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Abstract
Coherent beam combination (CBC) is a promising technology for achieving several hundred petawatts and even EW-level lasers. However, the measurement of the synchronization error and the time jitter of CBC is one of key technical issues, especially in the few-cycle PW-level laser facilities. In this paper, we demonstrate that the absolute time delay (ATD) and the relative time delay (RTD) for a tiled-aperture CBC can simultaneously be measured by using the double-humped spectral beam interferometry. The experimental study also was demonstrated. A root-mean-square deviation of approximately λ/38 (70 as) and a combining efficiency of 87.3% at 1 Hz closed feedback loop was obtained, respectively. Due to the wide adjustment range and a vast resisting beam energy disturbance capacity, this technique provide an effective and practical solution for measuring simultaneously the ATD and the RTD in the few-cycle PW-level laser pulses CBC.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The advent of the chirped pulse amplification (CPA) and the optical parametric chirped pulse amplification (OPCPA) over the past decades brought about a dramatic increase in the peak power of laser pulses [1,2]. Meanwhile, the ultra-intensity and ultra-short lasers play a significant role in many research fields, such as the laser-plasma electron and ion acceleration [3,4], fast ignition [5], and astrophysics in laboratory [6]. Nowadays, petawatt (PW)-level peak power lasers based on CPA and OPCPA technique have been achieved in many laboratories around the world by increasing the pulse output energy or decreasing the pulse duration [7–15], such as the output power was improved from 2 PW in 2013 to 10 PW in 2018 by upgrading output energy of the laser system [10,14]. Nevertheless, limited by nonlinear effects, damage threshold of materials and aperture of optical components, it is challenging to improve further the output capability of a single beam laser.
Coherent beam combination (CBC) was proposed and implemented to amplify the output power of laser pulses [16–23]. Meanwhile, the CBC of high-power laser has been achieved in the numerous laser systems based on CPA and OPCPA technique [15,24–26]. In theory, by employing CBC of several laser beams, the peak power can be increased N2-fold (N is the number of combined beams). However, in practice there are many technical obstacles, especially how to eliminate the synchronization error and the time jitter in the few-cycle PW-level laser pulses CBC. Many technologies had been researched and applied, such as the optical cross-correlation and the interferometry [17–21]. These techniques, however, all based on the measurement of the relative time delay (RTD) or carrier phase error, cannot provide the information of the absolute time delay (ATD) between the combined laser pulses. While this may be tolerated for relatively long pulses, i.e., when the ATD is much shorter than the pulse duration and will not significantly affect the peak power of combined beams, for the few-cycle laser pulses, the ATD of a cycle will dramatically change the peak power of the combined beams. Furthermore, when the ATD exists between the two laser pulses, the pulse electric field and carrier envelope after combining will be significantly changed, especially for few-cycle laser pulses CBC system [22]. Therefore, for few-cycle PW-level laser pulses CBC, the measurement of the ATD and RTD is an inevitable technical issue [15]. For example, the RTD will influence the stability of the combining efficiency in the high-power ultrafast laser pulses CBC [20,21].
In this work, we demonstrate a beam interferometry with double-humped spectrum that can simultaneously measure the ATD and the RTD of the tiled-aperture CBC. Moreover, for the few-cycle PW-level lasers with super long optical transmission systems and larger energy fluctuation, the proposed technique can provide a wide adjustment range and a vast resisting beam energy disturbance capacity. In the experiment, a reference laser beam with a double-humped spectrum was interfered with two other laser beams. The ATD and the RTD were estimated from the interference patterns. Finally, under the closed loop conditions at 1 Hz, the coherent combining of the two laser beams was achieved with a root-mean-square (RMS) deviation of approximately λ/38 (70 as) and a combining efficiency of 87.3%, respectively.
2. Theoretical analysis
According to the principle of interferometry [23,27]. The intensity distribution, I, of a two beam near-field interference pattern can be expressed as:
Fig. 1. The simulated results, (a) the near-field interference schematic (the insets show the difference of the interference patterns existing the delay), α is the incident angle between two laser beams, δ is the optical path difference (delay), Δ is the moving distance of interference fringe (the inset); (b) the initial and double-humped spectra; the simulated results of (c) the initial and (d) double-humped spectra in different delay conditions (left and right images show 2D and 1D interference patterns, respectively).
3. Experiment
To measure the ATD, two measured laser beams need to be interfered with a reference laser beam with the double-humped spectrum. The near-field interference patterns was recorded for estimating the ATD and controlling the RTD. Meanwhile, the far-field beam profile of the measured laser beams was recorded for calculating the combining efficiency. The experimental setup is explained in Fig. 2. Laser pulse with 35 fs pulse duration and 100 µJ pulse energy was split by a 50:50 beam splitter (BS 1). The transmission part (beam 1) was set as the reference beam and delayed by the delay line 1. The reflection part (beam 2) was split into two beams (beam 3 and 4) by a 50:50 beam splitter (BS 2). Beams 3 and 4 passed through beam splitter (BS 3) in parallel with a 90% transmittance and were focused on camera 2 (Spiricon, BeamGage) for recording the far-field beam profile by a convex lens with a 1 m focal length. Residual beams 3 and 4 passed through a spectral modulator to achieve a double-humped spectrum, and then interfered with beam 1. In here, in order to the experimental incident angle α close to the simulation, the propagation distance of beam 1 and beam 3 (4) incident camera 1 was set to 2.5 m. Finally, the near-field interference patterns were captured by camera 1 (Spiricon, BeamGage). As depicted in the inset in Fig. 2, the incident angle between beam 1 and beam 3 (4) was set to less than 1° to increase the interference fringe period d. The resolutions of cameras 1 and 2 were both 3.69 × 3.69 μm with 1569 × 1448 pixels. Limited by the aperture of camera 1, a 3:1 telescope 4-f system was used before laser beams entering the camera 1.
Fig. 2. The experimental setup for the ATD and RTD measurement and control of beams 3 and 4 (inset shows the spatial distribution of the reference beam and the measured beams of the blue grid).
The spectra before and after the application of spectral modulator are shown in Fig. 3 (a). The initial spectrum is centered around the 800 nm wavelength with an 80 nm bandwidth. After the application of spectral modulator, the two peaks of the modulated spectrum are at λ1 = 770 nm and λ2 = 820 nm, respectively. By adjusting the delay lines, 2D interference patterns are captured by camera 1 (Fig. 3 (b)). The 1D intensity distribution of the interference patterns on the y-axis (the red lines in Fig. 3 (b)) is analyzed to calculate the time delay, which is shown in Fig. 3 (c). And the interference patterns without the application of spectral modulator is depicted in Fig. 3 (d) as a contrast. In this experiment, the interference fringe period is d = 73 μm, meaning the incident angle α = 0.64°. Therefore, the measurement accuracy is 41 nm (136.7 as), which depend on the resolution of camera 1 and the incident angle α. From the results of Fig. 3, the measurements of the ATD have been successfully achieved by the near-filed interferometry with the double-humped spectrum. Moreover, due to no requirement for the laser beam intensity in the interferometry, the laser beam intensity hardly affects the measuring results, which implies that the technique can provide an effective solution for the few-cycle PW-level laser facilities with larger laser beam intensity disturbance.
Fig. 3. (a) The double-humped and initial spectra, (b) 2D and (c) 1D interference patterns with the application of spectral modulator, (d) 1D interference patterns without the application of spectral modulator recorded by camera 1.
To measure and control the RTD in the experiment, limited by the response speed of the camera and stepper motor (Sigma), a feedback loop of 1 Hz was built. The time difference between beams 3 and 4 is shown as the black line in Fig. 4 (a). Using a closed feedback loop, the time jitter was locked towards 0 for 1000 s with a RMS deviation of approximately λ/38 (70 as) (red line in Fig. 4 (a)). The inset in Fig. 4 (a) shows the control of the ATD when the feedback loop was closed or open. The results of Fig. 4 (a) demonstrates that the measurement of ATD is effective and accurate in the experiment, and that the ATD and the time jitter could be locked by a closed feedback loop. The focal spots of the single beam and the combined beam also were recorded by camera 2 and shown in Figs. 4 (b)–4 (e). When the time delay was locked, the interference fringes was observed in the focal spot, which proves the efficiency of the CBC of two laser beams. The combining efficiency, η, of 87.3% is obtained from the expression $\eta = I/\left( {{I_1} + {I_2} + 2\sqrt {{I_1}{I_2}} } \right)$ [28], where I is the peak intensity of the combined pulses, I1 and I2 are the peak intensity of the two of individual beams, respectively. Moreover, the time jitter in the experiment was potentially caused by the airflow and mechanical vibrations, and the fluctuation of active control of high frequency was lower compared to 1 Hz [20,21]. The closed-loop at a higher rate for locking RTD based on the interferometry can be realized by using the piezoelectric transducer and photo-sensitive devise [19]. Therefore, the combining efficiency could be further improved by increasing the closed loop feedback frequency.
Fig. 4. (a) Time difference measurement with open and closed feedback loop (inset shows the control of the ATD). The far-field spot of the two combined pulses recorded by camera 2: (b) beam 3, (c) beam 4, (d) two beams incoherently combined, (e) two beam coherently combined.
In the experiment, the control algorithm of closed feedback loop was introduced. First, the computer would always choose a part of the interference fringe for calculating the RTD. As shown in Fig. 5, the RTD δ could be calculated by the expression Δ=right(x)-left(x) and δ=λΔ / d, where right(x) and left(x) are the corresponding abscissa, respectively. Then, the stepper motor moved the corresponding distance L=δ / 2 to lock the RTD. For example, the Δ=30 µm indicated in Fig. 5, therefore, the stepper motor need to move L=171 nm. The stepper motor precision is 10 nm/step, which is effective for compensation of RTD. Meanwhile, from the black line in Fig. 4 (a), the control algorithm of closed feedback loop is feasible in the experiment.
Fig. 5. Schematic diagram of the RTD calculation based on 1D interference fringe (left(x) and right(x) are the corresponding abscissa, respectively).
4. Conclusions
We demonstrated a near-filed interferometry with a double-humped spectrum that can simultaneously measure the ATD and the RTD of the tiled-aperture CBC. The technique provides a wide adjustment range and good resistance against energy disturbance for few-cycle PW-level laser facilities with super long optical transmission systems and larger energy fluctuation. In the experiment, a reference laser beam was interfered with two other laser beams with a double-humped spectrum. The ATD and RTD between the two laser beams were first successfully measured and controlled using the proposed technique. Finally, using a closed feedback loop, we achieved the time jitter locking of the two laser beams at 1 Hz with a RMS deviation of approximately λ/38 (70 as) and a combining efficiency of 87.3%, respectively. The presented technique delivers a simple and practical solution for the simultaneous measurement of the ATD and RTD of the few-cycle PW-level laser pulses CBC. In future, we plan to apply the technique for the CBC of PW-level lasers.
Funding
National Key Research and Development Program of China (2017YFE0123700); The Strategic Priority Research Program of the Chinese Academy of Sciences (XDB1603); National Natural Science Foundation of China (61925507); Program of Shanghai Academic Research Leader (18XD1404200); Shanghai Municipal Science and Technology Major Project (2017SHZDZX02).
Disclosures
The authors declare no conflicts of interest.
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