A convenient polarization independent, broadband femtosecond optical gating technique utilizing transient Kerr lens effect is demonstrated by measuring the chirp structure of linearly polarized or non-polarized white light continuum generated in water and a photonic crystal fiber, respectively. Comparing with previous time-resolved spectroscopic techniques, this Kerr lens gating method is not limited by the requirement of specific nonlinear media with broadband response, critical phase-matching conditions, and especially the pump-probe polarization relationship. By replacing the white light continuum with other broadband light signals of interest, this method can be exploited in other femtosecond time-resolved spectroscopy, e.g., femtosecond photoluminescence.
© 2014 Optical Society of America
Study of the dynamics in the interactions of femtosecond laser with materials is essentially important for both fundamental research and applications. One important kind of the interactions is frequency conversion due to light induced electronic transitions or other nonlinear optical processes, e.g., femtosecond photoluminescence [1, 2], (second) harmonic generation [3, 4], and white light continuum (WLC) generation [5–9], which have been widely used in the applications of new frequency light sources [8–11], nonlinear optical imaging [12, 13], time-resolved nonlinear optical spectroscopy [14–17], etc.
To well understand the frequency conversion processes and to acquire accurate temporal response function for applications, the characterization of time-frequency properties of the emissions is necessary [15, 16]. Many time-resolved spectroscopic techniques were thus developed utilizing transient nonlinear optical effects, e.g., optical Kerr (polarization) gating (OKG) [1, 2, 18–20], frequency up-conversion [14, 21], transient absorption (TA) or (non degenerate) two-photon absorption (TPA) [15, 22, 23], frequency-resolved optical gating (FROG) [24–28]. In OKG technique, the pump induced birefringence is monitored by a probe beam using a polarization analyzer, where cross polarization of the pump and probe beams is required, and it was found recently that the OKG signal oscillated with the pump intensity and the thickness of the OKG medium [19, 20]. Frequency up-conversion has the advantage to transform infrared (IR) light into visible beam that can be detected by cheaper silicon detectors, but particular nonlinear crystals and critical phase matching conditions are necessary especially for broadband signal. For TA or TPA method, special nonlinear materials with both broadband nonlinear absorption and transient response are required. FROG has the unique advantage to measure both the amplitude and the phase of pulsed light fields, while a strong light pulse is required to generate a self-reference nonlinear signal, thus it is usually used for the characterization of intense laser pulses. Cross-correlation FROG based on sum frequency generation (SFG) [27, 28] was also developed to characterize relatively weak pulses, where special SFG crystals and phase matching conditions are also required. Moreover, all of the above techniques are polarization dependent.
In addition to Kerr birefringence, Kerr lens effect also occurs when an intense laser beam is focused into a Kerr medium due to the non-uniform distribution of the intensity-dependent nonlinear refractive index. This effect is widely used in the popular closed aperture Z-scan technique [29–32]. If another weak probe beam (usually at different wavelength) overlaps with the pump beam in the medium and is scanned in time, i.e., by a time-resolved Z-scan setup, both the nonlinear refraction and its transient dynamics of the medium can be obtained [33, 34]. But until recently only a few people noticed that Kerr lens effect could also be used as transient optical gating for time-resolved spectroscopy. Using a special tellurite glass as Kerr medium and with a slit in the middle of the pump beam, H. Zhang et al.  measured the chirp structure of WLC generated in water by monitoring the defocused and spatially separated WLC signal in the direction parallel to the slit. Although the Kerr lens gating effect was well represented, the polarization dependence was not discussed .
In this paper, with a traditional time-resolved closed aperture Z-scan setup, we further explore the capability of the optical Kerr lens gating (OKLG) using ordinary fused silica glass as Kerr medium. Instead of monitoring the spatially separated signal beam, we directly measure the transient change of the transmission spectrum passing through an aperture in the pump-probe Z-scan setup, thus both defocused and convergent signals can be used as the gating signals. Using linearly polarized WLC generated in water or non-polarized WLC generated in a photonic crystal fiber (PCF) as probe beam, we show that the OKLG method has the advantages of broadband response, no specific nonlinear medium and phase matching requirements, high sensitivity suitable for weak signal, and especially no requirement of pump-probe polarization relationship, comparing with previous time-resolved spectroscopic techniques.
2. Experimental setup
The experimental setup of the OKLG technique is shown in Fig. 1, which is similar to the traditional two-color pump-probe Z-scan setup [33, 34], except that the single-color probe beam is replaced by a broad bandwidth WLC beam. An IR laser beam (1 kHz, 800 nm, 150 fs) from a Ti: sapphire regenerative amplifier femtosecond laser system (MaiTai/Spitfire, Spectra Physics) is divided into two beams using a polarizing beam splitter. The reflected beam (IR pump) passes through an optical delay line and is focused by a lens L1 (f = 400 mm) to induce transient Kerr lens effect in a 3 mm-thick fused silica (FS) plate, which is mounted on a 1D translation stage to perform Z-scan. The transmitted beam is focused into a 5 mm-thick quartz cuvette filled with deionized water by a lens L2 (f = 100 mm) to generate the WLC probe, and an aperture is placed before a collimating lens L3 (f = 300 mm) to shape the WLC so that only the central homogenous part is used. For the WLC probe generated in PCF, the transmitted IR beam is coupled into a 300 mm-long solid core honeycomb PCF with zero dispersion wavelength at 800 nm (NL-2.4-800, Thorlabs) using a lens L5 (f = 50 mm), and the output WLC is collimated using a microscope objective (10X). Then either of the two WLC beams is focused by a lens L4 (f = 200 mm) and is overlapped with the IR pump collinearly in the FS plate using a dichroic mirror. After the FS plate, a shortpass filter (#47-585, Edmund Optics) is used to eliminate the IR pump. Then only the central part of the WLC probe is collected into a fiber spectrometer (USB4000, Ocean Optics) by a collimating lens (CL, diameter 5 mm, 74-UV, Ocean Optics), which also acts as the closed aperture in the Z-scan setup. The linear transmittance S of the closed aperture  is adjusted by moving CL along the Z direction to balance the spectral intensity and signal sensitivity. Larger S results in stronger spectral intensity but smaller ΔT/T0 (ΔT/T0 = (T-T0)/T0), and vice versa. Both the power and the polarization of the pump beam can be tuned using the combination of a half-wave plate HW2 and a polarizer P. The pulse duration of the IR pump is around 200 fs at the sample position due to the dispersion of the PBS cube and other optical elements, which is determined by cross-correlation in a thin BBO crystal.
3. Results and discussions
A typical spectrum of the WLC generated in water is measured after the FS plate by blocking the IR pump, as shown in Fig. 2(a) (black solid line). It spreads from 400 nm and cuts off at around 725 nm by the shortpass filter, and its polarization is linear and consistent with the excitation IR beam, which is determined by a polarizer. When the IR pump with polarization parallel to the WLC probe is unblocked to allow for the Kerr lens effect, by setting a proper temporal delay and moving the FS plate to Z- direction, a clear valley signal shows up on the transmission spectrum at a certain wavelength. By moving the FS plate to Z + direction, the valley will disappear and a peak signal will emerge at the same wavelength. Both the spectra with a valley or a peak signal are plotted in Fig. 2(a) labeled as ‘Z-, P//’ (black dotted line) and ‘Z + , P//’ (blue dashed line) respectively. By normalizing the two spectra with the reference spectrum (with pump off), relative transmission spectra are extracted as shown in Fig. 2(b). Except for the valley/peak signal of ∆T/T0~ ± 0.8 with a bandwidth of ~14 nm (FWHM), there is only a uniform background with a fluctuation of |∆T/T0|≤0.05, which is due to the instability of the WLC generation. Interestingly, when the polarization of the IR pump is rotated to be perpendicular to that of the WLC probe, there is still a very clear valley/peak signal with smaller amplitude for similar conditions, as shown in Fig. 2(a) labeled as ‘Z-, PX’ (red dashed dot line) for the spectrum taken at Z- for example. By normalizing with the same reference, we get the valley signal of ∆T/T0 ~-0.4 with the same bandwidth and background as in the case of parallel polarizations, as plotted in Fig. 2(b).
The phenomena can be easily understood using light-induced Kerr lens effect in the FS plate, which is confirmed by comparing a two-color with a single (pump) beam closed aperture Z-scan measurements. By scanning the FS plate along Z direction and setting proper optical delay, the normalized transmission T/T0 of the probe beam at 480 nm and the pump beam at 800 nm are detected, as shown in Fig. 2(c). As a Kerr medium with positive nonlinearity, the FS plate acts as a positive lens under the exposure of the focused IR pump. When the FS plate is located at a Z- position (as illustrated in Fig. 1), the actual focal point of the probe/pump beam is shifted towards Z-, thus the beam divergence at far field is increased, which results in a valley signal corresponding to a decrease of the closed aperture transmittance T. While when the FS plate is placed at a Z + position, it acts as a focal lens reducing the beam divergence since it is placed after the focal point of the input beams, thus resulting in an increase of T and a peak signal. The symmetric profiles of T/T0 for both probe and pump versus z indicate that mainly nonlinear refraction is induced. With the single (pump) beam Z-scan curve presented in Fig. 2(c), we calculate the nonlinear refractive index n2 of the FS glass using I0 = 1.5 × 1011 W/cm2, Leff = 3.0 mm, and ΔTpv = 0.6 ≈0.406 × n2I0Leff × 2π/λ for small aperture approximation . We get n2 ≈4.2 × 10−16 cm2/W, which is consistent with the previous results (n2 = 3.2 × 10−16 cm2/W) . As a technique similar to Z-scan measurements, the OKLG technique has very high sensitivity, i.e., a tiny change of the refractive index (Δn = n2I0) can result in a measurable change of the transmittance. Note that apparently larger ΔT/T0 amplitude for the probe in Fig. 2(c) is due to the effect that the cross-coupling nonlinear refractive index seen by the probe beam is twice as large as that seen by the pump beam itself [33, 36], which results in enhanced detection sensitivity for the OKLG. Thus cheap silica glass with low nonlinearity is good enough as the gating material and lower pump intensity can be used for gating materials with high nonlinearity .
Since the response of the Kerr lens effect in FS glass is transient due to nonresonant electronic polarization , it can be used as a gating in the time-resolved measurements analogous to the OKG technique. In our case, the WLC probe is a positive chirped pulse spreading around several picoseconds, and the pump induced Kerr lens effect only exists around 200fs (limited by the pump duration), thus the valley or peak signal only appears at the wavelength where the probe temporally overlap with the pump pulse. We first test this OKLG technique by using an IR pump with polarization parallel to the WLC probe. By scanning the optical delay and fixing the FS plate at Z + or Z- position where |ΔT/T| are maximum for the probe, time-resolved 3D normalized transmission spectrum is obtained. Since the measurements for Z + and Z- positions are almost identical except for the signs of ΔT/T signal are opposite, only the results taken at Z + are plotted as shown in Fig. 3(a). It is clear that the peak signals on the 3D spectra, taken at different delay, allow a straight measurement of the chirp structure of the WLC probe with high signal to noise ratio (SNR). To test the polarization dependence of the OKLG technique, we change the polarization of the IR pump to be perpendicular to the WLC probe and repeat the above measurements. Except for the amplitudes of the ΔT/T signals are reduced to about half of that taken for parallel polarizations, the 3D spectrum is almost the same, as plotted in Fig. 3(b) for the FS plate located at Z- for comparison. By fitting the dispersion of the peak (valley) delay positions using Twater(λ) = a + bλ + cλ2 + dλ3, we obtain a = −69.29 (−69.29) ps, b = 0.2999 (0.3007) ps/nm, c = −4.252 (−4.293) × 10−4 ps/nm2, and d = 2.071 (2.113) × 10−7 ps/nm3, respectively, as plotted in Fig. 3 with dashed lines. The quantitative agreement of the two fittings of the chirp structure indicates that the OKLG technique does not depend on the Z scan position of the Kerr medium or the pump-probe polarization relationship, although the sensitivity (ΔT/T0) does.
To test the capability of the OKLG technique in characterizing non-polarized pulses, the non-polarized WLC generated from a PCF is used as the probe. Unlike the WLC generated in water, the WLC polarization generated in PCF is strongly dependent on the input polarization  relative to the symmetric axis of the PCF, which is confirmed by rotating a half-wave plate before the coupling lens L5 and checking the output polarization using a plate polarizer. It turns out that WLC with linear polarization is obtained only for specific input polarizations and non-polarized WLC is generated for other cases. Moreover, the WLC output from the PCF is more fluctuant due to the competition among different nonlinear effects [27, 37], especially when the PCF is pumped by kilohertz amplifier as in our case, which poses extra challenge for characterizing its time-frequency structure.
The cross section of the NL-2.4-800 solid core honeycomb PCF is imaged using an optical microscope, and a typical non-polarized WLC spectrum is measured after the FS plate, as shown together in the right of Fig. 4. By locating the FS plate at Z- where -ΔT/T are maximum for the probe and scanning the pump in time, the chirp structure of the non-polarized WLC from the PCF is measured using the valley signal, as plotted in Fig. 4. It shows that except for a relatively bigger noise of the background |ΔT/T| due to shot to shot fluctuation of the WLC spectrum, there is a clear trace of the valley signal with amplitude of |ΔT/T| ~0.6, which is just between the two amplitudes of |ΔT/T| using probe beams of linear polarizations parallel and perpendicular to that of the pump. This result demonstrates obviously that the OKLG technique is also suitable for charactering non-polarized pulses, and thus has the unique advantage of polarization independence.
By fitting the valley positions using Tpcf(λ) = A + Bλ + Cλ2 + Dλ3, we get A = −167.49 ps, B = 0.5410 ps/nm, C = −5.174 × 10−4 ps/nm2, and D = 1.373 × 10−7 ps/nm3 respectively. The collinear pump-probe setup and the use of dichroic mirror and shortpass filter limit the measurable bandwidth of the WLC probe, which prevent us from a general discussion of the WLC chirp for its full wavelength range as in [27, 28]. However, it is worth noting that this limitation doesn’t blur the advantages of the OKLG technique, and it will be valuable to overcome this bandwidth limitation by modifying the current setup with a non-collinear alignment .
The nature of the polarization independence of the OKLG technique can be understood as follows. According to the general Z-scan theory, the normalized transmittance ΔT/T0 is proportional with nonlinear refractive index change Δn by 2ΔT/T0 = ΔTpv ≈0.406 × (2π/λ)LeffΔn for small aperture approximation , and Δn is determined by the effective nonlinear susceptibility χ(3)eff due to Δn = 3/(2n0)χ(3)effI0 , where I0 is the intensity of the pump beam. In principle, any measurable Δn induced by the pump can be used as a measure of a gating in the OKLG technique, no matter the effective susceptibility χ(3)eff is contributed by which and how many components, as long as the response is transient. For instance, if the gating medium is isotropic as in our case, χ(3)eff and thus Δn are contributed by χ(3)1111 for parallel polarization, or by χ(3)1122 for perpendicular polarization, or by the corresponding combination of both χ(3)1111 and χ(3)1122 if other polarized or non-polarized probe/pump is involved. Thus the OKLG technique has the unique advantage of no special requirement of the pump/probe polarization, or we say the OKLG is a polarization independent gating technique. While in other gating technique, only special susceptibility or combination is used, e.g., (χ(3)1111 - χ(3)1122) in a typical optical Kerr gating setup.
Using an IR pump-WLC probe closed aperture Z-scan setup, we demonstrate that the transient Kerr lens effect can be used as a polarization independent, broadband femtosecond optical gating by measuring the chirp structures of linearly polarized WLC generated from water and non-polarized WLC generated from a PCF respectively. By locating the Kerr medium (fused silica in our case) at different z positions, both the transient increase and the transient decrease of the transmission can be directly used as a measure of the optical gating signal. Comparing with previous time-resolved spectroscopic techniques, the OKLG method has the full advantages of broadband response, no specific nonlinear media and phase matching requirements, high sensitivity, and especially no requirement of gating-signal polarization relationship, i.e., polarization independent. The bandwidth limitation in current collinear setup due to the use of dichroic mirror and shortpass filter may be overcome with non-collinear alignment. This OKLG technique can also be further exploited in other femtosecond time-resolved spectroscopy by replacing the white light continuum with other broadband light signal of interest, e.g., femtosecond photoluminescence.
We gratefully acknowledge financial support for this work by the National Basic Research Programs of China (2010CB934101, 2013CB328702), the National Natural Science Foundation of China (61205035, 11174161), International S&T cooperation program of China (2011DFA52870), the 111 Project (B07013), and Oversea Famous Teacher Project (MS2010NKDX023). We also thank Peter Hertel for valuable advice.
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