1. Introduction

Human history has taught us that the invention of novel light sources and related technologies would lead to breakthroughs in science and impact the society and civilization tremendously. X-rays and lasers are good examples of such technologies. High-power laser systems are a class of coherent light sources that play a major role in the advancement of science and

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

technology, ranging from inertial nuclear fusion, laboratory astrophysics to laser weapons and 3D printing. Such lasers emit continuous wave (CW), nanosecond (ns), picosecond (ps) and femtosecond (fs) pulsed output. Single or near-single cycle electromagnetic radiation can now be generated by laser-based techniques from the terahertz (1 THz = 1012 Hz) to the soft x-ray regions of the spectrum. The spectra of the latter yield attosecond (1 as = 10–18 s) pulses. Such novel sources are expected to have a wide range of potential applications. Attosecond sources [1, 2] are perhaps among the most exciting new laser sources currently under development. In the near future, controlled light wave can steer electrons inside and around atoms. This emerging technology has been dubbed as "lightwave electronics" [3]. Nonetheless, study of condensed matter with attosecond time-resolution remains a challenge [4]. While the potential of microfabrication and nanostructuring of materials by ultrafast lasers were recognized and demonstrated more than a decade ago [5], there have not been reports of real-world applications of attosecond pulses to date. Primarily, this is limited by the lack of powerful attosecond sources.

We further show that the relative phase among the optical fields of the harmonics can be maintained a constant at least for thousands of nanosecond pulses. The worst-case relative phase fluctuation is 0.04 π rad. It is shown that sub-femtosecond (360 attosecond) pulses with carrier-envelope phase (CEP) control can be generated in this manner. Synthesis of arbitrary

Frequency-Synthesized Approach to High-Power Attosecond Pulse Generation and Applications: Generation…

Compared to the mainstream method of generating attosecond pulses by higher-harmonic generation (HHG) of few-cycle femtosecond pulses, this novel light source has advantages of compactness and simplicity. Further, arbitrary optical waveform can be synthesized while the attosecond pulse generated in this way is sub-single-cycle with full CEP control. In Section 2 of the chapter, we describe the basic principle for generation of attosecond pulses by synthesis of cascaded harmonics. The prototype system is described. The diagnostics of such broadband sources is nontrivial. Experimental methods for relative phase control among the harmonics are presented in Section 3. This is followed by a review of the synthesis of arbitrary waveforms and their diagnostics by the linear cross-correlation method. Finally, we summarize in Section 5 of the chapter. Applications of this novel high-power laser system can be found in part 2 of this work (the following chapter), in which we discuss coherently controlled harmonic generation [12] as well as phase-sensitive 2-color

2. Generation of attosecond pulses by synthesis of cascaded harmonics

EqðÞ¼ t Aqe

rewrite it as ϕ<sup>q</sup> = ϕ<sup>0</sup> + qϕm. The synthesized pulse could then be expressed as:

X q Aqe

<sup>i</sup>ð Þ <sup>ω</sup>0tþϕ<sup>0</sup>

Fundamentally, an optical pulse train with a repetition rate of ωm can be viewed as the sum of a set of frequency components that form an arithmetic series [13]. The electric field of each

where ω<sup>q</sup> = ω<sup>0</sup> + qωm, for q = 0, 1, 2, … To shape the pulse envelope, the phase term ϕ<sup>q</sup> and amplitude term Aq of each component are controlled. One can set the phase term ϕ<sup>q</sup> and

with frequency of ω0. In the commensurate case, the CEP is equal to ϕ<sup>0</sup> for all ultrashort pulses belonging to the same attosecond pulse train or within the ns pulse envelope in the HSRS approach since ω<sup>0</sup> equals to zero. As a result, CEP will be randomly changing if ϕ<sup>0</sup> is random from 1 ns pulse to another. For instance, a 802 nm and a 602 nm laser with pulsewidth around ns and repetition rate of 30 Hz (corresponding to q = 3 and 4 of the Raman resonance of molecular hydrogen) were employed to stimulate the Raman sidebands in early work by one of the co-authors [14, 15]. Because the phases of the two driving lasers, denoted as ϕ<sup>3</sup> and ϕ4, are random and independent of each other in individual ns pulses, both ϕ<sup>m</sup> = ϕ<sup>4</sup> � ϕ<sup>3</sup> and

<sup>i</sup>ϕ<sup>q</sup> e iωqt

iqω<sup>m</sup> <sup>t</sup>þϕ<sup>m</sup> ωm � �

¼ e

<sup>q</sup> Aqeiqωmt is a typical cosine pulse train and <sup>ω</sup>0<sup>t</sup> <sup>þ</sup> <sup>ϕ</sup><sup>0</sup> is the time-varying CEP

, (1)

http://dx.doi.org/10.5772/intechopen.78269

139

Þ, (2)

<sup>i</sup>ð Þ <sup>ω</sup>0tþϕ<sup>0</sup> Ec <sup>t</sup> <sup>þ</sup> <sup>ϕ</sup><sup>m</sup> <sup>=</sup><sup>ω</sup><sup>m</sup> �

waveforms, for example, square and sawtooth waveforms are possible [11].

ablation of copper and stainless steel by this multi-colour laser system.

component can be written in the following form:

EqðÞ¼ t e

E tðÞ¼ <sup>X</sup> q

where EcðÞ� <sup>t</sup> <sup>P</sup>

Among the approaches that allow generation of attosecond pulses, the high-order harmonic generation (HHG) [6] seems to be the most promising one. HHG can serve as a source of intense attosecond pulses that extending from the Vacuum Ultraviolet (VUV) or extreme ultraviolet (EUV) to the soft X-ray region [7]. Alternatively, Chen et al. [8] and Hsieh et al. [9] showed that carrier-envelope-phase (CEP) controlled sub-cycle pulse train can be generated by high-order stimulated Raman scattering (HSRS) process. Recently, we demonstrated the generation of attosecond pulses through pulse synthesis of harmonics of the same laser up to the fifth order. These harmonics were generated through second-order nonlinear optical processes, that is, second harmonic generation (SHG) or sum frequency generation (SFG). This novel source is able to generate 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 attosecond with carrier-envelopephase (CEP) control [10]. Waveform (purple trace) and intensity (red traces) of such ultrashort pulses are shown in Figure 1.

Figure 1. Waveform (blue trace) and intensity (red traces) of sub-femtosecond pulses synthesized by cascaded harmonics of an injection-seed high-power Q-switched laser.

We further show that the relative phase among the optical fields of the harmonics can be maintained a constant at least for thousands of nanosecond pulses. The worst-case relative phase fluctuation is 0.04 π rad. It is shown that sub-femtosecond (360 attosecond) pulses with carrier-envelope phase (CEP) control can be generated in this manner. Synthesis of arbitrary waveforms, for example, square and sawtooth waveforms are possible [11].

technology, ranging from inertial nuclear fusion, laboratory astrophysics to laser weapons and 3D printing. Such lasers emit continuous wave (CW), nanosecond (ns), picosecond (ps) and femtosecond (fs) pulsed output. Single or near-single cycle electromagnetic radiation can now be generated by laser-based techniques from the terahertz (1 THz = 1012 Hz) to the soft x-ray regions of the spectrum. The spectra of the latter yield attosecond (1 as = 10–18 s) pulses. Such novel sources are expected to have a wide range of potential applications. Attosecond sources [1, 2] are perhaps among the most exciting new laser sources currently under development. In the near future, controlled light wave can steer electrons inside and around atoms. This emerging technology has been dubbed as "lightwave electronics" [3]. Nonetheless, study of condensed matter with attosecond time-resolution remains a challenge [4]. While the potential of microfabrication and nanostructuring of materials by ultrafast lasers were recognized and demonstrated more than a decade ago [5], there have not been reports of real-world applications of attosecond

pulses to date. Primarily, this is limited by the lack of powerful attosecond sources.

pulse as high as 1014W/cm2

138 High Power Laser Systems

pulses are shown in Figure 1.

of an injection-seed high-power Q-switched laser.

Among the approaches that allow generation of attosecond pulses, the high-order harmonic generation (HHG) [6] seems to be the most promising one. HHG can serve as a source of intense attosecond pulses that extending from the Vacuum Ultraviolet (VUV) or extreme ultraviolet (EUV) to the soft X-ray region [7]. Alternatively, Chen et al. [8] and Hsieh et al. [9] showed that carrier-envelope-phase (CEP) controlled sub-cycle pulse train can be generated by high-order stimulated Raman scattering (HSRS) process. Recently, we demonstrated the generation of attosecond pulses through pulse synthesis of harmonics of the same laser up to the fifth order. These harmonics were generated through second-order nonlinear optical processes, that is, second harmonic generation (SHG) or sum frequency generation (SFG). This novel source is able to generate sub-single-cycle (0.37 cycle) pulses with peak intensity of a single

phase (CEP) control [10]. Waveform (purple trace) and intensity (red traces) of such ultrashort

Figure 1. Waveform (blue trace) and intensity (red traces) of sub-femtosecond pulses synthesized by cascaded harmonics

, pulse width as short as 400 attosecond with carrier-envelope-

Compared to the mainstream method of generating attosecond pulses by higher-harmonic generation (HHG) of few-cycle femtosecond pulses, this novel light source has advantages of compactness and simplicity. Further, arbitrary optical waveform can be synthesized while the attosecond pulse generated in this way is sub-single-cycle with full CEP control. In Section 2 of the chapter, we describe the basic principle for generation of attosecond pulses by synthesis of cascaded harmonics. The prototype system is described. The diagnostics of such broadband sources is nontrivial. Experimental methods for relative phase control among the harmonics are presented in Section 3. This is followed by a review of the synthesis of arbitrary waveforms and their diagnostics by the linear cross-correlation method. Finally, we summarize in Section 5 of the chapter. Applications of this novel high-power laser system can be found in part 2 of this work (the following chapter), in which we discuss coherently controlled harmonic generation [12] as well as phase-sensitive 2-color ablation of copper and stainless steel by this multi-colour laser system.
