation in the ZnO film whereas the IFRAC signal in the blue-green region in Fig. 4(a) reflects multiphoton-absorption in the ZnO film followed by incoherent, spontaneous emission from below-bandgap defect states. The short fringe spacing of $T=2.4$ fs and the strong power dependence of the of the optical nonlinearity $b2=3.5$ indicates that, here, multiphoton-absorption creates carriers in the conduction band of ZnO which then relax into the light-emitting below-bandgap defect states.

For a more quantitative analysis of the data in Fig. 4(a), we have simulated these results within the framework of optical Bloch equations. As schematically illustrated in Fig. 5
, we model the ZnO film as an effective 4-level-system with a ground state $|0\u3009$ and three excited states $|1\u3009$-$|3\u3009$. We assume that state $|1\u3009$ is coupled to the ground state by two-photon absorption, whereas $|2\u3009$ couples to $|0\u3009$ by three-photon absorption. We also assume that carriers $|2\u3009$ can relax at a rate ${k}_{r}$ to the low-lying state $|3\u3009$ from where they can spontaneously emit light. The Hamiltonian of the isolated system is then given as ${H}_{0}={\displaystyle \sum \hslash {\omega}_{i}|i\u3009\u3008i|}$, $i=\mathrm{0...3}$, and that for light-matter interaction is ${H}_{I}=\hslash {\Omega}_{r1}\left(t\right)\left(|0\u3009\u30081|+|1\u3009\u30080|\right)+\hslash {\Omega}_{r2}\left(|0\u3009\u30082|+|2\u3009\u30080|\right)$, with generalized Rabi frequencies ${\Omega}_{r1}\left(t\right)=\alpha E{\left(t\right)}^{2}/\hslash $ and ${\Omega}_{r2}\left(t\right)=\beta E{\left(t\right)}^{3}/\hslash $. Here *α* (*β*) denotes the matrix element for two-photon (three-photon) interaction between states $|0\u3009$ and $|1\u3009$ ($|0\u3009$ and $|2\u3009$). For simplicity, we assume real matrix elements. The time-evolution of the density matrix of the system is obtained by solving the Liouville-von Neumann equation $\frac{\partial}{\partial t}\rho =-\frac{i}{\hslash}\left[H,\rho \right]+{\frac{\partial}{\partial t}\rho |}_{rel}$. The last term includes possible dephasing and relaxation processes. The equations of motion for the relevant polarizations then read

Polarization dephasing times $T{2}_{1}$ and $T{2}_{2}$ are introduced phenomenologically. The population dynamics are deduced from

Here ${k}_{em}^{-1}$ denotes the radiative lifetime of state$|3\u3009$. The second harmonic field emitted from the sample is taken as ${E}_{SH}\left(t\right)={d}_{1}\cdot \mathrm{Re}\left({\rho}_{01}\left(t\right)\right)$ with ${d}_{1}$ being the one-photon transition dipole matrix element of states $|0\u3009$ and $|1\u3009$. The spontaneous emission intensity from level $|3\u3009$ is modeled as ${I}_{PL}\left(\lambda \right)\propto {\rho}_{33}\left({t}_{0}\right)\cdot PL\left(\lambda \right)$ with ${\rho}_{33}\left({t}_{0}\right)$ being the population in level $|3\u3009$ at a finite delay time ${t}_{0}$ after the arrival of the laser pulse and $PL\left(\lambda \right)$ being the emission spectrum in the blue-green region deduced from Figs. 3 and 4. The experimental data are modeled by taking a phase-locked pair of unchirped 6-fs-pulses as the input field $E\left(t\right)$. The IFRAC traces are then simulated using ${I}_{IF}\left(\tau ,{\omega}_{d}\right)={\left|{\displaystyle \int {E}_{SH}\left(\tau \right)\mathrm{exp}\left(-i{\omega}_{d}t\right)}dt\right|}^{2}+{I}_{PL}\left(\tau ,{\omega}_{d}\right)$. Model simulations have been performed taking unchirped laser pulses with a Gaussian spectrum and with the spectrum seen in Fig. 1(c). Results of such simulations for optimized system parameters are shown in Fig. 6(a) . Obviously the salient features of the experiment, specifically the different wavelength dependence of the fringe spacings in the blue and blue-green emission band are rather well reproduced. To reach good agreement with experiment, a few assumptions about the properties of the four-level-system are necessary: (i) The energy of the SH-emitting state $|1\u3009$ should be chosen around 3.1 eV (400 nm), slightly below the ZnO bandgap, and a short, yet finite, dephasing time $T{2}_{1}=7\pm 2$ fs should be assumed to match the IFRAC traces in the blue range. Good agreement is found when taking bandwidth-limited pulses with the spectrum shown in Fig. 1(c) and a dephasing time of 7 fs. (ii) A large energy of the three-photon active state $|2\u3009$ of 5.1 eV (240 nm), far above the ZnO bandgap, should be chosen to match the detection-wavelength independent fringe spacing of 2.4 fs in the blue-green emission band. The dephasing time $T{2}_{2}$ should not be longer than 3 fs to match the time dynamics of the experimentally-recorded IFRAC trace.

With these assumptions the wavelength-dependence and the dynamics of the IFRAC traces are reasonably well reproduced. Also the dynamics of the spectrally-integrated IAC traces in Fig. 6(c,d) are similar to those in the experiment (Fig. 4(c,d)). The IFRAC signal in the blue range shows a fringe spacing $T=4\pi /{\omega}_{d}$. Clearly, the blue emission results almost entirely from coherent second harmonic emission. A closer comparison between the IFRAC simulations for coherent second harmonic emission (Fig. 6a) and the experimental data in the blue emission band (Fig. 4a) shows the following important features: (i) At sufficiently long delay times, all fringes have comparable signal intensities. These fringes persist even if the pulse delay *τ* is much larger than the dephasing time $T{2}_{1}$. They result from the interference of the second harmonic fields ${E}_{SH}$ generated by each of the two temporally well-separated pulses (s. Eq. (4) in Ref. 20). They persist until *τ* becomes larger than the inverse spectral resolution of the monochromator used for IFRAC detection. These fringes give rise to the spectrally narrow second order sideband in the Fourier spectra.
(ii) At early times also second harmonic signals induced by the direct interference of the laser fields of the two pulses on the sample contribute. These signals results in a rather complex temporal and spectral IFRAC pattern arising from the interference between both pulses and the coherent polarizations induced in the nonlinear medium. They therefore persist only for delays similar to $T{2}_{1}$. Essentially, we find that “even” fringes at $\tau =4n\pi /{\omega}_{d},\text{\hspace{0.17em} \hspace{0.17em} \hspace{0.17em}}n\in \mathbb{Z}$ extend over the full range of detection wavelength range. The “odd” fringes at $\tau =\left(2n+1\right)2\pi /{\omega}_{d},\text{\hspace{0.17em} \hspace{0.17em} \hspace{0.17em}}n\in \mathbb{Z}$, however, have high intensity only for short detection wavelengths, ${\omega}_{d}\le {\omega}_{1}-{\omega}_{0}$, yet weak intensity for longer wavelengths. For the “even” harmonics, the fields at the fundamental laser frequency and at the second harmonic frequency are in phase, and constructive interference is seen for all detection wavelengths. For the “odd” harmonics, however, the interference pattern apparently depends on the phase of the second harmonic polarization ${\rho}_{01}$ which exhibits a phase jump at ${\omega}_{d}$ and hence gives rise to constructive interference for ${\omega}_{d}\le {\omega}_{1}-{\omega}_{0}$, yet destructive interference at longer wavelengths. A full analysis of these interference patterns is currently underway and will be given elsewhere.

In the region of the blue-green emission, the data in Fig. 6(a) show interference fringes with a spacing which is independent on the detection-wavelength. We take this a a clear signature that the blue-green emission arises predominantly from an incoherent photoluminescence process. A closer comparison between the Fourier-transformed IFRAC signals in Fig. 4(b) and 6(b) indicates, however, that the microscopic mechanisms resulting in the blue-green emission are certainly much more complicated than a three-photon-induced absorption into a higher-lying electronic state far above the bandgap. The strong power dependence of the nonlinear optical signal ($b2=3.5$) and the complex IFRAC-spectrum in Fig. 6(b) may probably be explained by an interference between different nonlinear optical processes. It is likely that this strong power dependence results from field-induced ionization processes, i.e., the generation of a dense electron-hole plasma in the ZnO film by below-band gap excitation. Its effect on the optical nonlinearities of ZnO nanostructures will be subject of further investigations.

## 5. Conclusions

In summary, we have studied the nonlinear optical properties of thin zinc oxide films using interferometric frequency-resolved autocorrelation (IFRAC) microscopy following impulsive excitation with 6-fs optical pulses focused to a spot size of 1 µm. Two emission bands with distinctly different coherence properties are observed in the blue and blue-green emission region. Both bands display very different wavelength dependencies of the interference patterns of their IFRAC signals. A new IFRAC analysis based on solutions of optical Bloch equations shows that this can directly be traced back to the different coherence properties of the two emission channels. This analysis allows us to unambiguously assign the blue band as resonantly enhanced coherent second harmonic emission close to the band gap of ZnO. The blue-green emission band, displaying detection-wavelength independent fringes, results from multiphoton-absorption-induced incoherent spontaneous emission from below bandgap defect states. Our results show that IFRAC microscopy is a new and elegant way to fully characterize the coherence properties of the optical emission from nanostructures. With its high time resolution of a few fs only, it can directly probe the dynamics of coherent optical polarizations in nanostructures in the time domain. Its high spatial resolution makes it interesting for studying the nonlinear optical properties of single nanostructure and/or for coherent nonlinear optical microscopy.

## Acknowledgments

This research was supported by the Japan Science and Technology Agency (JST) and the Deutsche Forschungsgemeinschaft (DFG) under the strategic Japanese-German Cooperative program on "Nanoelectronics". Support by the DFG (SPP 1391) and by the Korea Foundation for International Cooperation of Science & Technology (Global Research Laboratory project, K20815000003) is acknowledged.

## References and links

**1. **M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B **68**(11543), 1–10 (2003). [CrossRef]

**2. **D. Coquillat, G. Vecchi, C. Comaschi, A. M. Malvezzi, J. Torres, and M. Le Vassor d’Yerville, “Enhanced second- and third-harmonic generation and induced photoluminescence in a two-dimensional GaN photonic crystal,” Appl. Phys. Lett. **87**(10), 101106 (2005). [CrossRef]

**3. **A. B. Djurišić and Y. H. Leung, “Optical properties of ZnO nanostructures,” Small **2**(8-9), 944–961 (2006). [CrossRef] [PubMed]

**4. **Ü. Özgür, Ya. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Dŏgan, V. Avrutin, S.-J. Cho, and H. Morkoç, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. **98**(4), 041301 (2005). [CrossRef]

**5. **J. Fallert, R. J. B. Dietz, J. Sartor, D. Schneider, C. Klingshirn, and H. Kalt, “Co-existence of strongly and weakly localized random laser modes,” Nature Photon. **3**(5), 279–282 (2009). [CrossRef]

**6. **C. F. Zhang, Z. W. Dong, K. J. Liu, Y. L. Yan, S. X. Qian, and H. Deng, “Multiphoton absorption pumped ultraviolet stimulated emission from ZnO microtubes,” Appl. Phys. Lett. **91**(14), 142109 (2007). [CrossRef]

**7. **T. Tritschler, O. D. Mücke, M. Wegener, U. Morgner, and F. X. Kärtner, “Evidence for third-harmonic generation in disguise of second-harmonic generation in extreme nonlinear optics,” Phys. Rev. Lett. **90**(21), 217404 (2003). [CrossRef] [PubMed]

**8. **U. Neumann, R. Grunwald, U. Griebner, G. Steinmeyer, and W. Seeber, “Second-harmonic efficiency of ZnO nanolayers,” Appl. Phys. Lett. **84**(2), 170–172 (2004). [CrossRef]

**9. **D. C. Dai, S. J. Xu, S. J. Shi, M. H. Xie, and C. M. Che, “Observation of Both Second-Harmonic and Multiphoton-Absorption-Induced Luminescence In ZnO,” IEEE Photon. Technol. Lett. **18**(14), 1533–1535 (2006). [CrossRef]

**10. **N. S. Han, H. S. Shim, S. Min Park, and J. K. Song, “Second-harmonic Generation and Multiphoton Induced Photoluminescence in ZnO,” Bull. Korean Chem. Soc. Vol. **30**(10), 2199–2200 (2009). [CrossRef]

**11. **C. F. Zhang, Z. W. Dong, G. J. You, R. Y. Zhu, S. X. Qiana, H. Deng, H. Cheng, and J. C. Wang, “Femtosecond pulse excited two-photon photoluminescence and second harmonic generation in ZnO nanowires,” App, Phys. Lett. **89**, 042117 (2006). [CrossRef]

**12. **S. W. Liu, H. J. Zhou, A. Ricca, R. Tian, and M. Xiao, “Far-field second-harmonic fingerprint of twinning in single ZnO rods,” Phys. Rev. B **77**(11), 113311 (2008). [CrossRef]

**13. **K. Pedersen, C. Fisker, and T. G. Pedersen, “Second-harmonic generation from ZnO nanowires,” Phys. Status Solidi **5**(8), 2671–2674 (2008). [CrossRef]

**14. **S. K. Das, M. Bock, C. O’Neill, R. Grunwald, K. M. Lee, H. W. Lee, S. Lee, and F. Rotermund, “Efficient second harmonic generation in ZnO nanorod arrays with broadband ultrashort pulses,” Appl. Phys. Lett. **93**(18), 181112 (2008). [CrossRef]

**15. **Y. C. Zhong, K. S. Wong, A. B. Djurisic, and Y. F. Hsu, “Study of optical transitions in an individual ZnO tetrapod using two-photon photoluminescence excitation spectrum,” Appl. Phys. B **97**(1), 125–128 (2009). [CrossRef]

**16. **A. F. Kohan, G. Ceder, D. Morgan, and C. G. Van de Walle, “First-principles study of native point defects in ZnO,” Phys. Rev. B **61**(22), 15019–15027 (2000). [CrossRef]

**17. **H. L. Wang, J. Shah, T. C. Damen, and L. N. Pfeiffer, “Spontaneous emission of excitons in GaAs quantum wells: The role of momentum scattering,” Phys. Rev. Lett. **74**(15), 3065–3068 (1995). [CrossRef] [PubMed]

**18. **S. Haacke, R. A. Taylor, R. Zimmermann, I. Bar-Joseph, and B. Deveaud, “Resonant femtosecond emission from quantum well excitons: The role of Rayleigh scattering and luminescence,” Phys. Rev. Lett. **78**(11), 2228–2231 (1997). [CrossRef]

**19. **M. Gurioli, F. Bogani, S. Ceccherini, and M. Colocci, “Coherent vs Incoherent Emission from Semiconductor Structures after Resonant Femtosecond Excitation,” Phys. Rev. Lett. **78**(16), 3205–3208 (1997). [CrossRef]

**20. **G. Stibenz and G. Steinmeyer, “Interferometric frequency-resolved optical gating,” Opt. Express **13**(7), 2617–2626 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-7-2617. [CrossRef] [PubMed]

**21. **A. B. Djurišić, W. C. H. Choy, V. A. L. Roy, Y. H. Leung, C. Y. Kwong, K. W. Cheah, T. K. Gundu Rao, W. K. Chan, H. Fei Lui, and C. Surya, “Photoluminescence and Electron Paramagnetic Resonance of ZnO Tetrapod Structures,” Adv. Funct. Mater. **14**(9), 856–864 (2004) (and references therein). [CrossRef]

**22. **G. Stibenz, C. Ropers, C. Lienau, C. Warmuth, A. S. Wyatt, I. A. Walmsley, and G. Steinmeyer, “Advanced methods for the characterization of few-cycle light pulses: a comparison,” Appl. Phys. B **83**(4), 511–519 (2006). [CrossRef]

**23. **A. Anderson, K. S. Deryckx, X. G. Xu, G. Steinmeyer, and M. B. Raschke, “Few-femtosecond plasmon dephasing of a single metallic nanostructure from optical response function reconstruction by interferometric frequency resolved optical gating,” Nano Lett. **10**(7), 2519–2524 (2010). [CrossRef] [PubMed]

**24. **C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, *Atom-photon interactions: Basic processes and Applications* (Wiley, 1998).