Quasi-supercontinuum source in the extreme ultraviolet using multiple frequency combs from high-harmonic generation

Martin Wünsche; Silvio Fuchs; Stefan Aull; Jan Nathanael; Max Möller; Christian Rödel; Gerhard G. Paulus

doi:10.1364/OE.25.006936

1. Introduction

Light sources with smooth, continuous spectra covering a large bandwidth are often referred to as supercontinuum sources and have many applications in spectroscopy and imaging. Prominently, visible and near-infrared supercontinuum sources are used in Optical Coherence Tomography (OCT) [1]. Many applications of supercontinua do not necessarily require temporal coherent light. Therefore, incoherent swept source quasi-supercontinua have been used for example in OCT devices [2]. The extension of OCT to the extreme ultraviolet (XUV), so-called XUV Coherence Tomography (XCT), has proven remarkable potential [3]. For example, silicon-based multilayer systems have recently been investigated with a depth resolution of better than 8 nm [4]. Another XUV application that can take advantage of XUV quasi-supercontinuum sources is near-edge x-ray absorption fine structure spectroscopy (NEXAFS) [5]. In NEXAFS studies, the absorption of XUV and soft x-ray radiation is measured beyond the absorption edges of materials and is typically used to investigate the electronic structure of solid-state systems. So far, both applications typically require large-scale synchrotron radiation sources [6, 7]. Applications such as XCT or NEXAFS would greatly benefit from laboratory-scale quasi-supercontinuum XUV sources with high flux, since higher availability in comparison to synchrotron sources would provide access to these methods to a much larger community.

Fortunately, high-harmonic generation (HHG) in suitable gas targets [8] driven by state-of-the-art femtosecond laser systems can provide photon fluxes in the XUV, which become competitive to synchrotrons [9, 10]. However, due to the high-harmonic process itself, the resulting XUV spectra are normally strongly modulated with twice the fundamental frequency and thus form combs of harmonic lines with a large spectral range but relatively small bandwidth of the individual harmonics. Consequently, HHG spectra are typically non-continuous, which limit their usability for applications such as NEXAFS or XCT.

One strategy to generate continuous HHG spectra is to temporally gate the generation process to a single emission event resulting in an isolated XUV attosecond radiation burst. Several gating methods such as temporal gating or polarization gating have been developed to confine the emission of the XUV radiation to one laser half-cycle while other half-cycles are unused [11–13]. A review is given in [14], Sansone et al., and in [15], Chini et al.. However, all these methods are technically demanding and reduce the overall-efficiency, which leads to lower XUV photon fluxes.

Here we present a new scheme for generating supercontinuous HHG spectra by temporally averaging over multiple laser pulses with different fundamental frequencies [16]. The setup utilizes an optical parametric amplifier (OPA) to shift the HHG driving wavelength in an easy, fast and reliable way. To this end, the pulses of the Ti:Sapphire laser are down-converted by the OPA into the near-infrared (NIR) up to the mid-infrared (mid-wave IR, MWIR). This has two advantages. Firstly, due to the longer wavelengths of the driving pulses, the ponderomotive potential $U_{P} \propto λ^{2}$ and thus the high-harmonic cutoff ( $\propto 3.17 \cdot U_{P}$ ) increases. Accordingly, photon energies readily exceeding 100 eV can be generated in a broad spectral range using the OPA [17]. Secondly, a shift of the driving wavelength leads to a slightly different spacing of the XUV harmonic combs. By time-averaging over several driving wavelengths, a supercontinuous XUV spectrum can be generated which is well suited for XCT in the silicon transmission window and also for NEXAFS studies, for example, at the silicon L-edge [18,19].

2. Frequency combs by high-harmonic generation in gases

High-harmonic generation in gaseous media can be described by a three-step process [20]. In the first step, a strong laser field ionizes the gas atoms. Subsequently, in the second step, electrons are accelerated in the oscillating laser field and thus gain kinetic energy. Certain electron trajectories lead back to the parent ion where the electrons finally can recombine and high-energetic photons are emitted on a sub-femtosecond time-scale [21].

This process is repeated in every half-cycle of the laser pulse with an optical period $T$ . Thus, an attosecond pulse train with a spacing of $T / 2$ is generated. The spectral representation (i.e. Fourier transform) of this light field is a modulated harmonic comb structure with odd harmonic frequencies,

ω_{N} = (2 N - 1) ω_{L},

where

(2 N - 1)

is the harmonic order and

N = 1, 2, 3, ...

. In order to evaluate the magnitude of modulation of a harmonic spectrum, the harmonic peaks can be compared to their neighboring valleys. An expression for this is the contrast or the modulation depth

M = \frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}} .

For typical (strongly modulated) HHG spectra the modulation depth is almost $M = 1$ . A recorded spectrum is shown in Fig. 1. The driving laser pulse with a central wavelength of 800 nm has a pulse energy of 1.7 mJ and a pulse duration of 35 fs. The modulation depth in this case is $M = 0.99$ and thus, this source is not suited for applications that require continuous spectra.

Fig. 1 Example of a high-harmonic spectrum generated in neon using a Ti:Sa laser at 800 nm with a pulse energy of 1.7 mJ and a pulse duration of 35 fs. Due to the high-harmonic generation, the resulting XUV spectrum is strongly modulated with the fundamental frequency. The harmonic lines of the fundamental frequency have a small individual bandwidth of 0.4 eV (FWHM), such that there is a negligible photon flux between two harmonics. The modulation depth or contrast between the harmonic lines and their valleys describes the smoothness and thus the continuity of the XUV spectrum. This strongly modulated XUV spectrum has a contrast of $M = 0.99$ .

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By changing the driving laser frequency $ω_{D} = ω_{L} + Δ ω$ , the harmonic frequencies can be shifted to

{\tilde{ω}}_{N} = (2 N - 1) (ω_{L} + Δ ω)

When several harmonic combs with different driving frequencies are accumulated, a continuous spectrum can be generated. In order to cover the spectral range between neighboring harmonics, i.e.

{\tilde{ω}}_{N}

and

{\tilde{ω}}_{N + 1} = {\tilde{ω}}_{N} + 2 ω_{D}

the fundamental needs to be shifted by

Δ ω = 2 ω_{L} / N

This means, the required spectral shift is smaller for higher photon energies. For the silicon transmission window from 30 to 100 eV and a driving laser frequency of 1.3 µm (0.95 eV), the required shift can be calculated as follows.

The 31st harmonic (29.6 eV) reaches the neighboring harmonic (33rd at 31.5 eV) at a shift of the driving fundamental wavelength by 80 nm. For the harmonics around 100 eV, a wavelength shift of only 25 nm is required. The mean of many slightly differently spaced harmonic spectra is shown in Fig. 2. For this calculation, a bandwidth (FWHM) of 0.4 eV for an individual harmonic is assumed as suggested by the experimental data of Fig. 1. The blue curve in Fig. 2 shows a modeled single harmonic comb with a large modulation depth of $M = 1$ . An almost flat spectrum with a low modulation depth can be obtained by averaging over the generated combs of harmonics with fundamental wavelengths of 1260 nm to 1340 nm using a step size of 10 nm as shown by the red curve. The modulation depth is reduced to $M = 0.35$ . Most importantly, a high spectral power density is realized for each frequency within the continuum. The shape of the residual spectral modulation is similar to a spectral beating due to the different harmonic spacing for the different frequency combs.

Fig. 2 The principle idea of generating an XUV quasi-supercontinuum by averaging over different high-harmonic spectra with different driver wavelengths is shown. For this, every single harmonic comb is calculated as a comb of Gaussian shaped harmonics with an individual harmonic bandwidth (FWHM) of 0.4 eV and a driver wavelength between 1260 nm and 1340 nm. Typically, a high-harmonic spectrum generated by a multi-cycle laser pulse is strongly modulated such that there is no photon flux between two harmonics (blue curve, driver wavelength is 1300 nm). To generate an XUV quasi-supercontinuum the average of different harmonic combs with different driver wavelengths should cover the spectral area between two neighbored harmonics. With a scan of the driving laser wavelength in the range of 1260 nm to 1340 nm and steps of 10 nm the resultant XUV spectrum (red curve) is quasi-supercontinuous and less modulated than a single harmonic comb. To evaluate a continuum the modulation depth or contrast $M = (I_{\max} - I_{\min}) / (I_{\max} + I_{\min})$ can be used. While, the contrast for the single harmonic comb is $M = 1$ , it is reduced to $M = 0.35$ for the averaged comb.

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3. Experimental setup

We use a femtosecond Ti:Sapphire laser system with a repetition rate of 1 kHz. The laser pulses have a pulse duration of 35 fs and a pulse energy of up to 12 mJ. The central wavelength of this laser system is 800 nm and cannot be changed significantly to perform the wavelength scan. Therefore, the laser pulses from the Ti:Sapphire laser are used to pump an optical parametric amplifier (OPA) [22] whose output wavelength can be remotely tuned. Our setup is shown in Fig. 3. In the OPA, focusing a fraction of the 800 nm pulses into a sapphire plate generates a broad spectrum. The generated white light from 0.5 µm to 4 µm is then amplified in three OPA stages using barium borate (BBO) crystals. Stepper motors enable the adjustment of the phase matching angle by tilting the crystals. At 9.5 W pump energy, we typically achieve 2.5 W at a signal wavelength of 1.3 µm and a pulse duration of approximately 55 fs.

Fig. 3 The OPA (colored in green) is pumped by a two-stage Ti:Sa system. The pump pulses enter the OPA with a pulse energy of 9 to 9.7 mJ and a pulse duration of 35 fs. After several beam splitters, the pump beam is focused via a lens (L1) into a sapphire plate (white light generation, WLG) where the supercontinuum radiation (white light continuum, WLC) from 0.5 µm to 4 µm is generated. A dispersive element (DC1) chirps the WLC afterwards. The chirped WLC is then overlapped with a second pump beam in a BBO crystal. The signal wave is selected by the adjustment of the temporal delay (Δt) of the second pump to the WLC via stepper motors. Together with the proper phase matching angle of the BBO crystal (Δφ), which is also set by stepper motors, the signal wave is amplified and the idler wave is generated in the BBO. Another dispersive element (DC2) compensates the chirp afterwards. After two additional OPA stages the signal and idler wave are separated by a dichroitic mirror (DM). In our experiment the output energy of the signal wave (here 1300 nm) is optimized to 2.5 mJ. By shifting the wavelength λ remotely with a computer to $λ + Δ λ (Δ φ, Δ t)$ , high-harmonics are generated for each driver wavelength λ respectively $λ + Δ λ (Δ φ, Δ t)$ . In comparison to the original harmonic spectrum of λ the one of the shifted wavelength $λ + Δ λ (Δ φ, Δ t)$ appears stretched or compressed along the photon energy.

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Laser pulses with a varying central wavelength at 1.3 µm are focused with a lens ( $f = 25$ cm) into a gas capillary of argon or neon. The usable pulse energy in front of the lens is 1.7 mJ. The peak intensity in the focus is $4 \times 10^{14} W / c m^{2}$ . The backing pressure of the gas is set to 700 mbar and the position of the focus regarding the gas capillary is adjusted to optimize the HHG efficiency.

The harmonic spectra are recorded using an XUV spectrometer that consists of a nickel coated toroidal mirror and a transmission gold grating (1000 lines/mm). The XUV spectrometer has been calibrated regarding the photon flux [23]. A CCD camera is used as a detector (Andor DO940P-BN). Aluminum or zirconium foils are applied to separate the XUV light from the infrared light.

We modified and improved the control interface of the OPA such that the output wavelength can be tuned on a sub-second time-scale without compromising efficiency. In comparison to swept source supercontinua in the visible and NIR/IR regime, where megahertz scanning is demonstrated [2], speed is not a crucial issue for the presented XUV light source, because the required time to record a single measurement in many XUV application is typically in the order of seconds. Therefore, we chose a time step per wavelength of 50 ms, which enables sweeping the wavelength over the full range several times per measurement.

4. Experimental results

Harmonic spectra, each of them with an individual driving wavelength in the range of 1260 nm to 1340 nm, are plotted in Fig. 4. For every individual harmonic line the measured spectral bandwidth (FWHM) is below 1.1 eV. It should be noticed that in our XUV spectrometer stray light from the transmission grating, higher diffraction orders, and a support grid on the grating broaden the spectrometer (instrument) function and thus also decrease the modulation depth. Therefore, the modulation depth of the harmonic combs is strongly underestimated owing to the instrument function of the spectrometer. It varies from $M = 0.55$ in the aluminum transmission window, here in the range below 70 eV (Fig. 4, left), down to $M = 0.17$ using zirconium as a transmission filter for photon energies above 70 eV (Fig. 4, right).

Fig. 4 The recorded high-harmonic XUV spectra generated in argon with individual driving wavelengths are shown in the aluminum transmission (left) and also in the zirconium transmission window (right). (left) Every single harmonic comb has a strong spectral modulation with a contrast up to $M = 0.55$ . In comparison to each other, the different combs show slightly different modulation frequencies, so the spectral overlap of harmonics from different combs changes over the photon energy. For example, a harmonic of the 1260 nm (blue curve) and a harmonic of the 1320 nm (yellow curve) driving pulses are located around 42.4 eV (violet vertical line), while the positions of the nearby harmonics of the 1300 nm are shifted. In contrast, the harmonic radiation at 60.2 eV (green vertical line) is primarily generated by the 1260 nm driver. While the harmonic of the 1300 nm is shifted a bit and the spectrum of 1320 nm shows even a minimum between two harmonics. (right) High-harmonic spectra using the zirconium filter are plotted. The modulation depth is reduced to $M = 0.17$ due to the insufficient spectrometer resolution. The cut-off energy is around 90 eV.

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During the non-automated wavelength sweep, the XUV photon numbers remain approximately constant. We obtain a maximum photon flux of $5.5 \times 10^{8}$ photons per $e V \cdot s$ at 40 eV. Also the harmonic cut-off keeps constant around 90 eV providing a flux of $1 \times 10^{6}$ photons per $e V \cdot s$ . The total photon flux (averaged over the wavelength sweep) is around $6.4 \times 10^{9}$ photons/s in the range of 30 eV to 100 eV.

Because slightly different driving wavelengths are used, all harmonic spectra show slightly different modulation frequencies. These differences in the individual XUV spectra can be exploited to generate an XUV quasi-supercontinuum. By averaging the individual spectra as shown in Fig. 5 the modulation depth can be decreased significantly. In this example, the modulation depth is reduced from $M = 0.55$ to $M = 0.24$ . Thus, the smoothness of the XUV spectrum is increased by at least a factor of two. A Fourier analysis of the averaged spectrum (Fig. 5, right) also shows that the modulation depth of the frequency comb is reduced in comparison to a single XUV spectrum.

Fig. 5 Different high-harmonic spectra generated in argon are averaged to a smooth averaged spectrum with a reduced spectral modulation of $M = 0.24$ . (left) Exemplary, the single harmonic spectra of 1260 nm, 1300 nm and 1320 nm are plotted together with the mean spectrum of all involved wavelengths (violet curve). The modulation contrast shows a reduction by a factor of two in comparison to a single harmonic spectrum. (right) A frequency analysis of the modulated spectra is performed. In particular at the modulation frequency of the harmonic comb at $0.53 e V = 1 / (2 \cdot 0.95 e V)$ (green vertical line), the modulation depth is strongly reduced.

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Quasi-supercontinuous spectra can be obtained in a single acquisition cycle, when the driving wavelength of the OPA is scanned automatically during an exposure time of the XUV spectrometer. With a remote control interface it is possible to drive the optics of the OPA using stepper motors. Thus, single wavelength steps in the wavelength scan can be realized very fast, here on millisecond time-scale. This allows the direct accumulation of many different harmonic combs within an acquisition cycle using the XUV spectrometer. The time-averaging leads to a quasi-supercontinuous smooth XUV spectrum in a single exposure. Theoretically, the time-scale to obtain a quasi-supercontinuum XUV spectrum with ten wavelength steps is around 500 ms. However, relating to XCT and its signal to noise ratio, a chosen averaging time of some seconds is more adequate.

To cover a broad spectral range such as the silicon transmission window from 30 eV to 100 eV, the scan range of 1220 nm to 1320 nm was used for the highest HHG efficiency. The averaged XUV spectrum of the automatic scan is depicted in Fig. 6. The resulting modulation depth is $M = 0.08$ in the aluminum transmission window (Fig. 6, left), which is a reduction by a factor of 7 compared to a single harmonic comb, while the photon number of up to $3 \times 10^{8}$ photons per $e V \cdot s$ around 40 eV is still comparable to a single harmonic comb. Furthermore, the averaged total photon flux is $4 \times 10^{9}$ photons/s in the range of 30 to 100 eV.

Fig. 6 Recorded harmonic spectra generated in argon (left) or in neon (right) while an automatic sweeping over the laser wavelength are shown. The scan is performed automatically from 1220 to 1320 nm in 10 nm steps. We get a modulation depth of $M = 0.08$ for this scan in the Al window (left). Due to the reduced resolution of the spectrometer for higher photon energies with 0.25 eV round 80 eV and 1.4 eV around 200 eV an almost flat distribution in the Zr window is produced (right). The photon flux is up to $3 \times 10^{8}$ photons per $e V \cdot s$ around 40 eV and $2 \times 10^{5}$ photons per $e V \cdot s$ at 180 eV.

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For reaching photon energies higher than 100 eV, neon is used for high-harmonic generation. Using a backing pressure of 700 mbar the cut-off energy is increased to $> 180$ eV (Fig. 6, right), which corresponds to the upper limit of the zirconium transmission window. The generated harmonic spectra in this spectral window show a negligible modulation. However, due to the low resolution of the XUV spectrometer (0.25 eV at 80 eV and 1.4 eV at 200 eV) the continuity of the spectrum cannot be evaluated in this range. The photon number in the cut-off region is $2 \times 10^{5}$ photons per $e V \cdot s$ and the total photon flux is $1 \times 10^{7}$ photons/s in the range of 100 to 200 eV.

5. Conclusion

We have demonstrated a quasi-supercontinuous XUV light source with high photon flux (up to $3 \times 10^{8}$ photons per $e V \cdot s$ in the range of 30 to 200 eV). The total photon flux is $4 \times 10^{9}$ photons/s in the range of 30 eV to 100 eV and $1 \times 10^{7}$ photons/s in the range of 100 eV to 200 eV. The HHG light source is driven by a table-top femtosecond laser together with a fast tunable OPA. For optimized efficiency, the OPA delivers signal pulses at 1300 nm with 2.5 mJ and 55 fs. The spectral modulations of the individual harmonic combs are strongly reduced by an automated sweep of the driving wavelengths during an acquisition cycle. The resulting XUV spectrum is quasi-continuous and has a remaining modulation depth of $M = 0.08$ in the range of 30 eV to 70 eV, which does not limit the use of the radiation source for the envisaged application.

The simplicity, reliability and the table-top footprint of our quasi-supercontinuum XUV source allows to use it for lab-based microscopy methods like XCT or spectral absorption measurements like NEXAFS. Especially in the XUV, the harmonic source can be an alternative to large-scale synchrotron facilities [24, 25].

Funding

Deutsche Forschungsgemeinschaft (DFG PA-730/5); Thüringer Aufbaubank (TAB Forschergruppe 2015FGR0094); Helmholtz Institute Jena; German Federal Ministry for Education (BMBF project VIP X-CoherenT); Volkswagen Foundation (501100001663).

Acknowledgments

The authors thank Michael Zürch and Christian Spielmann for the help with the construction of the HHG source.

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Quasi-supercontinuum source in the extreme ultraviolet using multiple frequency combs from high-harmonic generation

Abstract

1. Introduction

2. Frequency combs by high-harmonic generation in gases

3. Experimental setup

4. Experimental results

5. Conclusion

Funding

Acknowledgments

References and links

Cited By

Figures (6)

Equations (5)

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