1 Introduction

The characterization of femtosecond laser pulse shapes is a practical concern in all ultrafast optics laboratories. Precise knowledge of the pulse shape can help control nonlinear optical phenomenon. From a practical point of view, pulse characterization often serves as a diagnostic tool to optimize the laser source. With the advent of commercial multi-millijoules short Ti:Sapphire laser systems, the possibilities for pumping tunable parametric sources have become enormous. Optical parametric amplifiers (OPA) and subsequent frequency mixers are now routinely found in most optics centers around the world. The huge spectra that these tunable sources can cover, spanning from ultraviolet to terahertz frequency ranges, poses a unique problem for pulse characterization. To completely characterize these pulses up to an additional phase factor, FROG or SPIDER techniques must be used.

Frequency-resolved optical gating (FROG) has been one of the first successful method to fully retrieve femtosecond pulse shapes [1]. Several variations of FROG have been invented. The most widely used is second-harmonic generation (SHG) FROG [2] since it relies on the strong second-order nonlinearity. Third harmonic generation, self-diffraction and polarization-gating FROG [1] are also classical examples relying on third-order nonlinearities. More complex forms of FROG also include second-harmonic interferometric FROG [3], which uses a collinear geometry thus causing interference fringes at the carrier frequency. More sophisticated methods applicable in completely different frequency ranges have emerged since the 2000s such as the FROG-CRAB [4], used to measure the duration of attosecond pulses through electron streaking in the XUV range. In contrast to the SHG-FROG technique, which involves time-gating the pulse with itself, cross-correlation FROG (XFROG) gates the unknown pulse with a well-known reference laser pulse. The second-harmonic generation process is replaced by a sum-frequency generation for the XFROG setup. This technique allowed the measurement of the intensity and phase of supercontinuum from a microstructured fiber [5]. The authors used angle-dithered BBO crystal to achieve phase matching at all wavelengths. One major advantage of this technique is that with strong pump intensity, you only need a faint probe to generate the sum-frequency signal. Another advantage is that it does not require as large a range of output wavelengths as SHG-FROG. One major disadvantage of XFROG when applied to measuring pulses from an OPA is that the temporal overlap between the pump pulse and the OPA pulse changes at every wavelength setting, making time synchronization experimentally inconvenient. In the following experiment, the source is an amplified femtosecond laser pulse with millijoule-scale pulse energy. Since the intensity is sufficient for several stages of cascaded second-harmonic generation, the SHG-FROG is experimentally simpler to implement than the XFROG.

Other methods for pulse characterization based on spectral interferometry have also been developed. The most important of them is SPIDER [6, 7]. This technique has some advantages, such as the possibility to do fast single-shot determination of pulse shapes and spatiotemporal characterization [8] without the use of any 2D imaging technique. FROG-based single-shot measurements are also possible with an advanced FROG setup [9]. One of the drawbacks of SPIDER is that it generally requires three beams. To characterize tunable laser sources that can span several optical octaves, properly synchronizing these pulses could be an issue, as well as the choice of the beam splitter, and the precise interferometric stabilization of the delay arms. SPIDER also requires a high-resolution spectrometer to resolve fringes in very different wavelength regions, which can be costly. Most importantly, when measuring time-fluctuating pulses, SPIDER retrieves only the coherent artifact and poorly underestimates the pulse durations. Simulations carried out by Ratner et al. [10] demonstrate that FROG is better than SPIDER for determining the pulse durations from averaging time-varying complex pulses.

In this work, we present a SHG-FROG setup in the visible and near-infrared region of the spectrum that relies on Type I phase matching in BBO and cascaded frequency up-conversions. A Ti:Sapphire laser amplifier (Femtopower PRO V CEP, 26 fs, 1 kHz) was used to pump a commercial optical parametric amplifier (TOPAS-C, Light Conversion). We report measurements of pulse shapes of both the second harmonic of the signal (580–800 nm) and of the idler (800–1100 nm), of the fundamental signal (1140–1600 nm) and idler waves (1600–2200 nm). We also report measurements of the difference frequency signal between the signal and idler (N-DFG, Light Conversion) from 2400 to 3250 nm. In the latter cases, another frequency doubling was performed to keep the FROG measurement within the range of the spectrometer. The procedure to retrieve the pulse shape before this additional frequency conversion is detailed. The role of phase matching is explained, as well as the corrections for the beam splitters filtering effect and dispersion. The tilt angles of the various crystals were also measured and compared to phase-matching curves of Type I SHG in BBO. We demonstrate pulse characterization over 2.5 optical octaves, mainly limited by the transparency range of the doubling crystals and by the lack of powerful sources at both ends of the spectrum.

2 Experimental setup

The experimental setup is presented in Fig. 1a–g. The primary laser source is a commercial Ti:Sapphire amplifier (Femtopower PRO V CEP, Femtolasers GmbH.) producing 26 fs, 5 mJ, carrier-envelope phase (CEP) stabilized laser pulses at 1 kHz. The CEP was not locked since it was unnecessary for this work. From this source, 3 mJ was sent to pump a commercial white light seeded OPA (TOPAS-C, Light Conversion) and a maximal efficiency of about 40 % was achieved around 1300 nm. In Fig. 1a–f, the idler and signal waves were separated after the OPA using a pair of dichroic dielectric mirrors provided by the OPA manufacturer. A periscope was used at zero degree to change only the beam height, or at \(90^{\circ }\) to flip the polarization. The output wave (signal or idler) was directed to the FROG setup using a glass wedge (Fig. 1a, b). An input iris was used to limit the energy at the focus of the FROG apparatus, and the angle of incidence of the wedge was adjusted to tune the energy to get in the proper range. A miniature spectrometer (Blue Wave, Stellarnet) covering the range 190–1037 nm was used to collect the light after frequency doubling inside a 12 \(\upmu {}\hbox {m}\) BBO cut at \(31.3^{\circ }\). All BBO crystals were set in rotation stages, and the tilt angle was adjusted in each case to maximize second-harmonic yield. In Fig. 1 c(d), a \(300\,\upmu {}\hbox {m}\) BBO cut at \(20^{\circ }\) was used to frequency double the signal (idler) wave, thus covering the range 570–800 nm (800–1100 nm). Focusing was employed (Fig. 1f, g) when the intensity of the unfocused beam was insufficient to make the measurement. In Fig. 1e–g, the fundamental signal, idler or DFG beam were, respectively, focused inside a \(100\,\upmu {}\hbox {m}\,\hbox {BBO}\) crystal only for pulse characterization purposes. To avoid damaging the FROG crystal in Fig. 1e–g, up-converted beams (S-pol.) were separated from their fundamental counterparts (P-pol.) through reflection off a silicon wafer at Brewster angle (\(74^{\circ }\)). The excellent polarizing properties of intrinsic silicon are shown on Fig. 2.

Fig. 1
figure 1

Experimental setups for the SHG-FROG measurements. The upper part of the figure shows the generation and measurement of laser pulses from 580 to 2200 nm and the lower part shows the setup for the generation and measurement of laser pulses from 2400 to 3250 nm. Upper part The OPA (TOPAS-C from Light Conversion) generate a horizontally polarized idler (H-pol.) and a vertically polarized signal (V-pol). The laser beams are separated by a dichroic beam splitter and can be used independently. a The signal is directly sent to the SHG-FROG apparatus (1140–1600 nm). b The idler is directly used for the measurement (1600–2200 nm). c The signal is frequency doubled by a \(300\,\upmu \hbox {m}\) thick BBO. The resulting beam is filtered by a reflection off a silicon wafer at Brewster angle to remove the fundamental beam. The second harmonic of the signal is used as the input of the SHG-FROG setup (580–800 nm). d The idler is frequency doubled by a 300 \(\upmu \hbox {m}\) BBO, and the resulting second-harmonic beam is used for the measurement (800–1100 nm). e Same as in c but with a \(100\,\upmu \hbox {m}\) thick BBO crystal. f Same as in d but with a \(100\,\upmu \hbox {m}\) BBO. In the cases b, c and e, a periscope rotates the polarization by \(90^{\circ }\) to fit the requirement of the SHG-FROG beam splitters. Lower part g The idler and the signal are sent together into a commercial non-collinear difference frequency generation module (N-DFG, Light Conversion). The output pulses (2400–3250 nm) are doubled by a \(100\,\upmu \hbox {m}\) BBO, and the output is sent to the SHG-FROG apparatus. Legend: BS beam splitter, DFG difference frequency generation module, OPA optical parametric amplifier, S spectrometer, \(\tau\): time difference between the two branches of the SHG-FROG, Si silicon wafer, W wedge, P periscope

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Fig. 2
figure 2

Reflectivity of an intrinsic silicon wafer at an angle of incidence of \(74^{\circ }\). The P-polarization is strongly suppressed and the S-polarization is reflected with little attenuation

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3 Data analysis

We describe here the whole data analysis used to retrieve the pulse shape at the position that we will refer to as the source. This position is different for the different setups (Fig. 1a–g), and we therefore define it explicitly here. In the case of Fig. 1a, b, the source position is taken to be just after the reflection on or the transmission through the beam separator of the OPA. In the case of Fig. 1c, d, the \(300\,\upmu {}\hbox {m}\,\hbox {BBO}\) position was taken as the source position. In the case of Fig. 1e–g, the up-conversion in the \(100\,\upmu {}\hbox {m}\,\hbox {BBO}\) was corrected for and dispersion was compensated up to the OPA beam separator (e–f) or up to the DFG crystal (g).

The first step of the data analysis is to take the measured spectrogram and to correct it for the instrumental broadening of the spectrometer through a deconvolution. Then, the resulting trace can be corrected (Eq. 1) for the phase-matching efficiency of the FROG BBO [11]. The different angles are defined on Fig. 3. Refraction is fully taken into account. The correction factor \(R(2\omega )\) (Eq. 2) in turns depends mainly on the phase mismatch \(\Delta {}k\) (Eq. 3), which is related to the refractive index of BBO [12] in the direction of propagation in the crystal (Eq. 4-6, \(\lambda\) in \(\mu \hbox {m}\)). After this phase-matching correction, we are left with the so-called FROG spectrogram defined by Eq. 7. The next step is to invert the FROG trace with an homemade version of the generalized projection algorithm [1], yielding the spectral and temporal phase and intensity and the corresponding complex electric fields up to an additional phase offset (Eq. 8, 9).

$$\begin{aligned} I_\text{FROG}^\text{SHG} (2\omega ,\tau )= & {} I(2\omega ,\tau )_\text{measured}/R(2\omega )\end{aligned}$$
(1)
$$\begin{aligned} R(2\omega )= & {} \frac{\omega ^3L^2}{n_\text{eff}(2\omega )}\left( (n_{eff}^2(2\omega )-1)(n_{0}^2(\omega )-1)^2)\right) ^2\hbox {sinc}^2 \left( \frac{\Delta {}kL}{2}\right) \end{aligned}$$
(2)
$$\begin{aligned} \Delta {}k (2\omega )= & {} 2k_0(\omega )-k_\text{eff}(2\omega ); k = \omega n/c_0\end{aligned}$$
(3)
$$\begin{aligned} n_\text{o,BBO}^2= & {} 2.7359+\frac{0.01878}{\lambda ^2-0.01822}-0.01354\lambda ^2\end{aligned}$$
(4)
$$\begin{aligned} n_\text{e,BBO}^2= & {} 2.3753+\frac{0.01224}{\lambda ^2-0.01667}-0.01516\lambda ^2\end{aligned}$$
(5)
$$\begin{aligned} n_\text{eff,BBO}^2= & {} \frac{1}{\left( \frac{{{\text{cos}}}(\beta )}{n_\text{o,BBO}} \right) ^2+ \left( \frac{{{\text{sin}}}(\beta )}{n_\text{e,BBO}} \right) ^2}\end{aligned}$$
(6)
$$\begin{aligned} I_\text{FROG}^\text{SHG} (2\omega ,\tau )= & {} \left| \int _{-\infty }^\infty \tilde{E}(t)\tilde{E}(t-\tau ){{\text{exp}}}(-2i\omega {}t){{\text{d}}}t \right| ^2\end{aligned}$$
(7)
$$\begin{aligned} \tilde{E}_1(t)= & {} \sqrt{I_1(t)}{{\text{exp}}}(i\omega _0t-i\phi _1t)\end{aligned}$$
(8)
$$\begin{aligned} \tilde{E}_1(\omega -\omega _0)= & {} \sqrt{I_1(\omega -\omega _0)}{{\text{exp}}}\left( i\phi _1(\omega -\omega _0)\right) \end{aligned}$$
(9)

Since SHG-FROG has an ambiguity on the sign of chirp [1], two traces with a known differential dispersion are needed to retrieve the proper chirp sign. Therefore, for each measurement, two FROG traces were recorded. The second trace had either a 6.35-mm fused silica or a 0.245-mm silicon window added before the FROG input iris. Silicon was used as a dispersive material in the infrared where it is transparent (\(\lambda > 1.2\, \upmu \hbox {m}\)) because fused silica is much less dispersive in this range than in the visible.

Fig. 3
figure 3

Definition of the angles for phase-matching calculation. Legend: L: thickness; \(\psi {}\): tilt; \(\beta\): angle between the wavevector \(\mathbf{k}\) and the optical axis; \(\varLambda {}\): crystal cut angle

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The next step is to correct the retrieved spectral intensity \(I_1(\omega )\) for the beam splitter intensity response (Eq. 10). In the Mach-Zehnder geometry of our SHG-FROG apparatus (Fig. 1), each beam is reflected once and transmitted once through our identical beam splitters, and it could be shown that the total associated spectral filtering is given by \(4R_\text{BS}(\omega )T_\text{BS}(\omega )\). The reflectivity, transmission and correction factors of our beam splitters are shown at an angle of incidence of \(45^{\circ }\) for S-polarization at Fig. 4a. The intensity correction factor \(4R_\text{BS}(\omega )T_\text{BS}\) is smooth and steadily above 76 % from 500 to 2500 nm.

$$\begin{aligned} I_2(\omega )=\frac{I_1(\omega )}{4R_\text{BS}(\omega )T_\text{BS}(\omega )} \end{aligned}$$
(10)

The group delay dispersion (GDD) of the beam splitters was measured both in transmission and in reflection at \(45^{\circ }\) under S-polarization using a homemade white light interferometer (Fig. 4b). The dispersion of the beam splitter in transmission is almost identical to the dispersion of a 1.6-mm-thick fused silica substrate on which the coating was deposited, except for small deviations above (669, 889 nm) and below that curve (606, 793 nm) peaking at the indicated wavelengths. The deviations of the dispersion from zero are larger for the reflected beam. The total dispersive effect of the beam splitters accounts for one transmission and one reflection (Fig. 4b, blue curve). The total spectral phase attributed to the beam splitters was then computed by two successive integrations with respect to the angular frequency over the range from 535 to 2560 nm following the equation:

$$\begin{aligned} \phi _\text{BS}(\omega )= & {} \int {{\text{d}}}\omega \int {{\text{d}}}\omega \Big (\text {GDDr}(\omega )+\text {GDDt}(\omega )\Big )\end{aligned}$$
(11)
$$\begin{aligned} \phi _2(\omega )= & {} \phi _1(\omega )-\phi _\text{BS}(\omega ) \end{aligned}$$
(12)
Fig. 4
figure 4

Optical properties of the beam splitter used in the SHG-FROG setup measured at \(45^{\circ }\) S. a Reflectivity (black line), transmission (red line) and spectral intensity correction factor resulting from one transmission and one reflection through the beam splitter coating, given by 4RT. b Group delay dispersion in reflection (GDDr, black line), in transmission (GDDt, red line) and their sum (blue line). Large GDD oscillations at 1064 and at 805 nm are caused by contamination in the white light interferometer signal and can be disregarded. Oscillations below 600 and above 1800 nm are caused by a low signal-to-noise ratio and can also be disregarded

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The next step is to correct the spectrum for the phase-matching efficiency of the \(100\,\upmu \hbox {m}\,\hbox {BBO}\) (Eq. 13), the denominator being given by Eq. 2. This step only applies to measurements taken with the setups of Fig. 1e–g. The dispersion inside the crystal can be neglected for our purpose.

$$\begin{aligned} I_3(\omega )=\frac{I_2(\omega )}{R(\omega ,L,\varLambda ,\psi )} \end{aligned}$$
(13)

Then, we subtracted the dispersion (Eq. 14) introduced by propagation in air between the FROG crystal and the \(100\,\upmu \hbox {m}\,\hbox {BBO}\) crystal (Fig. 1e–g) or up to the defined source position (Fig. 1a–d). The air path is typically 1–2 m long depending on the particular case. The index of refraction of air [13] is given for completeness (Eq. 15).

Fourier transformations are then applied (Eq. 16) to find the temporal pulse properties. The frequency up-conversion in the \(100\,\upmu \hbox {m}\,\hbox {BBO}\) can then be inverted (Eq. 17–19) if applicable. We are therefore left with the fundamental wave (of interest) at the position of the \(100\,\upmu \hbox {m}\,\hbox {BBO}\). The final step is to correct for the dispersion caused by propagation in air between the source position and the \(100\,\upmu \hbox {m}\,\hbox {BBO}\) (Eq. 20). Temporal profiles can be computed through inverse Fourier transforms (Eq. 21). The final pulse duration is measured numerically from \(I_5(t)\) and the group delay dispersion is found through a second-order polynomial fit of the spectral phase \(\phi _5(\omega /2)\).

$$\begin{aligned} \phi _3(\omega )= & {} \phi _2(\omega )-\frac{1}{2}L_\text{Air}\left[ \frac{{{\text{d}}}^2k}{{{\text{d}}}\omega ^2}\right] _\text{Air}\end{aligned}$$
(14)
$$\begin{aligned} n_\text{Air}= & {} 1+\frac{0.05792105}{238.0185-\lambda ^{-2}}+\frac{0.00167917}{57.362-\lambda ^{-2}}\end{aligned}$$
(15)
$$\begin{aligned} I_3(t)= & {} \left| {{\mathcal {F}}}^{-1}\{ \tilde{E}_3(\omega )\} \right| ^2; \phi _3(t)=\angle {{\mathcal {F}}}^{-1}\{ \tilde{E}_3(\omega )\}\end{aligned}$$
(16)
$$\begin{aligned} I_4(t)= & {} \sqrt{I_3(t)}; \phi _4(t)=\phi _3(t)/2;\end{aligned}$$
(17)
$$\begin{aligned} \tilde{E}_4(t)= & {} \sqrt{I_4(t)}{{\text{exp}}} \left( i\frac{\omega }{2}t-i\phi _4(t)\right) \end{aligned}$$
(18)
$$\begin{aligned} I_4(\omega /2)= & {} \left| {{\mathcal {F}}}\{ \tilde{E}_4(t)\} \right| ; \phi _4(\omega /2)=\angle {{\mathcal {F}}}\{ \tilde{E}_4(t)\}\end{aligned}$$
(19)
$$\begin{aligned} I_5(\omega /2)= & {} I_4(\omega /2); \phi _5(\omega /2)=\phi _4(\omega /2)-\frac{1}{2}L_\text{Air} \left[ \frac{{{\text{d}}}^2k}{{{\text{d}}}\omega ^2}\right] _{Air}\end{aligned}$$
(20)
$$\begin{aligned} I_5(t)= & {} \left| {{\mathcal {F}}}^{-1}\{ \tilde{E}_5(\omega )\} \right| ^2; \phi _5(t)=\angle {{\mathcal {F}}}^{-1}\{ \tilde{E}_5(\omega )\} \end{aligned}$$
(21)

4 Results and discussion

A selection of corrected FROG traces and their respective fits taken from the different data sets are shown in Fig. 5. The labels indicate the fundamental centroid wavelength before the frequency up-conversions. We generally observe good agreement between the experimental and fitted traces. In each case, two experimental traces corresponding to the trace without glass (top) and the trace with additional dispersive window (bottom) are shown.

Fig. 5
figure 5

A sample of experimental (Exp.) and retrieved (Fit) FROG traces with (w/ w.) and without (w/o w.) additional dispersive windows. For cases a, b, e, f, the window was a 6.35-mm-thick piece of fused silica and for cases c, d, g, h, the window was a 0.245-mm-thick piece of intrinsic silicon. The centroid wavelength at the laser source position and the corresponding series name is indicated next to each set of figures. \(\sqrt{I_\text{FROG}^\text{SHG}}\) is shown on a logarithmic color scale spanning two orders of magnitude. The grid is \(64\times 64\) with time steps of 2.5 fs

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At each step of the experiment, we optimized the different BBO crystal tilt angles to maximize second-harmonic yield. The measured tilt angles are reported in Fig. 6 for each of the crystals, where they are compared to phase-matching charts computed with Eq. 2–6. We observe a good overall agreement between theory and experiment.

Fig. 6
figure 6

Type I second-harmonic generation phase-matching charts of three BBO crystals as a function of the tilt angle and the second-harmonic wavelength. The symbols indicate the measured tilt angles in each case. a \(300\,\mu {}\hbox {m}\,\hbox {BBO}\) cut at \(20^{\circ }\). b \(100\, \upmu {}\hbox {m}\,\hbox {BBO}\) cut at \(20^{\circ }\). c \(12\,\upmu {}\hbox {m}\,\hbox {BBO}\) cut at \(31.3^{\circ }\)

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The final results for the fundamental pulse parameters at the source position are found at Fig. 7. The pulse duration of the fundamental wave at source position is given in Fig. 7a, and the fitted group delay dispersion at the same position is given at Fig. 7b. Figure 7c specifies the available pulse energy measured with a power meter at each wavelength. We observe that pulse durations range from about 20–120 fs. We observe that the signal wave out of the OPA is more or less transform-limited, with durations between 20 and 40 fs. The idler wave has comparable durations below 1800 nm, but then its (negative) chirp grows while going toward 2000 nm and above. This could be attributed in part to the transmission through the 6-mm-thick fused silica filter used to separate idler and signal. This increasingly negative chirp for increasing wavelength of the idler is also very neatly seen in the curve “\(\hbox {idler} \times 2300\,\upmu {}\hbox {m}\,\hbox {BBO}\)” at Fig. 7b. Note that the second harmonic of a Gaussian pulse is 1.41 times shorter than its generating wave, which could account for some of the relatively short durations seen in the curves “\(\hbox {signal} \times 2300\,\upmu {}\hbox {m}\,\hbox {BBO}\)” and “\(\hbox {idler} \times 2300\,\upmu {}\hbox {m}\,\hbox {BBO}\).” We observe at Fig. 7a, b that the cascaded second-harmonic generation in a \(100\,\upmu {}\hbox {m}\,\hbox {BBO}\) before the FROG setup leads to overestimations of the chirp and the pulse durations below 1450 nm (curves “signal” and “\(\hbox {signal}\,\times 2100\,\upmu {}\hbox {m}\,\hbox {BBO}\)”). It is increasingly accurate as the wavelength is increased toward 2000 nm as seen by comparing the curves “idler” and “\(\hbox {idler}\times 2100 \,\upmu {}\hbox {m}\,\hbox {BBO}\).” The probable explanation for the discrepancy between the curves “signal” and “\(\hbox {signal} \times 2100\,\upmu {}\hbox {m}\,\hbox {BBO}\)” is the limited bandwidth of the second-harmonic process in the \(100\,\upmu {}\hbox {m}\,\hbox {BBO}\), even after correction, that is affecting much more the shorter than the longer wavelengths. The data set dubbed “\(\hbox {DFG} \times 2100\, \upmu {}\hbox {m}\,\hbox {BBO}\)” shows pulse durations in the 60–100 fs range, which corresponds at \(3\,\upmu {}\hbox {m}\) to 6–10 cycles. An independent experiment using a completely different detection scheme, namely four-wave mixing in air [17], had found around 80–120 fs pulses at the wavelengths that we selected here between 2100 and 3300 nm. In [17], we could not correct for the longer air path dispersion and absorption loss because the spectral phase remained unknown. The results presented here and in [17] are consistent with each other. For this reason, we believe in the accuracy of the measurement technique presented here above \(2000\,\upmu {}\hbox {m}\).

Fig. 7
figure 7

Results after full correction for dispersion and phase-matching efficiency. a Pulse durations, defined by the full width at half maximum of the intensity profile. b Group delay dispersion fitted using a second-order polynomial of the spectral phase. c Energy per pulse available at each wavelength

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5 Conclusion

We have measured laser pulse shapes over 2.5 optical octaves (580–3250 nm) using a SHG-FROG setup equipped only with a single inexpensive visible-NIR spectrometer and a pair of homemade beam splitters. The algorithm to retrieve the initial pulse shape was detailed. Corrections for the resolution of the spectrometer, the phase-matching efficiency, the filtering and dispersive effects of the beam splitter and the air dispersion were fully taken into account. Pulse durations ranging from 20 to 120 fs were retrieved. We have shown that the output pulses from parametric amplifiers and difference frequency generators can differ greatly in pulse duration from the Ti:Sapphire pump. Four-wave mixing in air can be used to extend the pulse shape characterization range from 3250 to 18,000 nm [17].