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Acousto-optic modulator based dispersion scan for phase characterization and shaping of femtosecond mid-infrared pulses

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Abstract

Compression, shaping and characterization of broadband mid-infrared (MIR) pulses based on an acousto-optic modulator (AOM) pulse shaper is presented. Characterization of the spectral phase is achieved by an AOM-shaper based implementation of a dispersion scan (d-scan). The abilities of the setup are demonstrated by imprinting several test phases with increasing complexity on broadband MIR pulses centered at 3.2 µm and retrieval of the imprinted phases with the presented d-scan method. Phase characterization with d-scan in combination with an evolutionary algorithm allows us to compress the MIR pulses below 50 fs FWHM autocorrelation after the shaper.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Shaped mid-infrared (MIR) ultrashort laser pulses have shown their value in a broad range of applications, such as in the investigation of vibrational dynamics of molecules [1] and coherent control over the excitation of vibrational levels [2,3] or over the functional properties of solids [4]. In all those applications, the spectral phase of the laser pulse is a key parameter in the experiment. Several techniques have been proposed and successfully applied throughout the years to determine the spectral phase, such as frequency resolved optical gating (FROG) [5,6], spectral phase interferometry for direct electric-field reconstruction (SPIDER) [7,8] and multiphoton intrapulse interference phase scan (MIIPS) [9,10].

Successful pulse characterization by FROG and SPIDER has been demonstrated for pulses ranging from ultraviolet to MIR [11]. By up- or down-conversion with a reference (XFROG) or a chirped pulse (SPIDER) the signal to be measured can be spectrally shifted into the visible region, which facilitates detection [1214]. MIIPS, on the other hand, is a convenient method for phase characterization if a pulse shaper is available. It relies on the iterative determination and subsequent compensation of the pulse’s group delay dispersion (GDD). In this way, the pulse can be compressed to its transform limit and its original phase is just the phase applied by the shaper.

In recent years, another technique for phase characterization of ultrashort pulses has drawn the attention of the community: dispersion scan (d-scan). In d-scan, similarly to MIIPS, a known phase is imprinted on the pulse and its effect on the second harmonic (SH) spectrum is recorded [15]. In contrast to MIIPS, the phase reconstruction in d-scan does not rely on the second derivative of the applied test phase, thus making the technique more robust for pulses with complex phases [9,15]. The popularity of d-scan arises from its simple setup and minimum alignment requirements, as it relies on a single beam geometry and does not require interferometric delay precision [15]. Furthermore, d-scan is able to simultaneously measure and compress the test pulse and has a high tolerance to noise [16,17].

Despite the widespread and successful use of d-scan in the visible (VIS) and near-infrared (NIR) spectral ranges, it has not yet been extensively applied for phase characterization in the MIR. The lack of off-the-shelf optics like mirrors and wedges for dispersion control has hampered its broad application in the MIR. There have been approaches to partially mitigate these issues, e.g. by using a grating compressor for dispersion control [18], or changing the dispersion only in discrete and fixed steps by varying the number of passes through a sapphire plate, [19] or by inserting flat windows of various thickness with a filter wheel [20].

In the present work, the challenge of dispersion control for MIR d-scan is addressed by using an acousto-optic modulator (AOM) based pulse shaper, which is capable not only of MIR pulse characterization, but also of a nearly arbitrary modification of the MIR pulse’s spectral phase and amplitude. The presented setup uses a strictly collinear geometry and no multiple reflections from chirped mirrors are necessary. Both are advantageous with respect to the ease of alignment. The phase of broadband MIR pulses, ranging from 2.8 to 3.6 µm, is manipulated by several test phases and characterized. Compression of the MIR pulses by the shaper gives pulses with an autocorrelation below 50 fs (FWHM). For experiments which already include a pulse shaper in the beamline, our approach offers an in-line pulse characterization tool with a minimum of additional alignment and components necessary.

2. AOM shaper based d-scan

The electric field of an ultrashort laser pulse can be described in the frequency domain by its spectral amplitude $|{E(\omega )} |$ and spectral phase $\varphi (\omega )$ [15]

$$E(\omega )= |{E(\omega )} |\textrm{exp}[{i\varphi (\omega )} ]$$

The spectral amplitude $|{E(\omega )} |\; \propto \sqrt {I(\omega )} $ can be relatively easily determined by measuring the intensity spectrum $I(\omega )$, whereas the determination of $\varphi (\omega )$ requires more sophisticated techniques. For the d-scan method, several known frequency dependent phases ${\phi _j}(\omega )$ are added onto the pulse and for each ${\phi _j}(\omega )$ the spectrum of a non-linearly generated signal (usually the SH) is recorded [1517]. This gives a two-dimensional trace of the non-linearly generated spectra vs. the imprinted phases ${\phi _j}(\omega )$. From the measured d-scan trace ${S_{meas}}({\omega ,{\phi_j}(\omega )} )$ and an independent measurement of the fundamental wavelength (FW) spectrum $I(\omega )$, the spectral phase $\varphi (\omega )$ can be determined by fitting a simulated trace ${S_{sim}}({\omega ,{\phi_j}(\omega )} )$ to the measured trace ${S_{meas}}({\omega ,{\phi_j}(\omega )} )$, taking into account the dependence of the non-linearly generated signal on the spectral phase of the laser pulse. In practice, spectrum and phase are often not given as continuous functions, but their values are given at discrete angular frequencies ${\omega _i}$. The fit minimizes the error function [15,17]

$$G = \sqrt {\frac{1}{{{N_i}{N_j}}}\mathop \sum \limits_{i,j} {{[{{S_{meas}}({{\omega_i},{\phi_j}} )- {\mu_i}{S_{sim}}({{\omega_i},{\phi_j}} )} ]}^2}} $$
where ${N_i},\; {N_j}$ denote the total number of frequency points and imprinted phases, respectively. ${\mu _i}$ is updated at every iteration of the fit and accounts for phase matching and detection efficiency of the non-linearly generated signal:
$${\mu _i} = \frac{{\mathop \sum \nolimits_j {S_{meas}}({{\omega_i},{\phi_j}} ){S_{sim}}({{\omega_i},{\phi_j}} )}}{{\mathop \sum \nolimits_j {S_{sim}}{{({{\omega_i},{\phi_j}} )}^2}}}$$

In the VIS/NIR spectral region, usually a combination of chirped mirrors and glass wedges is used to realize d-scan. The thickness of the glass wedges is chosen in such a way that the dispersion of the chirped mirrors and the dispersion of the glass wedges cancel out up to first order. ${\phi _j}(\omega )$ is then imprinted on the compressed pulse by varying the thickness of the transmitted glass.

In our setup, the spectral phase $\varphi (\omega )$ of broadband MIR pulses is controlled by a pulse shaper. Unlike in traditional d-scan implementations, an AOM in the Fourier plane of a 4f pulse shaper geometry is used to imprint ${\phi _j}(\omega )$ onto the pulses. In this way, the use of wedges and chirped mirrors, which are challenging to produce in the MIR, is circumvented. Moreover, many experiments rely on a pulse shaper anyway and the phases ${\phi _j}(\omega )$ can be readily imprinted on the pulses without the need of additional alignment or optics to introduce the dispersion. Finally, with the pulse shaper it is not only possible to characterize the pulse, but also to imprint virtually any phase on it.

For characterization, pure quadratic phases are imprinted on the MIR pulses

$${\phi _j}(\omega )= \frac{1}{2}{c_j}{({\omega - {\omega_0}} )^2}$$
and the GDD ${c_j}$ is scanned. Figure 1 shows a scheme of how our implementation of d-scan works: Pulses with some initial unknown phase enter the AOM pulse shaper. The shaper modifies the pulses’ phase by ${\phi _{AOM}}$ (in the example shown in Fig. 1, the combination of the pulse’s initial phase before the shaper and ${\phi _{AOM}}$ generates a pulse with flat spectral phase). In order to perform d-scan, the AOM in addition successively imprints several quadratic phases on the pulses by scanning the GDD ${c_j}$. For each ${c_j}$ the spectrum of the SH is recorded, resulting in a two-dimensional trace. From the d-scan trace and an independent measurement of the FW spectrum, the phase $\varphi (\omega )$ of the pulses after the shaper is retrieved.

 figure: Fig. 1.

Fig. 1. Scheme of the AOM shaper based d-scan technique: Pulses with an initial phase enter the shaping setup. The shaper imprints some phase ${\phi _{AOM}}$ on the pulses. In addition to ${\phi _{AOM}}$ several quadratic phases ${\phi _j}$ are imprinted successively on the pulses (represented by the parabolas of different colors) and for each ${\phi _j}$ a spectrum of the SH is recorded. This gives a d-scan trace of the shaped pulses. For the sake of clarity, the manipulation of the phase by ${\phi _{AOM}}$ and ${\phi _j}$ is shown separately; in the experiment, they are imprinted in a single step as ${\phi _{AOM}} + {\phi _j}$.

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The approach to d-scan described here is also known as chirp scan. A demonstration of chirp scan for pulses centered at 800 nm with an acousto-optic programmable dispersive filter has been presented in Ref. [21].

3. Experimental setup and methods

3.1. Experimental details

The experimental setup is shown in Fig. 2. It consists of an optical parametric amplifier (OPA) that generates the MIR pulses, a pulse shaper and a part for characterization of the shaped pulses. The OPA is pumped by a commercial 1 kHz Ti:Sapphire chirped pulse amplification system (Coherent Astrella) and is a two-stage design using in the second stage a periodically poled lithium niobate crystal designed to provide broadband phase matching. It delivers vertically polarized idler pulses with 1.5 µJ energy and a spectrum spanning from 2.6 to 3.6 µm (FWHM) with passive carrier-envelope phase stabilization. Its architecture is based on the designs presented in [22,23]. A periscope flips the polarization from vertical to horizontal. A CaF2 lens collimates the MIR beam, which is then coupled into a pulse shaping setup using a folded reflective 4f geometry capable of phase and amplitude shaping [24,25]. The 4f setup comprises gratings with 150 grooves/mm, f=170 mm cylindrical mirrors and a germanium AOM (ISOMET LS600-1109-10-W). Mirrors and gratings are gold coated. This choice of gratings and mirrors allows to image the MIR spectrum onto the whole AOM active aperture. The number of pixels of our shaper is estimated to be around 180, limited by the finite spot size of the optical beam at the interaction region with the acoustic wave. The radio frequency (RF) waveform for the acoustic wave with 75 MHz carrier frequency is generated by a computer controlled arbitrary waveform generator with 1 GHz sampling rate (Chase Scientific Company, DA11000). After the 4f setup an iris is used to let pass only the -1st diffraction order with the imprinted spectral phase, while all other orders are blocked. In addition, a razor blade blocks wings of the 0th diffraction order that are not properly blocked by the iris. Two folding mirrors guide the shaped MIR beam into the characterization setup. The MIR beam exiting the shaper has ca. 400 nJ energy and its spectrum spans from 2.8 to 3.6 µm (FWHM).

 figure: Fig. 2.

Fig. 2. Experimental setup: an OPA acts as a source for MIR pulses which are sent into a Germanium AOM 4f pulse shaper setup. With a flip mirror, the shaped MIR beam can either be sent into a spectrometer to record its spectrum or into an arrangement to measure a d-scan trace or an interferometric autocorrelation trace, respectively. A 50 mm lithium fluoride rod (LiF) compensates for the dispersion introduced by the shaper up to first order. CL: collimation lens, FL: focusing lens, RF: radio frequency, PM: parabolic mirror, MCT: mercury cadmium telluride, AGS: Silver thiogallate (AgGaS2) non-linear optical crystal, SP: shortpass filter, PD: photodiode.

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A flip mirror is used to either let the MIR beam pass, in order to record the FW spectrum, or to send it via a f=50.8 mm gold coated parabolic mirror into a 100 µm thick AgGaS2 (AGS) crystal (Eksma Optics, $\theta $=39°, $\varphi $=45°) for SH generation (SHG). Before the AGS crystal, a 50 mm LiF rod introduces a GDD of -15.000 fs2 at 3.2 µm [26], which compensates for the GDD introduced by the Ge substrate of the AOM and a Bragg angle correction phase mask applied by the AOM [27], see Section 3.2. In order to account for the wavelength dependent losses of the LiF rod in the measurement of the FW spectrum, another 50 mm LiF rod is placed in the path where the FW spectrum is recorded. After SHG in the AGS crystal, a CaF2 lens (f=50.0 mm) collimates the beam and an IR short wave pass filter (Laser Components, cut-off wavelength 2.3 µm) removes the fundamental MIR component. The transmitted SH beam is then either guided into a spectrometer to record its spectrum for d-scan or, via a flip mirror, sent to an InGaAs photodiode (THORLABS DET10D/M) to record a collinear SH autocorrelation. Neutral density (ND) filters before photodiode and spectrometer avoid saturation of the detectors (not shown in Fig. 2). Both for the d-scan and autocorrelation measurement, the AOM shaper scans the GDD and the delay of the pulse pair, respectively. The spectrometer is a spectrograph (Acton Research Corporation, SpectraPro-500i, f=0.5 m) with a mercury cadmium telluride (MCT) array detector. It records both the FW and the SH spectrum by changing between different gratings inside the spectrograph (150 grooves/mm for the FW and 300 grooves/mm for the SH).

3.2. Bragg compensation mask

A 4f pulse shaper setup with an AOM in the Fourier plane is used. In pulse shaping with AOM, the desired phase and amplitude modulations are imprinted on the laser pulse by Bragg diffraction of the optical wave from the travelling acoustic wave [28,29]. A known issue with Bragg diffraction of a broadband laser pulse by an AOM crystal in a 4f pulse shaper setup is that for a constant acoustic frequency over the whole AOM aperture, the Bragg diffraction angle of the optical wave varies with optical wavelength, which leads to angular dispersion of the diffracted optical wave. This in turn results in spatial dispersion of the outgoing beam after the 4f setup and thus may hamper effective pulse shaping [27,30]. In order to reduce the angular dispersion of the diffracted optical wave, a Bragg mask is applied on the AOM as described in Refs. [27,30], in addition to the quadratic phases for d-scan.

3.3. Phase retrieval

In the work presented, a Nelder-Mead algorithm (also known as downhill simplex) [31] is almost exclusively used for retrieval of the spectral phase from the d-scan traces. In our implementation of the retrieval algorithm, the spectral phase is represented by its values at certain frequencies. Similar to Ref. [16], the phase is first optimized at only few frequencies and interpolated in between. When the algorithm converges or gets stuck, the frequency resolution is increased. This is repeated until the desired resolution given by the user (which in our case is 6 cm-1) is reached.

Some d-scan traces show features that suggest that the phase imprinted on the pulse can be described by a Taylor series. This is the case if the trace is for example shifted (second order dispersion), tilted (third order dispersion) or curved (fourth order dispersion) compared to the trace of a transform-limited (TL) pulse. If a trace shows such features, the phase is first represented by a Taylor series with 40 coefficients to get a first estimation of it. After the algorithm converges or stalls for the Taylor representation, the phase is represented by its values at certain frequencies and the procedure described above takes place. This allows for a more accurate retrieval as deviations from a pure Taylor phase can be represented as well.

The measured d-scan trace and FW spectrum are corrected for grating efficiency of the spectrograph, efficiency of the detector and, in the case of the d-scan trace, also for transmission of ND and short-pass filters (data is obtained from the manufacturers’ data sheets).

3.4. Autocorrelation

In order to measure the duration of the shaped pulses, the shaper itself is used to measure an interferometric autocorrelation [32]. The double pulses are created by applying a mask [33]

$$M\left( \omega \right) = cos \left( {\displaystyle{{\omega \tau } \over 2}} \right) = \left| {cos \left( {\displaystyle{{\omega \tau } \over 2}} \right)} \right| \times exp\left\{ {i\underbrace{{arg\left[ {cos \left( {\displaystyle{{\omega \tau } \over 2}} \right)} \right]}}_{{0{\rm \; }or{\rm \; }\pi }}} \right\}$$
on the AOM. $\tau $ is the variable delay between the pulses. The SH signal is generated in the same AGS crystal as used for the d-scan measurements and recorded by an InGaAs photodiode. By employing the pulse shaper for double pulse creation, there is no need to set up an additional mechanical delay line that would increase the demands on alignment of the setup.

4. Results

4.1. Pulse compression

The AOM shaper based d-scan is used to determine the spectral phase of MIR pulses after the shaper. Then a corresponding phase is applied to compress the MIR pulses. This is done in an iterative manner: In a first d-scan measurement, a large range of GDDs with big step size is scanned. The retrieved phase is fitted by a polynomial function up to third order and the corresponding GDD and third order dispersion (TOD) are applied by the shaper. An autocorrelation measurement of the up-to–TOD-corrected pulses is measured. In a second d-scan measurement, the phase of the roughly compressed pulse is determined by scanning a smaller range of GDDs with finer resolution. This time, no fit is performed on the retrieved phase, the corresponding phase mask is written on the AOM and an autocorrelation measurement is performed again. Our experience shows that more iterations do not lead to shorter pulses.

Figure 3(a) shows the measured spectrum and retrieved phases of pulses after the AOM shaper setup. The retrieved phase of the first d-scan measurement (red) shows hardly any GDD, but strong TOD. This is not surprising, as for the first d-scan, only a Bragg compensation mask is applied on the AOM and the length of the LiF rod is chosen such that it compensates the GDD introduced by the Ge substrate and Bragg mask of the AOM. In contrast, the TOD introduced by the shaper has the same sign as the TOD of LiF and the two contributions add up. The retrieved phase of the second d-scan (green) has some contribution from negative fourth order dispersion (FOD), which can also be seen by the curved look of its trace (Fig. 3(b)). This makes sense as in this iteration corrections up to third order are already applied by the AOM. From the retrieved phase of d-scan 2 (green) it can be seen that the retrieval becomes unreliable below ca. 2.8 µm. The reason for this is that the detector used to record the spectrum of the SH consists of a MCT array in combination with a coated ZnSe window. The window has very low transmission below ca. 1.5 µm, leading to a very small and noisy SH signal which corresponds to wavelengths shorter than 3 µm. This can only be partly compensated by correction of the measured signal by the detector sensitivity according to the data sheet, as from some point on the measured signal is too low and noise gets strongly amplified.

 figure: Fig. 3.

Fig. 3. a) Measured spectrum (grey shaded) and retrieved phases for iterative d-scan measurements. For a discussion of the large absolute value of the phase in d-scan 2 (green) and 3 (blue), see text. Retrieved phases are not shown for spectral regions where the spectrum is smaller than 10% of the maximum intensity. For better visibility, the retrieved phase of d-scan 3 is shifted by $2\pi $ below $0.52 \times {10^{15}}rad/s$ (3.6 µm). b) Measured and retrieved trace of d-scan 2. The matrix size for retrieval is $321 \times 61$ (frequency ${\times} $ dispersion axis), retrieval error G=0.0280. c) Interferometric (black) and intensity (red) autocorrelation trace of the compressed pulses. The intensity trace was obtained from the measured interferometric trace by applying a Fourier filter. A Lorentzian fit (blue) to the intensity autocorrelation trace gives a FWHM of 46 fs. ACT: autocorrelation trace.

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It should be noted that phase retrieval with d-scan has been shown to possess some tolerance against bandwidth limitations of the SH detection [34,35]. This is because the phase information of a certain fundamental wavelength is not only encoded in the corresponding SH wavelength, but also at wavelengths resulting from mixing with other parts of the spectrum. With this redundancy of information contained within the d-scan trace, phase retrieval over the whole spectrum might be possible even if parts of the SH spectrum are missing. However, for the retrieval to be successful, the information of an uncalibrated d-scan trace needs to be sufficiently redundant [36]. In our case, the unreliable part of the SH spectrum is too large for the retrieval to be successful below 2.8 µm.

A solution to extend the reliable region of phase retrieval to shorter wavelengths of the spectrum would be a detector with good sensitivity for both the MIR FW and SH spectrum. MCT detectors with appropriately coated windows are in principle available. With such a detector, it would be possible to reliably retrieve the phase over the full spectrum.

Another way to address the issue is to apply an amplitude mask in the AOM and let only spectral components of the unreliable retrieval region pass. In this situation, only the SH intensity of the spectrally clipped FW spectrum is recorded by an InGaAs photodiode. In addition to the amplitude mask, the AOM also applies both GDD and TOD to the spectrally clipped pulse and an evolutionary algorithm is used to find values for GDD and TOD that maximize the SH signal on the photodiode [37]. The optimization of the phase with the evolutionary algorithm is separately done in the blue wing of the pulse (where the retrieval becomes unreliable due to low detector response) and the red edge (where the retrieval eventually becomes unreliable due to low signal of the FW spectrum). By using the combination of d-scan and evolutionary algorithm to determine the phase, the MIR pulse can be further compressed. A Lorentzian fit to the intensity autocorrelation trace of the compressed pulse yields 46 fs FWHM autocorrelation after the AOM (Fig. 3(c)). By fitting a Lorentzian to the simulated autocorrelation trace [38] of the TL-pulse, its autocorrelation is estimated to be 28 fs FWHM. The TL-pulse has a duration of 22 fs FWHM. The main reason for the discrepancy between the theoretically possible and the experimentally achieved pulse duration is the breakdown of the d-scan retrieval below 2.8 µm. The phase estimation with the evolutionary algorithm can only partly mitigate that problem, as the applied third order Taylor phase is only a rough estimation. This point is further illustrated by simulating the autocorrelation trace of the TL pulse with its spectrum restricted between 2.8-3.9 µm and set to zero beyond (beyond 3.9 µm the spectral intensity is less than 10% of its maximum value). A Lorentzian fit to this autocorrelation trace results in 40 fs FWHM, closer to the value that was experimentally achieved for the full spectrum.

4.2. AOM based characterization of tailored phases

To further demonstrate the AOM shaper based d-scan characterization, several phases are imprinted with the AOM on the compressed MIR pulses, d-scan traces are measured and the retrieved phases are compared with the applied phases. Second (${\pm} \; 2000\; fs^2$), third (${\pm} {10^5}\; f{s^3}$) and fourth order dispersion (${\pm} 2 \times {10^6}\; f{s^4}$) are applied to the pulses. In addition, a two-color double pulse is created by delaying the blue part of the spectrum by 500 fs. A reference measurement of the compressed pulse without any additional imprinted phase is also acquired (not shown). The retrieved phase of the reference measurement is subtracted from the retrieved phases of the pulses with the imprinted phases mentioned above. With the sole exception of the 500 fs two-color double pulse, all retrievals are done using a Nelder-Mead algorithm; for the retrieval of the 500 fs two-color double pulse, a differential evolution scheme is employed [17].

Figure 4 shows the measured and fitted traces together with the phases and fundamental spectra of pulses with imprinted phase of $+ 2000\; f{s^2}$ (Fig. 4(a)-(c)), $- 2000\; f{s^2}$ (Fig. 4(d)-(f)), $+ {10^5}\; f{s^3}$ (Fig. 4(g)-(i)) and $- {10^5}\; f{s^3}$ (Fig. 4(j)-(l)). As can be seen, the d-scan traces show the typical features corresponding to GDD and TOD, i.e. a shift from zero GDD and tilt, respectively. The reconstruction of the spectral phase works well for the major part of the spectrum; deviations from the applied phase are only seen for short wavelengths for the reason mentioned above.

 figure: Fig. 4.

Fig. 4. Shaper based d-scan measurements of MIR pulses with imprinted phases. If not noted otherwise, no initial guess was made on the phase to retrieve and no noise was added on the simulated traces. a)-c) pulse with imprinted phase of 2000 fs2, G=0.0415, d)-f) -2000 fs2, for the retrieval, 1% of the d-scan trace’s maximum value was added as noise on the simulated trace and an initial guess of −2000 fs2 with 20% noise on the phase was used. Such a guess can be readily obtained by observing that the measured d-scan trace is centered around $2 \times {10^3}$ fs2, G=0.0574, g)-i) 105 fs3, G=0.0201, j)-l) -105 fs3, G=0.02363. The first row a), d), g), j) shows measured d-scan traces, the second row b), e), h), k) fitted d-scan traces. The third row c), f), i), l) shows the measured spectra (grey shaded), the retrieved phase (red squares) and the phase imprinted by the AOM shaper (blue line). The retrieval algorithm sometimes introduces jumps by $2\pi $ in the retrieved phase that have no physical meaning. Thus, for better comparison with the applied phase, in f) (-2000 fs2) and l) (-105 fs3), the retrieved phase of angular frequencies above $0.66 \times {10^{15}} rad/s$ (2.8 µm) was shifted by $2\pi $. Imprinted and retrieved phase are not shown for spectral regions where the spectrum is smaller than 10% of the maximum intensity.

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Figure 5 shows the results for pulses with fourth order dispersion $+ 2 \times {10^6}\; f{s^4}$ (Fig. 5(a)-(c)), $- 2 \times {10^6}\; f{s^4}$ (Fig. 5(d)-(f)), and the 500 fs two-color double pulse (Fig. 5(g)-(i)). The group delay of the 500 fs two-color pulse has a discontinuity at the separation frequency $0.58 \times {10^{15}}\textrm{\; rad}/\textrm{s}$ (3.24 µm), which would make retrieval with MIIPS challenging. For the 500 fs two-color double pulse, a shaper based autocorrelation is also measured. The measured pulse separation agrees well with the adjusted one (inset Fig. 5(i), which displays the intensity autocorrelation), which demonstrates the setup’s fidelity in phase tailoring.

 figure: Fig. 5.

Fig. 5. Shaper based d-scan measurements of MIR pulses with imprinted phases. No initial guess was made on the phase to retrieve and no noise was added on the simulated traces. a)-c) pulse with imprinted phase of $2 \times {10^6}$ fs4, G=0.0325, d)-f) -$2 \times {10^6}$ fs4, G=0.0329 g)-i) 500 fs two-color double pulse with separation frequency $0.58 \times {10^{15}} rad/s$ (3.24 µm) that corresponds to the center of the spectrum, G=0.0266. The inset in i) shows an intensity autocorrelation measurement of the 500 fs two-color-double pulse. In f) and i), the retrieved phase is shifted by $2\pi $ in the region above $0.64 \times {10^{15}} rad/s$ (3.0 µm) and $0.67 \times {10^{15}} rad/s$ (2.8 µm) respectively, for better comparison with the applied phase. Imprinted and retrieved phase are not shown for spectral regions where the spectrum is smaller than 10% of the maximum intensity.

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5. Conclusion

Phase tailoring and in-line characterization with an AOM shaper-based variant of d-scan for broadband MIR pulses centered at 3.2 µm has been demonstrated. For experiments comprising a pulse shaper, our method only calls for minimum additional alignment to characterize the MIR pulses, as no delay stages, splitting and combining of beams etc. are involved. Moreover, no further components to introduce the dispersion on the MIR pulses are needed. This makes our characterization setup particularly attractive for the MIR spectral region, where alignment is more challenging than in the VIS/NIR. Combination of the d-scan technique and an evolutionary algorithm allows for generation of broadband shapeable pulses with autocorrelation shorter than 50 fs FWHM. The presented AOM-shaper based d-scan implementation can thus be a convenient, easy-to-set-up alternative to other phase characterization methods for MIR experiments that involve a pulse shaper.

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)

Fig. 1.
Fig. 1. Scheme of the AOM shaper based d-scan technique: Pulses with an initial phase enter the shaping setup. The shaper imprints some phase ${\phi _{AOM}}$ on the pulses. In addition to ${\phi _{AOM}}$ several quadratic phases ${\phi _j}$ are imprinted successively on the pulses (represented by the parabolas of different colors) and for each ${\phi _j}$ a spectrum of the SH is recorded. This gives a d-scan trace of the shaped pulses. For the sake of clarity, the manipulation of the phase by ${\phi _{AOM}}$ and ${\phi _j}$ is shown separately; in the experiment, they are imprinted in a single step as ${\phi _{AOM}} + {\phi _j}$.
Fig. 2.
Fig. 2. Experimental setup: an OPA acts as a source for MIR pulses which are sent into a Germanium AOM 4f pulse shaper setup. With a flip mirror, the shaped MIR beam can either be sent into a spectrometer to record its spectrum or into an arrangement to measure a d-scan trace or an interferometric autocorrelation trace, respectively. A 50 mm lithium fluoride rod (LiF) compensates for the dispersion introduced by the shaper up to first order. CL: collimation lens, FL: focusing lens, RF: radio frequency, PM: parabolic mirror, MCT: mercury cadmium telluride, AGS: Silver thiogallate (AgGaS2) non-linear optical crystal, SP: shortpass filter, PD: photodiode.
Fig. 3.
Fig. 3. a) Measured spectrum (grey shaded) and retrieved phases for iterative d-scan measurements. For a discussion of the large absolute value of the phase in d-scan 2 (green) and 3 (blue), see text. Retrieved phases are not shown for spectral regions where the spectrum is smaller than 10% of the maximum intensity. For better visibility, the retrieved phase of d-scan 3 is shifted by $2\pi $ below $0.52 \times {10^{15}}rad/s$ (3.6 µm). b) Measured and retrieved trace of d-scan 2. The matrix size for retrieval is $321 \times 61$ (frequency ${\times} $ dispersion axis), retrieval error G=0.0280. c) Interferometric (black) and intensity (red) autocorrelation trace of the compressed pulses. The intensity trace was obtained from the measured interferometric trace by applying a Fourier filter. A Lorentzian fit (blue) to the intensity autocorrelation trace gives a FWHM of 46 fs. ACT: autocorrelation trace.
Fig. 4.
Fig. 4. Shaper based d-scan measurements of MIR pulses with imprinted phases. If not noted otherwise, no initial guess was made on the phase to retrieve and no noise was added on the simulated traces. a)-c) pulse with imprinted phase of 2000 fs2, G=0.0415, d)-f) -2000 fs2, for the retrieval, 1% of the d-scan trace’s maximum value was added as noise on the simulated trace and an initial guess of −2000 fs2 with 20% noise on the phase was used. Such a guess can be readily obtained by observing that the measured d-scan trace is centered around $2 \times {10^3}$ fs2, G=0.0574, g)-i) 105 fs3, G=0.0201, j)-l) -105 fs3, G=0.02363. The first row a), d), g), j) shows measured d-scan traces, the second row b), e), h), k) fitted d-scan traces. The third row c), f), i), l) shows the measured spectra (grey shaded), the retrieved phase (red squares) and the phase imprinted by the AOM shaper (blue line). The retrieval algorithm sometimes introduces jumps by $2\pi $ in the retrieved phase that have no physical meaning. Thus, for better comparison with the applied phase, in f) (-2000 fs2) and l) (-105 fs3), the retrieved phase of angular frequencies above $0.66 \times {10^{15}} rad/s$ (2.8 µm) was shifted by $2\pi $. Imprinted and retrieved phase are not shown for spectral regions where the spectrum is smaller than 10% of the maximum intensity.
Fig. 5.
Fig. 5. Shaper based d-scan measurements of MIR pulses with imprinted phases. No initial guess was made on the phase to retrieve and no noise was added on the simulated traces. a)-c) pulse with imprinted phase of $2 \times {10^6}$ fs4, G=0.0325, d)-f) -$2 \times {10^6}$ fs4, G=0.0329 g)-i) 500 fs two-color double pulse with separation frequency $0.58 \times {10^{15}} rad/s$ (3.24 µm) that corresponds to the center of the spectrum, G=0.0266. The inset in i) shows an intensity autocorrelation measurement of the 500 fs two-color-double pulse. In f) and i), the retrieved phase is shifted by $2\pi $ in the region above $0.64 \times {10^{15}} rad/s$ (3.0 µm) and $0.67 \times {10^{15}} rad/s$ (2.8 µm) respectively, for better comparison with the applied phase. Imprinted and retrieved phase are not shown for spectral regions where the spectrum is smaller than 10% of the maximum intensity.

Equations (5)

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E ( ω ) = | E ( ω ) | exp [ i φ ( ω ) ]
G = 1 N i N j i , j [ S m e a s ( ω i , ϕ j ) μ i S s i m ( ω i , ϕ j ) ] 2
μ i = j S m e a s ( ω i , ϕ j ) S s i m ( ω i , ϕ j ) j S s i m ( ω i , ϕ j ) 2
ϕ j ( ω ) = 1 2 c j ( ω ω 0 ) 2
M ( ω ) = c o s ( ω τ 2 ) = | c o s ( ω τ 2 ) | × e x p { i a r g [ c o s ( ω τ 2 ) ] 0 o r π }
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