Open Access
Add to BibSonomyAbstract
A simple but robust ultra-broadband femtosecond optical gating method utilizing transient beam deflection effect is demonstrated with direct CCD imaging of the distorted single-color probe and the measurement of the chirp structure of a white light continuum generated from a CaF2 plate. The non-collinear configured beam deflection gating technique not only preserves all the advantages of the previous optical Kerr lens based gating methods, such as having no phase matching conditions, little dependence on probe intensity or special nonlinear media, and no requirements on the pump-probe polarization relationship, but it also extends the measurable probe bandwidth. Meanwhile, it is also proved that the current gating technique is easy-aligned, free from the influence of the pump-probe pulse-front mismatch and the probe beam profile, which is much convenient for the characterization of ultra-broadband light pulses in the applications of ultrafast spectroscopy.
© 2014 Optical Society of America
1. Introduction
Understanding of the dynamics in the interaction of femtosecond laser pulses with various materials is essentially important for both fundamental research and applications [1–4]. One approach is characterizing the time-frequency property of the generated radiation such as photoluminescence [5–7], harmonic generation [8, 9], and white light continuum (WLC) [10–12]. Many time-resolved spectroscopic techniques were thus developed, including optical Kerr (polarization) gating (OKG) [5, 13–15], frequency up- or down-conversion [6, 7, 16], non-degenerate two-photon absorption [17, 18], transient grating [19, 20], frequency-resolved optical gating (FROG) [21–24] etc. Although these techniques were extensively used, there are some limitations in applications such as pump-probe polarization relationship, measurable bandwidth and phase matching conditions etc. due to their respective gating mechanisms [25]. For instance, particular nonlinear crystals and phase matching conditions are required in frequency up-conversion and cross-correlation FROG techniques [23, 24] using sum frequency generation. Therefore, it is still an exciting topic to develop robust optical gating techniques to overcome all the restrictions of polarization relationship, light intensity, bandwidth, phase matching conditions, and the requirement of special nonlinear media etc.
In addition to Kerr birefringence effect, Kerr lens effect also occurs in the interaction of intense laser pulse with Kerr medium [26], which has been widely used in the mode-locked laser systems [3, 27] and the closed aperture Z-scan techniques [28, 29]. But until recently only a few groups noticed that Kerr lens effect can also be utilized as transient optical gating. By putting a slit in the pump beam and monitoring the defocused probe light in the direction parallel to the slit due to pump induced transient Kerr lens, H. Zhang et al. measured the chirp structure of a WLC generated in a sapphire plate [30]. With a collinear two-color closed aperture Z-scan setup and by monitoring transmission spectrum of the WLC probe, we systematically demonstrated that the transient Kerr lens gating has unique advantages of broadband response, high sensitivity suitable for weak signal, no specific nonlinear media and phase matching requirements, and no pump-probe polarization relationship restriction [25]. In principle, there is no bandwidth limitation for the Kerr lens effect, as the dispersion of the nonlinear refractivity due to the non-resonant electronic response is very small, e.g., the nonlinear refractive dispersion curve of the fused silica is almost a constant from 400 nm to 1600 nm [31]. But unfortunately, the collinear configuration and the use of short-pass filter for blocking the pump in [25] and [30] limited the measurable bandwidth of these Kerr lens based gating techniques. For the specific example in [25], our bandwidth limits for WLC chirp measurements are from UV (400nm) to about 720 nm.
Very recently, M. R. Ferdinandus et al. [32] demonstrated that transient beam deflection of a single-color probe in a non-collinear pump-probe scheme due to Kerr lens effect can be used to characterize both the temporal response and the amplitude of the ultrafast nonlinear refraction. Inspired by this idea, with an updated setup using a fiber spectrometer and a WLC probe, we demonstrate in the current manuscript that the transient beam deflection effect can also be utilized as an excellent ultrafast optical gating, which not only possesses all the advantages of the previous collinear pump-probe closed aperture Z-scan method, but can also circumvent the restriction of measurable bandwidth.
2. Experimental setup
The experimental setup (top view) of the transient beam deflection gating technique is illustrated in Fig. 1, which is modified from M. R. Ferdinandus et al.’s experiments [32], mainly by replacing the single color probe with a WLC and monitoring its spectrum with a fiber spectrometer. A laser beam (1 kHz, 800 nm, 120 fs) from a Ti: sapphire femtosecond laser system (MaiTai/Spitfire, Spectra Physics) is split into two beams using a plate beam splitter. One beam (the pump) passing through the optical delay line is focused by a lens L1 (f = 400mm) into a 3 mm-thick fused silica (FS) plate to induce transient Kerr lens. The other beam (the seed beam) is focused into a 3 mm-thick calcium fluoride plate (CaF2) by a lens L2 (f = 100 mm) to generate the WLC probe, which is then collimated by a lens L3 (f = 150 mm) and refocused by a lens L4 (f = 300 mm) into the FS plate overlapping off-centered with the pump. Note that the CaF2 plate is translated slowly normal to the seed beam with a 2D stage to avoid damage during the experiments. A hot mirror HM (FM201, Thorlabs) between the lenses L3 and L4 is used to modify the WLC spectrum, so that the residual seed light is highly attenuated, otherwise the intensity of the residual seed beam at 800 nm will be two orders of magnitude higher than that of the generated WLC, and self-induced nonlinearity might occur. The FWHM beam diameters of pump and the WLC probe in the FS plate are about 115 μm and 50 μm respectively, which are determined using a CCD beam profiler (SP620, Ophir-Spiricon). The cross angle between the two beams is around 6°, which ensures the spatial separation of the pump and the WLC probe at far field and thus no spectrum filter is required to block the pump during the experiments.
Fig. 1 Sketch of the experimental setup (top view). BS: beam splitter; NDF1-NDF3: neutral density filters; M1-M6: mirrors; L1-L5: focal lenses; HW: half wave plate; HM: hot mirror; BPF: band pass (laser line) filter; CCD: laser beam profiler.
After the FS plate, the WLC probe is collected by a lens L5 and is split using a neutral density filter (NDF3). The reflected beam (~10%) passes through a 633 nm laser line filter (FL632.8-10, Thorlabs) and is monitored by a CCD beam profiler (SP620, Ophir-Spiricon), which provides direct transverse intensity profile of the single color probe. A very small part of the transmitted WLC beam is directly coupled into a fiber spectrometer with an optical fiber of 200 μm in core diameter (USB4000 + QP200-2-VIS/NIR, Ocean Optics), which provides the gated WLC spectrum signal. Note that either the fiber entrance or the CCD sensor isn’t at the focus.
3. Results and discussion
3.1 Measurement of transient beam deflection of single color probe using CCD imaging
The transient beam deflection of the pulsed single color probe at 633 nm filtered from the WLC is firstly characterized using CCD imaging. The initial transverse intensity profile of the single-color probe is almost a 2D Gaussian distribution, as shown in Fig. 2(a), which is measured by blocking the IR pump before the FS plate. This profile keeps unchanged even when the pump is unblocked, until the beam distortion occurs when the pump and probe arrive at the FS plate coincidently in time by setting a proper temporal delay. A typical distortion image of the probe for a pump power at 0.8 mW is shown in Fig. 2(b), where the intensity on the upper part (A) is reduced while the intensity on the lower part (B) is increased.
Fig. 2 Direct imaging of the transient beam deflection of the single color probe. (a) Initial profile of the probe; (b) distorted beam profile of the probe due to beam deflection for an average pump power at 0.8 mW; (c) illustration of the deflection mechanism using side view picture of the pump (red) and probe (yellow); (d) intensity profile of the probe in (c) with (blue dashed line) and without (black solid line) deflection effect.
This phenomenon can be understood using a side-view picture of the pump and probe beams, as illustrated in Fig. 2(c). Due to the intensity-dependent nonlinear index change, the pulsed IR pump introduces a transient Kerr lens inside the Kerr medium (the FS plate). When the probe with finite beam diameter off-axially irradiates on this lens, each part will experience different deflection. The light passing through the optical center of the lens or far from the center does not deflect where the transverse gradient of the refractive index is equal to or approaches zero. While as deduced in [32], the light passing through around ωe/2 of the pump beam (A’) experiences maximum bending towards the axis of the pump (or the induced lens), and thus results in a decrease of intensity at far field (part A in Fig. 2(b)), where ωe is the radius at 1/e2 of the peak intensity of the pump beam. Meanwhile, the deflected light superposes with the non-bending light passing nearby the optical center of the transient lens (B’), and leads to an increase in intensity at far field corresponding to part B in Fig. 2(b).
In analogy with the measurement using a bi-cell photodiode in [32], the magnitude of the beam deflection of the single color probe can be evaluated with the asymmetry S of the CCD image defined by,
where Cup and Cdown are the integral intensities (sum of the pixel counts) of the up and down parts of the CCD images. The asymmetry S is directly proportional to the pump power as plotted in Fig. 3(a) together with corresponding CCD images, where co-polarized pump and probe are used. Such a result agrees well with the theory deduced in [32], as S is proportional to the third order nonlinear refractivity n2I, where n2 is the non-degenerate nonlinear refractive index and I is the pump intensity. Note that a pump power of 1 mW corresponds to a peak intensity of about 78 GW/cm2 at the FS plate.Fig. 3 The pump power dependence of the beam deflection of the single color probe measured with (a) S - up and down asymmetry and (b) S’ - relative change of the intensity within a specific area marked by a square frame, of the CCD images. An average pump power of 1 mW corresponds to about 78 GW/cm2 in peak intensity. Red dashed lines: linear fitting of the dependence of S or S’ on pump power. Note that the beam sizes in all the images are the same; the enlarged images are just for better illustration.
For cross-polarized beams, the deflection of the probe is weaker, and the ratio between the two polarization configurations under the same conditions is measured to be S///S⊥ = 3.16 ± 0.32, which results from the fact that the bound electronic nonlinearity dominates the nonlinear response in the isotropic FS plate, and thus S// /S⊥ = n2,co/n2,cross = χ(3)1111/χ(3)1122 = 3 [26, 32]. It also indicates that a probe light with any polarization can be deflected by the pump-induced Kerr lens, although the degree (magnitude) of the defection varies.
Alternatively, the degree of the beam deflection can be characterized using the relative change of the beam intensity within a small region where the maximum deflection occurs, as marked in the CCD images in Fig. 3(b) with squares. The magnitude of the beam deflection is then re-defined as S’ = (C0-Cp)/C0, where Cp and C0 are the integral counts in the selected region with and without pump respectively. The signal S’ is also proportional to the pump power as shown in Fig. 3(b), but the value is more than twice of S for the same CCD images. This indicates that a point detector instead of a bi-cell detector can be used to simplify the characterization of transient beam deflection and the behind nonlinearity, as in the traditional closed aperture Z-scan measurements [28], where only the central part of the beam is detected.
3.2 Differential transmission spectrum of the WLC due to transient beam deflection gating
The entrance of the optical fiber with a core of 200 μm in diameter acts as a pinhole of a detector, which is put where the beam diameter of the WLC probe is about 2 mm. This condition is approximately equivalent to the situation in Fig. 3(b), where 40 × 40 pixels in the square are selected from the 500 × 500 pixels of the full image.
A typical (reference) spectrum of the WLC generated in CaF2 with pump off is shown in Fig. 4(a) (solid black line), and the cutoff at about 850 nm is limited by the hot mirror. When the pump (0.8 mW) is on, a clear dip appears on the spectrum (red dashed line). By calculating the differential transmission spectrum with ΔT/T0(λ) = [I(λ)-I0(λ)]/I0(λ), where λ is the probe wavelength, I(λ) and I0(λ) are the two spectra measured with and without pump respectively, a probe spectrum independent signal ΔT/T0(λ) is extracted, as shown in Fig. 4(b). Except for the dip signal of ΔT/T0(λ) ≈− 0.31 at λ = 633 nm with a bandwidth of ~14 nm, there is only a flat background with a fluctuation of |ΔT/T0(λ)| ≤ 0.05, which is due to the fluctuation of the WLC generation and the non-synchronous measurement of the reference and the signal spectra.
Fig. 4 (a) Typical WLC spectra with (dashed red line) and without (solid black line) the influence from the transient beam deflection effect; (b) a differential transmission spectrum due to transient beam deflection; (c) temporal resolution of the deflection gating.
This gating phenomenon can be understood by considering the non-coaxial interaction of the chirped WLC with the transient Kerr lens. Since the response of Kerr effect in FS glass is due to non-resonant electronic polarization [32], the pump induced Kerr lens only exists for about 120fs (limited by the pump duration); while the WLC probe is a positively chirped pulse, light at different wavelengths is separated in time spreading around several picoseconds, thus only the light at the wavelength temporally overlapping with the transient Kerr lens can be deflected, which results in a dip signal on the spectrum.
Technically, the background fluctuation on the differential transmission spectrum can be highly reduced by modulating the pump and measuring the differential spectrum of the WLC probe with a fast response spectrometer (e.g., optical multichannel analyzer) that can be coincident with the modulation [33], or by splitting the WLC probe into reference and probe beams, and then monitoring both beams at the same time with two-channel spectrometer or two spectrometers, as in the pump-probe setup for transient absorption measurement [34]. Despite of the very strong fluctuation of the WLC generation in the current setup, the distinct gating signal demonstrates that the beam deflection gating method is also an anti-fluctuation gating technique.
As only a small portion within the intensity-decreased region (part A in Fig. 2(b)) is monitored for the optical gating, the gating signal, i.e., the relative change of the transmittance (ΔT/T0(λ)) only depends on the “local” intensity at that region, and thus is free from the influence of the spatial inhomogeneity and the possible spatial chirp of the WLC probe, which indicates that the current gating technique utilizing beam deflection also has no requirement on the beam profile of the probe for the ultrafast spectroscopies.
The temporal resolution of the transient beam deflection gating is characterized by monitoring the dependence of the dip signal around 490 nm (FWHM ≈10nm) on the optical delay, as plotted in Fig. 4(c). The dip signals at negative and positive delay between the pump and probe are quite symmetric and can be well fitted using a Gaussian profile with a FWHM about 176 fs, which indicates that there is no distinguishable relaxation process of the induced Kerr lens and only the convolution of the durations of the pump and probe contributes to the temporal resolution (The FWHM duration of the probe can be evaluated with τprobe = (τ2con – τ2pump)1/2 = 129 fs assuming it’s also a Gaussian profile within the selected narrow bandwidth, where τcon = 176 fs and τpump = 120 fs are the FWHM durations of the convolution signal and the pump respectively.) Higher temporal resolution is expected if shorter pump pulse is used, as the Kerr lens effect due to non-resonant electronic response is transient (in femtosecond time scale) [26].
The non-collinear pump-probe geometry may introduce a pulse-front mismatch of dprobesinθ/c in time along the finite diameter of the probe within the intersection plane, as illustrated in Fig. 5, where dprobe is the diameter of the probe, θ is the cross angle of the pump and the probe outside of the FS plate, and c is the light speed in vacuum respectively. In our case, such a pulse-front mismatch is about 17 fs across the full probe using dprobe = 50 μm and θ = 6°. If the full section of the probe is measured, one will get an integral signal of the interaction, and thus a broadened gating signal and lower temporal resolution. But as only 1/10 portion of the probe diameter is monitored by the fiber spectrometer, the corresponding pulse-front mismatch is only about 2 fs, and such a gating broadening effect can be ignored.
Fig. 5 Illustration of the pulse-front mismatch effect due to the non-collinear pump-probe geometry from top view.
3.3 Time-frequency property (chirp structure) of the WLC probe characterized using the transient beam deflection gating
A straightforward application of the transient beam deflection gating is the measurement of the time-frequency property (chirp structure) of the WLC generated from dielectric media, as from the CaF2 plate in our case. By combining a series of differential transmission spectra at different optical delays measured with the transient beam deflection gating as demonstrated in section 3.2, a time-frequency 2D spectrum is obtained, as shown in Fig. 6.
Fig. 6 Time-frequency 2D spectrum of the WLC generated from CaF2 plate measured by the transient beam deflection gating, where a pump power of about 0.65 mW is used. The fitting curve of the chirp structure is plotted with scattered squares. Insert: zoom-in spectrum of the selected area for better illustration of the dip signal.
Except for a flat background, the dip signals on the 2D spectrum illustrated with blue color present an intuitive view of the relationship between the delay and the wavelength, which can be well fitted using a fourth order dispersion curve τ(λ) = a + bλ + cλ2 + dλ3 + eλ4, as plotted in Fig. 6 with scattered squares, where τ(λ) is the delay at the wavelength λ relative to the excitation wavelength (λ = 800nm); a = −96.15 ps, b = 0.5183 ps/nm, c = −1.083 × 10−3 ps/nm2, d = 1.023 × 10−6 ps/nm3, and e = −3.636 × 10−10 ps/nm4 are the fitting parameters. Such a positive chirp is mainly due to the complex mechanism of the WLC generation [10, 11], as the chirp due to linear dispersion in the propagation between the CaF2 plate and the Kerr medium (FS plate) can be neglected. The chirp measurement for the shorter wavelengths region up to about 720 nm is also performed using the collinear Z-scan setup [25]. Except for the relative timing shift due to the difference of the pump-probe distance between the two alignments, e.g., the insert of the dichroic mirror in the pump beam, the two chirp curves are completely identical for the measurable bandwidth. This result is more than evidently reasonable, as the two measurements are due to the same nonlinear optical effect – the Kerr lens effect and no extra dispersion optics is inserted in the WLC probe. Note that the gating signal (ΔT/T0) presented in Fig. 6 looks weaker than that of our previous collinear Z-scan setup [25] mostly because the pump intensities used in the two measurements are different. A pump intensity of about 150 GW/cm2 was used in Ref. 25, while a pump intensity of about 51 GW/cm2 (a pump power of 0.65 mW) is used for the current measurement presented in Fig. 6. As ΔT/T0 is proportional to the pump intensity in both systems, the gating sensitivities (namely the gating signal per pump intensity) of the two techniques are actually comparable.
Comparing with previous optical gating techniques based on Kerr lens effect [25, 30], the main improvement of the current method is the break of the measurable bandwidth limitation, thanks to the direct separation of the pump and the probe pulses after the non-collinear interaction. With this improvement, one can obtain the entire time-frequency information of the WLC and thus to get a better understanding of the generation process.
It should be emphasized that although both the beam deflection gating technique and the Z-scan method [25] are based on the pump induced Kerr lens effect, the interaction mechanisms and corresponding phenomena are very different. In the collinear pump-probe Z-scan setup, the probe should pass through the center of the pump beam, and the interaction mechanism is the defocusing or refocusing of the probe due to the Kerr lens induced by the pump, thus the focus location of the probe beam along the Z direction is crucial. One can get a maximum gating signal when the focus locates several millimeters before (a positive ΔT/T0) or after (a negative ΔT/T0) the Kerr lens, and the signal will approach zero if the focus of the probe locates overlapping with the Kerr lens or far from it [25]. While in the current beam deflection technique, the probe should off-axially pass through the Kerr lens induced by the pump beam, then part of the probe beam passing through around ωe/2 of the pump beam experiences maximum bending towards the axis of the pump (or the induced Kerr lens) and results in a decrease of intensity at far field. Thus the lateral offset of the pump and the probe within the Kerr media is crucial, while the focus location of the probe is less important. Technically, as long as any part of the probe can pass through the ωe/2 radius of the pump beam, one can get the distinct beam deflection signal, i.e., the gating signal, thus the beam deflection alignment is also simpler than the Z-scan method.
4. Conclusion
With a non-collinear, off-axial pump-probe alignment, we show that the transient beam deflection due to the pump-induced Kerr lens can be used as an excellent ultra-broadband optical gating. The principle of the transient beam deflection effect is firstly illustrated using direct CCD imaging of a single-color probe, and the dependences of the deflection degree on pump power and polarization are discussed. Then the optical gating utilizing the transient beam deflection is presented using differential transmission spectrum of a broadband WLC, which is obtained by monitoring a small portion of the transmitted WLC with a fiber spectrometer, and the temporal resolution of this optical gating is proved to be on 100 femtoseconds time scale limited by the pump duration of our laser system. A straightforward application of the transient beam deflection gating is performed by measuring the chirp structure of the WLC generated from a CaF2 plate with its bandwidth covering the pump wavelength (800nm), and we thus prove that the current setup has no limitation of the signal bandwidth. These results demonstrate that the transient beam deflection gating technique not only preserves all the advantages of the previous optical Kerr lens based gating methods including no restrictions on pump-probe polarization relationship, phase matching conditions, special nonlinear media, probe intensity etc., but also extends the measurable bandwidth of the signal, which can be much helpful to understand the underlying mechanism of the radiation generated from the interaction of intense pulse with materials. Meanwhile, it is also proved that the current gating technique is free from the influence of the pump-probe pulse-front mismatch and has no requirement on the probe beam profile, which is much convenient for the time-frequency characterization of ultra-broadband light pulses.
Acknowledgments
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 (11404173, 61205035, 11174161), International S&T cooperation program of China (2011DFA52870), the 111 Project (B07013), and Oversea Famous Teacher Project (MS2010NKDX023).
References and links
1. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Theberge, N. Akozbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83(9), 863–905 (2005). [CrossRef]
2. D. Majus, G. Tamošauskas, I. Gražulevičiūtė, N. Garejev, A. Lotti, A. Couairon, D. Faccio, and A. Dubietis, “Nature of spatiotemporal light bullets in bulk Kerr media,” Phys. Rev. Lett. 112(19), 193901 (2014). [CrossRef] [PubMed]
3. T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000). [CrossRef]
4. H. H. Tu and S. A. Boppart, “Coherent fiber supercontinuum for biophotonics,” Laser Photon Rev 7(5), 628–645 (2013). [CrossRef] [PubMed]
5. W. M. Kwok, C. Ma, and D. L. Phillips, “Femtosecond time- and wavelength-resolved fluorescence and absorption spectroscopic study of the excited states of adenosine and an adenine Oligomer,” J. Am. Chem. Soc. 128(36), 11894–11905 (2006). [CrossRef] [PubMed]
6. T. Koyama, Y. Ito, K. Yoshida, M. Tsuji, H. Ago, H. Kishida, and A. Nakamura, “Near-infrared photoluminescence in the femtosecond time region in monolayer graphene on SiO₂,” ACS Nano 7(3), 2335–2343 (2013). [CrossRef] [PubMed]
7. M. Sajadi, M. Quick, and N. P. Ernsting, “Femtosecond broadband fluorescence spectroscopy by down- and up-conversion in beta-barium borate crystals,” Appl. Phys. Lett. 103(17), 173514 (2013). [CrossRef]
8. R. A. Ganeev, “High-order harmonic generation in a laser plasma: a review of recent achievements,” J. Phys. B 40(22), R213–R253 (2007). [CrossRef]
9. S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008). [CrossRef] [PubMed]
10. A. Brodeur and S. L. Chin, “Ultrafast white-light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16(4), 637–650 (1999). [CrossRef]
11. C. Nagura, A. Suda, H. Kawano, M. Obara, and K. Midorikawa, “Generation and characterization of ultrafast white-light continuum in condensed media,” Appl. Opt. 41(18), 3735–3742 (2002). [CrossRef] [PubMed]
12. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
13. R. Righini, “Ultrafast Optical Kerr Effect in liquids and solids,” Science 262(5138), 1386–1390 (1993). [CrossRef] [PubMed]
14. J. Takeda, K. Nakajima, S. Kurita, S. Tomimoto, S. Saito, and T. Suemoto, “Time-resolved luminescence spectroscopy by the optical Kerr-gate method applicable to ultrafast relaxation processes,” Phys. Rev. B 62(15), 10083–10087 (2000). [CrossRef]
15. S. Arzhantsev and M. Maroncelli, “Design and characterization of a femtosecond fluorescence spectrometer based on optical Kerr gating,” Appl. Spectrosc. 59(2), 206–220 (2005). [CrossRef] [PubMed]
16. J. Shah, “Ultrafast luminescence spectroscopy using sum frequency generation,” IEEE J. Quantum Electron. 24(2), 276–288 (1988). [CrossRef]
17. M. A. M. Versteegh and J. I. Dijkhuis, “Ultrafast all-optical shutter based on two-photon absorption,” Opt. Lett. 36(15), 2776–2778 (2011). [CrossRef] [PubMed]
18. D. A. Fishman, C. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5(9), 561–565 (2011). [CrossRef]
19. D. Lee, P. Gabolde, and R. Trebino, “Toward single-shot measurement of a broadband ultrafast continuum,” J. Opt. Soc. Am. B 25(6), A34–A40 (2008). [CrossRef]
20. K. Chen, J. K. Gallaher, A. J. Barker, and J. M. Hodgkiss, “Transient grating photoluminescence spectroscopy: an ultrafast method of gating broadband spectra,” J. Phys. Chem. Lett. 5(10), 1732–1737 (2014). [CrossRef]
21. R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10(5), 1101–1111 (1993). [CrossRef]
22. M. Li, J. P. Nibarger, C. Guo, and G. N. Gibson, “Dispersion-free transient-grating frequency-resolved optical gating,” Appl. Opt. 38(24), 5250–5253 (1999). [CrossRef] [PubMed]
23. X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. 27(13), 1174–1176 (2002). [CrossRef] [PubMed]
24. E. P. Power, A. M. March, F. Catoire, E. Sistrunk, K. Krushelnick, P. Agostini, and L. F. DiMauro, “XFROG phase measurement of threshold harmonics in a Keldysh-scaled system,” Nat. Photonics 4(6), 352–356 (2010). [CrossRef]
25. Y.-E. Wu, Z. Wang, X. Zhang, W. Li, L. Huang, F. Gao, W. Li, Q. Wu, and J. Xu, “Polarization independent broadband femtosecond optical gating using transient Kerr lens effect,” Opt. Express 22(6), 6691–6698 (2014). [CrossRef] [PubMed]
26. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, 2008) Chap. 4.
27. U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424(6950), 831–838 (2003). [CrossRef] [PubMed]
28. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990). [CrossRef]
29. M. Balu, J. Hales, D. J. Hagan, and E. W. Van Stryland, “Dispersion of nonlinear refraction and two-photon absorption using a white-light continuum Z-scan,” Opt. Express 13(10), 3594–3599 (2005). [CrossRef] [PubMed]
30. H. Zhang, Z. G. Zhou, A. X. Lin, J. Cheng, L. H. Yan, J. H. Si, F. Chen, and X. Hou, “Chirp structure measurement of a supercontinuum pulse based on transient lens effect in tellurite glass,” J. Appl. Phys. 113(11), 113106 (2013). [CrossRef]
31. D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” Appl. Opt. 37(3), 546–550 (1998). [CrossRef] [PubMed]
32. M. R. Ferdinandus, H. Hu, M. Reichert, D. J. Hagan, and E. W. Van Stryland, “Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction,” Opt. Lett. 38(18), 3518–3521 (2013). [CrossRef] [PubMed]
33. D. Polli, L. Lüer, and G. Cerullo, “High-time-resolution pump-probe system with broadband detection for the study of time-domain vibrational dynamics,” Rev. Sci. Instrum. 78(10), 103108 (2007). [CrossRef] [PubMed]
34. A. L. Dobryakov, S. A. Kovalenko, A. Weigel, J. L. Pérez-Lustres, J. Lange, A. Müller, and N. P. Ernsting, “Femtosecond pump/supercontinuum-probe spectroscopy: Optimized setup and signal analysis for single-shot spectral referencing,” Rev. Sci. Instrum. 81(11), 113106 (2010). [CrossRef] [PubMed]
