Third harmonic generation (THG) of femtosecond laser pulses in sputtered nanocrystalline TiO2 thin films is investigated. Using layers of graded thickness, the dependence of THG on the film parameters is studied. The maximum THG signal is observed at a thickness of 180 nm. The corresponding conversion efficiency is 26 times larger compared to THG at the air-glass interface. For a demonstration of the capabilities of such a highly nonlinear material for pulse characterization, third-order autocorrelation and interferometric frequency-resolved optical gating (IFROG) traces are recorded with unamplified nanojoule pulses directly from a broadband femtosecond laser oscillator.
© 2011 OSA
Nanocrystalline thin films constitute important functional materials and exhibit a vast potential for applications in photovoltaics, chemical sensors, or photocatalysis. A further intriguing application of nanocrystalline films lies in the highly efficient nonlinear frequency conversion of laser pulses, enabling the use of sub-micron films in advanced detection and diagnostics systems. The extremely short path lengths in the highly nonlinear films essentially removes all phase-matching constraints of traditional nonlinear optics, enabling conversion of broadband spectra without detrimental spectral filtering nor temporal broadening due to dispersion. These characteristics are of particular interest for the measurements of few-cycle optical pulses, using techniques like autocorrelation or frequency-resolved gating (FROG) where spectral filtering may easily corrupt the measured pulse shape or width. While materials research has mostly concentrated on films with enhanced χ(2) nonlinear susceptibility suitable for second-harmonic generation, thin films with enhanced χ(3) would further improve the capabilities in characterization techniques such as FROG. Using third-order nonlinear conversion rather than a χ(2) process, it is immediately possible to resolve the direction-of-time ambiguity [1,2], which enables detection of pulse asymmetry  and distinction between pre- and post-pulses . For third-order characterization of femtosecond pulses, surface third harmonic generation (STHG) at the air-glass transition [4,5] defines the standard for near-infrared laser wavelengths, featuring a number of advantages as (i) independence on wavelength and bandwidth, (ii) relatively high efficiency, and (iii) strongly reduced phase-matching requirements. STHG has been used for various third-order pulse characterization techniques such as third-order autocorrelation, third harmonic frequency-resolved optical gating (THG-FROG) [6–8] and related techniques. THG in specifically designed nanocrystalline films is more than an alternative to STHG and offers a greatly increased conversion efficiency compared to standard STHG [9,10]. Previous work employing a thin Ta2O5 film (thickness ~180 nm) demonstrated tenfold enhancement of the THG signal compared to air-glass STHG .
Here we report essential progress in this field. Employing nanocrystalline TiO2 thin films, THG signal enhancement up to 26 times above the value for the air-glass interface is observed. The properties of the THG are discussed, and immediate application for ultrashort-pulse characterization by third-order autocorrelation and interferometric frequency-resolved optical gating (IFROG) is presented.
2. Experimental details
2.1. Preparation and characterization of nanocrystalline layers
Thin TiO2 nanolayers were deposited by reactive dc-sputtering in a vacuum chamber using a two-inch metallic titanium target. Before depositing, the chamber was evacuated to a base pressure below 10−4 Pa. Sputtering was performed in the low pressure region with an argon-oxygen-atmosphere at a partial pressure ratio of 2:1 (argon partial pressure about 1,5*10−3 mbar and an oxygen partial pressure of about 0,7 * 10−3 mbar, respectively) with constant power of 200 W and a target-to-substrate distance of 5 cm. Formerly, the total sputtering pressure was varied to influence the morphology of the growing film as well as the formation and the amount of crystalline phases in the films . The thin films were deposited onto thin glass substrates (microscope slides). Prior to this deposition, a reactively sputtered SiO2 barrier layer was deposited to prevent unwanted alkali migration from the glass into the TiO2-layer. The samples were investigated (a) as-deposited and (b) after annealing at 723 K for one hour in air. As the annealed samples exhibit slightly higher nonlinearities, we focus on their discussion in the following. Film thickness and optical properties were characterized by a mechanical stylus profilometer (Dektak 3 ST, Veeco) and spectral ellipsometry (SE850, Sentech). The first main objective of this work was to experimentally identify the optimum thickness for efficient THG. For a sufficiently large thickness difference over the sputtered area, glass substrates with dimensions of about 70 x 22 mm2 were used. Measurements indicate a well-defined variation in layer thickness ranging from 105 to 420 nm. Thickness data and refractive indices determined at discrete positions (step width 6.25 mm) of the sample are plotted in Fig. 1(a) . Over a large thickness range between 150 and 375 nm, the refractive index was found to remain nearly constant, i.e. n ≈2.3, close to the value reported for TiO2 thin films grown by electron beam evaporation . The SEM images in Figs. 1(b)–1(c) reveal the differences in the surface structure at two different positions of a graded thickness TiO2 thin film. At a thickness of 180 nm, the surface consists of nanograins with an average size of about 20 nm [Fig. 1(b)], whereas the layer appears to be much smoother at a thickness of 400 nm [Fig. 1(c)]. We attribute the higher index of refraction measured for large thickness to this change of morphology. The inset of Fig. 1(a) shows the optical image of a gradient layer sample. The thickness variation is directly visible from the differently colored zones (Newton's rings).
The X-ray diffraction pattern for the sample with 180 nm thickness is shown in Fig. 2 . For higher thickness, a nearly identical pattern was observed, indicating anatase (101) as the prevalent phase together with a small amount of the rutile (110) phase. The damage threshold fluence of TiO2 thin film is ~0.3 J/cm2 for a pulse duration of 150 fs . This value is expected to further reduce for the shorter pulses.
2.2. Third-harmonic generation
THG studies were performed by exciting the samples with a Ti:sapphire laser oscillator (Femtosource) capable of emitting linearly polarized 15 fs pulses at a repetition rate of 75.3 MHz, a pulse energy of 4 nJ, and a central wavelength near 800 nm. The experimental setup is schematically shown in Fig. 3 . The experiments were done either without the Michelson interferometer (for THG study) or with it (for pulse characterizations). The laser pulses were tightly focused onto the samples under normal incidence. The generated THG signal was collected in transmission direction by a UV transmitting microscope objective. The THG spectrum was mostly separated from residual pump radiation by two interference filters. In some cases one or two additional highly reflecting mirrors at 266 nm were also used. The generated signal was analyzed with a fiber-coupled grating spectrometer (HR 2000, Ocean Optics) and a high-sensitivity electron multiplier charge coupled device (EMCCD) based spectrometer (Newton, Andor Technology). All experiments were carried out at room temperature. The EMCCD detector was thermo-electrically cooled down to −75°C. The input power dependence was studied by varying the intensity with a set of neutral density filters.
2.3. Third-order pulse characterization
To demonstrate the applicability to the characterization of ultrashort pulses, third-order interferometric autocorrelation  and frequency-resolved optical gating (IFROG) [15–20] were implemented experimentally. Using the Michelson interferometer, the input pulses were split into two replicas using a broadband dielectric beam splitter (Venteon). A 25 mm focal length concave mirror or a lens of focal length 12 mm was used to generate the THG, and the EMCCD based spectrometer served for frequency-resolved detection. The total THG signal was deduced from this signal by spectral integration, yielding the autocorrelation signal as a function of temporal delay.
3. Results and discussion
3.1. Optimum thickness for efficient THG
The thickness-dependent THG is depicted in Fig. 4(a) , clearly illustrating increasing dephasing between fundamental and THG signal for increasing length. From this oscillating curve we deduce a thickness of 180 nm for the strongest THG signal.
In general, the highest frequency conversion efficiency is achieved when the thickness is equal to the coherence length (LC) of the nonlinear optical interaction. For the THG process, this length is defined byEq. (1) was found to be 190 nm, thereby approximately confirming the experimental value of thickness for highest THG. For this calculation the refractive indices were taken from , in which the data for the transmission region were similar to our experimental findings for lower thickness. To further verify the result, the thickness dependence was tested with a discrete set of TiO2 nanolayer samples of different, but uniform thickness. As in the first experiment with graded layers, a thickness close to 180 nm is found to exhibit the highest THG efficiency. All details on THG signal analysis and applications to pulse diagnostics reported below refer to this one optimized uniform sample. The appearance of a second peak according to the signal dependence on the coherence length was expected for a larger thickness than 350 nm as it is indicated by the experimental results in Fig. 4(a).
The fast damped oscillation behavior and the appearance of a second peak at 350 nm deviates from the expected ideal characteristics, according to which the THG signal should show a gradual decrease with subsequent gradual increase towards 570 nm position. The fast deviating signal after the peak at 180 nm is explained by a significant contribution the Fabry-Pérot interference of the fundamental in the layer. This was verified by numerical simulations.
The reason for the modified curve at larger thickness, however, may only be understood by assuming a distinct change of the stoichiometry. Indeed, this becomes obvious from Fig. 1(a) in which the refractive index undergoes an extremely steep rise toward higher thickness, and from the corresponding structural change (strongly decreasing roughness, Figs. 1(b) and 1(c)). The local intra-layer variation of stoichiometry, however, is still the subject of investigations by independent physico-chemical analytical techniques.
3.2. Analysis of the THG signal
According to the expectations, the generated THG signal strength scales with third power of the input signal strength (straight line in the logarithmic plot in Fig. 4(b)). The THG spectrum generated from the thin film [Fig. 4(c)] exhibits a FWHM bandwidth of 22 nm and is centered at a wavelength of 272 nm. For comparison, the air-glass interface THG signal detected under the same experimental conditions is displayed in the inset of Fig. 4(c). For the latter case, the spectral properties appeared to be quite similar to those obtained with the TiO2 thin films.
The spectral characteristics corroborate that the TiO2 thin films are, in fact, a viable alternative for obtaining reliable THG over the full bandwidth of a broadband Ti:sapphire laser oscillator. From Fig. 4(c) an enhancement factor of about 26 (ratio between the THG from 180 nm TiO2 nanolayers and the value for the air-glass interface) was found. The estimation of third-order nonlinearity from a comparison of THG signals in the presence and absence of the thin film is a proven standard method . For focused Gaussian beams, the THG intensities without and with film can be expressed by Eqs. (2) and (3), respectively:
For our case, the THG contribution from the thin film is much larger compared to the STHG from the interface. The film thickness L was much smaller than the confocal parameter b(~150 µm) and the refractive indices of the thin film are much different from the values for the substrate. Under these conditions, Eqs. (2) and (3) take the form10,21]Eqs. (4) and (5), the absolute value of third-order nonlinearity of the TiO2 thin film was estimated to be χ(3) = 7.1 x 10−11 esu (in SI units:χ(3) = 9.94 x 10−19 m2V−2). The parameters used for this estimation and corresponding references are given in Table 1 . A similarly high value of third-order nonlinearity in nanocrystalline TiO2 thin film was recently reported for a z-scan experiment with 50 fs pulses at wavelengths around 800 nm . This value significantly exceeds the third-order nonlinearity of bulk TiO2 at 1064 nm and 532 nm [24,25] (χ(3) = 3.4 x 10−13 esu and χ(3) = 4.6 x 10−12 esu, respectively, calculated from n2 data). By simulations based on  we found that the value at 532 nm is less reliable because of being related to a wavelength range with a rapidly changing third-order nonlinearity whereas the value at 1064 nm is expected to be very close to that at 800 nm. The large third-order nonlinearities in TiO2 found in our experiments as well as by other groups (see ) can only be explained by a major contribution from surface effects, i.e. higher charge densities and stronger electrostatic potential gradients caused by grain boundaries. These effects result in an increase of total dipole moment and nonlinear coefficients . Surface enhancement of both, second-order [28,29] and third-order nonlinearity [29,30] has also been reported for materials like BBO or ZnO. The role of possible intrinsic (volume) inhomogeneities for the enhancement has still to be investigated.
3.3. Application to third-order ultrashort pulse characterization
Figure 5(a) shows a third-order interferometric autocorrelation trace recorded for with a pulse energy of 0.6 nJ (EMCCD detector exposure time 10 ms, gain = 0). For generating this trace, the concave mirror of f = 25 mm was used, and only interference filters were employed to suppress the residual fundamental. In accordance with theory , the peak-to-background ratio is found to be close to 32:1. Figure 5(b) shows a spectrally resolved representation of the same measurement, yielding a high-contrast third-order IFROG trace. IFROG is a collinear variant of FROG that is particularly suited for few-cycle pulses [16–18]. IFROG offers two independent ways of retrieving pulse shapes and offers added internal consistency checks, in particular for calibrating the delay axis. Here we restrict ourselves to analyzing the unmodulated dc part of the trace that we extract by Fourier filtering. The resulting THG-FROG trace can then directly be processed by a standard pulse retrieval software (Femtosoft Technologies, FROG 3.0).The retrieved spectral signal and spectral phase are shown in Fig. 5(c). The corresponding pulse duration is determined as 22 fs. The spectral phase information [red circles, Fig. 5(c)] indicates the presence of a positive quadratic chirp. Due to this chirp, the measured pulse duration is found to be larger than the input duration of 15 fs, which we attribute mostly to the beam splitters used in this study.
We performed a marginal test, comparing the retrieved and an independently measured fundamental spectrum [dashed line Fig. 5(c)]. Even though the agreement may not be perfect, there are no indications of a major loss of bandwidth. As the retrieved spectrum appears enhanced on the short wavelength side, the deviations are indicative of an increase of nonlinearity with shorter wavelength, which may be explained by resonant enhancement of the nonlinearity in the vicinity of the bandgap. A certain influence may also come from the relatively strong filtering required for rejection of the fundamental in collinear techniques. Considering the challenges of measuring oscillator pulses with third-order FROG methods , we therefore believe that nanocrystalline TiO2 thin films provide a viable alternative for characterizing ultrashort pulses, with the added advantage of time-symmetry disambiguation.
In order to demonstrate the performance of the TiO2 THG based pulse characterization system relative to STHG at the air-glass interface, we did the comparative study of linear chirp measurements. For these measurements, we employed tighter focusing with the 4 mm thick flint glass lens (f = 12 mm), which exhibits a group-delay dispersion of 500 fs2. In the case of air-glass STHG, it was considerably more difficult to suppress residual fundamental light. Therefore an additional filter (HR at 266 nm) was used, and the same condition was maintained for THG of TiO2 to ensure equal experimental conditions in both cases. The interferometric autocorrelation trace measured with STHG (exposure time = 200 ms) and THG in TiO2 (exposure time = 10 ms) are shown in Figs. 6(a) and 6(b), respectively. Both traces exhibit a nearly perfect 32:1 peak to background ratio, with clear indications of somewhat elevated noise levels on the STHG trace. Despite a 20 times lower integration time, the absolute signal levels (shown as lefthand ordinates) are 1.2 times higher for THG in TiO2, yielding a ratio of ~24 between the THG of our TiO2 thin film and STHG at the air-glass interface, which is very close to the value reported in section 3.2.
Extracting the unmodulated dc part from the IFROG traces in Figs. 7(a) and 7(c), we retrieved the pulse shapes shown in Figs. 7(b) and 7(d), respectively. The FROG errors observed in the retrieval are in the range of 0.01 to 0.02. Regardless of the nonlinear material used, similar slightly asymmetric pulse shapes with 150 fs pulse duration are retrieved [Figs. 7(b) and 7(d)]. In the spectral representation, the phase curvature is indicative of a group delay dispersion of 500-600 fs2, which agrees well with the additional dispersion introduced by the 4 mm thick lens.
In summary, we investigated highly efficient third harmonic generation of near-infrared ultrashort pulses in sputtered TiO2 nanolayers towards their suitability for pulse characterization applications. Using graded thickness layers we determined an optimum film thickness of 180 nm for THG in close agreement with the theoretically calculated coherence length. The optimized samples provided an ~26 times higher THG efficiency than air-glass interface STHG. As such thin films do not require stringent phase-matching criteria for THG, their application for characterization of ultrashort pulses lies at hand and is relative insensitive of central wavelength and bandwidth of the pulses. We further demonstrated the use of the efficient THG for the characterization of broadband nanojoule ultrashort pulses. To the best of our knowledge, this constitutes the first demonstration of third-order interferometric FROG and the first measurement of a THG FROG trace using a broadband and easy-to-produce thin-film material at sub-nJ pulse energy. Contrary to most of the known third-order pulse characterization techniques based on four-wave mixing processes (polarization-gating FROG, self-diffraction FROG, transient-grating FROG) which utilize volume χ(3) nonlinearities , nanocrystalline TiO2 thin films enable THG FROG measurements at significantly enhanced efficiency. Previous approaches like heterodyne four-wave mixing , semiconductor amplifiers or THG in liquids required far more complicated arrangements (e.g., multiple interferometers), or they were restricted to long wavelengths. Therefore, setups incorporating thin films with nanoscale substructures are a simple but highly efficient alternative.
The authors thank Dr. M. Albrecht, A. Kwasniewski and M. Schmidbauer (IKZ Berlin), M. Tischer, and C. Poppe (MBI Berlin) and Prof. Rüssel (OSI, FSU Jena) for stimulating discussions and support. The work was in part financially supported by DFG (projects no. GR 1782/12-1 and GR 1782/13-1).
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