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Attosecond Pulse Synthesis: Fundamentals and Applications
Ci-Ling Pan
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DOI: 10.22661/AAPPSBL.2018.28.6.09

Attosecond Pulse Synthesis:
Fundamentals and Applications



We present an alternative approach to generating attosecond pulses and arbitrary waveform synthesis by cascaded harmonics of a single-frequency high power laser. Sub-single-cycle (~ 0.37 cycle) sub-femtosecond (360 attosecond) pulses with carrier-envelope phase (CEP) control and arbitrary waveforms are generated. We also present examples of coherently controlled harmonic generation and phase-sensitive 2-color ablation of copper and stainless steel by this approach.


Ultrafast phenomena, particularly the generation of the shortest possible pulses [1, 2], is currently one of the most exciting and important fields of physics. In the near future, controlled light waves will be used to steer electrons inside and around atoms. This emerging technology has been dubbed as "lightwave electronics" [3]. Nonetheless, the study of material systems with attosecond time-resolution remains a challenge [4]. On the application side, the processing and manipulation of materials by ultrafast lasers were achievements that were recognized and demonstrated more than a decade ago [5]. To date, however, there have not been reports of real-world applications of attosecond pulses.

Among the approaches that allow generation of attosecond pulses, high-order harmonic generation (HHG) [6] seems to be the most promising one. HHG can serve as a source for intense attosecond pulses that extend from the vacuum ultraviolet (VUV) or extreme ultraviolet (EUV) region to the soft X-ray region [7]. Alternatively, Chen et al. [8], and Hsieh et al. [9], showed that a carrier-envelope-phase (CEP) controlled sub-cycle pulse train can be generated by the high-order stimulated Raman scattering (HSRS) process.

An alternative approach to the generation of attosecond pulses is found through pulse synthesis. Sub-single-cycle (~ 0.37 cycle) pulses, with peak intensity of a single pulse as high as 1014W/cm2, pulse width as short as 400 attoseconds and with carrier-envelope-phase (CEP) control was reported [10]. We further show that the relative phase among the optical fields of the harmonics can be constantly maintained for, at minimum, thousands of nanosecond pulses. The worst-case relative phase fluctuation is 0.04 π rad. It has been shown that sub-femtosecond (360 attosecond) pulses with carrier-envelope phase (CEP) control can be generated in this manner. Synthesis of arbitrary waveforms, e.g., square and saw-tooth waveforms, are possible [11]. To demonstrate applications of this approach, coherently controlled harmonic generation [12] as well as phase-sensitive 2-color ablation of copper and stainless steel by this novel light source was reported [13].

In this paper, we briefly review our work on the generation and selected applications of attosecond pulses by synthesis of cascaded harmonics. Details can be found in chapters of the recently published book, entitled High Power Laser Systems {14,15}.


Fundamentally, an optical pulse train can be viewed as the sum of a set of frequency components that form an arithmetic series. To shape the pulse envelope, one can control the phase and amplitude of each component.

Our experimental set-up is shown in Fig. 1. The fundamental frequency component at ω1 is from a custom-made injection-seeded, narrow-band high-power Q-switched Nd:YAG laser (λ = 1064 nm) operating at 10 Hz. The pulse duration is about 10 ns. The nonlinear optical crystals for generating the 2nd through the 5th harmonics of the laser fundamental beam are arranged in a cascaded layout. Thus, the 5-color output of the laser system covers optical spectra from the near infrared range (NIR), or 1064 nm, to the ultraviolet range (UV), i.e., 213 nm. The cascade setup was adopted to ensure that the second-order nonlinear optical process occurred entirely collinearly. As a result, the fundamental and harmonics overlapped spatially. The five colors are horizontally polarized light. It is possible to adjust the amplitude and relative phase of these harmonics separately.


Fig. 1: An attosecond source based on frequency synthesis of cascaded in-line harmonics of a single-frequency laser. Amplitude and phase modulation of each of the harmonics can be controlled. Insets (a) and (b) show predicted and experimentally generated square waveforms. (adapted with permission from ref [14], Fig. 6)

Figure 2(a) shows sub-cycle transform-limited cosine waveforms, each spanning a 0.37 optical cycle with a temporal full width at half maximum (FWHM) of 520 attoseconds. Adding the phases of all harmonic frequencies by 3π / 2, the pulse envelope profile does not change, but the carrier electric field waveform will change to a sine function as shown in Fig. 2(b). Figure 2(c) shows the square waveform that was synthesized by just three harmonic frequencies. The amplitudes of the harmonics relative to that of the fundamental for the three are {1, 0, 1/3}. Figure 2(d) shows the sawtooth waveform that was synthesized by four harmonic frequencies. The corresponding amplitude ratio is {1, 1/2, 1/3, 1/4}. These figures show that commonly used periodic waveforms, such as square and sawtooth, can be synthesized closely resembling the real waveform with just a few harmonics. It is possible to generate transform-limited cosine waveform with a temporal FWHM as short 480 attoseconds. The intensity of each attosecond pulse will exceed 1014 W/cm2 when it is focused to a spot size of 20 關m. If the pulse energy of all the harmonics were the same, e.g., 22 mJ, the transform-limited cosine waveform would exhibit a temporal FWHM of 360 attoseconds. This would be the shortest pulse duration in the optical region so far, to the best of our knowledge.


Fig. 2: The electric field of synthesized waveforms: (a) transform-limited cosine waveform at CEP = 0, (b) transform-limited sine waveform at CEP = 3π/2, (c) square waveform, and (d) sawtooth waveform. The inset figures show the simulation of the electric field waveform as a black solid line and the pulse envelope as a blue line with dashes. (adapted with permission from ref [11])

Coherent-controlled Non-linear Optics
The coherent control of nonlinear optical processes, such as harmonic generation by the waveform-controlled laser field, is important for both fundamental science and technological applications. As a first example, we demonstrate generation of the third-harmonic (TH, ω3 = 355nm) signal by two-color excitation (ω1 = 1064nm and its second-harmonic, ω2 = 532nm) in argon gas, with emphasis on the influence of the relative phases and intensities of the two-color pump on the third-order nonlinear frequency conversion process. Perturbative nonlinear optics predicts that the relative amplitude and the relative phase between the fundamental and second harmonic laser pulses will influence the intensity of the TH signal. Figure 3(a) - (c) shows the experimental and theoretically simulated results. The relative phase between ω1 and ω2 was varied over a range of about 4π. For comparison, only TH signals of the fundamental pulses are also shown. The solid curve in figure 3(a)-(c) is the theoretically predicted sinusoidal variation of the TH signal by two-color excitation. The experimentally measured TH signals all show a modulation with a period of 0.89 fs or a phase change of π. These data points have been normalized to the maxima of the TH signals.


Fig. 3: TH signal is measured as a function of the relative phase, Δ𝜙. The solid squares are the TH signals generated by two-color excitation. The disks are the TH signal generated by only the fundamental pulse. The solid curve is the theoretically predicted sinusoidal modulation of the TH signal by two-color excitation. Figure 3(d)-(f) show electrical-field waveforms of the two-color exciting laser for the corresponding data in Fig. 3(a)-(c), respectively. The solid curve shows the two-color electric-field waveform when the relative phase is 0π. The dash curve shows the two-color electric-field waveform when the relative phase 3 is 0.5π. (adapted with permission, ref. [12])

We also observed that the enhancement of the TH signal is substantial for 2-color excitation. Meanwhile, plasma emission was found to be visible to the naked eye in such cases. It is reasonable to assume that laser-induced multi-photon ionization in the inert gases, e.g., argon, contributes to the enhancement. It can be shown that the enhancement of the TH signal is due to the plasma-enhanced susceptibility of the FWM process. On the other hand, when the plasma density is high enough, the wave-vector mismatch Δk becomes significant due to the plasma-induced refractive index change, which is linearly proportional to the plasma density. The experimental data are in good agreement with the simulated values using the above theoretical formulism. This is shown in Fig. 4.


Fig. 4: The comparison of the experimental and simulation results for a two-color excited third harmonic signal in argon as a function of the second-harmonic pulse energy. (adapted with permission, ref [15])

The enhancement of the third harmonic signal is due to the plasma-enhanced susceptibility for the FWM process. On the other hand, when the plasma density is high enough, the wave-vector mismatch Δk becomes significant due to the plasma-induced refractive index change, which is linearly proportional to the plasma density. Note that the theoretically predicted threshold for plasma enhancement does not match that of the experimental data. This may be explained by the dependence of the threshold on the step-like enhanced ionization probability. The step-like behavior caused by new absorption processes becomes dominant when the effective photon energy (effective frequency) reaches the threshold of this process. However, in reality, there actually exist many quantum processes involving the absorption of several photons at frequencies of ω and 2ω. The different quantum processes have different ionization rates. When the power ratio of the two-color field is changed, the ionization probability of the different quantum processes is also changed. It could be argued that the variation of the ionization rate with the second-harmonic pulse energy is continuous rather than step-like when the plasma density increases. This in turn should shift the threshold pulse energy.

Waveform control of an electric-field is advantageous for ultrafast nonlinear optical processes such as the generation of attosecond pulses by high-order harmonic generation (HHG). The HHG technique is also widely used for generation of vacuum ultraviolet (VUV) light. Such VUV light sources are essential in atomic and molecular spectroscopy. To date, the reported HHG conversion efficiency is still very low. We showed that further enhancement of HHG is possible using a synthesized waveform from the present multi-color laser system. Figure 5 shows the HHG and VUV spectra signal generated by the fundamental (1064 nm), second harmonic (532 nm), and the synthesized two-color laser fields, respectively. We note that there is no signal when only the second harmonic field is applied. When both the fundamental and second harmonic fields are driven (two-color field), however, the emission spectrum is enhanced to a state that is about an order of magnitude larger than the state of argon excited only by the fundamental laser.


Fig. 5: Comparison of the HHG and VUV spectra of Ar generated by the single-color 1064 nm pulse (black solid line), the single-color 532 nm pulse (red solid line), and the synthesized two-color laser fields (green solid line). The ratio of intensity for the fundamental and second harmonic is 1 : 0.2 (횞 1013 W/cm2).


Lately, high energy laser beams have been used increasingly for processing and fabrication of material and devices. Those uses include the fabrication of microelectromechanical systems, optoelectronic components, biomedical micro fluid chips and silicon chip processing, electronic packages and the drilling of circuit boards, to name just a few.

Basically, there are two kinds of mechanisms occurring during laser processing of materials: a photo-thermal mechanism and a photo-chemical mechanism. In the photo-thermal mechanism, laser beams with high power density are used as a thermal source, which is focused on an object in an extremely short time period. The energy absorbed on the surface of the object is introduced into bulk of the object via thermal conduction. Thereafter, a part of the object is melted or vaporized by the deposited thermal energy. Meanwhile, the laser spot is moved to another part of the work piece that is ready for further processing. In the photo-chemical mechanism, the bonding in the material to be processed is broken after absorption of one or more photons, which makes electrons hop between energy levels and break bonding in a molecule as a result [16].

In laser material processing, the laser is chosen according to characteristics such as energy absorption, thermal diffusion and the melting point of the material. For example, ablation is performed on various materials using lasers at different frequencies. It is interesting, therefore, to investigate whether synthesized waveforms proposed and demonstrated in our work could be advantageous for laser processing.


Fig. 6: Numerical simulation of the peak strength of the laser waveform synthesized by two-color laser fields with various relative phases between the fundamental and the second harmonic (a) Δ𝜑= 0, (b) Δ𝜑 = π/2, (c) Δ𝜑 = π, and (d) Δ𝜑 = 3π/2, respectively.

We conducted preliminary experiments on the drilling of copper and stainless steel with the laser system described in Fig. 1 to demonstrate the feasibility of the approach. Figures 6(a) to 6(d) show the simulated results of the peak strengths of the synthesized laser field with various relative phases (Δ𝜑 = 0, 0.5π, π, and 1.5π). As can be seen in Fig. 6(b) and 6(d), the synthesized laser field is expected to exhibit a higher peak strength at relative phases of Δ𝜑= 0.5π, and 1.5π. Therefore, ablation is expected to be more efficient for these waveforms.

In Fig.7(a), we plotted diameters of holes drilled in copper sheets as a function of relative phases between the fundamental (ω1) and second (ω2) harmonics of the synthesizing laser. Pictures of the drilled holes are also presented. Similar results for stainless steel are shown in Fig. 7(b). These data clearly show the dependence of ablation rate on the synthesized waveform, i.e., relative phase of the fundamental (ω1) and second (ω2) harmonics of the single-frequency Nd: YAG laser.


Fig. 7: The diameters of holes drilled in (a) copper, and (b) stainless steel by synthesized laser fields with different relative phases between the fundamental (ω1) and second (ω2) harmonics of the Q-switched laser. Pictures of the drilled holes are also shown.


We review our works on an alternative scheme of attosecond pulses by frequency synthesis. The experimental configuration is based on a narrow-band transform-limited high-power Q-switched Nd:YAG laser and its 2nd (λ = 532nm) through 5th harmonics, (λ = 213 nm). The laser system was designed such that the cascaded harmonics spatially overlap and co-propagate to the far fields. The spectral bandwidth of this coherent laser source thus exceeds two octaves or 32,200 cm-1. The amplitude and phase of the comb, consisting of the five frequency components, can be independently controlled. Sub-single-cycle (~ 0.37 cycle) sub-femtosecond (360 attosecond) pulses with carrier-envelope phase (CEP) control can be generated in this manner. The peak intensity of each pulse exceeds 1014 W/cm2 with a focused spot size of 20 關m. It is also possible to synthesize arbitrary optical waveforms, e.g., a square or sawtooth wave. The synthesized waveform is stable for, at minimum, thousands of nanoseconds.

To illustrate applications of this novel source, we studied the influence of relative phases and intensities of the two-color pump on the third-order nonlinear frequency conversion process. It was shown that the third-harmonic (TH) signal oscillates periodically with the relative phases of the two-color driving laser fields due to the interference of TH signals from a direct third-harmonic-generation (THG) channel and a four-wave mixing (FWM) channel. In an intense laser field, however, plasma can be generated through the ionization process. In the multiphoton ionization regime, the plasma density was estimated by the Perelomov, Popov, and Terent'ev (PPT) model [17] where the instantaneous laser field and frequency of laser are taken into account. Working under the assumption that susceptibility and wave-vector mismatch depend on the plasma density, we show that plasma plays a significant role in the generated third harmonic signal. The simulation results are in good agreement with the experiments.

Finally, we showed preliminary data indicating that the synthesized two-color laser fields are critical in enhancing the conversion efficiency of HHG and VUV spectra. We also demonstrated phase-sensitive 2-color ablation of copper and stainless steel. Our results show that hole drilling is more efficient with the use of optimized waveforms.

Acknowledgements: This work was supported by grants sponsored by the National Science Council of Taiwan (NSC 98-2112-M-009-015-MY3) and Phase II of the Academic Top University Program of the Ministry of Education, Taiwan. The author would also like to express his appreciation for the assistance and contributions of Hong-Zhe Wang, Rui-Yin Lin, Chan-Shan Yang, Alexey Zatazev, Wei-Jan Chen, and Chao-Kuei Lee.


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[13] Ci-Ling Pan et al., US patent 9,031,101, 2015.
[14] Ci-Ling Pan et al., Chap. 7, pp. 137-151 in Maoun Harooni ed., High Power Laser Systems, IntechOpen, London, 2018
[15] ibid., Chap. 8, pp. 154-171
[16] C.-L. Pan, C.-H. Lin, C.-S. Yang and A. Zaytsev, Chap. 15, in Dongfang Yang ed., Applications of Laser Ablation - Thin Film Deposition, Nanomaterial Synthesis and Surface Modification, IntechOpen, London, 2016.
[17] A. M. Perelomov, V. S. Popov, and M. V. Terent'ev, Soviet Physics JETP 23(5), 924 (1966).


Ci-Ling Pan is a Tsing Hua Chair professor at National Tsing Hua University in Hsinchu, Taiwan. Prof. Pan received his PhD in physics from Colorado State University, in Ft. Collins, Colorado, USA in 1979. His main research interests are laser science, ultrafast and THz photonics, fiber photonics and liquid crystal photonics. Prof. Pan is a fellow of SPIE, OSA, IEEE and APS; a member of the Asia Pacific Academy of Materials and corresponding member of the International Academy of Engineering. He served on the editorial board of the AAPPS Bulletin (2011-2013) and serves as a member of Commission C17 (Quantum Electronic) of IUPAP (2012-2014, 2018-2020) and Commission D (Electronics and Photonics) of URSI (2013 to date). Prof. Pan has published more than 260 refereed journal papers to date. He also holds 21 Taiwan patents and 14 US patents. More information about Professor Pan is available at the following website: http://www.phys.nthu.edu.tw/e_teacher/clpan.html.

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