Attosecond Nonlinear Optics in Plasmas for Coherent Xray GenerationXiaoshi Zhang, Amy L. Lytle, Oren Cohen, David M. Gaudiosi, Tenio Popmintchev et al. Citation: AIP Conf. Proc. 926, 145 (2007); doi: 10.1063/1.2768845 View online: http://dx.doi.org/10.1063/1.2768845 View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=926&Issue=1 Published by the American Institute of Physics. Related ArticlesUltra low bending loss equiangular spiral photonic crystal fibers in the terahertz regime AIP Advances 2, 022140 (2012) Optically recorded tunable microlenses based on dye-doped liquid crystal cells Appl. Phys. Lett. 100, 181111 (2012) Derivation of second-order nonlinear optical conductivity by the projection-diagram method AIP Advances 2, 012161 (2012) Fabrication of disconnected threedimensional silver nanostructures in a polymer matrix Appl. Phys. Lett. 100, 063120 (2012) Enhancement of linear and nonlinear optical properties of deoxyribonucleic acid-silica thin films doped withrhodamine Appl. Phys. Lett. 99, 243304 (2011) Additional information on AIP Conf. Proc.Journal Homepage: http://proceedings.aip.org/ Journal Information: http://proceedings.aip.org/about/about_the_proceedings Top downloads: http://proceedings.aip.org/dbt/most_downloaded.jsp?KEY=APCPCS Information for Authors: http://proceedings.aip.org/authors/information_for_authors

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Attosecond Nonlinear Optics in Plasmas for Coherent X-ray Generation

Xiaoshi Zhang, Amy L. Lytle, Oren Cohen, David M. Gaudiosi, Tenio Popmintchev, Ariel Paul, Margaret M. Murnane, and Henry C. Kapteyn

Department of Physics and JILA, and NSF Engineering Research Center in Extreme Ultraviolet Science and Technology, University of Colorado and NIST, Boulder, CO 80309-0440

kapteyn@jila.colorado.edu

Brendan Reagan, Mike Grisham, and Jorge J. Rocca

Department of Electrical and Computer Engineering, and NSF Engineering Research Center in Extreme Ultraviolet Science and Technology, Colorado State University, Ft. Collins, CO

Abstract. The process of high-order harmonic generation (HHG) can be used to generate bright, coherent beams of light in the extreme-ultraviolet and soft x-ray region of the spectrum by upconverting intense femtosecond pulses to very short wavelengths. These high-order harmonics result from ionization of the gas used as a nonlinear medium; thus, a full understanding of the process involves incorporating atomic physics, quantum dynamics, and plasma physics into an already non-trivial nonlinear optics problem. In the past several years, we have developed a new technology of “extreme” nonlinear optics that uses the rich, attosecond time-scale physics of the process in novel ways to manipulate the characteristics of this source, improving both the flux and the spectral characteristics. Most recently, we have (1) demonstrated that quasi phase matching of the high-order harmonic conversion process can be accomplished by the use of weak counterpropagating pulse trains that modulate the conversion process, constituting a nonlinear-optical “crystal” made of light; and (2) we have demonstrated that high-order harmonics can be generated by ionization of ions in a guided-wave geometry, using a discharge-created plasma waveguide to pre-ionize the gas and form a guiding electron density profile.

High-order harmonic generation (HHG) driven by ultrashort laser pulses is a source of extreme-ulraviolet and soft x-ray light with the unique properties of ultrashort pulse duration and high spatial and temporal coherence.1 This source has made possible a number of new ultrafast spectroscopic probes of atoms, molecules and materials. To date, however, most applications use relatively long wavelengths (>10nm), due to the fact that the efficiency of the HHG process decreases rapidly at shorter wavelengths. This decrease in efficiency is not due primarily to the very high-order nonlinearity of the process, but as a result of the phase mismatch between the fundamental laser field and high order harmonic field. Dispersion of the free-electron plasma produced by ionization creates a phase mismatch that speeds up the phase velocity of the driving laser with respect to the generated harmonics, and that cannot be compensated using conventional phase matching techniques. This limits efficient harmonic generation to

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relatively low levels of ionization, below a “critical” ionization level of ≈ 5% for argon, or ≈ 0.5% for helium, corresponding to photon energies of ≈ 50eV and 130eV, respectively.1,3

Recent work as shown that a weak counterpropagating pulse can disrupt harmonic emission in a gas cell.2 Although a number of reasons for this counterpropagating pulse interaction could be contemplated, the work presented herein definitively confirms that the interaction is due to field interferences that interact with the high order harmonic generation process itself. The superposition of a pump beam and a counterpropagating pulse results in a standing wave field that amplitude and phase modulates the driving laser with a periodicity corresponding to half the laser wavelength. These rapid variations prevent the coherent buildup of the harmonic field, suppressing the generation process in regions where the counterpropagating pulses intersect.4 Therefore, if the laser beams collide in a region where the harmonic polarization is out of phase with the pump, then the harmonic signal is enhanced.

Our work shows for the first time that this interaction can be used to increase the brightness of high-order harmonic generation. We observe a substantial enhancement (300x) using this all-optical quasi phase matching (QPM) implemented using a train of counterpropagating pulses.4 In our first experiment, we used harmonic generation in a 6 cm long hollow waveguide filled with 7 torr of argon.5 The driving laser pulse, with an energy of 0.5 mJ and a pulse duration of ~25 fs, drives the generation process. The length of each counterpropagating pulse (sent through the waveguide in the opposite direction) was 0.34 mm, with a separation of 1.1 mm, and with energy 0.12mJ. Figures 1a and c show the measured enhancement in the output EUV signal as a function of harmonic order, using one, two or three counterpropagating pulses. A large, 300x enhancement of the 41st harmonic is shown in Fig. 1c. To benchmark the output flux, we compare the brightness of harmonics emitted from 3-pulse QPM with conventionally phase-matched harmonic generation in helium at the same energy (Fig. 1b). Helium is the brightest emitter that can be phase matched at this photon energy using conventional approaches. We find that the brightness of the 39th, 41st and 43rd harmonics are comparable to or brighter than those from phase matched HHG in helium, showing that this technique can result in brighter emission than any other geometry in this spectral range. This demonstrates that all-optical QPM does significantly enhance the harmonic flux harmonic flux in regimes that cannot normally be phase-matched, such as those involving highly ionized plasmas.3 Since the three-pulse sequence is not yet near the maximum enhancement possible in this wavelength range, further improvements should be possible.

In further work, we enhanced harmonic emission at energies up to 150 eV, also using a 6cm-long hollow waveguide filled with 200 torr of helium. In this experiment, a pulse train with 3 pulses (each 0.16 mm long) and a separation of 0.45 mm is used. The pulse energy of the pump pulse and each of the counterpropagating pulses was 1.24 mJ and 0.1 mJ, respectively. Figure 2a shows these data. An enhancement of 60x is observed for the 95th harmonic around 150eV.

Finally, we demonstrate selective enhancement of the two different quantum trajectories that generate a given harmonic (the long and short trajectories) by varying the counterpropagating pulse separation. In this experiment, using three counterpropagating pulses, each separated by 0.45 mm, the long trajectory or high

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frequency peak of a harmonic is selectively enhanced (Fig. 2c, red curve); When blocking the middle of the three counterpropagating pulses to increase the separation to 0.9 mm, the short trajectory (low frequency peak of the harmonic order) is selectively enhanced (Fig. 2c. blue curve). Since the two quantum trajectories spend slightly different times in the field (slightly less and slightly greater than 1fs) and since the quantum phase of the two trajectories is different, they respond differently to the counterpropagating field. This allows for coherent control over the radiating electron wavefunction on attosecond timescales.

Fig. 1: Quasi phase matching of high harmonic generation using either one, two, or three counterpropagating pulses in a 6cm hollow waveguide filled with 7 torr of Ar. a) HHG emission for no (grey), one (blue), and three (red) counterpropagating pulses, each of width 0.34 mm, spaced by 1.1 mm. b) Comparison of brightness between 3-pulse QPM (red), no counterpropagating pulses, (grey) in argon at 7 torr, and the phase matched emission from 100 torr of He (blue) under same conditions; c) Enhancement factor as a function of harmonic order, for one (blue), two (black) and three (red) counterpropagating pulses.

75 79 83 87 91 95 99 103 107

10

20

30

40

50

60

70

Enh

ance

men

t Fac

tor

Harmonic Order

3 Pulses 2 Pulses 1 Pulse

(b)

65 71 77 83 89 95 101 107 1130

200

400

600

Inte

nsity

[A. U

.]

Harmonic Order

3P QPM Long Traj. 2P QPM Short Traj. W/O CP Pulse

(c)

Fig. 2: Quasi phase matching of high harmonic generation using either one, two or three counterpropagating pulses in a long hollow waveguide (6 cm) filled with 200 torr of He. a) Observed HHG emission for no (grey), one (green), two (blue) and three (red) counterpropagating pulses, each of width 0.16mm, spaced by 0.45mm. b) Enhancement factor as a function of harmonic order, for one (blue), two (black) and three (red) counterpropagating pulses. c) Quasi phase matching of different quantum trajectories: long trajectories using 3 counterpropagating pulses with a separation of 0.45 mm (red); short trajectories using 2 counterpropagating pulses with a separation of 0.9 mm (blue); Non-phasematched harmonic spectrum without counterpropagating pulses (grey).

This work demonstrates that phase-matching in high-order harmonic generation can

be obtained even for very high-energy harmonics where the gas is highly ionized and plasma dispersion prevents conventional phase matching. It is thus of interest to push these novel phase matching techniques to higher energies in the soft x-ray region of the spectrum. In other recent work,6 we showed that it is possible to generate very high energy harmonics from further ionization of a plasma pre-ionised using a capillary discharge. This allows one to tailor the electron density radial profile to guide the

(a)

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pulse. This guiding avoids plasma-induced defocusing that would otherwise limit the peak intensity. Figure 3 shows that, using such a discharge, significantly higher photon energies can be obtained than without the discharge. Other experimental data show that the effects of ionization self-phase-modulation are suppressed in a discharge preionized plasma.7 The next step in these experiments is to implement the quasi phase matching techniques introduced earlier to the case of the plasma waveguide.

100 125 150 175 200 225 250 275 30010

0

101

102

103

Photon Energy (eV)

g(

)

no discharge5 A 2μsbackground

Argon

Fig. 3. High harmonic spectrum obtained from 6.0 Torr argon when the discharge is pulsed with a 5 A current pulse (red). The harmonic spectrum obtained in a hollow core waveguide with no discharge is also shown (black).

In summary, this work represents an important advance in overcoming a critical

challenge in laser science, for implementing useful coherent EUV sources at wavelengths of interest to advanced lithography, and for high-resolution imaging. Promising future directions include the application of this technique to very high-order harmonics, the use of multiple pulse trains and pulse sequences that are shaped in time, amplitude, and polarization to optimize EUV efficiency, as well as attosecond pulse generation by enhancing selected quantum paths while applying gated phase matching techniques.

REFERENCES 1 H.C. Kapteyn, M.M. Murnane, and I.P. Christov, Physics Today (March), March Issue (2005). 2 S. Voronov et al., Phys. Rev. Lett. 87, 133902 (2001). 3 E. A. Gibson, A. Paul, N. Wagner et al., Science 302 (5642), 95 (2003). 4 X. Zhang, A. L. Lytle, H. C. Kapteyn, M. M. Murnane, and O. Cohen, Nature Physics 3, 270-275 (2007). 5 A. Rundquist, C.G. Durfee III, S. Backus et al., Science 280 (5368), 1412 (1998). 6 D. M. Gaudiosi, B. Reagan, T. Popmintchev et al., Physical Review Letters 96 (20), 203001 (2006). 7 B. A. Reagan, T. Popmintchev, M. E. Grisham, D. M. Gaudiosi, M. Berrill, O. Cohen, B. C. Walker, M.

M. Murnane, J. J. Rocca, and H. C. Kapteyn, Physical Review A TBP(2007).

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