Some temporal and spectral properties of femtosecond supercontinuum important in pump probe spectroscopy

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1 Optics Communications xxx (2004) xxx xxx Some temporal and spectral properties of femtosecond supercontinuum important in pump probe spectroscopy M. Ziolek a, *, R. Naskrecki b, *, J. Karolczak a,b a Center for Ultrafast Laser Spectroscopy, Adam Mickiewicz University, Poznan, Poland b Quantum Electronics Laboratory, Faculty of Physics, Adam Mickiewicz University, Poznan, Poland 1 Received 20 January 2004; received in revised form 11 June 2004; accepted 30 June 2004 Abstract We present an investigation into the femtosecond supercontinuum properties, generated with 100 fs laser pulses in a condensed phase. The influence of different generation conditions on spectral and temporal properties of the supercontinuum is presented. Particularly, various media (water, fused silica, calcium fluoride), laser wavelength (800 and 400 nm), pulse energy, and focusing lens displacement are used. The experimental results are analyzed in view of current theories, with the focus on the role of multiphoton ionization in the generation process. A semi-quantitative explanation of the frequency broadening is proposed. Finally, the implications of the results for pump probe spectroscopy are also discussed. Ó 2004 Elsevier B.V. All rights reserved. PACS: J; J; J Keywords: Supercontinuum; Femtosecond; Pump probe 1. Introduction Many models have been introduced over the years in an attempt to explain the supercontinuum (SC) generation. In the femtosecond time regime, the self-phase modulation (SPM), enhanced by * Corresponding authors. Tel.: ; fax: addresses: marziol@amu.edu.pl (M. Ziolek), (R. Naskrecki). self-focusing, played a prominent role in the past theoretical assumption [1]. The frequency change Dx of the pulse is given by: Dx ¼ oð/ nl Þ=ot; ð1þ where the nonlinear phase / nl accumulated during propagation over a distance L, may be written as: / nl ¼ Dnx 0 L=c: ð2þ In Eq. (2), c is the velocity of light in vacuum, x 0 is the central frequency of the pulse, and Dn is the /$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi: /j.optcom

2 2 M. Ziolek et al. / Optics Communications xxx (2004) xxx xxx change of refractive index due to nonlinear processes. If Dn depends on the distance L, a proper calculus to Eq. (2) has to be added. The change of the refractive index in the case of Kerr nonlinear effect is proportional to pulse intensity I: Dn Kerr ¼ n 2 I; ð3þ where n 2 is called the nonlinear refractive index. Thus, in the leading part of the laser pulse the refractive index increases with time, which causes the generation of lower frequencies (negative Dx), called Stokes broadening. The opposite situation is in the trailing part of the pulse, which becomes blue-shifted (anti-stokes broadening). When the laser pulse power exceeds the critical power for self-focusing, the beam diameter can be decreased to or even less than 10 lm. This results in an even 100 times larger intensity than that with normal focusing (by lenses) and causes larger broadening. The Stokes anti-stokes asymmetry of the SC spectrum was believed to be a result of a self-steepening [2,3]. The back of the pulse travels faster than its central part (due to different refractive index) so that the intensity slope becomes steeper at the back. In this way, the decrease of Dn at the back of the pulse (anti-stokes broadening) is more rapid than its increase in front of the pulse (Stokes broadening). However, the experimentally observed asymmetry is larger than calculated. Furthermore, the anti-stokes frequency broadening increases with decreasing of n 2, and is independent of the initial pulse intensity. These observations are contrary to the predictions of usual SPM theory [1]. Recent reports suggest that the supercontinuum generation is much more complicated and many other processes should be considered. One of them is the plasma formation caused by the multiphoton absorption [4 6]. During the selffocusing and filament formation the pulse intensity as well as Dn increase relatively slowly, which brings about relatively small Stokes broadening. When the intensity reaches the critical value for the multiphoton ionization, free electrons are generated in a very short time (single femtoseconds). The free electrons induce a negative change of the refractive index, which can be approximated by [6]: Dn e ¼ 2pe2 N e ; ð4þ m e x 2 0 where N e is electron density and e and m e are the charge and mass of the electron in CGS units, respectively. The electron density is proportional to Kth power of light intensity, N e µi K [4 6], where K is the order of multiphoton process. This number of photons required to ionize the medium can be calculated when its energy bandgap, E g,is known: K ¼ Intð1 þ E g =hx 0 Þ; ð5þ where Int(x) denotes the integer part of x. As a result of multiphoton ionization, the rapid drop in Dn causes defocusing and large anti-stokes broadening. This mechanism explains the observed increase of SC spectral width together with the increase mediumõs energy bandgap. Larger bandgap requires higher order of multiphoton ionization, which means larger critical intensity and larger maximal Dn. In media with energy bandgap lower than the bandgap threshold, self-focusing is stopped by free electron defocusing before an intensity sufficient for SC generation is achieved. In such media only small broadening of the pulse spectrum due to the SPM is observed [7]. Another important process in the SC generation is the group velocity dispersion, which may cause pulse splitting [8,9] and a new coalescence [10]. Very recently, it has been shown that the linear chromatic dispersion plays an important role in the achievable spectral extent of the SC [11]. It is worth noticing that Raman processes and four-wave mixing are the dominant mechanisms in SC generation in longer time scales, for pico [12,13] and nanosecond [14] laser pulses. Moreover, ultrashort pulses might be significantly spectrally broadened by the SPM effect alone in optical fibers due to the relatively long propagation distances [15]. In this paper, we do not consider these two cases of the SC generation. 2. Experimental results A series of experiments with femtosecond supercontinuum generated under different conditions

3 M. Ziolek et al. / Optics Communications xxx (2004) xxx xxx 3 were performed. Time-resolved studies (SC chirp measurements) were made with the transient absorption experimental setup, described in detail before [16]. In order to collect the SC spectra, a CCD camera from the same experimental setup was used. The output of the laser system (femtosecond titanium sapphire) was set at 1 khz repetition rate providing pulses of about 100 fs duration, with the energy up to 1 mj. The probe beam passed through an optical delay line consisting of a retroreflector mounted on a computer-controlled motorised translation stage, and then converted to SC, which diameter was 2 5 times smaller than that of the pump. Both pump and probe pulses intersect at an angle of 2 3 and spatially overlap into a sample (0.3 mm BK7 plate for pump wavelength 400 nm or 2 mm cell filled with methanol for pump wavelength 266 nm) with slight focusing of pump beam and no focusing of probe beam. A grating polichromator was used in conjunction with thermoelectrically cooled CCD camera to record the spectra. In order to improve the signal-to-noise ratio the transient absorption measurements were performed in two-beam geometry (probe and reference) with two synchronized choppers in the pump and probe paths, respectively. This allowed the substantial elimination of the influence of the laser beam fluctuations and, consequently, the measurements of the very small values of optical density changes, DOD < SC was generated either in 10 mm quartz cuvette filled with water or in rotating (with frequency of a few Hz) fused silica or calcium fluoride plates of 2 mm thickness. The spatial distribution of generated SC has a radial structure it contains a number of colored rings around a common white center. A diaphragm with a variable aperture shapes the white light continuum beam and fixes the beam diameter between 0.2 and 0.4 mm. The vertical and horizontal translation of this aperture allows to cut out from the spatial distribution of the generated SC the central most homogenous part. It is worth mentioning that several mechanisms for the conical emission accompanying the SC have been proposed [17 20], but its investigation is beyond the interest of our paper. The geometry for SC generation in water is shown schematically in the inset of Fig. 1(a). The displacement Dx between the lens of focal length 10 cm and the medium for SC generation causes the change of the focus position in the medium by the amount of Dx/n 0, where n 0 is the linear refractive index of the medium [4]. The SC spectra generated with 800 nm, 100 fs laser pulses in 10 mm long cuvette filled with water, for different displacements are presented in Fig. 1(a). Long- Fig. 1. (a) The spectrum of the supercontinuum generated with 800 nm, 100 fs laser pulses in 10 mm cuvette filled with water, measured for different displacements Dx of focusing lens; longwavelength part of the spectrum is modified by optical filters; (a) inset: experimental scheme for the supercontinuum generation. (b) The chirp of the supercontinuum generated with 800 nm, 100 fs laser pulses in 10 mm cuvette filled with water, measured for different displacements Dx of focusing lens; inset: the change of the measured supercontinuum chirp compared to the calculated group velocity dispersion.

4 4 M. Ziolek et al. / Optics Communications xxx (2004) xxx xxx Fig. 2. The dependence of the temporal duration (FWHM) of the pump probe cross-correlation function (CCF) on the displacements Dx of focusing lens. The probe supercontinuum pulse was generated with 800 nm, 100 fs laser pulses in 10 mm cuvette filled with water. The linear fit to the data points is indicated by the dotted line. wavelength part of the spectrum is modified by optical filters, which remove from the SC the rest of the fundamental beam (the conversion efficiency was approximately 20 30%). The anti-stokes edge of the spectrum is constant and equals about 370 nm (in spite of early stages: Dx=0.5, where the light is blue, and Dx=0.9, where the light is green by eye). Similar results are obtained for the SC generation in calcium fluoride plate, but the cutoff wavelength is shorter and equals 300 nm. Fig. 1(b) shows the variation of SC chirp generated with 800 nm pulses in water as a function of the lens displacements. The chirp is determined by the fitting of Gaussian curve to the kinetics of pump probe cross-correlation function (CCF) measured using the two-photon absorption signal (in 0.3 mm BK7 glass plate, pumping 400 nm) in the spectral range nm. The measured chirp is also affected by the optics between the cuvette filled with water and BK7 plate (back window of the cuvette and lens behind the cuvette). In the inset of Fig. 1(b), the average change of the measured SC chirp (caused by the displacement of the lens by an amount Dx =1 mm) is compared to the calculated values. The squares with error bars are calculated from the data in Fig. 1(b) (the average of 6 differences between 2 time delays of adjacent lens displacements). The solid line represents the calculated group velocity dispersion assuming propagation of the laser pulse in 1 mm/1.33 water (1.33 is the linear refractive index of water at 800 nm). Besides the chirp, the duration of SC pulses also changes with Dx since the CCF duration (the mean of 70 fitted wavelength results) varies from 110±4 fs for Dx=0 to 128±4 fs for Dx =6 mm, see Fig. 2. As can be seen from this figure, the CCF duration changes linearly with Dx (with the increase of about 3 fs per 1 mm lens displacement). It should be noted that, within the experimental error, the CCF temporal broadening is independent of probing wavelength. The SC properties dependence on wavelength is presented in Fig. 3(a) (spectral properties) and Fig. 3(b) (temporal properties). The spectral range of the anti-stokes part of the spectrum (Fig. 3(a)) is about 2 times narrower when 400 nm instead of 800 nm wavelength pulses are used in 2 mm calcium fluoride or fused silica plates. In both cases, the range of the spectrum is broader for calcium fluoride than for fused silica plate. The chirp (Fig. 3(b)) was measured applying the two photon absorption signal in 2 mm sample cell filled with methanol at excitation wavelength 266 nm. It was possibly to determine precisely the time zero for each wavelength of the supercontinuum (in spite of broadening of the signal due to significant pump probe velocity mismatch and thickness of the sample) with the help of formula presented in [21]. The measured chirp is also affected by the optics between the calcium fluoride plate and sample cell (methanol). As seen in Fig. 3(b), the chirp of SC is slightly smaller for SC generation with 400 nm pulses (50 fs difference in spectral range nm for generation in 2 mm calcium fluoride plate). The influence of pulse energy on the SC spectrum generated with 800 nm laser pulses in 10 mm cuvette filled with water was also experimentally measured. Similarly to the displacement dependence, the anti-stokes edge of the spectrum stays constant for pulse energy ranging from 4 to 17 lj, while relative intensities change in different parts of the spectrum. Furthermore, the change of pulse energy from 6 to 9 lj causes the increase

5 M. Ziolek et al. / Optics Communications xxx (2004) xxx xxx 5 Fig. 3. (a) The intensity of the anti-stokes part of the supercontinuum spectrum generated with 100 fs laser pulses of two different wavelengths (400 and 800 nm) in 2 mm calcium fluoride or 2 mm fused silica plate. (b) The chirp of the supercontinuum generated with 100 fs laser pulses of two different wavelengths (400 and 800 nm) in 2 mm calcium fluoride plate. of the measured SC chirp by the amount of 90 fs at 380 nm (related to 800 nm), which is equivalent to the dispersion of 0.4 mm of water. 3. Discussion Our results appear to be consistent with the multiphoton ionization model [4]. One of the most important predictions from this model is that the anti-stokes part of the spectrum is generated over a very small distance in the medium, about 200 lm. Thus, the spectrum width is independent of the position of the beam focus in the medium (Fig. 1(a)). By increasing the distance between lens and medium, SC is generated at the position closer to the medium entrance, and the remaining part of the medium contributes only to additional chirp of SC (due to the group velocity dispersion effect). The different spectrum at early stages (Dx <1 mm) might be explained by the stimulated Raman scattering, which contributes to the generation before the filament is formed, as has been recently observed [22]. Displacing the lens by Dx is equivalent to moving the focus by Dx/n 0 in the medium, where n 0 is the linear refractive index [4]. In other words, such displacement changes the chirp of SC by the amount of dispersion in the medium of Dx/n 0 thickness, which is confirmed in Fig. 1(b). Similar results were reported before [23], but under slightly different geometrical conditions (geometrical focus was in front of the sample so that the position of the generation volume was moving towards the end of the sample while the displacement Dx was increasing), which are less often used in the pump probe spectroscopy. Moreover, the changes of the chirp are also in agreement with the changes in the duration of the pump probe CCF since additional dispersion causes temporal broadening of the SC pulses (Fig. 2). To our knowledge, this is the first report on such dependence of CCF duration. The increase of CCF duration (from 110 to 128 fs for lens displacement of 6 mm) with its independence of the probe wavelength in the range nm reveals yet another interesting property of SC, important in the pump probe spectroscopy. Both these facts together cannot be explained under the assumption that the duration of a part of SC pulse at particular wavelength changes in similar fashion to that of the normal pulse duration. The duration pffiffiffiffiffiffiffiffiffiffiffiffiffiffiof CCF of two Gaussian pulses is equal s 2 1 þ s2 2, where s 1 and s 2 are the durations of pump and probe pulses. In our experiment the pump pulse duration is not precisely known, so, to satisfy the initial 110 fs value of CCF duration both the pump and SC probe pulses might be 78 fs as well as, for example, the pump pulse might be 105 fs and probe pulse much shorter 30 fs. A temporal duration increase of the unchirped, transform limited Gaussian pulse due to

6 6 M. Ziolek et al. / Optics Communications xxx (2004) xxx xxx the group velocity dispersion in the medium of a given thickness can be easily calculated (for example, with the help of formula (12) from [24]). Although, if we take the probe pulse duration as 78 fs, the change of CCF after passage of 6 mm of water is nearly independent of probe wavelength, but it is too small (113 fs for 370 nm) compared to the experimental value 128 fs. Otherwise, if we take shorter probe pulse duration (30 fs), the CCF broadening is more significant, but strongly dependent on the wavelength (for example, 128 fs for 370 nm but only 112 fs for 700 nm). Thus, because of unusual nature of wavelength components of SC pulses, their temporal duration have to be treated differently from the duration of other pulses in pump probe spectroscopy. In the ionization model, the anti-stokes spectrum width is independent of the pulse energy (if the pulse power exceeds the critical power for self-focusing), which was experimentally verified in line with the results of other groups [6,25,26]. However, increasing the energy causes earlier focusing (and greater chirp) since the self-focusing of the beam acts faster. Such behaviour of the chirp of SC pulse has not been explicitly reported so far. The precise absolute value of the distance between the lens and medium for SC generation is not determined in our experiment, so we can only perform a very rough calculation. The self-focusing distance in the continuous beam and paraxial approximation can be written as [27]: rffiffiffiffiffiffiffiffiffiffiffi n 0 z sf ¼ r 0 ; ð6þ 2n 2 I 0 where r 0 is the initial beam radius and I 0 is the initial intensity. Assuming that r 0 equals 50 lm at the entrance of the medium due to external focusing, the self-focusing distance for 100 fs pulses in water (n 0 =1.33, n 2 = m 2 /W) is equal 4.7 and 3.8 mm for the pulse energy 6 and 9 lj, respectively. Thus, the difference of self-focusing distances is 0.9 mm, which is not far away from the experimentally determined value 0.4 mm (see Section 2) and confirms the fact that anti-stokes broadening of SC occurs near the self-focus point. Next, doubling the pulse frequency (from 800 to 400 nm wavelength) means that the multiphoton ionization occurs for the lower order of multiphoton process. Thus, the lower intensity is sufficient for the free electron defocusing, and the anti- Stokes spectrum is narrower. This is in agreement with the results presented in Fig. 3(a), where the anti-stokes broadening becomes about twice smaller when changing the wavelength from 800 to 400 nm in both fused silica and calcium fluoride plates. On the contrary, in the usual SPM theory the SC spectrum should broaden with increasing pulse intensity I, pulse frequency x 0, and propagation distance L in the medium. The results are consistent with the observation that the ratio of the mediumõs bandgap energy to the photon energy of the incident wavelength determines the amount of anti-stokes broadening [28]. The spectrum comparison between 400 and 800 nm generated SC was also theoretically studied in [25], but, to our knowledge, the comparison of the chirp (Fig. 3(b)) has not been reported so far. So far, many theoretical models and simulations including numerous physical processes have been proposed to explain the SC spectrum [4,5,11,22,25,26,29]. However, there is still no satisfactory agreement between the theory and the experiment. Also, different authors focus their attention at the role of different factors and processes, which, taking into account the complex dependence of the numerical solutions on the initial parameters, makes their conclusions difficult to compare. Thus, we want to propose a simple, semi-quantitative analysis of SC generation with the explanation of the frequency broadening. After [4] we assume that during the self-focusing of the pulse its intensity (as well as the refractive index change in Eq. (3)) grows linearly within the propagation distance. The nonlinear positive phase accumulation stops when the intensity reaches the threshold intensity I th for multiphoton ionization, and rapid drop in Dn occurs due to the free electrons generation (Eq. (4)). Assuming that the initial intensity is much lower than I th, the maximum anti-stokes frequency broadening (Eqs. (1) and (2)) is proportional to n 2 I th (maximum refractive index change). In order to verify our estimation the analytical expression for I th is needed for calculations. In the absence of avalanche ionization contribution (in the femtosecond time regime it can be often neglected because the

7 M. Ziolek et al. / Optics Communications xxx (2004) xxx xxx 7 ionization requires time to build up from the collisions of electrons in the case of avalanche process), the intensity threshold for multiphoton ionization in condensed phase may be written in the following analytical way [30] (in MKS units): 1=K I th ¼ B 1 q cr ; ð7þ Að0:5sÞ where q cr is the critical free carrier density, s is the pulse duration, K is defined by Eq. (5) and A and B coefficients are given by: A ¼ 2 9p x m 0 3=2 K x 0 0 e 2K 1 UðzÞ ; h 16 B ¼ e 2 m 0 E g x 2 0 ce 0n 0 : In the above expressions, 1/m 0 =1/m e +1/m h, with m e and m h denoting electron and hole masses, respectively, and both the function U(z) and its argument z are defined as: z ¼ 2K 2E 1=2 g ; hx 0 Z z UðzÞ ¼e z2 e y2 dy: 0 To verify the proportionality of the SC anti-stokes broadening to the n 2 I th term, we performed the calculations of the ionization threshold intensities with Eq. (7) and compared the results to our experimental data of SC broadening. The pulse duration was taken as s=100 fs, the standard value of critical free carrier density q cr =10 18 cm 3 was used, and it was assumed that the m e equals m h [31]. Table 1 presents the calculated values of I th for two materials of different energy bandgap (E g ) at two different wavelengths of the pulse that generates the SC. The table also contains the nonlinear refractive index values of these materials and the experimentally measured maximum anti- Stokes broadening (Dx max ), from the data of Fig. 3(a). As can be seen from the values presented in the last column of Table 1, the ratio n 2 I th /Dx max is similar under different SC generating conditions, except for one slightly larger value for 400 nm generation in calcium fluoride. This confirms the fact that the term n 2 I th is really proportional to the anti-stokes broadening, which should be the general property of SC generation. The dependence of intensity threshold I th on the order of multiphoton process K is plotted in Fig. 4. The two curves (for 800 and 400 nm generating wavelength) are calculated for the parameters of fused silica (E g =7.5 ev, n 0 =1.45 for 800 nm or n 0 =1.51 for 400 nm). However, they can be easily used for the estimation of I th for other media since, according to Eq. (7), the I th value has to be multiplied by energy bandgap ratio and refractive index ratio. In principle, the values of function U(z) changes for different materials as well, but for most of the E g and x 0 combinations they are in the range of Taking into account that the U(z) is raised to the power of (1/K), such changes are of minor importance. Therefore, we took the mean value U(z) = 0.5 for the plots in Fig. 4. As can be seen from Fig. 4 for both 800 and 400 nm wavelength, the intensity threshold grows linearly with K for the values K P 3, but Table 1 Different parameters of supercontinuum generation and multiphoton ionization for calcium fluoride and fused silica: wavelength (k), energy bandgap (E g, from [4]), order of multiphoton process (K, calculated from Eq. (5)), maximum anti-stokes broadening (Dx max, from experimental results in Fig. 3(a)), intensity threshold for multiphoton process (I th, calculated from Eq. (7)), nonlinear refractive index (n 2 ) and the ratio n 2 I th /Dx max Material k (nm) E g (ev) K Dx max (cm 1 ) I th (10 12 W/cm 2 ) n 2 (10 16 cm 2 /W) n 2 I th /Dx max (10 7 cm) Calcium fluoride , , Fused silica ,

8 8 M. Ziolek et al. / Optics Communications xxx (2004) xxx xxx Fig. 4. The dependence of intensity threshold I th on the order of multiphoton process K for the optical parameters of fused silica material (E g =7.5 ev, n 0 =1.45 for 800 nm or n 0 =1.51 for 400 nm), calculated from Eq. (7). The filled circles show the intensity thresholds in fused silica for 800 and 400 nm pulses. for smaller values of K it drops rapidly. For example, I th (K=3) is about 10 times greater than I th (K = 2). This explains why the SC generation is not observed in the materials of small energy bandgap [4] and is consistent with the observation of the threshold for SC generation for E g /hx 0 =2 [28]. Thus, although many other things that we didnõt take into account in our consideration (for example, the moving focus model which describes the self-focusing process for ultrashort pulses) might also contribute to the broadening value, we believe that intensity threshold for multiphoton ionization process multiplied by nonlinear refractive index plays a major role in the SC broadening. One of the most important applications of the femtosecond SC pulses are probing pulses in various pump probe methods. It is desired to have the probe pulse spectrum as wide as possible to get more information about the studied samples in such experimental techniques. Thus, in view of the above analysis, the best choice is the use of longer wavelength pulses since they give better anti-stokes broadening. Particularly, it is better to use 800 nm from Ti:Sapphire laser rather than its second harmonic unless probing wavelength below 300 nm are needed [28]. What is more, the chirp of SC in pump probe methods should be precisely determined to make proper zero time correction [32]. Optimum conditions for SC generation require careful adjusting of incoming pulse energy, beam diameter, and focal point relative to the generating material. Only then is the white light sufficiently stable for transient absorption experiments. However, usually the absolute values of these parameters are not verified, and only the stability of SC is controlled. The above results indicate that the chirp (as well as the temporal duration of pump probe cross-correlation function) depends on pulse intensity and distance (between the lens and the material for SC generation), which has been neglected so far. Thus, in principle, the chirp of probe pulses and the temporal duration of pump probe cross-correlation function should be measured whenever these parameters are changed. It is especially important when relatively thick media for SC generation are used. 4. Conclusions The investigations into temporal and spectral properties of the femtosecond supercontinuum were presented. The spectral range of the anti- Stokes part of the supercontinuum depends on the laser wavelength and the optical properties (energy bandgap, refractive index) of medium in which the supercontinuum is generated. The spectral range does not depend on the generating pulse energy and focusing lens displacement but varying both of them may strongly influence the chirp and temporal duration of the supercontinuum pulse. The results are consistent with the multiphoton ionization model of the supercontinuum generation process and are contrary to the predictions of simply self-phase modulation model. A semi quantitative calculations revealed that the frequency broadening is proportional to intensity threshold for multiphoton ionization process multiplied by nonlinear refractive index of the generating medium. The variations of the spectral range, the chirp and temporal duration of the supercontinuum pulse investigated in the paper are of significant importance in the pump probe spectroscopy.

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