The strong electric field of intense laser light induces ionization in matter, and ultrashort pulses with attosecond-scale resolution can be used to probe electronic processes in atoms, molecules, and condensed matter. If we could control the shape of such a pulse, we could achieve coherent control of electronic motion. For this, we need to generate a broadband spectrum with a bandwidth of over two octaves (an octave is a doubling of frequency). Several methods have already been demonstrated. One such technique is high-order stimulated Raman scattering (HSRS), by which microjoule-powered attosecond pulses spanning more than two octaves can be created.1 This opens the window for strong electric field laser-matter interaction, which requires a pulse duration shorter than the cycle length. HSRS can be used for ultrafast waveform synthesis, but subcycle nonlinear optics requires a pulse energy of hundreds of millijoules.2 This requires a new high-intensity light source with suitable bandwidth and a way to control its waveform.
Recently, we proposed and demonstrated such a light source with an output pulse energy of hundreds of millijoules.3 We use a frequency comb consisting of the fundamental (λ=1064nm) and harmonics of a high-power laser. This can be used to synthesize an attosecond pulse train with stable carrier-envelope phase (CEP)4—the phase difference between the peaks of the carrier wave (the laser light) and the ‘envelope profile’—and so automatically meets our requirements. However, the quality of the pulse shaping and the number of channels are also important for coherent control. We therefore assessed the synthesized pulse shape quality we obtained. We used the image quality index widely used in pattern recognition, which showed that good quality simulations of commonly used periodic waveforms can be synthesized with just the fundamental and the next few harmonics.5 We considered pulse shaping quality obtained with various numbers of harmonics and found we could achieve a quality factor of 92% for an optical sawtooth waveform with just the fundamental and four harmonics.
Figure 1. Experimental setup. The harmonic generator (HG) consists of four nonlinear optical crystals for generating the second, third, fourth, and fifth harmonics of the Nd:YAG (neodymium-doped yttrium aluminum garnet) laser. The amplitude modulator (AM) consists of half-wave plate and polarizer, and the phase modulator (PM) consists of a pair of prisms. P: Power meter.
We demonstrated this experimentally using our harmonic frequency comb (see Figure 1). The fundamental frequency component at ω1 is from a single-frequency neodymium-doped yttrium aluminum garnet (commonly known as Nd:YAG) laser. We adopted a ‘cascade’ setup to ensure that it overlapped spatially with its coherent harmonics overlap. To adjust the amplitude and the phase of each frequency component independently, we spatially dispersed the harmonic frequencies by passing them through a fused silica prism before re-collimating them into parallel (but spatially separated) beams with another, larger prism. In the parallel co-propagating region, we inserted an amplitude modulator and a phase modulator for each of the harmonics to adjust their amplitude and relative phase individually. Finally, we recombined and collimated these five harmonic beams with another pair of prisms set out symmetrically to the first pair. This setup of amplitude and phase modulation is similar to the ‘4f system’ widely used in image processing and pulse shaping.6
Superposition of these harmonics creates a train of shaped pulses. We used the shaper-assistant linear cross-correlation process to retrieve a subcycle pulse waveform.7 It will be possible to record directly the relation of the pulse's electric field to the alternating current part of the linear cross-correlation signal.
Figure 2. Electric field waveforms. Transform-limited cosine waveform at zero carrier-envelope phase, CEP =0 (a). Transform-limited sine waveform at CEP =3π/2 (b). Square waveform (c). Sawtooth waveform (d). The inset figures show the simulation of electric field waveform in black solid line and pulse envelope in blue dash line. a.u.: Arbitrary units.
The spectrum of our harmonic frequency comb is more than two octaves. Thus, the shortest pulses we can synthesize are transform-limited subcycle cosine pulses. Figure 2(a) shows the subcycle transform-limited cosine waveform each spanning 0.37 optical cycle with a temporal field (full width at half-maximum) of 520as. If we increase the phases of all harmonic frequencies by 3π/2, the pulse envelope profile does not change, but the carrier electric field waveform changes to a sine function as shown in Figure 2(b). Figure 2(c) shows a square waveform, which we synthesized using just three harmonic frequencies. Figure 2(d) shows the sawtooth waveform that was synthesized by four harmonic frequencies. If we were using the optimized condition of full power distribution of five harmonics at 380, 178, 70, 41, and 22mJ, the intensity of each attosecond pulse will exceed 1014W/cm2 when it is focused to a spot size of 20μm.
In summary, we have devised and demonstrated a source of a high-peak-power, waveform-controllable light. The bandwidth is more than two octaves, so the electric field oscillation in the pulse envelope is close to half-cycle. This may be suitable for generating high-order harmonics and investigating subcycle nonlinear optics. In addition, the electric field's subcycle nature makes it possible to explore coherent control of electronic motion. Our next step is to generate extreme UV radiation and use our pulse-shaping technique to develop even shorter, more energetic light pulses for probing atomic and molecular processes.
Department of Photonics
National Sun Yat-Sen University
Chao-Kuei Lee is currently an associate professor. His research interests focus on ultrafast photonics, including generating and characterizing ultrafast photonic signals by pulse shaping.
Department of Physics
National Tsing Hua University
Wei-Jan Chen is an assistant research scientist whose research focuses on high-power waveform synthesis and application.
Department of Physics and Institute of Astronomy
National Tsing Hua University
Ci-Ling Pan's main research interests are ultrafast and terahertz photonics. He is currently a Tsing Hua Chair Professor and chair of the Department of Physics and the Institute of Astronomy.
1. S. E. Harris, A. V. Sokolove, Subfemtosecond pulse generation by molecular modulation, Phys. Rev. Lett. 81, p. 2894-2897, 1998.
2. J. Mauritsson, J. M. Dahlström, E. Mansten, T. Fordell, Sub-cycle control of attosecond pulse generation using two-colour laser fields, J. Phys. B: Atom. Mol. Opt. Phys. 42, p. 134003, 2009.
3. W. J. Chen, H. Z. Wang, R. Y. Lin, C. K. Lee, C. L. Pan, Attosecond pulse synthesis and arbitrary waveform generation with cascaded harmonics of an injection-seeded high-power Q-switched Nd:YAG laser, Laser Phys. Lett. 9, p. 212, 2012.
4. W. J. Chen, Z. M. Hsieh, S. W. Huang, H. Y. Su, C. J. Lai, T. T. Tang, C. H. Lin, C. K. Lee, R. P. Pan, C. L. Pan, A. H. Kung, Sub-single-cycle optical pulse train with constant carrier envelope phase, Phys. Rev. Lett.
100, p. 163906, 2008. doi:10.1103/PhysRevLett.100.163906
5. Z. Wang, A. C. Bovik, A universal image quality index, IEEE Signal Proc. Lett. 9, p. 81-84, 2002.
6. A. M. Weiner, Femtosecond pulse shaping using spatial light modulators, Rev. Sci. Instrum. 71, p. 1929-1960, 2000.
7. H. S. Chan, Z. M. Hsieh, W. H. Liang, A. H. Kung, C. K. Lee, C. J. Lai, R. P. Pan, L. H. Peng, Synthesis and measurement of ultrafast waveforms from five discrete optical harmonics, Science 331, p. 1165-1168, 2011.