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Abstract
Naturally down-chirped superradiance pulses, with mirco-pulse energy, peak wavelength, and micropulse duration of 40 µJ, 8.7 μm, and 5.1 optical cycles, respectively, emitted from a free-electron laser (FEL) oscillator were nonlinearly compressed down to 3.7 optical cycles using a 30-mm-thick Ge plate. The peak power enhancement owing to nonlinear compression was found to be 40%. The achieved peak power and pulse duration were comparable to those of recently developed high-intensity and few-cycle long-wavelength infrared sources based on solid-state lasers. FEL oscillators operating in the superradiance regime can serve as unique tools for studying strong-field physics in long-wavelength infrared regions.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The collective scientific focus is gradually shifting to strong-field physics in the long-wavelength infrared (LWIR) region, which corresponds to 8–14 µm in wavelength, because attosecond soft X-rays can be generated via high-harmonic generation (HHG) [1,2], applied to ultrafast nonlinear spectroscopy [3], pump-probe experiments of solid [4,5] or gaseous samples [6], and laser-induced electron diffraction [7,8] or holography [9]. In recent years, significant progress has been made in the generation of intense few-cycle LWIR pulses [3,10–15]. Most studies have used optical parametric chirped-pulse amplifiers (OPCPAs). A free-electron laser (FEL) oscillator operating in the superradiance regime has been proposed as an alternative light source [16]. An FEL oscillator operating in the superradiance regime can directly provide highly intense ultrashort pulses with a high repetition rate (>10 MHz) without using the CPA technique. The generation of few-cycle pulses from an FEL oscillator operating in the superradiance regime was demonstrated [17,18]. Some of the applications listed above require carrier-envelope phase (CEP) stable pulses. FEL oscillators are considered a non-CEP stable source since they are normally started from spontaneous radiations. There are some studies on the CEP stabilization of the FEL oscillator via external seeding of CEP stable pulse [19] or starting up from coherent undulator radiation emitted by sharp edges of electron bunches [20].
An FEL operating in the superradiance regime naturally has a down-chirp [17,18]. In addition to the natural down-chirp, the FEL pulse duration is further prolonged by a vacuum window to extract laser pulses from an electron accelerator in an ultra-high vacuum environment, as most useful optical materials in the LWIR region, except for Ge, have negative group velocity dispersion (GVD). To achieve a few-cycle pulse duration at the focus point of the FEL beam, the natural down-chirp and the down-chirp introduced by the window or lens should be compensated. Dispersion management, or pulse compression, is commonly conducted in ultrafast lasers using grating pairs, prism pairs, chirped mirror pairs, and dispersive media. In the field of FEL oscillators, chirped-pulse generation and compression using a pulse compressor have been proposed so far [21–25]. In another study, naturally chirped pulses were generated from an FEL oscillator operated in the superradiance regime and compression by a pulse compressor was proposed [17]. Chirped pulse generation and pulse compression using a grating pair were realized in the FELIX facility in 1997 [26], where intentionally up-chirped 1.5 ps pulses were generated and compressed to 1.2 ps. To introduce the up-chirp, the electron beam energy was ramped up, and 10-µm optical cavity detuning was introduced. These modified operational conditions led to a decrease in the total energy of the FEL pulses, rendering this scheme ineffective for increasing the peak power of the FEL.
The pulse compression by chirp compensation of naturally down-chirped few-cycle pulses generated from an FEL oscillator operating in the superradiance regime has been proposed so far [17] but has not been demonstrated. In this study, we attempted to compensate for the naturally introduced down-chirp in the superradiance regime operation of an FEL oscillator by inserting a thick Ge plate with a positive group delay dispersion (GDD) in the LWIR region for the first time. The advantage of using a thick Ge plate is its high transmittance; however, it has no tunability of the GDD. To examine the pulse manipulation with different GDD, experiments were performed with Ge plates of three different thicknesses. In addition to the chirp compensation, occurrence of a spectral broadening in the thick Ge plate assists further compression of the FEL pulse via nonlinear compression.
2. Methods
The experiments were performed at the Kyoto University free-electron laser (KU-FEL) [27]. The electron beam energy was set to 31.5 MeV to drive the KU-FEL at a wavelength of 8.7 µm. Electron beams with 7-µs-long macro-pulses under photocathode conditions [28] were used for generating FEL pulses. The operating parameters are listed in Table 1. The parameters of the major components of the KU-FEL are summarized elsewhere [27,28]. A typical macropulse structures of the electron beam and FEL pulse are shown in Fig. 1(a). In the photocathode-mode operation of the KU-FEL, burst pulses with a micropulse repetition rate of 29.75 MHz and a macropulse duration of 3.8 µs were generated. In the experiment, the peak micropulse energy of the FEL was approximately 40 µJ with a macropulse energy of 4.5 mJ. The average power during the macropulse was approximately 1.2 kW.
Fig. 1. (a) Typical macro-pulse structures of the electron beam (gray) and FEL pulse (red). The inset shows the magnified timing of approximately 6.35 µs to show the electron bunch interval (∼33.6 ns). The FEL pulse was measured with a fast pyroelectric detector, and the 29.75 MHz repetition rate could not be fully resolved owing to an insufficient temporal resolution. (b) and (c) are horizontal and vertical beam sizes measured by the knife edge method, respectively.
Table 1. Operational parameters of the KU-FEL set during the experiment
An autocorrelation apparatus for pulse-shape characterization of the KU-FEL [18] was used to simultaneously obtain linear and nonlinear autocorrelation traces. The phase distributions in the frequency domain were retrieved using the same phase retrieval method as in a previous study [18]. The time domain intensity and phase distributions were obtained using a complex inverse Fourier transformation of the intensity and phase distributions obtained in the frequency domain.
To study the variation in the FEL pulse properties due to the insertion of the Ge plate, Ge plates with thicknesses of 5, 30, and 60 mm were used in the experiment. Both sides of the Ge plates were coated with an antireflection coating to minimize the attenuation of the FEL pulses due to the surface reflection of the Ge plates. The FEL beam sizes (1/e2 radius) on the entrance surface of the Ge plates were around 8.6 mm both in the horizontal and vertical directions as shown in Fig. 1(b) and (c). A variable aperture installed immediately after the vacuum window to extract the FEL beam from the FEL vacuum system into the air was used to remove the higher-order transverse modes [29]. This makes the transverse profile of the FEL very similar to that of the fundamental Gaussian mode. The 5-mm-thick Ge plate (WG91050-G, Thorlabs) had a diameter of 25.4 mm. The 30-mm-thick and 60-mm-thick Ge plates with a diameter of 25.4 mm were purchased from IR System Co., Ltd., Japan. The frequency and time-domain distributions of the FEL pulses with and without the Ge plates were measured.
3. Results
The frequency- and time-domain distributions of the FEL pulses with and without the 5-mm-thick Ge plate are shown in Fig. 2. The vertical scales of these results were normalized by considering the integrated results and the measured transmittance of the 5-mm-thick Ge plate (97.5%). As a result of the insertion of the 5-mm-thick Ge plate, the frequency spectrum was slightly modified, i.e., small reduction at around 35.5 THz (8.45 µm), and small increases at approximately 31.5 THz (9.5 µm) and 37.5 THz (8.0 µm). From the time-domain distribution, the full width at half maximum (FWHM) pulse duration was reduced from 146 to 130 fs, and the peak intensity increased by a factor of 1.25. The phase distributions in both the frequency and time domains flattened with the insertion of the 5-mm-thick Ge plate. This means that the down chirp is compensated after passing through the 5-mm-thick Ge plate because the Ge plate has a positive GDD in this frequency region.
Fig. 2. Observed frequency-domain (left) and time-domain (right) distributions of FEL pulses with and without the 5-mm-thick Ge plate. The solid and dashed lines show the intensity and phase distributions, respectively. The vertical scales of these graphs are normalized with taking into account considering the integrated results and the transmittance of the 5-mm-thick Ge plate (97.5 %).
The frequency- and time-domain distributions of the FEL pulses with and without the 30-mm-thick Ge plate are shown in Fig. 3. The vertical scales of these results were normalized by considering the integrated results and the measured transmittance of the 30-mm-thick Ge plate (96.2%). As a result of the insertion of the 30-mm-thick Ge plate, the frequency spectrum was significantly modified, and the FWHM spectral bandwidth was broadened from 4.1 to 7.9 THz. There was a significant reduction in the frequency region from 33.5 THz (9.0 µm) to 36 THz (8.3 µm) and a significant increase in the frequency region from 28.5 THz (10.5 µm) to 31.5 THz (9.5 µm). Simultaneously, the FWHM pulse duration was reduced from 146 to 106 fs, and the peak intensity was increased by a factor of 1.4.
Fig. 3. Observed frequency-domain (left) and time-domain (right) distributions of FEL pulses with and without the 30-mm-thick Ge plate. The solid and dashed lines show the intensity and phase distributions, respectively. The vertical scales of these graphs are normalized considering the integrated results and transmittance of the 30-mm-thick Ge plate (96.2%).
We did not expect strong nonlinear optical phenomena to occur on the Ge plate, because nonlinear optical phenomena had never been observed in our experiments with the beam size of 8.6 mm before the present study. However, we observed a large spectral broadening for the Ge plate. Spectral broadening contributes to the further compression of the pulse duration in addition to chirp compensation. This is known as nonlinear compression [30–32]. Nonlinear compression is widely used for pulses generated from femtosecond laser systems based on solid-state and fiber lasers to achieve a pulse duration of a few cycles. However, to the best of our knowledge, there are no reports on the nonlinear pulse compression of FEL pulses. This could be the first observation and implementation of nonlinear compression for pulses generated by an FEL. The chirp direction of the FEL pulses after they passed through the Ge plate cannot be determined because of time-direction ambiguity in the autocorrelation measurement. In Fig. 3, we assumed the time direction so that the tail follows the main peak. According to this assumption, the FEL pulse with the 30-mm-thick Ge has a slight up chirp. In a future experiment, we will examine the chirp direction of the FEL pulses after passing through a 30-mm-thick Ge plate by measuring the pulse duration after passing through an additional ZnSe plate with a large negative GVD, as in a previous study [18].
The frequency- and time-domain distributions of the FEL pulses with and without the 60-mm-thick Ge plate are shown in Fig. 4. The vertical scales of these results were normalized by considering the integrated results and the measured transmittance of the 60-mm-thick Ge plate (94.4%). The frequency-domain distribution of the FEL pulse after passing through the 60-mm-thick Ge plate has a similar spectral bandwidth as that of the 30-mm-thick one with intensity attenuation around 29 to 34 THz (10.3 to 8.8 µm) and a slight increase of intensity around 34.5 to 36.5 THz (8.7 to 8.2 µm). This implies that further modification of the frequency spectrum occurred in the latter half of the 60-mm-thick Ge plate, but the effect was not as strong as that in the first half of the plate. Because of the large GDD (13,470 fs2 @9 µm [33]) in the latter half of the 60-mm-thick Ge plate, the FEL pulses after passing through the 60-mm-thick Ge plate were strongly up-chirped. The FWHM pulse duration with the 60 mm Ge plate was 244 fs, which is much longer than that of the other conditions. Owing to pulse elongation, the peak intensity was reduced by a factor of 2.3.
Fig. 4. Observed frequency-domain (left) and time-domain (right) distributions of FEL pulses with and without the 60-mm-thick Ge plate. The solid and dashed lines show the intensity and phase distributions, respectively. On the left panel, the result with the 30-mm-thick Ge plate is also shown for the convenience of comparison. The vertical scales of these graphs are normalized considering the integrated results and transmittance of the 60-mm-thick Ge plate (94.4%).
4. Discussion and conclusion
Because the phase distribution in the frequency domain without a Ge plate was retrieved, the FEL pulse duration after a Ge plate with different thicknesses and without spectral broadening can be easily calculated based on the wavelength-dependent variation in the refractive index given by the Sellmeier equation for Ge [33]. The results are shown in Fig. 5, along with the experimentally observed pulse durations. The minimum pulse duration without spectral broadening was approximately 123 fs when the thickness of the Ge plate was 25 mm. The experimentally observed minimum pulse duration was 106 fs with a 30-mm-thick Ge plate, which was approximately 86% of the minimum value obtained in the linear calculation.
Fig. 5. Pulse duration dependence on the thickness of the Ge plate. The black dots represent the result of linear calculation based on the measured pulse shape and phase without the Ge plate.
Based on the previous research on spectral broadening in Ge plates [34], we examined whether the FEL intensity on the Ge plate was sufficiently high to induce spectral broadening. With the assumption of the Gaussian temporal profile given by $I(t )= {I_\textrm{p}}\textrm{exp}({ - ({2{t^2}} )/{\tau^2}\; } )$, the maximum frequency shift can be estimated to be $|{\mathrm{\Delta }\omega {{(t )}_{\textrm{max}}}} |= |{\mathrm{\Delta }\omega ({\tau /2} )} |\sim 0.5{|{\mathrm{\Delta }\phi } |_{\textrm{max}}}\mathrm{\Delta }{\omega _0}$, in which ${|{\mathrm{\Delta }\phi } |_{\textrm{max}}} = ({\omega /c} ){n_2}{I_p}L$ is the maximum phase shift, τ, Ip , L and Δω0 are 1/e2 pulse duration (=Δt/(2ln2)1/2, Δt: FWHM pulse duration), peak intensity, effective propagation length in the Ge plate, and the bandwidth of the FEL pulses at the entrance of the Ge plate, respectively [35]. By substituting the nonlinear refractive index ${n_2} = 9900 \times {10^{ - 16}}$ cm2/W for Ge at a wavelength of 10 µm [36], the peak intensity Ip = 1.2 × 108 W/cm2 (270 MW divided by the area of the FEL beam with a 1/e2 beam radius of 8.6 mm), and the Ge plate thickness L = 3 cm, we can estimate the ${|{\mathrm{\Delta }\phi } |_{\textrm{max}}}$ as 2.5. This leads to the maximum spectral broadening $|{\mathrm{\Delta }\omega {{(t )}_{\textrm{max}}}} |/\mathrm{\Delta }{\omega _0}$ with 1.3. This simple evaluation implies that significant spectral broadening of the FEL pulse can be expected when the thickness of the Ge plate is 30 mm, despite the large FEL beam size. Furthermore, the observation of no significant spectral broadening for the case of the 5-mm-thick Ge plate is consistent with the above simple calculation. A more precise simulation, including the non-Gaussian temporal structure of the FEL, complex initial spectrum, initial down-chirp, pulse shape evolution in the Ge plate, and linear and nonlinear absorption, must be performed to reproduce the experimentally observed pulse structure and phase after passing through a thick Ge plate. In addition, since the amount of the spectral broadening depends on the intensity of the pulse in the Ge plate, the study on the intensity dependence is an important subject for understanding the observed process and further optimization of the nonlinear compression of the few-cycle FEL pulses. A comparison of the simulation and the experiments for the intensity dependence will give us a deeper understanding of the nonlinear compression in the Ge plates. However, these are beyond the scope of the present study.
The measured FWHM pulse durations Δtmeas with Ge plates of different thicknesses are summarized in Table 2 together with the transform-limited pulse durations ΔtTL calculated from the measured spectrum. The ratio of the measured pulse durations to transform-limited pulse durations (Δtmeas/ΔtTL) is also listed in Table 2. Owing to the spectral broadening, the transform-limited pulse duration decreased with the increased thickness of the Ge plate. The ratio Δtmeas/ΔtTL showed the smallest value with the 30-mm-thick Ge plate. Under these conditions, the pulse duration was 23% longer than that of the transform-limited pulse. The ratio Δtmeas/ΔtTL increased significantly when the thickness of the Ge plate was 60 mm. This is due to the overcompression of the FEL pulse. Further optimization of the Ge plate thickness and compensation of the higher-order frequency chirp will enable us to reduce the FEL pulse duration. Therefore, we plan to design a special chirped mirror pair to compensate for the higher-order dispersion observed in the experimental results.
Table 2. Summary of the measured pulse duration and calculated transform-limited pulse duration with different thicknesses of the Ge plate. All the pulse durations in this table are in FWHM
When a 30-mm-thick Ge plate was inserted, the enhancement factor of the FEL peak power was 1.40. The effect of this enhancement is not significant for linear optical processes but can be significant for higher-order nonlinear optical processes. For example, the yield of 10th order nonlinear process can be 29 times higher than without enhancement. The developed pulse compression scheme will contribute to the exploration of LWIR applications, particularly in the strong-field regime, using the KU-FEL.
Other groups have developed few-cycle and intense LWIR sources with pulse energies exceeding several tens of µJ [3,10,15]. Except for the pulse obtained by photon deceleration in plasma [10], the results obtained in the present work were comparable to the LWIR pulses generated from OPA- (optical parametric amplifier-) or OPCPA-based sources and had a unique burst pulse structure with high average power in the burst.
Here, we note future prospects for the development of few-cycle and high-intensity LWIR sources based on oscillator FELs. There are two possible directions for upgradation. The first is a further increase in intensity. This can be achieved by increasing the bunch charge of the driving accelerator system. This would lead to an increase in the FEL gain and extraction efficiency. By increasing the bunch charge to 1 nC, the KU-FEL intensity could possibly be increased to 500 µJ or even higher with half the micropulse duration because of the doubled extraction efficiency [16]. The other direction is an increase in the macro-pulse duration. The KU-FEL uses a normal conducting accelerator, and the macropulse duration of the electron beam is limited to 7 µs with the macro-pulse repetition rate of 2 Hz and the electron bunch repetition rate of 29.75 MHz in the macropulse. A continuous wave (CW) operation is possible if a superconducting accelerator is used to drive an oscillator FEL system in the superradiance regime. As an example, the Free-electron laser at the Electron Linear Accelerator with high Brilliance and low Emittance (FELBE) uses a superconducting accelerator and can be operated under CW conditions with a repetition rate of 13 MHz [37]. Highly charged CW electron bunches provided by a superconducting accelerator can supply highly intense and extremely short LWIR pulses with a repetition rate >10-MHz under CW conditions. A millijoule-class >10-MHz few-cycle LWIR source can be realized using a superconducting accelerator-based FEL oscillator, and begin a new era of strong-field science in the LWIR region.
Funding
Ministry of Education, Culture, Sports, Science and Technology (Q-LEAP, Grant Number JPMXS0118070271).
Disclosures
The authors declare no conflicts of interest.
Data availability
The 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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