OSA's Digital Library

Optics Express

Optics Express

  • Vol. 17, Iss. 7 — Mar. 30, 2009
  • pp: 5139–5146

Optics InfoBase > Optics Express > Volume 17 > Issue 7 > Page 5139

« Show journal navigation

Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field

Weiyi Hong, Peixiang Lu, Pengfei Lan, Qingbin Zhang, and Xinbing Wang  »View Author Affiliations


Optics Express, Vol. 17, Issue 7, pp. 5139-5146 (2009)
http://dx.doi.org/10.1364/OE.17.005139


View Full Text Article

Acrobat PDF (300 KB)


Advanced Search

Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

High-order harmonic generation in the presence of a strong terahertz field is investigated, and phase stabilization of the few-cycle laser pulses is extended to the extremely ultraviolet region. It is found that the strong terahertz field significantly breaks the symmetry between the consecutive half-cycle and greatly extends the harmonic cutoff, producing both odd and even harmonics which are covered with an extremely broad bandwidth and well locked in phase. These results can support the generation of few-cycle attosecond pulse trains with stabilized carrier-envelope phase from pulse to pulse, and also enables the generation of phase-stabilized pulse train with tunable wavelength.

© 2009 Optical Society of America

1. Introduction

Current laser technology enables the generation of optical pulses containing only a few cycles[1

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997). [CrossRef] [PubMed]

]. The carrier-envelope phase(CEP), which is determined as the phase shift between the peak of the envelope and the closest peak of the carrier wave, has significant implications for some highly nonlinear phenomena induced by the electric field in the few-cycle regime. CEP control has been achieved in the visible and near-infrared (ir) region [2

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635 (2000). [CrossRef] [PubMed]

, 3

A. Apolonski, A. Poppe1, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85, 740–743 (2000). [CrossRef] [PubMed]

] and the phase-stabilized few-cycle pulses have been widely used to study and manipulate the electron dynamics in the intense laser field [4

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003). [CrossRef]

]. In this paper, the concept of CEP stabilization of the few-cycle pulses is extended to the extreme ultraviolet (xuv) regime, providing a powerful tool for study and control the ultrafast process in attosecond time scale, and also for the generation of the xuv frequency comb.

Driven by a intense laser field, atomic or molecular systems can emit lights with the frequency multiplying of that of the driving field. This highly nonlinear process, known as high-order harmonic generation (HHG), produces a radiation source covered by a broad spectral bandwidth from infrared to xuv region with equidistant frequencies. Analogous to the mode-locked laser, this frequency comb structure in the xuv region can be used to produce an attosecond pulse train via synthesizing several harmonics [5

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292, 1689–1692 (2001). [CrossRef] [PubMed]

]. The appearance of attosecond pulses has made a breakthrough on metrology and pump-probe technology, allowing one to study and control the ultrafast electron dynamics with unprecedented resolution [6

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. West-erwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature (London) 427, 817–821 (2004). [CrossRef]

]. The mechanism of HHG can be explained well by the “three-step” model [7

P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]

]: the electron first tunnels through the barrier formed by the Coulomb potential and the laser field, then it oscillates and returns to the parent ion with emission of a energetic photon. As is well known, this process repeats per half-cycle in one color driving field, which gives rise to an attosecond pulse train (APT) with two pulses per cycle [5

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292, 1689–1692 (2001). [CrossRef] [PubMed]

]. Since the one color driving field yields a spectrum of odd harmonics due to the inversion symmetry, the mode spacing of ωrep = 2ω 0 (ω 0 is the frequency of the driving field) will lead to a phase flip of π from pulse to pulse in the attosecond pulse train [8

Y. Nabekawa, T. Shimizu, T, Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train in the single cycle regime,” Phys. Rev. Lett. 97, 153904 (2006). [CrossRef] [PubMed]

]. The phase ambiguity of the APT limits the precision in its applications, and how to produce an APT with the same CEP is an issue of great interest.

Phase stabilization of attosecond pulses has been investigated both experimentally [9

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature (London) 436, 234–237 (2005). [CrossRef]

, 10

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97, 031001 (2006). [CrossRef]

] and theoretically [11

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A 76, 021801(R) (2007). [CrossRef]

]. In analogy to the mode-locked laser, the CEP difference ∆ϕ between consecutive pulses is related to the frequency offset δ through 2πδ = ωrep ∆ϕ [2

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635 (2000). [CrossRef] [PubMed]

]. If only the odd harmonics are included, δ = ω 0, leading to a phase flip of π from pulse to pulse in the train. When the odd and even harmonics are both included, then the frequency offset is equal to zero, thereby avoiding the pulse-to-pulse phase flip. This can be realized by breaking the inversion symmetry during the interaction. According to the “three-step” model of HHG, symmetry breaking can be achieved in different steps. For the ionization step, adopting asymmetric molecules can break the symmetry of ionization process in consecutive half-cycles [11

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A 76, 021801(R) (2007). [CrossRef]

], which results in an APT with one pulse per cycle and the same CEP from pulse to pulse. Similar results has been obtained via controlling the acceleration process in the laser field by using an additional second harmonic field [10

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97, 031001 (2006). [CrossRef]

]. However, the generated APT contains many optical cycles, and the CEP effect of few-cycle attosecond pulse would have more significant impacts on study and control of the electron dynamics inside atoms. This can be easily understood via the analogy with that in the visible and ir region [6

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. West-erwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature (London) 427, 817–821 (2004). [CrossRef]

, 12

Q. Liao, P. Lu, P. Lan, W. Cao, and Y. Li, “Phase dependence of high-order above-threshold ionization in asymmetric molecules,” Phys. Rev. A , 77, 013408 (2008). [CrossRef]

]. Then how to manipulate the HHG process and generate a few-cycle APT with stabilized CEP is desired.

In the present work, we focus on the generation of a few-cycle APT with stabilized pulse-to-pulse CEP. Our method is based on the non-coherent control of the HHG quantum paths using a strong terahertz (THz) pulse, which is currently a hot subject of research due to its dramatic potential applications [13

R. A. Kaindl, M. A. Carnahan, J. Orenstein, D. S. Chemla, H. M. Christen, H. Zhai, M. Paranthaman, and D. H. Lowndes, “Far-infrared optical conductivity gap in superconducting MgB2 films,” Phys. Rev. Lett. 88, 023001 (2001). [CrossRef]

, 14

T. Löffler, T. Bauer, K. Siebert, H. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Opt. Express 9, 616–621 (2001). [CrossRef] [PubMed]

, 15

B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. Zhang, “T-ray computed tomography,” Opt. Lett. 27, 1312–1314 (2002). [CrossRef]

, 16

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature (London) 410, 60 (2001). [CrossRef]

]. Schemes for powerful THz pulse generation with the peak strength reaching tens of kV/cm and even exceeding MV/cm have been achieved [17

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805–2807 (2005). [CrossRef] [PubMed]

, 18

X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006). [CrossRef] [PubMed]

, 19

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007). [CrossRef] [PubMed]

, 20

M. S. Sherwin, C. A. Schmuttenmaer, and P. H. Bucksbaum, DOE-NSF-NIH Workshop on Opportunities in THz Science.

]. Recently, it has been theoretically proposed that a THz source with field strength of MV/cm-GV/cm can be realized from a transient net current driven by the laser ponderomotive force in the plasma slab [21

H. Wu, Z. Sheng, and J. Zhang, “Single-cycle powerful megawatt to gigawatt terahertz pulse radiated from a wavelength-scale plasma oscillator,” Phys. Rev. E 77, 046405 (2008). [CrossRef]

]. A strong THz field can also be used to significantly manipulate the HHG process. In our previous work, it has been theoretically shown that a strong static field can greatly modulate the electron trajectories of HHG [22

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B 40, 2321–2331 (2007). [CrossRef]

]. However, such strong static fields are not experimentally possible, and strong THz fields can work instead. Figure 1 illustrate the electron dynamics of HHG in one color field [Fig.1 (a)] and in the presence of a strong THz field with 15% peak intensity of the driving field [Fig. 1(b)]. This intensity of the THz field is chosen to reach the highest kinetic energy of the electron’s first return (see reference[22

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B 40, 2321–2331 (2007). [CrossRef]

] for more details). As shown in Fig. 1(a), one color driving field yields two couples of ionization and recombination times per half-cycle, known as long and short trajectories, characterized by different travelling times of the electrons in the laser field. The symmetry of electron trajectories in consecutive half-cycles is much broken by the strong THz field, as shown in Fig. 1(b). Since the wavelength of the THz field (30μm–300μm) is much longer than the driving field (here a 800-nm field is used), the THz field can be treated as a quasi-static field during the interaction within many cycles of the driving pulse. When the driving and the THz fields point along the same direction, the electrons accelerating here can gain much more energy than the well-known value of 3.17Up , and vice versa. One can clearly see that the maximum kinetic energy of the electrons reaches 9.1Up , while that in the consecutive half-cycle decreases to 0.7Up . Moreover, for the trajectories with the kinetic energy of 9.1Up , the recombination times of the electrons are almost the same. Note that here we considered all the possible multi-returns [plotted in red in Fig. 1(b)]. Taking account all of the above results, It is easy to conclude that the HHG spectrum in the presence of a strong THz field is extended to Ip + 9.1Up and the harmonics higher than Ip + 0.7Up are well locked in phase with the mode spacing of ωrep = ω 0. Synthesizing several harmonics higher than Ip + 0.7Up results in an APT with a periodicity of full cycle and same pulse-to-pulse CEPs. This scheme provides harmonics covered with much broader bandwidth and much less intrinsic chirp, which can support few-cycle APT generation.

Fig. 1. (a) electron trajectories of HHG in one-color driving field. Blue dots and blue crosses present the ionization and the recombination times, respectively. (b) electron trajectories of HHG in the presence of a strong THz field with the 15% peak intensity of the driving pulse. Blue dots and blue crosses present the ionization and the recombination times for the electron’s first return, and red dots and red circles present the ionization and the recombination times for the electron’s second return, respectively.

2. Result and discussion

In this paper, we consider the interaction between the atom and the combined laser pulse in the single active electron approximation, and numerically solve the one-dimensional time-dependent Schrödinger equation in terms of the split-operator method [23

M. D. Ferr, J. A. Fleck JR., and A. Steiger, “Solution of the Schrǒdinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982). [CrossRef]

]. In our simulation, we use a soft-core potential model V(x) = - 1/(α + x 2)1/2 and choose the softening parameter α to be 0.484 corresponding to the ionization energy of 24.6 eV for the ground state of helium atom. Here we consider a multicycle 800-nm driving pulse with 20 cycles in combination with a 100-μm THz field. The peak intensities of the driving pulse and the THz field are chosen to be 3 × 1014 W / cm 2 and 4.5 × 1013 W/cm 2 The electric field is express by E(t) = f(t)E 0 sin(ω 0 t)X̂ + ETHzSin(ωTHzt)X̂. Here E 0 and ETHz are the amplitudes and ω 0 and ωTHz are the frequencies of the driving pulse and the THz field. Note that one half-cycle of the THz field is several times longer than the the duration of the driving pulse, therefore the delay between two fields and the envelope of the driving pulse have little impact. f(t) is the envelope of the driving pulse and is considered to a trapezoidal shape with three-cycle linear ramps.

The HHG spectrum in the presence of a strong THz field is shown in Fig. 2(a) (red line). For comparison, we also performed a simulation of HHG in the driving pulse alone, and the harmonic spectrum is shown by the blue line in Fig. 2(a). These spectra here show the typical structure: The harmonic yield in the first few orders decreases rapidly, then remains nearly constant for many orders forming a plateau, and sharply drops at the cutoff. Comparing to the harmonic spectrum in one-color driving pulse, there are two plateaus in the presence of the strong THz field . The first cutoff is at Ip + 0.7UP and the second one is significantly extended to 122nd harmonic, corresponding to the energy of Ip + 9.1UP , which is in great agreement with the classical approach shown in Fig. 1(b). In contrast to the HHG in one-color case, both odd and even harmonics are observed, forming a frequency-comb-like structure in the plateau. The structure detail is shown in Fig. 2(b). This phenomena is well explained with the selection role of HHG [24

O. E. Alon1, V. Averbukh1, and N. Moiseyev, “Selection Rules for the High Harmonic Generation Spectra,” Phys. Rev. Lett. 80, 3743–3746 (1998). [CrossRef]

].

Fig. 2. (a) The harmonic spectrum in the presence of a strong THz field with 15% peak intensity of the driving pulse (red line) and in the driving pulse alone(blue line). The intensity of the driving pulse is 3 × 1014 W/cm 2. (b) Detail structure (blue line) of the spectrum and the harmonic phases as a function of harmonic orders.

Next we further investigate the phase-locking properties of the harmonics in the second plateau, which is a critical factor in the generation of an APT. Note that phase-locking means that the phase difference between the harmonics with the same mode spacing is constant. To address this factor, the harmonic phases of the second plateau are presented in Fig. 2(b) (green circles). One can clearly see that the harmonic phases decrease almost linearly, which means the harmonics in the second plateau are well phase-locked. To further measure the quantities of phase-locking degree of the harmonics in the second plateau, we introduce a parameter η which is defined by [25

M. B. Gaarde and K. J. Schafer, “Space-time consideration in the phase locking of high harmonics,” Phys. Rev. Lett. 89, 213901 (2002). [CrossRef] [PubMed]

]

η= ∫ τNdtI (t) ∫ T0/2dtI (t),
(1)

where I(t) is the intensity of the attosecond pulses, and τN = T 0/2N. Here T 0 is the optical cycle of the driving pulse and N = 5 is the number of the harmonics including in I(t). We then normalize η to η̃ = (η - 2τN /T 0)/(0.775 -2τN /T 0). Here 0.775 is the value in the case of Fourier transform limit, i.e, the perfect phase-locking. η̃ measures the proportion of the τN energy emitted within τN during one half-cycle. η˜ = 1 stands for the perfect phase-locking and η̃ = 0 if I(t) is a constant. The dependence of the phase-locking degree η̃ on the harmonic order is shown in Fig. 3 (blue open squares). For comparison, η̃ of the harmonics in one-color driving field is also presented (red closed circles). One can clearly see that η̃ for the case of one-color driving field is less than 0.6 and rapidly increases to 0.95 in the highest harmonics near 55th, which is at the cutoff [See Fig. 2(a)]. For the case in the strong THz field, η̃ drifts for the lower harmonic orders and dramatically increases to 0.95 and remains nearly constant as the harmonic order increases. These results provide phase-locking harmonics covered with a bandwidth broader than 100 eV, which has a potential for the generation of few-cycle APT, as expected in Fig. 1(b). Note that the harmonics in the second plateau are not perfectly phase-locked, since there are still little intrinsic chirps [estimated from Fig. 1(b) to be 4.3 as/eV].

It is well-known that the harmonic phases in one-color field are chaotic (i.e., poor phase-locked) in the plateau and become linear (i.e., phase-locked) near the cutoff [11

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A 76, 021801(R) (2007). [CrossRef]

]. Then regular APT can only be produced by synthesizing the harmonics near the cutoff. As shown in Fig. 2(a), only odd harmonics are produced in one-color driving pulse, then near the cutoff the frequency offset δ = ω 0, and the CEP difference ∆ϕ of the generated APT is calculated to be π through the equation 2πδ = ωrep ∆ϕ. Figures 4(a) and (b) show the temporal shape and the electric field of the APT obtained by synthesizing five harmonics near the cutoff, respectively. There are two attosecond pulses in each optical cycle of the driving pulse, and CEPs of the consecutive pulses shift by π from pulse to pulse [10

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97, 031001 (2006). [CrossRef]

]. For the case in the presence of the strong THz field, both odd and even harmonics are included, then the frequency offset δ = 0, which avoids the CEP flip from pulse to pulse in the train. The results are shown in Fig. 5. Figure 5(a) presents the temporal profiles of the APTs from the second plateau and near the cutoff, obtained by synthesizing the harmonics from 75th–85th (red line), 120th – 130th (grey line) and 69th-105th (blue line), respectively. One can clearly see that the periodicity of the generated APTs is one optical cycle of the driving pulse, as expected from the classical approach shown in Fig. 1(b). The pulse duration of the APT by synthesizing 69th–105th harmonic is approximately 72 as, which is very closed to the Fourier-transform limit (68 as). Since the central wavelength of the selected harmonics is approximately 9.2 nm (30.7 as of the optical cycle), each pulse in the train contains only 2.4 cycles. Figures 5(b)–(d) are the electric waveforms of three APTs shown in Fig. 5(a). As shown in these figures, the CEP differences between the consecutive pulses of these three APTs become zero. This indicates that CEP-stabilized APTs with different bandwidths and different central wavelengths can be produced. Such CEP-stabilized APTs with tunable central wavelengths play an important role in the manipulating the ultrafast electron dynamics inside atoms.

Fig. 3. Normalized phase-locking degree of the harmonics in the presence of a strong THz field (open squares) and in one-color driving pulse (closed circles). The parameters are the same as in Fig. 2(a).
Fig. 4. (a)The temporal shape and (b) the electric waveform of the attosecond pulse train in one-color driving pulse via synthesizing the harmonics near the cutoff. The parameters are the same as in Fig. 2(a).
Fig. 5. (a)The temporal shapes of the attosecond pulse train in the presence of a strong THz field via synthesizing the harmonics from 75th–85th (red line), 120th–130th (grey line) and 69th–105th (blue line), respectively. (b)–(d) are the corresponding electric waveforms. The parameters are the same as in Fig. 2(a).

Finally, we would like to qualitatively discuss the influence of the propagation effect in our scheme. Actually, propagation both affects the fundamental pulse and the harmonic field [26

M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B 41, 132001 (2008). [CrossRef]

]. First, dispersion will change the delay between the THz field and the driving pulse. But in low-density gas medium, this change is small and can be tolerant in our scheme, since this change has little impact to the XUV radiations even when the delay varies within 20 fs. On the other hand, propagation also affects the time-frequency structure of the harmonics due to different phase-matching conditions for different quantum paths [26

M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B 41, 132001 (2008). [CrossRef]

]. In our scheme, the harmonics from two different paths are synchronously emitted, as show in Fig. 1(b). Then the time-frequency structures of the harmonics in the second plateau will hardly change under different phase-matching conditions.

3. Conclusion

In conclusion, the HHG in the presence of a strong THz field was investigated. HHG quantum paths are significantly manipulated and the symmetry of HHG in the consecutive half-cycles is much broken: the maximum photon energy is greatly extended to Ip +9.1Up while that in the consecutive half-cycle decreases to Ip +0.7Up . Moreover, the harmonics higher than Ip +0.7Up are well locked in phase. These scheme provides phase-locked harmonics covered with an extremely broad bandwidth and with the mode-spacing of ω 0, which supports the generation of a few-cycle APT with stabilized CEP from pulse to pulse and also enables the generation of CEP-stabilized APTs with tunable wavelength. Such APTs allow one to study and control the ultrafast phenomena induced by the waveform with much highly precision. Moreover, in analogy to the frequency comb in the visible and ir region, the extension of CEP stabilization may pave the way to precise xuv spectroscopy.

In this work, the delay between the THz field and the driving pulse is fixed to zero. Although slight fluctuation of this delay can be tolerant due to the much longer wavelength of the THz field, the relative phase between these two fields need to be locked in experiment, otherwise delay will dramatically fluctuate from pulse to pulse and leads to some unexpected consequences. It is still hard to lock the phase of a THz pulse to a 800-nm laser pulse at the moment. We would like to address one possible solution: Splitting an 800-nm intense femtosecond pulse into two beams. One is used to produce a strong THz field by ionization-induced transient currents in air[19

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007). [CrossRef] [PubMed]

], or, maybe in the future, by transient net current in the plasma slab[21

H. Wu, Z. Sheng, and J. Zhang, “Single-cycle powerful megawatt to gigawatt terahertz pulse radiated from a wavelength-scale plasma oscillator,” Phys. Rev. E 77, 046405 (2008). [CrossRef]

]. Another one is used as a driving pulse. Then after properly adjusting the delay between these two beams, the THz field can be locked in phase with the driving pulse from shot to shot.

Acknowledgment

This work was supported by the National Natural Science Foundation of China under Grant No. 10774054, 10734080 and the National Basic Research Program of China under Grant No. 2006CB806006. This work was partial supported by the State Key Laboratory of Precision Spectroscopy of Huadong Normal university.

References and links

1.

M. Nisoli, S. De Silvestri, O. Svelto, R. Szipöcs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, “Compression of high-energy laser pulses below 5 fs,” Opt. Lett. 22, 522–524 (1997). [CrossRef] [PubMed]

2.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis,” Science 288, 635 (2000). [CrossRef] [PubMed]

3.

A. Apolonski, A. Poppe1, G. Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, “Controlling the Phase Evolution of Few-Cycle Light Pulses,” Phys. Rev. Lett. 85, 740–743 (2000). [CrossRef] [PubMed]

4.

A. Baltuška, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature (London) 421, 611–615 (2003). [CrossRef]

5.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug, Ph. Balcou, H. G. Muller, and P. Agostini, “Observation of a Train of Attosecond Pulses from High Harmonic Generation,” Science 292, 1689–1692 (2001). [CrossRef] [PubMed]

6.

R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. West-erwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, “Atomic transient recorder,” Nature (London) 427, 817–821 (2004). [CrossRef]

7.

P. B. Corkum, “Plasma Perspective on Strong-Field Multiphoton Ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]

8.

Y. Nabekawa, T. Shimizu, T, Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, “Interferometric autocorrelation of an attosecond pulse train in the single cycle regime,” Phys. Rev. Lett. 97, 153904 (2006). [CrossRef] [PubMed]

9.

Ch. Gohle, Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, and T. W. Hänsch, “A frequency comb in the extreme ultraviolet,” Nature (London) 436, 234–237 (2005). [CrossRef]

10.

J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, “Attosecond pulse trains generated using two color laser fields,” Phys. Rev. Lett. 97, 031001 (2006). [CrossRef]

11.

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules,” Phys. Rev. A 76, 021801(R) (2007). [CrossRef]

12.

Q. Liao, P. Lu, P. Lan, W. Cao, and Y. Li, “Phase dependence of high-order above-threshold ionization in asymmetric molecules,” Phys. Rev. A , 77, 013408 (2008). [CrossRef]

13.

R. A. Kaindl, M. A. Carnahan, J. Orenstein, D. S. Chemla, H. M. Christen, H. Zhai, M. Paranthaman, and D. H. Lowndes, “Far-infrared optical conductivity gap in superconducting MgB2 films,” Phys. Rev. Lett. 88, 023001 (2001). [CrossRef]

14.

T. Löffler, T. Bauer, K. Siebert, H. Roskos, A. Fitzgerald, and S. Czasch, “Terahertz dark-field imaging of biomedical tissue,” Opt. Express 9, 616–621 (2001). [CrossRef] [PubMed]

15.

B. Ferguson, S. Wang, D. Gray, D. Abbot, and X. Zhang, “T-ray computed tomography,” Opt. Lett. 27, 1312–1314 (2002). [CrossRef]

16.

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature (London) 410, 60 (2001). [CrossRef]

17.

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805–2807 (2005). [CrossRef] [PubMed]

18.

X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006). [CrossRef] [PubMed]

19.

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007). [CrossRef] [PubMed]

20.

M. S. Sherwin, C. A. Schmuttenmaer, and P. H. Bucksbaum, DOE-NSF-NIH Workshop on Opportunities in THz Science.

21.

H. Wu, Z. Sheng, and J. Zhang, “Single-cycle powerful megawatt to gigawatt terahertz pulse radiated from a wavelength-scale plasma oscillator,” Phys. Rev. E 77, 046405 (2008). [CrossRef]

22.

W. Hong, P. Lu, W. Cao, P. Lan, and X. Wang, “Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field,” J. Phys. B 40, 2321–2331 (2007). [CrossRef]

23.

M. D. Ferr, J. A. Fleck JR., and A. Steiger, “Solution of the Schrǒdinger equation by a spectral method,” J. Comput. Phys. 47, 412–433 (1982). [CrossRef]

24.

O. E. Alon1, V. Averbukh1, and N. Moiseyev, “Selection Rules for the High Harmonic Generation Spectra,” Phys. Rev. Lett. 80, 3743–3746 (1998). [CrossRef]

25.

M. B. Gaarde and K. J. Schafer, “Space-time consideration in the phase locking of high harmonics,” Phys. Rev. Lett. 89, 213901 (2002). [CrossRef] [PubMed]

26.

M. B. Gaarde, J. L. Tate, and K. J. Schafer, “Macroscopic aspects of attosecond pulse generation,” J. Phys. B 41, 132001 (2008). [CrossRef]

OCIS Codes
(190.4160) Nonlinear optics : Multiharmonic generation
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(300.6560) Spectroscopy : Spectroscopy, x-ray

ToC Category:
Nonlinear Optics

History
Original Manuscript: November 18, 2008
Revised Manuscript: February 9, 2009
Manuscript Accepted: March 11, 2009
Published: March 17, 2009

Citation
Weiyi Hong, Peixiang Lu, Pengfei Lan, Qingbin Zhang, and Xinbing Wang, "Few-cycle attosecond pulses with stabilized-carrier-envelope phase in the presence of a strong terahertz field," Opt. Express 17, 5139-5146 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5139


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Nisoli, S. De Silvestri, O. Svelto, R. Szipocs, K. Ferencz, Ch. Spielmann, S. Sartania, and F. Krausz, "Compression of high-energy laser pulses below 5 fs," Opt. Lett. 22, 522-524 (1997). [CrossRef] [PubMed]
  2. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-Envelope Phase Control of Femtosecond Mode-Locked Lasers and Direct Optical Frequency Synthesis," Science 288, 635 (2000). [CrossRef] [PubMed]
  3. A. Apolonski, A. Poppe, G . Tempea, Ch. Spielmann, Th. Udem, R. Holzwarth, T. W. Hansch, and F. Krausz, "Controlling the Phase Evolution of Few-Cycle Light Pulses," Phys. Rev. Lett. 85, 740-743 (2000). [CrossRef] [PubMed]
  4. A. Baltuska, Th. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis,Ch. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature (London) 421, 611-615 (2003). [CrossRef]
  5. P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Aug, Ph. Balcou, H. G. Muller, and P. Agostini, "Observation of a Train of Attosecond Pulses from High Harmonic Generation," Science 292, 1689-1692 (2001). [CrossRef] [PubMed]
  6. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, and F. Krausz, "Atomic transient recorder," Nature (London) 427, 817-821 (2004). [CrossRef]
  7. P. B. Corkum, "Plasma Perspective on Strong-Field Multiphoton Ionization," Phys. Rev. Lett. 71, 1994-1997 (1993). [CrossRef] [PubMed]
  8. Y. Nabekawa, T. Shimizu, T, Okino, K. Furusawa, H. Hasegawa, K. Yamanouchi, and K. Midorikawa, "Interferometric autocorrelation of an attosecond pulse train in the single cycle regime," Phys. Rev. Lett. 97, 153904 (2006). [CrossRef] [PubMed]
  9. Ch. Gohle,Th. Udem, M. Herrmann, J. Rauschenberger, R. Holzwarth, H. A. Schuessler, F. Krausz, T. W. Hansch, "A frequency comb in the extreme ultraviolet," Nature (London) 436, 234-237 (2005). [CrossRef]
  10. J. Mauritsson, P. Johnsson, E. Gustafsson, A. L’Huillier, K. J. Schafer, and M. B. Gaarde, "Attosecond pulse trains generated using two color laser fields," Phys. Rev. Lett. 97, 031001 (2006). [CrossRef]
  11. P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, "Carrier-envelope phase-stabilized attosecond pulses from asymmetric molecules," Phys. Rev. A 76, 021801(R) (2007). [CrossRef]
  12. Q. Liao, P. Lu, P. Lan, W. Cao, and Y. Li, "Phase dependence of high-order above-threshold ionization in asymmetric molecules," Phys. Rev. A,  77, 013408 (2008). [CrossRef]
  13. R. A. Kaindl, M. A. Carnahan, J. Orenstein, D. S. Chemla, H. M. Christen, H. Zhai, M. Paranthaman and D. H. Lowndes, "Far-infrared optical conductivity gap in superconducting MgB2 films," Phys. Rev. Lett. 88, 023001 (2001). [CrossRef]
  14. T. Loffler, T. Bauer, K. Siebert, H. Roskos, A. Fitzgerald, S. Czasch, "Terahertz dark-field imaging of biomedical tissue," Opt. Express 9, 616-621 (2001). [CrossRef] [PubMed]
  15. B. Ferguson, S. Wang, D. Gray, D. Abbot, and X  Zhang, "T-ray computed tomography," Opt. Lett. 27, 1312-1314 (2002). [CrossRef]
  16. B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, C. R. Stanley, "Coherent manipulation of semiconductor quantum bits with terahertz radiation," Nature (London) 410, 60 (2001). [CrossRef]
  17. T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, "Generation of single-cycle THz transients with high electric-field amplitudes," Opt. Lett. 30, 2805-2807 (2005). [CrossRef] [PubMed]
  18. X. Xie, J. Dai, and X.-C. Zhang, "Coherent control of THz wave generation in ambient air," Phys. Rev. Lett. 96, 075005 (2006). [CrossRef] [PubMed]
  19. K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, "Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields," Opt. Express 15, 4577-4584 (2007). [CrossRef] [PubMed]
  20. M. S. Sherwin, C. A. Schmuttenmaer, and P. H. Bucksbaum, DOE-NSF-NIH Workshop on Opportunities in THz Science.
  21. H. Wu, Z. Sheng, and J. Zhang, "Single-cycle powerful megawatt to gigawatt terahertz pulse radiated from a wavelength-scale plasma oscillator," Phys. Rev. E 77, 046405 (2008). [CrossRef]
  22. W. Hong, P. Lu,W. Cao, P. Lan, and X. Wang, "Control of quantum paths of high-order harmonics and attosecond pulse generation in the presence of a static electric field," J. Phys. B 40, 2321-2331 (2007). [CrossRef]
  23. M. D. Ferr, J. A. Fleck, JR., and A. Steiger, "Solution of the Schrˇodinger equation by a spectral method," J. Comput. Phys. 47, 412-433 (1982). [CrossRef]
  24. O. E. Alon1, V. Averbukh1, and N. Moiseyev, "Selection Rules for the High Harmonic Generation Spectra," Phys. Rev. Lett. 80, 3743 - 3746 (1998). [CrossRef]
  25. M. B. Gaarde and K. J. Schafer, "Space-time consideration in the phase locking of high harmonics," Phys. Rev. Lett. 89, 213901 (2002). [CrossRef] [PubMed]
  26. M. B. Gaarde, J. L. Tate, and K. J. Schafer, "Macroscopic aspects of attosecond pulse generation," J. Phys. B 41, 132001 (2008). [CrossRef]

Cited By

 Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited