Advancement of laser technology has led to the generation of ultrashort pulses of few-10 femtosecond (fs) duration with attainable intensities of ${10}^{19}–{10}^{22}{\mathrm{W}/\mathrm{cm}}^2$ [1,2]. Recently, few-cycle pulses with relativistic intensity have been produced [3–5]. Such high intensity lasers are capable of accelerating protons and ions to high energy [6,7], generating relativistic high-order harmonics [8,9], or accelerating electron bunches with TV/m fields to relativistic energies in solid nanoplasmas [10], which demand a high temporal-intensity contrast. Methods such as Cross-Polarized Wave (XPW) generation [11–13], Nonlinear Elliptical polarization Rotation (NER) [14–16], and the application of saturable absorbers [17] are commonly used for improving the pulse contrast [18]. XPW employs the third-order non-linearity of a crystal with additional focusing/collimating optics for pulse cleaning. Ultra-broadband, few-cycle pulses can also be used as an input to the XPW [19], which are created from a narrow spectrum via the process of self-phase modulation in a noble-gas-filled hollow-core fiber (HCF) wave-guide [20,21]. Whereas, NER uses the existing HCF with a couple of additional optics, thereby promising a better throughput and a much simpler setup than XPW for ultra-broadband pulses. However, pulse broadening and contrast improvement with NER have not yet been realized at the same time.

The response of a nonlinear medium to an intense electric field in terms of refractive index is given by $n=n_0+n_{2}I(r,t)$, where $n_0$ is the ordinary refractive index, $n_2$ (${\mathrm{cm}}^2/\mathrm{W}$) is the nonlinear index of refraction, and $I(r,t)$ (${\mathrm{W}/\mathrm{cm}}^2$) is the cycle-averaged intensity of the laser [22]. When an elliptically polarized (EP) laser pulse propagates through an isotropic medium, the intensity-dependent refractive index rotates the orientation of the polarization ellipse. The rotation of the polarization ellipse is dependent on the nonlinear phase change ($\mathrm{\Delta }\varphi$) between left- and right-circular (LC and RC) polarized components. This is given by $\mathrm{\Delta }\varphi =\omega z\mathrm{\Delta }n/c$, where $\omega$ is the angular frequency of the laser, $z$ is the path length, $c$ is the speed of light in vacuum, and $\mathrm{\Delta }n$ is the difference in refractive indices of the LC and RC. $\mathrm{\Delta }n=(4{ϵ}_{0}c/3)n_0{n}_2({|E_{-}|}^2-{|E_{+}|}^2)$, where ${ϵ}_0$, $E_{-}$ and $E_{+}$ are the vacuum permittivity, and the magnitude of electric fields of the LC and RC polarized components, respectively [22]. Hence, the intense part of the pulse after interaction has a different polarization ellipse than the unrotated low intensity part. Thus, the contrast of the intense laser pulse can be improved based on this intensity-dependent rotation. Careful selection of the rotated polarization components is, therefore, important to improve the contrast with NER. Therefore, the contrast improvement is highly dependent on the extinction ratio of the polarizers and the overall setup. Previous investigation on NER with xenon filled HCF proves a 3 orders of magnitude (OOM) contrast improvement of a 60 fs pulse having roughly 1% signal level of the main peak as pre-pulses [14]. Further, $>3$ OOM contrast enhancement to a level of 8 OOM was reported with 42 fs pulses in air [15]. In these studies, angle between the fast axis of the quarter waveplate and the input linear polarization is fixed to about 22.5° in order to maximize the NER efficiency [14,15]. However, the selection of this angle is not valid for the generation of few-cycle pulses that demand a significant spectral broadening, which will be considered in the current investigations.

In this Letter, the contrast improvement of a 75 mJ, 4.7 fs optical parametric synthesizer (OPS) [3] seeded by spectrally-broadened NER-cleaned pulses from a HCF is presented. The contrast is improved by 3 OOM via NER.

The schematic of the experiment is shown in Fig. 1. The polarization of a linear horizontally (LH) polarized light from a 1 kHz repetition rate, 24 fs pulse duration, multipass Ti:Sapphire chirped-pulse-amplifier (CPA) system (Femtopower Compact Pro) having an energy of 800 μJ is filtered by a 525 μm thin Si-wafer (LP1). LP1 removes the unwanted polarization components, if any, via reflection ($R=74.6\%$) leading to a better (linear) polarization degree $\ge {10}^4$. Further, the pulse passes through a quarter waveplate (QWP1) that generates EP. The ellipticity can be tuned by varying the angle (${\theta }_{\mathrm{NER}}$) between the fast axis of QWP1 and the input polarization, which is optimized for better efficiency in the current study. The EP light is then focused by an achromatic plano-convex lens of focal length $f=100\mathrm{cm}$ to a full width at half maximum (FWHM) spot size of $\approx 190\mathrm{\mu m}$ to couple it to the HCF. HCF filled with argon gas acts as a non-linear medium capable of producing a broad spectrum and generates NER at the same time. The pressure of Ar should be appropriately selected to have a large broadening and to avoid any spatio-temporal distortion of the pulse. The 1 m long HCF has an inner diameter of 250 μm. The pressure inside the HCF can be adjusted manually, which influences the polarization rotation since the rotation angle, $\alpha$, of the polarization ellipse is given by $\alpha =(\omega /c)(\tan {\theta }_{\mathrm{NER}}/(1-{\tan }^2{\theta }_{\mathrm{NER}}))(n_2/3)zI$, in which $n_2$ is pressure dependent, and $I$ is the intensity of the elliptically polarized light [23]. Due to this intensity dependent non-linearity, the polarization ellipse of the pulse is rotated around the peak while keeping the rest of the pulse intact. The pulse after the HCF is re-collimated and passes through a second $\lambda /4$ retarder (QWP2). The angle of QWP2 is suitably selected, such that it returns the output polarization state back to the input, i.e., to LH, except for the intense portion around the peak. Hence, weaker pulses and pedestals can be filtered using a glan polarizer (LP2) positioned cross to the input polarization. While pressure is scanned to optimize spectral broadening with a good beam profile, the ellipticity is scanned in order to maximize the NER efficiency. However, for maximum energy, the two properties, spectral broadening and efficiency depend on the two parameters, pressure and ellipticity. Therefore, generally a 2D optimization is required. Once optimized, the NER pulse is amplified using the four-stage OPS system, Light Wave Synthesizer 20 (LWS-20) [3], to $\approx 75\mathrm{mJ}$ and compressed to $\approx 4.7\mathrm{fs}$ for the contrast measurement using a third-harmonic generation autocorrelator [24].

 

Fig. 1. Experimental setup for cleaning sub-4 fs pulses via nonlinear elliptical polarization rotation (NER) in a hollow-core fiber (HCF). The quarter waveplates (QWP) set the polarization for the process and the polarizers (LP) used in the input and output in cross configuration select the rotated polarization component. Optimized NER pulses are stretched using a grism stretcher (GS) and Dazzler acousto-optic dispersive filter (DAZ), amplified in four optical parametric synthesizer stages (OPS) and compressed before employing third-order autocorrelator (THG-AC) for the temporal-intensity contrast measurements.

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A global optimum of the spectral broadening and efficiency is found at 650 mbar pressure and ${\theta }_{\mathrm{NER}}=7°$ for an input energy of $\approx 540\mathrm{\mu J}$. The parameters scanned around this optimum value are presented as follows. The pressure inside the HCF is varied from 250 mbar to 1000 mbar in order to optimize both the spectrum and the stability of the spatial-intensity distribution (beam profile) for ${\theta }_{\mathrm{NER}}=7°$. Figures 2(a) and 2(b) show the spectral broadening at various pressures for the rotated (crossed, NER) and unrotated (parallel to original) polarization components. The NER spectra are smoother such that the modulation around the original Ti:Sapphire spectrum of the HCF input is negligible. While spectral broadening is evident with an increase of pressure, the beam profile becomes unstable for pressures $>650\mathrm{mbar}$, where the bandwidth supports even sub-3 fs pulses. This is attributed to the plasma formation at the HCF input due to high intensity. The internal efficiency ($\eta$) of NER process is given by the equation, $\eta =P_{\perp }/(P_{\parallel }+P_{\perp })$, where $P_{\parallel }$ and $P_{\perp }$ are the power of non-rotated (parallel) and rotated (perpendicular, NER) components, and is measured after LP2. $\eta$ of NER as a function of pressure is shown in Fig. 2(c), in which it is found to maximize at 650 mbar with $\approx 57\%$ internal efficiency. It is also clear from Fig. 2(c) that the Fourier limit (FL) decreases with increasing pressure in the measured range. Efficiency as well as NER power ($P_{\mathrm{NER}}$) have a maximum at 650 mbar, as shown in Figs. 2(c) and 2(d). It should be noted that $\eta$ and $P_{\mathrm{NER}}$ are not proportional to each other since the overall transmission of the HCF varies upon increasing the pressure. Consequently, the optimal conditions support a spectral bandwidth for sub-4 fs pulses with $\eta \ge 50\%$.

 

Fig. 2. Spectral broadening measured for various Ar pressures from 250 mbar to 1 bar for (a) NER and (b) unrotated (parallel) component at the output of the HCF. (c) Fourier limit (FL) of NER calculated from the spectra (red-squares) assuming constant phase, NER internal efficiency (blue-triangles) with standard deviation, and (d) NER power (blue-triangles) with standard deviation measured as a function of Ar pressure. The efficiency maximizes around 650 mbar when the measurement is performed with ${\theta }_{\mathrm{NER}}=7°$ for 540 μJ input pulse energy.

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The measurement is repeated around the optimum of 650 mbar for various ellipticities, corresponding to different ${\theta }_{\mathrm{NER}}$, to investigate its influence. The NER spectra shows relatively small variation upon changing ${\theta }_{\mathrm{NER}}$, as plotted in Fig. 3(a), compared to the variation in pressure except for 10°. The spectral bandwidth displays an improvement of the FL from 4.01 fs to 3.73 fs for a variation of ${\theta }_{\mathrm{NER}}$ from 3° to10°, as given in Fig. 3(c). In addition, $\eta$ increases with an increase in ${\theta }_{\mathrm{NER}}$ and reaches a maximum at 7°, as shown in Fig. 3(c). It is also noted from Fig. 3(d) that $P_{\mathrm{NER}}$ also maximizes at ${\theta }_{\mathrm{NER}}=7°$. Similarly, as earlier, $\eta$ and $P_{\mathrm{NER}}$ are not proportional to each other since the overall transmission of the HCF varies upon varying the ellipticity. The optimized Ar pressure of 650 mbar and angle ${\theta }_{\mathrm{NER}}=7°$ with an internal efficiency $\approx 57\%$ were used later in the contrast investigations. A recent work on the generation of high-fidelity few-cycle laser pulses via NER in a stretched HCF by Khodakovskiy et al. supports the presented results [25].

 

Fig. 3. HCF spectra measured for (a) NER and (b) parallel-polarized pulses with various ellipticities for 540 μJ, 24 fs input pulses at 800 nm. The pressure inside the HCF is 650 mbar. (c) Fourier limit of NER component (red squares) and its internal efficiency (blue triangles) as a function of ellipticity. (d) NER power (blue triangles) and extinction coefficient of the setup (red square) measured with vacuum in the HCF versus ellipticity of the input pulse.

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The extinction ratio (degree of polarization suppression) is an important parameter that determines the contrast enhancement. As the ellipticity is controlled by optics influencing polarization, dependence of the extinction ratio on the ellipticity is relevant. To investigate this, ${\theta }_{\mathrm{NER}}$ is varied from 0° to 10° by keeping the HCF in vacuum. For ${\theta }_{\mathrm{NER}}=0°$, the extinction ratio is found to be $\approx {10}^4$, and it decreases with increasing ${\theta }_{\mathrm{NER}}$, as shown in Fig. 3(d). The extinction ratio used for the current NER based contrast measurements is $1.03\times {10}^3$ for 7°.

The NER pulse with energy $\approx 35\mathrm{\mu J}$ is seeded to the four stage OPS system for further amplification. The pulse is stretched to about $\approx 65\text{ps}$ using a grating-prism (GS, grism) stretcher and an acousto-optic programmable dispersive filter (DAZ; Dazzler, Fastlite) combination before amplification [26]. The red and blue part of the pulses are separately amplified in a serial OPS to attain pulse energies $\approx 75\mathrm{mJ}$. The red and blue part of the pulses are separately amplified in a serial OPS to attain pulse energies ≈75 mJ [3]. Importantly, the spectral gain bandwidth is limited to about 580 nm-960 nm upon amplification, leading to an increased pulse duration such that the FL is modified to sub-5 fs from the sub-4 fs seed. The amplified pulse from the OPS is compressed using the combination of block of glasses and chirped mirrors together with the Dazzler. Figure 4(a) shows the spectra of NER, original output (HCF, i.e., QWPs in 0 deg), and the corresponding amplified pulses after the OPS stages. The chirp scan technique [27] is used to characterize the spectral phase of the pulse with a feedback to the Dazzler, pulse durations close to ($<0.1\mathrm{fs}$) Fourier transform limit are reached. In order to achieve this, the second harmonic spectra are recorded while scanning the chirp of the laser pulse using the Dazzler. The spectral phase of the laser pulse is retrieved with the help of an iterative algorithm [28]. This retrieved spectral phase and independently measured spectrum are then utilized for the calculation of the pulse duration, which is found to be $\approx 4.7\mathrm{fs}$. The inset of Fig. 4(a) shows the retrieved and FL temporal intensity.

 

Fig. 4. (a) NER at 7° (NER, green) and original spectra from HCF at 0° (HCF, black). The corresponding amplified spectra in four OPS stages are presented here for NER (red) and HCF (blue). Inset: temporal intensity of amplified NER pulses with 4.7 fs FWHM duration (red) and Fourier limit (gray). (b) Contrast measurements using a third-order correlator for amplified NER (red) and HCF (blue) pulses. The NER pulses display 3 OOM contrast improvement when compared to that of HCF. Here, parts highlighted in gray color in the NER correlation are measurement artifacts.

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The NER spectrum is found to be smoother (without modulation) compared to the spectrum of the original component before and after the amplification. In order to measure the contrast that characterize pedestals/pre-pulses, defined as the intensity ratio at a certain time before or after the pulse and the peak of the pulse, a third-harmonic generation based autocorrelator (THG-AC) having a dynamic range $>{10}^9$ is used [24]. Figure 4(b) shows the measured contrast for the amplified NER and HCF. The HCF seed pulse has a nanosecond pedestal due to the amplified spontaneous emission from the CPA-based multipass amplifier, which increases significantly in the saturated OPS and is the reason for the base line in the autocorrelation trace for all time delays (${\tau }_{\mathrm{d}}$). The THG-AC signal for NER shows 3 OOM better contrast in average compared to the HCF. The peak around $-5.4\mathrm{ps}$ in NER correlation is attributed to the Dazzler, which is after the NER process. The gray colored parts at $-2.3\mathrm{ps}$ and 2.3 ps in the correlation trace for NER pulse are attributed to the parasitic internal reflection from the THG crystal, i.e., are measurement artifacts. Thus, the contrast is found to be 7 OOM in the present case for NER pulses. Though, NER is expected to produce a better contrast, the improvement in the current study is limited by the lower extinction ratio ($\approx 1.03\times {10}^3$) of the experimental setup. The contrast and the overall efficiency of NER could be improved if the following changes are implemented from the current setup. (1) The use of thin silicon wafer beyond its moderate reflectivity degrades the focal spot at the HCF input. This affects the light coupling into the HCF and its throughput. A better LP1 can therefore improve the overall efficiency of the process. (2) The size of the glan polarizer (LP2) used in the experiment is small and hence $\approx 50\%$of the energy was cut using an aperture. Therefore, with a bigger glan polarizer, $P_{\mathrm{NER}}$ and the overall efficiency can be improved. (3) The contrast could be improved if polarization optics with better extinction ratios are used. All three points can be fulfilled with (multiple reflections on) existing high quality reflective polarizers that support beyond an octave.

In conclusion, NER is employed in an Ar-filled HCF to improve the contrast of sub-4 fs pulses. The Ar pressure and ellipticity are optimized to obtain the spectral bandwidth supporting sub-4 fs laser pulses with an internal efficiency better than 50% for NER process. The optimized NER pulses are then amplified in an OPS, compressed and temporally characterized with the chirp scan technique and an advanced iterative phase retrieval algorithm. Thus, pulse duration of the compressed pulses are estimated to be $\approx 4.7\mathrm{fs}$ slightly longer than the sub-4 fs NER pulses due to the bandwidth limit introduced by the OPS gain bandwidth. A third-order autocorrelation device is used for the contrast measurement, which is found to be 3 OOM better than the amplified original HCF seed. For NER, it is important to have a high extinction ratio, which is investigated for various input ellipticities, and a value of $\approx {10}^3$ is measured with the applied parameters. It is expected to have even higher contrast enhancement with using better polarization optics, which makes this method well suited to clean seed pulses for Petawatt laser systems.