1. Introduction

Time-resolved fluorescence (TRF) is one of the most important optical spectroscopic methods for the study of various photo-induced physical, chemical, and biological processes [1–5]. Since the TRF probes the excited state dynamics exclusively, it provides direct information on the photo-induced reaction dynamics occurring in the excited state, whereas transient absorption (TA) may be complicated by the ground state dynamics and excited state absorption. Among a number of TRF measurement techniques, fluorescence upconversion [6–11] and Kerr shutter [12–15] have been widely used to obtain a femtosecond TRF signal at a fixed wavelength or TRF spectra with typically 200 fs time-resolution. Still higher time-resolution is essential to investigate many photochemical and electronic processes in molecules and semiconductors occurring faster than 100 fs. For example, observation of the coherent wave packet motions of molecules in electronic excited states, which gives detailed information on many photochemical processes, requires much higher time-resolution, because the period of a typical molecular vibration is in the range of 10~100 fs. Accordingly, TA has been used almost exclusively to study the coherent wave packet motions in molecules [16–18].

To achieve the ultrahigh time-resolution in the fluorescence upconversion, group velocity dispersion (GVD), group velocity mismatch (GVM), and phase front mismatch (PFM) should be minimized. We reported a TRF apparatus providing 50 fs time-resolution by employing noncollinear sum frequency generation (SFG) [9]. The time-resolution reported, however, was still larger by a factor of two from the ideal transform-limit. We found that one of the limiting factors in getting a higher time-resolution was the longer pump pulse duration, which is usually generated by the second harmonic generation (SHG) in an upconversion experiment. In this work, we have further improved and generalized the noncollinear fluorescence upconversion technique to achieve ~30 fs time-resolution, which is close to the limit imposed by the 20 fs pulse duration employed in this work. We used two photon absorption (TPA) as an ultrafast excitation method, although noncollinear SHG [19] or achromatic SHG [20] can be employed to generate short excitation pulses. Some of the advantages of the TPA excitation are the efficient fluorescence collection and imaging due to the small excitation volume and reduced photodamage due to the longer wavelength non-resonant pump pulses. The fluorescence near the one photon excitation wavelength can be fully obtained from time zero, which usually can not be recorded in one photon excitation TRF experiment due to the interference from the scattered excitation light. Note also that the theoretical time-resolution attainable by TPA as an excitation is better than that of the one-photon excitation by a factor of √2 for a Gaussian pulse because of the quadratic intensity dependence of the TPA [19].

2. Experiments

2.1 Optical setup

A home-made cavity-dumped Ti:sapphire oscillator pumped by a frequency doubled Nd:YVO₄ laser (Verdi, Coherent, Inc) was used as a femtosecond light source. Center wavelength and spectral width were adjusted to 800 nm and 55 nm, respectively. The output pulse duration was 20 fs. The positive GVD of the optical elements was compensated by negative GVD mirrors (Layertec, Inc) and a pair of fused silica Brewster prisms. A beam splitter divided the 800 nm beam into two portions to provide the pump and gate pulses. The pump pulse was passed through an additional fused silica Brewster prism pair to compensate the difference of the GVDs arising from the different optical paths of the pump and the gate pulses.

Figure 1 shows the schematic of the fluorescence upconversion setup using TPA. In order to increase the efficiency of TPA, a singlet lens of 1.5 cm focal length was used to focus the pump beam into a 200 µm path length sample cuvette. A reflective microscope objective (N.A.=0.28) by Cassegrainian design was used to image the excitation volume onto the SFG crystal, which reduces the numerical aperture of the fluorescence beam for the efficient SFG in the BBO crystal. For time-resolved anisotropy measurement, polarization of the pump pulse was rotated with respect to the gate pulse by using a λ/2 waveplate. For the ultrahigh time-resolution, a 100 µm thick BBO crystal and the noncollinear phase matching geometry with an external angle of 10° were employed to reduce the GVM and PFM effects in the SFG crystal. Although the best temporal resolution can be achieved in nearly collinear SFG for the thin BBO crystal, the noncollinear mixing scheme is advantageous in separating the SFG signal from the fluorescence and gate pulses without the use of a prism. It should be noted that at the external angle of 10°, experimental time-resolution is practically the same as that of the collinear case [9]. SFG signal was filtered by a UG11 (Schott) glass filter and detected by a blue enhanced photomultiplier tube and a gated photon counter (SR400, Stanford Research Systems, Inc.). The photon detection efficiency through the filter, monochromator, and the photomultiplier tube was about 3 %. With gated photon counting, background noise was virtually zero for fluorescence wavelengths from 400 nm to 650 nm to give the signal-to-noise ratio (S/N) of N, where √N is the number of photons detected.

 

Fig. 1. Schematic of the upconversion setup employing TPA. Frequencies of the two input pulses are the same (λ_p=λ_g=800 nm). Fluorescence (ω_f) following the TPA was collected by the Cassegrainian pair and focused onto the BBO crystal.

Download Full Size | PDF

Instrument response function (IRF) was estimated by two different methods. In one, the autocorrelation was measured by mixing the pump pulse scattered from the sample and the gate pulse in the BBO crystal. In the other, an ultrathin 20 µm BBO crystal was placed at the sample position to experimentally simulate the cross-correlation between the gate and the fluorescence at 400 nm. The former does not take into account the effect of GVM, and serves as the lower limit of the actual IRF in a TRF measurement, whereas the latter serves as the upper limit, since the GVM between the fluorescence at the wavelengths longer than 400 nm and the gate is smaller than the GVM between the 400 nm and the gate.

2.2 Numerical simulation

A full description of the simulation method considering the effects of both GVM and PFM has been reported elsewhere [9]. The pump (ω_p) and gate (ω_g) beams propagate along the y-axis, and they overlap with an external angle θ in the BBO SFG crystal. The SFG signal at ω_p+ω_g is proportional to the spatial and temporal overlap integral of the two pulse envelopes

where L is the crystal thickness, and I_p, I_g, and I_SFG are the intensities of the ω_p, ω_g, and SFG signals, respectively. In the calculation, the pump and gate pulses were assumed to be a Gaussian in shape with 20 fs (FWHM) pulse durations, and the beam diameters were set to 85 µm. Numerical simulations were performed for the BBO crystals of 100 and 580 µm thicknesses. The intensity of the SFG signal vs. time delay (τ_d) was calculated at an external crossing angle and a pump (fluorescence) wavelength to give the cross-correlation function.

3. Results and discussion

Figure 2 shows the experimental measurements of the cross-correlations between the scattered pump pulses and the gate pulses in 100 and 580 µm thick BBO crystals. The width of the cross-correlation between the scattered 800 nm pump pulse and the gate pulse in the 100 µm thick BBO crystal is 33 fs, which is 1.1 times the theoretical limit indicating near perfect imaging of the present setup. The width increases to 38.5 fs for the 580 µm thick crystal due to the GVD and PFM. For the 400 nm SHG signal (generated at the sample position) and the gate pulses, the width of the cross-correlation is 38 fs for the 100 µm thick SFG crystal, demonstrating the ultimate time-resolution in upconversion. The width, however, increases to 115 fs for the SFG in the 580 µm crystal, which establishes that GVM plays a major role to deteriorate the time-resolution in a TRF experiment (GVD alone broadens the 20 fs pulse to 26 fs at 400 nm in a 580 µm thick BBO crystal). Nonetheless, we found by the simulation and experiment as described below that the temporal resolution for the wavelengths longer than 500 nm are highly enhanced at the external angle of 10°, approaching that of the upconversion setup using the 100 µm thick BBO crystal.

 

Fig. 2. Cross-correlation measurements by the SFG signals and their Gaussian fitting results: (a) 800 nm+800 nm in a 100 µm crystal, (b) 400 nm+ 800 nm in a 100 µm crystal, (c) 800+800 nm in a 580 µm crystal, and (d) 400 nm+800 nm in a 580 µm crystal. Fitted FWHM of each Gaussian pulse is also shown in each panel.

Download Full Size | PDF

To investigate the wavelength dependent time-resolution in the upconversion experiment, we have simulated the cross-correlation of the SFG output in the noncollinear phase matching scheme by using the equation (1). Figure 3 shows the simulation results for the two different thickness BBO crystals. For the 100 µm thick BBO crystal, simulation results show time-resolution of 40 fs at all wavelengths at the external crossing angle of 10°. This is in good agreement with the experimental results shown in Fig. 2. On the other hand, for the 580 µm thick BBO crystal with the same crossing angle of 10°, time-resolution of about 40–60 fs can be achieved for the wavelengths longer than 500 nm. Note that the external crossing angle that gives the narrowest cross-correlation width for the 400 and 800 nm lights is 20°. The optimum cross angle, however, quickly shifts to smaller values as the fluorescence wavelength increases, because the GVM at longer wavelength decreases while the PFM effect is insensitive to the wavelength. The numerical simulations and experimental results suggest that upconversion with TPA using a thin 100 µm crystal can provide near transform-limited time-resolution of about 33 fs over the entire fluorescence wavelengths. In particular, even for a BBO crystal thicker than 500 µm, similar time-resolution of around 40 fs can be achieved at the wavelengths longer than 500 nm. This result is significant because the intensity of the SFG output is a fast growing function of the crystal thickness.

 

Fig. 3. Simulated width (FWHM) of the cross-correlation of the SFG output in the noncollinear phase matching scheme as a function of the fluorescence wavelength and the external crossing angle. Thicknesses of the BBO crystals are (a) 100 µm and (b) 580 µm.

Download Full Size | PDF

To verify the ultrahigh resolution of the fluorescence upconversion apparatus and the simulation results at the wavelengths other than 400 nm, we have measured the TRF of 5 mM coumarin 153 dissolved in methanol. The fluorescence quantum yield is 0.42 [21] and the TPA cross-section is 47 GM (10^–50 cm4·s·photon^-1). An absorption band at around 400 nm was excited via TPA with the fundamental at 800 nm. Detection wavelength was set to the red edge of the emission band at 580 nm to watch the vibrational wave packet motion in the electronic excited state clearly [22]. For the pump and gate pulse energies of 9 nJ at 380 kHz repetition rate, upconversion signal of 150 counts·s^-1 was attinable with the 100 µm thick BBO crystal to give the S/N of 12 with 5 nm detection bandwidth. Figure 4 shows the TRF signals for the two different BBO crystals. Exponential fits, residuals, and the Fourier power spectra of the residuals are also shown. Both TRFs show two rise components of 110 fs and 1.2 ps time constants due to the dynamic Stokes shift of the fluorescence spectrum originating from the solvation dynamics [2, 23]. The IRFs were assumed to be a Gaussian in shape, and the widths resulted from the fits are 35 and 39 fs for the TRFs using the 100 µm and 580 µm thick BBO crystals. More importantly, both residuals show the oscillations with a major frequency component at 375 cm^-1 (period, 89 fs). These oscillations must be due to the vibrational wave packet motions in the electronic excited state, because the spontaneous emission from the S₁ state is measured exclusively. In a pump/probe transient absorption signal, such an oscillation may originate from the vibrational wave packet motion in the electronic ground as well as in the excited states [24, 25], and in principle its origin cannot be differentiated. Since the oscillation period is longer than twice the width of the IRF, the wave packet oscillation can be well resolved in these measurements. The relative amplitudes of the 375 cm^-1 oscillation are comparable for both crystals suggesting that the time-resolution of the thicker 580 µm crystal is similar to that of the 100 µm crystal, which should be better than 38 fs. That is, the oscillation amplitude is not significantly diminished due to the limited time-resolution. Nonetheless, the Fourier power spectra in Fig. 4 show that the relative amplitude of the 375 cm^-1 mode for the 100 µm crystal is higher, indicating the higher time-resolution for the thin crystal. Dramatic improvement of the time-resolution from 115 fs (Fig. 2(d)) to close to 40 fs for the 580 µm crystal indicates that the effect of GVM on the time-resolution indeed decreases steeply as the wavelength increases, in agreement with the calculation shown in Fig. 3(b). Therefore, we estimate that the time-resolution for the 100 µm crystal at the wavelengths longer than 500 nm is close to the lower bound (33 fs) set by the cross-correlation between the scattered fundamental and the gate pulses (Fig. 1(a)).

 

Fig. 4. Time-resolved fluorescence of coumarin 153 in methanol. The molecule is excited by the two photon absorption with the 800 nm pulses, and the detection wavelength is 580 nm. Thicknesses of the BBO crystals are (a) 100 µm and (b) 580 µm, respectively. Red solid lines represent the exponential fits. Insets show the Fourier power spectra of the residuals.

Download Full Size | PDF

In conclusion, we have achieved ultimate time-resolution of 33 fs in a fluorescence upconversion experiment by exploiting TPA excitation and the noncollinear sum frequency generation. This opens up the possibility of observing the nuclear wave packet motions as high as 1000 cm^-1 for the molecules and semiconductors in their electronic excited states. It was also demonstrated that TPA can be employed routinely in a fluorescence upconversion experiment even for the molecules without one-photon resonance. Experiments and simulations of the instrumental response function indicate that time-resolution of 40 fs can be routinely achieved at a wavelength longer than 500 nm when a moderately thick 580 µm BBO crystal is used, which allows the fluorescence upconversion with high efficiency as well as high time-resolution.