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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 8 — Apr. 14, 2008
  • pp: 5868–5873
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Carrier-envelope phase measurement from half-cycle high harmonics

Pengfei Lan, Peixiang Lu, Fang Li, Yuhua Li, and Zhenyu Yang  »View Author Affiliations


Optics Express, Vol. 16, Issue 8, pp. 5868-5873 (2008)
http://dx.doi.org/10.1364/OE.16.005868


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Abstract

We present an efficient method to observe the high harmonics generated in individual half-cycle of the driving laser pulse by mixing a weak ultraviolet pulse, and then the cutoff of each half-cycle harmonic is imaged. The simulation shows that the information of the driving laser pulse, including the laser intensity, pulse duration and carrier-envelope phase, can be in situ retrieved from the harmonic spectrogram. In addition, our results show that this method also distinguishes the half-cycle high harmonics for a pulse longer than 10 fs, suggesting a potential to extend the CEP measurement to the multi-cycle regime.

© 2008 Optical Society of America

Nowadays, rapid advances in laser technology have made it possible to shape and control the intense laser pulse consisting only a few optical cycles (typically, 5 fs for the Ti:sapphira laser), opening up new frontiers for ultrafast physics [1

1. T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545 (2000). [CrossRef]

]. To fully characterize such few-cycle pulses, the methods for characterizing a multi-cycle pulse turn out to be not sufficient. A new quantity of the relative phase between the carrier wave and the pulse envelope, i.e., carrier-envelope phase (CEP), has to be introduced. In the few-cycle regime, the temporal evolution of the electric field depends sensitively on the CEP. And many strong-field interactions which are relevant to the electric field of laser pulse rather than the intensity profile can be precisely controlled with the phase-stabilized few-cycle pulse [2

2. 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 (2003). [CrossRef] [PubMed]

, 3

3. D. B. Milošević, G. G. Paulus, and W. Becker, “High-order above-threshold ionization with few-cycle pulse: a meter of the absolute phase,” Opt. Express 11, 1418 (2003). [PubMed]

]. The ability to measure and stabilize the CEP therefore becomes a crucial issue for all applications.

Many methods have been proposed for CEP measurement based on the photonionization [3

3. D. B. Milošević, G. G. Paulus, and W. Becker, “High-order above-threshold ionization with few-cycle pulse: a meter of the absolute phase,” Opt. Express 11, 1418 (2003). [PubMed]

, 4

4. G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle Laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003). [CrossRef]

, 5

5. A. D. Bandrauk, S. Chelkowski, and N. H. Shon, “Measuring the electric field of few-cycle laser pulses by attosecond cross correlation,” Phys. Rev. Lett. 89, 283903 (2002). [CrossRef]

, 6

6. A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of Light-Phase-Sensitive Photoemission from a Metal,” Phys. Rev. Lett. 92, 073902 (2004). [CrossRef] [PubMed]

, 7

7. C. Lemell, X. M. Tong, F. Krausz, and J. Burgdorfer, “Electron emission from metal surfaces by ultrashort pulses: Determination of the carrier-envelope phase,” Phys. Rev. Lett. 90, 076403 (2003). [CrossRef] [PubMed]

], ultraviolet (uv) and terahertz emissions [8

8. C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Kninght, J. P. Marangos, and J. W. G. Tisch, and “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nature Phys. 3, 52 (2007). [CrossRef]

, 9

9. M. Kress, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy,” Nature Phys. 2, 327 (2006). [CrossRef]

]. It was shown that the few-cycle laser pulse leads to a strong left-right asymmetry of photoelectrons [3

3. D. B. Milošević, G. G. Paulus, and W. Becker, “High-order above-threshold ionization with few-cycle pulse: a meter of the absolute phase,” Opt. Express 11, 1418 (2003). [PubMed]

], which has been observed and utilized as a meter of CEPs [4

4. G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle Laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003). [CrossRef]

]. The photonelectron emission from metal surfaces also shows a phase-sensitive property [6

6. A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of Light-Phase-Sensitive Photoemission from a Metal,” Phys. Rev. Lett. 92, 073902 (2004). [CrossRef] [PubMed]

], suggesting a potential to measure the CEP [7

7. C. Lemell, X. M. Tong, F. Krausz, and J. Burgdorfer, “Electron emission from metal surfaces by ultrashort pulses: Determination of the carrier-envelope phase,” Phys. Rev. Lett. 90, 076403 (2003). [CrossRef] [PubMed]

]. But for photonelectron signals, thousands of consecutive pulses measurement is usually required to achieve the required degree of accuracy. In recent work, Haworth et al. [8

8. C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Kninght, J. P. Marangos, and J. W. G. Tisch, and “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nature Phys. 3, 52 (2007). [CrossRef]

] experimentally demonstrated a method of spatio-filtering, which separated the high harmonic generation (HHG) in each half-cycle of the driving pulse in the spatio-domain and the CEP was retrieved form the harmonic spectrogram. Moreover, the high harmonic signal is more easily detected and single shot measurement becomes possible. In addition, the spatio-filtering indicates a potential to CEP measurement for a multi-cycle pulse (≥10 fs), i.e., better by half [10

10. S. T. Cundiff, “Better by half,” Nature Phys. 3, 16 (2007). [CrossRef]

]. However, the spatio-filtering did not separate the half-cycle harmonics (HCHs) with close cutoffs, so that Haworth et al. observed only 3 or 4 HCHs in an 8.5-fs pulse at some CEPs (e.g., 2 rad), and only 2 at some other CEPs (e.g., 3.2 rad).

In this work, we propose an alternative method to retrieve the information of the driving pulse from HHG. However, in contrast to Ref. [8

8. C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Kninght, J. P. Marangos, and J. W. G. Tisch, and “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nature Phys. 3, 52 (2007). [CrossRef]

], we separate the HCH in the time domain. It is numerically shown that this approach is more efficient and all HCHs can be clearly observed. Our method is based on the HHG in a two-color field [12

12. K. Ishikawa, “Photonemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003). [CrossRef] [PubMed]

, 13

13. P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801(R) (2007). [CrossRef]

], which is illustrated in Fig. 1(a). The red line shows the 5-fs laser field. From the three-step model [11

11. P. B. Corkum, “Plasma perspective on stong-field multphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993). [CrossRef] [PubMed]

], the electron is first set free via photonionization at the laser peak and then is accelerated in the following half-cycle of the laser field, accumulating a maximum kinetic energy of about 3.17Up=3.17E 2 0/(4ω 2 0). In this equation, Up is the ponderomotive energy, ω 0 and E 0 are the laser frequency and amplitude. Finally, the electron recombines with the parent ion by releasing its energy to high harmonics with the cutoff energy of Ip+3.17Up, where Ip is the atomic ionization energy. Such a process occurs periodically in each half-cycle of the driving field as shown by the dotted line in Fig. 1(a). However, how to observe the HCH still is a crucial issue and challenge. As shown in Fig. 1(a), ionization is the starter of HHG and each HCH corresponds to a specific ionization time near the laser peak. Therefore, we mix a uv pulse to the laser field (see the blue line). Due to the high photon energy and ultrashort duration, the uv pulse significantly enhances the photonionization [12

12. K. Ishikawa, “Photonemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003). [CrossRef] [PubMed]

] and also confines the ionization time in an interval of several hundred attoseconds, which has been demonstrated to control and enhance the HHG [14

14. K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004). [CrossRef] [PubMed]

, 15

15. P. Lan, P. Lu, W. Cao, and X. Wang, “Efficient generation of an isolated single-cycle attosecond pulse,” Phys. Rev. A 76, 043808 (2007). [CrossRef]

]. Here, we focus on how to distinguish the individual HCH and to extract the driving pulse information. In such a field shown in Fig. 1(a), the uv pulse firstly launches a free electron, initialing the HHG. The electron is then accelerated in the following half-cycle of the driving laser field, and finally recombines with the parent ion by releasing high harmonics. Since the ionization is enhanced and confined in a short interval by the uv pulse, high harmonics generated in a half-cycle can be selected. Scanning the uv pulse, each HCH will be separated in the time domain, which also inherits the information of the driving field. From the harmonic spectrogram, the laser intensity, pulse duration and CEP are therefore can be in situ retrieved during HHG.

Fig. 1. (a) Electric fields of the few-cycle pulse (red line) and the uv pulse (blue line). The dotted line shows the dependence of the electron energy (Ip+Ek) on the ionization time. (b) High harmonic spectrogram as a function of delay between the laser and uv pulses (see the movie for various CEPs). The colorbar shows the harmonic intensity in logarithmic scale. The laser intensity is 4×1014 Wcm-2, pulse duration is 5 fs and the CEP is 0. The uv pulse intensity is 1×1013 Wcm-2 and duration is 1 fs. [Media 1]

Figure 2 shows the HCOs as a function of CEPs. The bars from left to right correspond to the HCHs of H -1, H 0,H 1,H 2 in Fig. 1, respectively. Different colors are used for clarity. For comparison, we also calculated the corresponding HCOs (solid lines) with the three-step model [11

11. P. B. Corkum, “Plasma perspective on stong-field multphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993). [CrossRef] [PubMed]

], modified by taking account the initial energy when the electron is released. It can be estimated as ωuv-Ip-V(ti), where V(ti) is the height of the combined Coulomb and driving laser field barrier at the ionization time [14

14. K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004). [CrossRef] [PubMed]

]. Note that the initial energy is not significant for our parameters and is negligible if the uv photon energy is less than 8 eV (the central wavelength is about 135 nm). As shown in Fig. 2, the HCOs obtained from classical model agree quite well with those from TDSE. In addition, one can see that the HCO depends sensitively on the CEP of the driving field. Conversely, one can retrieve the CEP from the harmonic spectrogram. For illustration, we refer the harmonic spectrogram obtained from TDSE to the “raw” results without knowing the CEP, and then present an algorithm to retrieve the driving field information from “raw” spectrograms. Firstly, we calculate the HCO by the classical model for a 5-fs pulse with a range of intensities (3.5–4.5×1014 W/cm 2) and CEPs (0–2π), establishing a database of the “theoretical” HCOs. Afterward, we extract the HCOs from the “raw” spectrograms and then compare them with the “theoretical” ones. Each comparison returns a value proportional to how well the two agree, which is defined as the square of the offset between the “raw” and “theoretical” HCOs. Finally, the driving laser intensity and CEP can be taken from the best match and the error from the standard deviation of the degree of agreement from this value. The intensity returned by the algorithm is 4.1±0.1×1014 Wcm-2, which agrees quite well with the “known” value (4×1014 Wcm-2). Figure 3 presents the retrieved CEPs, which also agree well with the “known” ones. The largest deviation is 0.04π and the average deviation is only 0.01π.

Fig. 2. The dependence of HCOs obtained from TDSE (the bars) and classical model (solid lines) on the CEP. Parameters are the same as Fig. 1.
Fig. 3. Retrieved CEPs as a function of “known” ones. Parameters are the same as Fig. 1.

Figure 4 shows the harmonic spectrograms as a function of delay for a (a) 8- and (b) 11.5-fs laser pulse. One can clearly distinguish each HCH and HCO from these spectrograms. In Fig. 5, we show the HCOs near the pulse peak (-2.5T 0ω 0 τ ≤ 1.5T 0) for a range of CPEs obtained from TDSE (bars) and classical model (solid lines). Similarly, the information of the driving field can be retrieved from the harmonic spectrogram as the above algorithm. Our calculation shows that the HCO can be clearly observed in a 15-fs pulse and still is distinguishable further increasing the duration to 20 fs. Hence, our method indicates a potential to measure the CEP in the multi-cycle regime. For even longer pulse (25 fs), the HCH still is separated in the time domain, but the HCO shift becomes much smaller and more difficult to measure.

Fig. 4. High harmonic spectrogram as a function of delay between the driving laser and uv pulse in a (a) 8- and 11.5-fs laser pulse. See the movie for a range of CEPs. Other parameters are the same as Fig. 1. [Media 2][Media 3]
Fig. 5. Same as Fig. 2, but for a 11.5-fs laser pulse.

Pulse duration is another useful parameter for ultrashort pulses. Usually, it is measured by frequency-resolved optical gating [16

16. R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: using frequency-resolved optical gating,” J. Opt. Soc. Am. A , 10, 1011 (1993). [CrossRef]

] or spectral phase interferometry for direct-electric field reconstruction [17

17. C. Iaconis and I.A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792 (1998). [CrossRef]

], but both are not in situ measurement method. In principle, the comparison algorithm mentioned above and also Ref. [8

8. C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Kninght, J. P. Marangos, and J. W. G. Tisch, and “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nature Phys. 3, 52 (2007). [CrossRef]

] is capable of a complete self-referencing retrieval of the electric-field of the driving pulse, including the intensity, spectral phase and so on. However, this approach needs more parameters and entangles the CEP measurement, which not only enlarges the calculation but also reduces the precision of CEP measurement. Here we present an alternative method to retrieve the pulse duration from HCOs. Our method is benefit from that the temporal filter clearly records all the HCOs. For instance, the 8-fs pulse consists only about 3 cycles FWHM, and 8 HCOs are clearly shown in Fig. 4(a). By contrast, the spatio-filter only distinguishes less than 4 HCOs [8

8. C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Kninght, J. P. Marangos, and J. W. G. Tisch, and “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nature Phys. 3, 52 (2007). [CrossRef]

]. Therefore, our method of temporal filter is more efficient for CEP measurement. More importantly, such an improvement also suggests a new method for in situ pulse duration measurement during HHG. From the three-step model, the HCO≃Ip+3.17(Ep/2/ω 0)2, where Ep is the laser amplitude of each individual half cycle. We assume a Gaussian envelope, which is widely used both in simulation and experiments, the HCO-Ip≃3.17/4/ω 2 0 [E 0 exp(-t 2/T 2)]2. Thus, the pulse duration can be extracted by fitting the HCOs with a Gauss squared function. We devise a simple algorithm to deal with this issue. Firstly, normalize HCO-Ip by its maximum, consequently (HCO-Ip)N obeys the Gauss-squared function exp[-(t/T)2]2, which is then transformed as {-ln[(HCO-Ip)N]/2}0.5~t/T. Finally, the parameter T and pulse duration can be retrieved with the least squares fitting method. In Fig. 6(a), we shows the {-ln[(HCO-Ip)N]/2}0.5 for the 5-(circles), 8- (triangles) and 11.5-fs (squares) pulse with a CEP of 0, which are fitted by the red, green and blue lines, respectively. The slope is 0.6016, 0.3688, 0.2666, the parameter T is retrieved as 1.66, 2.71, 3.75 T 0 and the pulse duration is 5.18, 8.5, 11.77 fs, respectively, which all agree well with the known values in Figs. 1 and 4. Note that this method enables one to retrieve the pulse duration without knowing the CEP. Figure 6(b) shows the {-ln[(HCO-Ip)N]/2}0.5 and the fitted lines for the 5-, 8-, 11.5-fs pulses with a CEP of 0.5π. The retrieved pulse durations are 5.48, 8.6 and 12 fs, respectively. We have also calculated for other CEPs, the deviation is bellow 8%. Therefore, pulse duration can be in situ measured independently on the CEP with our method, which is another advantage in contrast to the spatio-filtering [8

8. C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Kninght, J. P. Marangos, and J. W. G. Tisch, and “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nature Phys. 3, 52 (2007). [CrossRef]

].

Fig. 6. The half-cycle harmonic cutoff ln[(HcIp)N]2~tT for a two- (circles), three- (triangle), four-(square) laser pulse with the CEP of (a) 0 and (b) π/2. The solid line presents the fitted results. Other parameters are the same as Fig. 1.

In summary, we present an alternative method to in situ retrieve the information of the driving pulse by mixing a weak uv pulse. The simulation shows that the uv pulse enhances and confines the photonionization in a short interval, and then the HCH is clearly separated in the time domain. This approach is more efficient than the spatio-filter, all the HCOs are recorded and also suggests a potential to measure the CEP in the multi-cycle regime. In addition, we present a new way to in situ measure the pulse duration during HHG and this method is independent on the CEP. We also investigate the influence of the fluctuation on our method. The test simulation shows that neither a variation of the intensity (5×1012–1×1014 Wcm-2), duration (0.6–1.3 fs) nor a variation of wavelength (80–150 nm) of the uv pulse change the above results significantly. Note that intense isolated attosecond pulses are achievable currently. In Ref. [18

18. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605 (2004). [CrossRef] [PubMed]

], an isolated 950 as pulse with the energy of 2 nJ were observed experimentally. Its intensity will approaches to 1×1014 Wcm-2 by focusing to a micrometer spot as Ref. [19

19. H. Mashiko, A. Suda, and K. Midorikawa, “Focusing coherent soft-x-ray radiation to a micrometer spot size with an intensity of 1014 W/cm2,” Opt. Lett. 29, 1927 (2004). [CrossRef] [PubMed]

]. Therefore, the uv pulse in our simulation is promising to be produced with the similar methods in Refs. [18

18. T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605 (2004). [CrossRef] [PubMed]

, 19

19. H. Mashiko, A. Suda, and K. Midorikawa, “Focusing coherent soft-x-ray radiation to a micrometer spot size with an intensity of 1014 W/cm2,” Opt. Lett. 29, 1927 (2004). [CrossRef] [PubMed]

]. Moreover, we also estimate the influence of the laser intensity distribution for a focused driving laser pulse. Our simulation shows that our results persist in a loosely focused field. Usually, the high harmonics are generated in a highly localized region (less than 1 mm) in the focus, and so the CEP slip is minimized. It is estimated about 0.03 π for the driving field with a beam waist of about 40 µm and even less for a more loosely focused geometry. In addition, we can clearly distinguish the HCH for a range of laser intensities of 1–6×1014 Wcm-2 and a broader range is possible by taking other target atoms (e.g., He+, Ne).

Acknowledgements

This work was supported by the National Natural Science Foundation of China under grant Nos. 10574050, 10774054, 10734080 and 973 program under grant No. 2006CB806006.

References and links

1.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72, 545 (2000). [CrossRef]

2.

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 (2003). [CrossRef] [PubMed]

3.

D. B. Milošević, G. G. Paulus, and W. Becker, “High-order above-threshold ionization with few-cycle pulse: a meter of the absolute phase,” Opt. Express 11, 1418 (2003). [PubMed]

4.

G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, “Measurement of the Phase of Few-Cycle Laser Pulses,” Phys. Rev. Lett. 91, 253004 (2003). [CrossRef]

5.

A. D. Bandrauk, S. Chelkowski, and N. H. Shon, “Measuring the electric field of few-cycle laser pulses by attosecond cross correlation,” Phys. Rev. Lett. 89, 283903 (2002). [CrossRef]

6.

A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, “Observation of Light-Phase-Sensitive Photoemission from a Metal,” Phys. Rev. Lett. 92, 073902 (2004). [CrossRef] [PubMed]

7.

C. Lemell, X. M. Tong, F. Krausz, and J. Burgdorfer, “Electron emission from metal surfaces by ultrashort pulses: Determination of the carrier-envelope phase,” Phys. Rev. Lett. 90, 076403 (2003). [CrossRef] [PubMed]

8.

C. A. Haworth, L. E. Chipperfield, J. S. Robinson, P. L. Kninght, J. P. Marangos, and J. W. G. Tisch, and “Half-cycle cutoffs in harmonic spectra and robust carrier-envelope phase retrieval,” Nature Phys. 3, 52 (2007). [CrossRef]

9.

M. Kress, T. Löffler, M. D. Thomson, R. Dörner, H. Gimpel, K. Zrost, T. Ergler, R. Moshammer, U. Morgner, J. Ullrich, and H. G. Roskos, “Determination of the carrier-envelope phase of few-cycle laser pulses with terahertz-emission spectroscopy,” Nature Phys. 2, 327 (2006). [CrossRef]

10.

S. T. Cundiff, “Better by half,” Nature Phys. 3, 16 (2007). [CrossRef]

11.

P. B. Corkum, “Plasma perspective on stong-field multphoton ionization,” Phys. Rev. Lett. 71, 1994 (1993). [CrossRef] [PubMed]

12.

K. Ishikawa, “Photonemission and ionization of He+ under simultaneous irradiation of fundamental laser and high-order harmonic pulses,” Phys. Rev. Lett. 91, 043002 (2003). [CrossRef] [PubMed]

13.

P. Lan, P. Lu, W. Cao, Y. Li, and X. Wang, “Attosecond ionization gating for isolated attosecond electron wave packet and broadband attosecond xuv pulses,” Phys. Rev. A 76, 051801(R) (2007). [CrossRef]

14.

K. J. Schafer, M. B. Gaarde, A. Heinrich, J. Biegert, and U. Keller, “Strong field quantum path control using attosecond pulse trains,” Phys. Rev. Lett. 92, 023003 (2004). [CrossRef] [PubMed]

15.

P. Lan, P. Lu, W. Cao, and X. Wang, “Efficient generation of an isolated single-cycle attosecond pulse,” Phys. Rev. A 76, 043808 (2007). [CrossRef]

16.

R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: using frequency-resolved optical gating,” J. Opt. Soc. Am. A , 10, 1011 (1993). [CrossRef]

17.

C. Iaconis and I.A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792 (1998). [CrossRef]

18.

T. Sekikawa, A. Kosuge, T. Kanai, and S. Watanabe, “Nonlinear optics in the extreme ultraviolet,” Nature 432, 605 (2004). [CrossRef] [PubMed]

19.

H. Mashiko, A. Suda, and K. Midorikawa, “Focusing coherent soft-x-ray radiation to a micrometer spot size with an intensity of 1014 W/cm2,” Opt. Lett. 29, 1927 (2004). [CrossRef] [PubMed]

OCIS Codes
(020.4180) Atomic and molecular physics : Multiphoton processes
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(190.4160) Nonlinear optics : Multiharmonic generation
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Nonlinear Optics

History
Original Manuscript: January 25, 2008
Revised Manuscript: March 29, 2008
Manuscript Accepted: March 31, 2008
Published: April 11, 2008

Citation
Pengfei Lan, Peixiang Lu, Fang Li, Yuhua Li, and Zhenyu Yang, "Carrier-envelope phase measurement from half-cycle high harmonics," Opt. Express 16, 5868-5873 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-8-5868


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References

  1. T. Brabec and F. Krausz, "Intense few-cycle laser fields: Frontiers of nonlinear optics," Rev. Mod. Phys. 72, 545 (2000). [CrossRef]
  2. 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 (2003). [CrossRef] [PubMed]
  3. D. B. Miloˇsevi’c, G. G. Paulus, and W. Becker, "High-order above-threshold ionization with few-cycle pulse: a meter of the absolute phase," Opt. Express 11, 1418 (2003). [PubMed]
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