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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 9 — May. 5, 2014
  • pp: 10191–10201
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Temporal and spectral structure of the infrared pulse during the high order harmonic generation

W. Holgado, B. Alonso, J. San Román, and I. J. Sola  »View Author Affiliations


Optics Express, Vol. 22, Issue 9, pp. 10191-10201 (2014)
http://dx.doi.org/10.1364/OE.22.010191


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Abstract

We present, for the first time, the complete pulse characterization of the infrared pulse after generating harmonics. A systematic study of the high harmonic generation process, and the generating infrared pulse characterization, has been done by changing the focus-gas-jet relative position. We have concluded, supported by nonlinear propagation simulations, that there is a correlation between the spectral and temporal nonlinear evolution of the infrared generating field and the structures shown in the harmonic signal. We have identified two different pressure regimes: the low pressure regime, characterized by the effects produced by the plasma generated by the infrared pulse, and the high pressure regime where the plasma and the Kerr effect generated by the infrared field are both present. These observations highlight the important role played by the nonlinear propagation of the generating field in the high harmonic generation context.

© 2014 Optical Society of America

1. Introduction

There are different effects of the HHG process that drastically affect the phase matching conditions. Several experiments demonstrate that the spatial phase of the generating field plays an important role on the phase matching conditions of the HHG process, showing that using a special pulse wavefront one can optimize the phase matching conditions and consequently the HHG efficiency. A classical example of such strategy consists in doing the generation in a hollow-core wave-guide, where the generating field behaves almost like a plane wave [5

5. A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1414 (1998). [CrossRef] [PubMed]

]. Another effect that plays an important role for the phase matching conditions is the amount of ionized electrons generated during the HHG process. Ceccherinni et al studied the spectral properties of the HHG signal while changing the focus-gas-jet relative position [6

6. P. Ceccherini, A. Boscolo, L. Poletto, G. Tondello, P. Villoresi, C. Altucci, R. Bruzzese, C. De Lisio, M. Nisoli, S. Stagira, S. De Silvestri, and O. Svelto, “Gas medium ionization and harmonic wavelength tunability in high-order harmonic generation with ultrashort laser pulses,” Laser and Particle Beams 18, 477–482 (2000). [CrossRef]

]. They observed a continuous blue-shift of the harmonic wavelength induced by the presence of the ionized electrons. This process can even lead to spectral splitting of the harmonics. Zhong et al reported this harmonic splitting [7

7. F. Zhong, J. Deng, X. Hu, Z. Li, Z. Zhang, and Z. Xu, “The effect of ionization of gases on the high harmonic splitting,” Phys. Lett. A 278, 35–43 (2000). [CrossRef]

] and attributed it to the ionization of the medium, which, as reported by Streingrube et al [8

8. D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, and M. Kovačev, “Phase matching of high-order harmonics in a semi-infinite gas cell,” Phys. Rev. A 80, 043819 (2009). [CrossRef]

], causes not only harmonic splitting, but also spectral broadening and blueshift. Cao et al observed this harmonic splitting remarking the importance of the macroscopic effects to be able to explain the observations [9

9. W. Cao, G. Laurent, C. Jin, H. Li, Z. Wang, C. D. Lin, I. Ben-Itzhak, and C. L. Cocke, “Spectral splitting and quantum path study of high-harmonic generation from a semi-infinite gas cell,” J. Phys. B 45, 074013 (2012). [CrossRef]

]. All these conclusions were obtained by comparing the experimental results with theoretical models, without doing a direct measurement of the generating field. The first HHG experiment, to our knowledge, that measures the generating beam during a HHG experiment was done in 2006 by J. C. Painter and coworkers [10

10. J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, “Direct observation of laser filamentation in high-order harmonic generation,” Opt. Lett. 31, 3471–3473 (2006). [CrossRef] [PubMed]

]. They investigated the spatial evolution of the laser pulse used to generate HHG in a semi-infinite gas cell showing the elongation of the focus region, which is characteristic of self-focusing and filamentation. However, self-guiding had previously been observed by Tamaki and coworkers in 1999 [11

11. Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1426 (1999). [CrossRef]

], where they detected laser beam self-guiding phenomenon by looking at the fluorescence of the plasma channel generated during the HHG process, but without reporting any data. All these experiments indicate that the propagation of the generating field can be quite complex due to the possible appearance of nonlinear effects.

It is worth to realize that the main nonlinear effects that could be the origin of the phenomena observed in [10

10. J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, “Direct observation of laser filamentation in high-order harmonic generation,” Opt. Lett. 31, 3471–3473 (2006). [CrossRef] [PubMed]

, 11

11. Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1426 (1999). [CrossRef]

], mainly the Kerr effect and the ionization of the medium, are the basic ingredients of another nonlinear phenomenon: filamentation. The filament appears when there is a balance between the self-focusing dynamics induced by the optical Kerr effect and the defocusing produced by the diffraction and the ionized plasma generated in the medium during its propagation. If this balance takes place the pulse propagates in a self-guided way for several Rayleigh lengths forming what is called a filament [12

12. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995).

, 13

13. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007). [CrossRef]

]. This filamentation phenomenon, which seems to be present in some HHG experiments during the generation process, has been extensively studied both experimentally and theoretically. Important spatio-temporal shaping of the field during its nonlinear propagation has been observed experimentally by using different techniques. Odhner et al directly observed a temporal pulse-splitting by using the Transient-grating (TG) FROG technique [14

14. J. Odhner and R. J. Levis, “Direct phase and amplitude characterization of femtosecond laser pulses undergoing filamentation in air,” Opt. Lett. 37, 1775–1777 (2012). [CrossRef] [PubMed]

]. They explained the effect as a domination of the defocus by plasma in the leading part of the pulse that induces a redshift and a Kerr refocusing of the rear part of the pulse which entails a blueshift. Minardi et al also reported this effect [15

15. S. Minardi, A. Gopal, A. Couairon, G. Tamoašuskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34, 3020–3022 (2009). [CrossRef] [PubMed]

], adding a measure showing that these two split pulses have also different velocities. Alonso et al studied the spatio-temporal dynamics of a filament during its propagation both experimentally and theoretically [16

16. B. Alonso, I. J. Sola, J. San Román, O. Varela, and L. Roso, “Spatiotemporal evolution of light during propagation in filamentation regime,” J. Opt. Soc. Am. B 28, 1807–1816 (2011). [CrossRef]

]. They show that at the beginning of the filament formation there is a pulse-splitting in which one of the peaks survives while the other vanishes until a self-compressed pulse is generated. These results agree with other works as [17

17. S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnürer, N. Zhanvoronkov, and G. Steinmeyer, “Self-compression by femtosecond pulse filamentation: experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006). [CrossRef]

, 18

18. C. Brée, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Plasma induced pulse breaking in filamentary self-compression,” Las. Phys. 20, 1107–1113 (2010). [CrossRef]

], which also reported a competition between the two peaks in the pulse splitting.

The main purpose of this paper is to apply all the tools used in the context of filamentation to directly observe the temporal structure of the generating field at the HHG process, together with the HHG spectrum. We have performed a systematic study where the focus-gas-jet relative position is changed to investigate the relation between the temporal structure of the infrared (IR) generating pulse and the spectral structure of the high order harmonics. A nonlinear propagation model has also been used to better understand the experimental observations.

2. Experimental setup for the observation of the generating field and the HHG process

The layout of the experiment is shown in Fig. 1. We use a CPA Ti:sapphire laser system (Spectra-Physics) which delivers 100 fs pulses centered at 795 nm with 9 nm FWHM and 10 Hz repetition rate. A beam splitter divides the incident beam into two: one used to generate the harmonics, which we call the test beam because it is the beam that we want to temporally characterize, and the other used as a reference pulse in the STARFISH, the spectral interferometry technique applied to characterize the test pulse [19

19. B. Alonso, I. J. Sola, O. Varela, J. Hernández-Toro, C. Méndez, J. San Román, A. Zaïr, and L. Roso, “Spatiotemporal amplitude-and-phase reconstruction by Fourier-transform of interference spectra of high-complex beams,” J. Opt. Soc. Am. B 27, 933–940 (2010). [CrossRef]

].

Fig. 1 Experimental setup used in the laboratory. The incoming pulse is divided into the test and reference pulse. The former is used to generate the high-order harmonics. The later is first temporally characterized with a GRENOUILLE and then is used to measure the test pulse with spectral interferometry

The input energy of the test pulse is adjustable up to 5 mJ by changing the energy before the beam splitter with a half-wave plate and a linear polarizer (not shown in the figure). We use an iris to optimize the harmonic generation process before focusing the beam with a 40-cm focal length to generate high-order harmonics in Xenon. With this configuration we estimate to achieve intensities of the order of 9 × 1014 W/cm2 [20

20. We estimate the intensity at the focus by doing linear Gaussian propagation. This estimation is clearly overestimating the intensity because assume perfect Gaussian spatial shape, aberration free focusing and linear propagation. Any of this effects will deteriorate the focusing process producing a bigger focal spot and a lower intensity.

], we chose this high intensity since it is necessary to observe the effects that we are looking for. The Xenon gas passed to the vacuum chamber through a nozzle of 500 μm diameter with the gas-jet backing pressure fixed at 5 bar. The harmonics generated in the interaction chamber are propagated trough a 150-nm thick aluminum foil to filter the IR radiation and the lower harmonics. A grazing-incidence Rowland circle XUV spectrometer (Model 248/310G, McPherson Inc.), of 1-m radius and 300-grooves/mm spherical diffraction grating, is used to measure the wavelength of each generated harmonic. We control the position of the focusing lens with a motorized linear stage, with which we observe the differences in the XUV radiation when changing the focus-gas-jet relative position due to complex propagation of the IR generating field, as we will show later.

In order to measure the generating IR pulse we place a mirror inside the generation chamber after the gas-jet and before the XUV spectrometer. The IR pulse interacts with the Xenon, in the same conditions as when generating the harmonics, and is reflected outwards from the chamber. Once the beam is out of the chamber, we characterize it with spatiotemporal amplitude-and-phase reconstruction by Fourier-transform of interference spectra of highly-complex-beams (STARFISH [19

19. B. Alonso, I. J. Sola, O. Varela, J. Hernández-Toro, C. Méndez, J. San Román, A. Zaïr, and L. Roso, “Spatiotemporal amplitude-and-phase reconstruction by Fourier-transform of interference spectra of high-complex beams,” J. Opt. Soc. Am. B 27, 933–940 (2010). [CrossRef]

]). We first make the z-scan measurement of the high-order harmonics and then, with the same configuration, we make a z-scan to measure the temporal structure of the laser pulse depending on the different focus-gas-jet relative distances.

The temporal characterization of the reference pulse, which is required by the STARFISH technique to characterize the test pulse, is done with a GRENOUILLE (20–120 fs, single-shot FROG, Swamp Optics) [21

21. P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort-pulse measurement,” Opt. Lett. 26, 932–934 (2001). [CrossRef]

]. Once the reference is known, it is sent into a fiber-connectorized spectrometer together with the test pulse (with a 2.5 ps delay) in a collinear configuration thanks to the fiber optic coupler. The phase structure of the test pulse is retrieved from the spectral fringes obtained in the interference spectrum of the two pulses. To extract it we use the fringe inversion algorithm proposed by Lepetit et al [22

22. L. Lepetit, G. Cheriaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995). [CrossRef]

].

3. Theoretical model of the propagation of the generating field

4. Results and Discussion

We present first the results of the theoretical modeling to better identify the different phenomena that could appear during the harmonic generation in the experimental data, which will be presented later.

4.1. Theoretical results

As we have explained in the Section 2, the IR pulse interacts with the gas coming from a gas-jet. Therefore, the IR pulse will see different gas pressures at the waist as we change the focus-gasjet relative position. To study the main effects that could appear under such situations we have done simulations of the propagation of the pulse at different pressures: the low pressure case representing the situation in which the beam-waist does not coincide with the gas-jet, and the high pressure case representing the situation in which the beam-waist and the gas-jet coincide. The input beam used in the simulations has the following form:
E(ρ,t,z=0)=E0exp(ρ4/w04)exp(t2/tp2)exp(ik0ρ2/2f)
(6)
where w0 = 2.5 mm represents the width of the beam, tp = 85 fs represents the temporal duration and f = 40 cm is focal length. The amplitude of the pulse is selected to have an energy of 1 mJ. This pulse interacts with Xe gas at two different pressures: 0.01 and 0.05 atm, which are enough to see the different regimes of interaction.

Fig. 2 Left and right column represent the 0.01 and 0.05 atm case, respectively. The top figures represent the temporal structure of the on-axis intensity at different propagation positions around the focus. The bottom figures represent the corresponding spectral structure of the above figures. All the pictures are shown in logarithmic scale.

Fig. 3 The thick (blue) and thin (green) solid curves represents the temporal intensity structure at 15 mm after the focus at the two different pressure regimes, the low pressure and the higher pressure regime, respectively. The thick (red) and thin (cyan) dashed curves correspond to the same two different pressure regimes but switching off the Kerr nonlinearity, thus using n2 = 0.

4.2. Experimental results

Fig. 4 High-order harmonics spectra obtained for each position of the focus. The harmonics shown are 13th, 15th, 17th and 19th of 795 nm. In the horizontal axis is presented the harmonic energy, while the vertical axis corresponds to the focus-gas-jet relative position, z. The z < 0 values represent the positions where the laser-beam-waist is placed before the gas-jet and vice versa. The side color bar represents the harmonics signal
Fig. 5 The left figure represents the normalized temporal intensity characterization of the infrared pulse while z is being varied. The right axis, z, indicates the focus-gas-jet relative position while the left axis shows the temporal reconstruction using STARFISH for each position. The right figure corresponds to the spectrum of the IR pulse after interacting with the gas. The right axis corresponds to the focus-gas-jet relative position and the left axis represents the spectral wavelengths.

Fig. 6 (a) Temporal characterization of the infrared pulse for different z-positions of the focus. In color we show the instantaneous wavelength of the pulse, from 780 nm (blue) to 820 nm (red). (b) Measured infrared spectrum for each position. (c) HHG signal obtained.

5. Conclusions

We have shown, for the first time, the complete pulse characterization of the pulse after generating harmonics. The HHG and IR characterization experiment is done during the interaction of an IR pulse with a Xe gas-jet. A systematic study of the HHG process and the generating IR pulse characterization has been done while changing the focus-gas-jet relative position. We have also used the standard model of nonlinear propagation to better understand the experimental results. Taking all these tools we conclude that there is a high correlation between the spectral and temporal nonlinear evolution of the IR generating field and the structures shown in the HHG signal. We have been able to identify two different pressure regimes during the z-scan. The low pressure regime is characterized by the effects produces by the plasma generated by the IR pulse, which is the main nonlinear phenomenon present. Consequently the pulse is temporally shifted to the front part and its spectrum is slightly blue-shifted. Contrarily, the higher pressure regime presents effects of both the plasma generated by the IR generating beam and the Kerr effect. The pulse, in this second regime, presents more complex structures in both the temporal and spectral domains. In our experiment we have been able to identify the typical asymmetric temporal pulse splitting generated by the replenishment dynamics, together with some traces of the self-phase modulation and the plasma in the spectrum of the IR. All these effects can be clearly correlated with the structure observed in the harmonics, indicating that the nonlinear propagation of the generating field is essential to correctly interpret the harmonics results in the parameters region used here.

Acknowledgments

The authors would like to thank Dr. David Novoa for the fruitful discussions on the results presented in this work.

The authors also acknowledge the support from Spanish Ministerio de Ciencia e Innovación (MICINN) through the Consolider Program SAUUL ( CSD2007-00013) and Research Project FIS2009-09522, from the Junta de Castilla y León (Project No. SA116U13) and from Centro de Láseres Pulsados. B. A. acknowledges Fundaçao para a Ciencia e a Tecnologia (FCT) through grant No. SFRH/BPD/88424/2012. W. H. and I. J. S. also acknowledge support from the Spanish Ministerio de Ciencia e Innovación through the Formación de Personal Investigador and Ramón y Cajal grant programs respectively.

References and links

1.

A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, and C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987). [CrossRef]

2.

M. Protopapas, C. H. Keitel, and P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997). [CrossRef]

3.

P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]

4.

K. J. Schafer, B. Yang, L. F. DiMauro, and K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993). [CrossRef] [PubMed]

5.

A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, and H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1414 (1998). [CrossRef] [PubMed]

6.

P. Ceccherini, A. Boscolo, L. Poletto, G. Tondello, P. Villoresi, C. Altucci, R. Bruzzese, C. De Lisio, M. Nisoli, S. Stagira, S. De Silvestri, and O. Svelto, “Gas medium ionization and harmonic wavelength tunability in high-order harmonic generation with ultrashort laser pulses,” Laser and Particle Beams 18, 477–482 (2000). [CrossRef]

7.

F. Zhong, J. Deng, X. Hu, Z. Li, Z. Zhang, and Z. Xu, “The effect of ionization of gases on the high harmonic splitting,” Phys. Lett. A 278, 35–43 (2000). [CrossRef]

8.

D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, and M. Kovačev, “Phase matching of high-order harmonics in a semi-infinite gas cell,” Phys. Rev. A 80, 043819 (2009). [CrossRef]

9.

W. Cao, G. Laurent, C. Jin, H. Li, Z. Wang, C. D. Lin, I. Ben-Itzhak, and C. L. Cocke, “Spectral splitting and quantum path study of high-harmonic generation from a semi-infinite gas cell,” J. Phys. B 45, 074013 (2012). [CrossRef]

10.

J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, and J. Peatross, “Direct observation of laser filamentation in high-order harmonic generation,” Opt. Lett. 31, 3471–3473 (2006). [CrossRef] [PubMed]

11.

Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, and K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1426 (1999). [CrossRef]

12.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995).

13.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007). [CrossRef]

14.

J. Odhner and R. J. Levis, “Direct phase and amplitude characterization of femtosecond laser pulses undergoing filamentation in air,” Opt. Lett. 37, 1775–1777 (2012). [CrossRef] [PubMed]

15.

S. Minardi, A. Gopal, A. Couairon, G. Tamoašuskas, R. Piskarskas, A. Dubietis, and P. Di Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34, 3020–3022 (2009). [CrossRef] [PubMed]

16.

B. Alonso, I. J. Sola, J. San Román, O. Varela, and L. Roso, “Spatiotemporal evolution of light during propagation in filamentation regime,” J. Opt. Soc. Am. B 28, 1807–1816 (2011). [CrossRef]

17.

S. Skupin, G. Stibenz, L. Bergé, F. Lederer, T. Sokollik, M. Schnürer, N. Zhanvoronkov, and G. Steinmeyer, “Self-compression by femtosecond pulse filamentation: experiments versus numerical simulations,” Phys. Rev. E 74, 056604 (2006). [CrossRef]

18.

C. Brée, A. Demircan, S. Skupin, L. Bergé, and G. Steinmeyer, “Plasma induced pulse breaking in filamentary self-compression,” Las. Phys. 20, 1107–1113 (2010). [CrossRef]

19.

B. Alonso, I. J. Sola, O. Varela, J. Hernández-Toro, C. Méndez, J. San Román, A. Zaïr, and L. Roso, “Spatiotemporal amplitude-and-phase reconstruction by Fourier-transform of interference spectra of high-complex beams,” J. Opt. Soc. Am. B 27, 933–940 (2010). [CrossRef]

20.

We estimate the intensity at the focus by doing linear Gaussian propagation. This estimation is clearly overestimating the intensity because assume perfect Gaussian spatial shape, aberration free focusing and linear propagation. Any of this effects will deteriorate the focusing process producing a bigger focal spot and a lower intensity.

21.

P. O’Shea, M. Kimmel, X. Gu, and R. Trebino, “Highly simplified device for ultrashort-pulse measurement,” Opt. Lett. 26, 932–934 (2001). [CrossRef]

22.

L. Lepetit, G. Cheriaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995). [CrossRef]

23.

A. Dalgarno and A.E. Kingston, “The refractive indices and Verdet constants of the inert gases,” Proc. Roy. Soc. A 259, 424–429 (1960). [CrossRef]

24.

A. Borzsonyi, Z. Heiner, A.P. Kovacs, M. P. Kalashnikov, and K. Osvay, “Measurement of pressure dependent nonlinear refractive index of inert gases,” Opt. Express 18, 25847–25855 (2010). [CrossRef] [PubMed]

25.

M. Mlejnek, E.M. Wright, and J.V. Moloney, “Dynamic spatial replenishment of femtosecond pulses propagating in air,” Opt. Lett. 23, 382384 (1998). [CrossRef]

OCIS Codes
(190.4160) Nonlinear optics : Multiharmonic generation
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
(320.5520) Ultrafast optics : Pulse compression
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Nonlinear Optics

History
Original Manuscript: February 12, 2014
Revised Manuscript: March 13, 2014
Manuscript Accepted: March 13, 2014
Published: April 21, 2014

Citation
W. Holgado, B. Alonso, J. San Román, and I. J. Sola, "Temporal and spectral structure of the infrared pulse during the high order harmonic generation," Opt. Express 22, 10191-10201 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-9-10191


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References

  1. A. McPherson, G. Gibson, H. Jara, U. Johann, T. S. Luk, I. A. McIntyre, K. Boyer, C. K. Rhodes, “Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases,” J. Opt. Soc. Am. B 4, 595–601 (1987). [CrossRef]
  2. M. Protopapas, C. H. Keitel, P. L. Knight, “Atomic physics with super-high intensity lasers,” Rep. Prog. Phys. 60, 389–486 (1997). [CrossRef]
  3. P. B. Corkum, “Plasma perspective on strong field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993). [CrossRef] [PubMed]
  4. K. J. Schafer, B. Yang, L. F. DiMauro, K. C. Kulander, “Above threshold ionization beyond the high harmonic cutoff,” Phys. Rev. Lett. 70, 1599–1602 (1993). [CrossRef] [PubMed]
  5. A. Rundquist, C. G. Durfee, Z. H. Chang, C. Herne, S. Backus, M. M. Murnane, H. C. Kapteyn, “Phase-matched generation of coherent soft x-rays,” Science 280, 1412–1414 (1998). [CrossRef] [PubMed]
  6. P. Ceccherini, A. Boscolo, L. Poletto, G. Tondello, P. Villoresi, C. Altucci, R. Bruzzese, C. De Lisio, M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, “Gas medium ionization and harmonic wavelength tunability in high-order harmonic generation with ultrashort laser pulses,” Laser and Particle Beams 18, 477–482 (2000). [CrossRef]
  7. F. Zhong, J. Deng, X. Hu, Z. Li, Z. Zhang, Z. Xu, “The effect of ionization of gases on the high harmonic splitting,” Phys. Lett. A 278, 35–43 (2000). [CrossRef]
  8. D. S. Steingrube, T. Vockerodt, E. Schulz, U. Morgner, M. Kovačev, “Phase matching of high-order harmonics in a semi-infinite gas cell,” Phys. Rev. A 80, 043819 (2009). [CrossRef]
  9. W. Cao, G. Laurent, C. Jin, H. Li, Z. Wang, C. D. Lin, I. Ben-Itzhak, C. L. Cocke, “Spectral splitting and quantum path study of high-harmonic generation from a semi-infinite gas cell,” J. Phys. B 45, 074013 (2012). [CrossRef]
  10. J. C. Painter, M. Adams, N. Brimhall, E. Christensen, G. Giraud, N. Powers, M. Turner, M. Ware, J. Peatross, “Direct observation of laser filamentation in high-order harmonic generation,” Opt. Lett. 31, 3471–3473 (2006). [CrossRef] [PubMed]
  11. Y. Tamaki, J. Itatani, Y. Nagata, M. Obara, K. Midorikawa, “Highly efficient, phase-matched high-harmonic generation by a self-guided laser beam,” Phys. Rev. Lett. 82, 1422–1426 (1999). [CrossRef]
  12. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995).
  13. A. Couairon, A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007). [CrossRef]
  14. J. Odhner, R. J. Levis, “Direct phase and amplitude characterization of femtosecond laser pulses undergoing filamentation in air,” Opt. Lett. 37, 1775–1777 (2012). [CrossRef] [PubMed]
  15. S. Minardi, A. Gopal, A. Couairon, G. Tamoašuskas, R. Piskarskas, A. Dubietis, P. Di Trapani, “Accurate retrieval of pulse-splitting dynamics of a femtosecond filament in water by time-resolved shadowgraphy,” Opt. Lett. 34, 3020–3022 (2009). [CrossRef] [PubMed]
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