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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 15 — Jul. 19, 2010
  • pp: 15467–15474
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Femtosecond multi-filamentation control by mixture of gases: towards synthesised nonlinearity

Benjamín Alonso, Amelle Zaïr, Julio San Román, Oscar Varela, and Luis Roso  »View Author Affiliations


Optics Express, Vol. 18, Issue 15, pp. 15467-15474 (2010)
http://dx.doi.org/10.1364/OE.18.015467


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Abstract

We have investigated femtosecond multi-filamentation process in a mixture of gases controlling the concentration of atoms versus molecules in the gas cell. The experimental results show that this control could provide a new freedom degree to deterministic spatial distribution control of the multiple filaments. Our simulation indicates surprisingly that only difference of the gases nonlinearity (referred to as “synthesised nonlinearity”) is sufficient to be responsible for this control. This study opens the way to provide few-cycle pulses spatial distributed source for spatially encoded measurements and experiments.

© 2010 Optical Society of America

1. Introduction

In filamentation experiments involving the propagation of high-power ultrashort laser pulses in transparent media, it is now well-known that when the input beam power exceeds several times the critical power for self-focusing (Pcr), the transverse spatial beam profile breaks up into multiple filaments (MF). For high input powers corresponding to hundred’s times Pcr, it has been demonstrated theoretically by Bespalov and Talanov [1

1. V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear media,” JETP Lett. 3, 307 (1966).

] that MF originate from initial random noise in the input beam profile. For input powers of few Pcr, commonly used now for post-compression of IR laser pulses [2–5

2. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense carrier-envelope phase-locked few-cycle laser pulses through filamentation,” App. Phys. B 79, 673–677 (2004). [CrossRef]

] and possibly extendible to mid-IR laser pulse [6

6. L. Bergé, “Self-compression of 2µ m laser filaments,” Opt. Express 16(26), 21529–21543 (2008). [CrossRef] [PubMed]

, 7

7. O. D. Mucke, S. Alisauskas, J. A. Verhoef, A. Pugzlys, A. Baltuska, V. Smilgevicius, J. Pocius, L. Giniunas, R. Danielius, and N. Forget, “Self-compression of millijoule 1.5µm pulses,” Opt. Lett. 34(16), 2498–2500 (2009). [PubMed]

], this initial random noise induces first a collaps as a single filament (SF) and after small propagation distance could break up into MF. In this regime the random noise induces only stochastic distribution of the transverse spatial beam profile that depends on each laser shot, minimising possible applications of such laser beam distribution. However, since many years, G. Fibich, B. Ilan and coworkers [8

8. G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamention in air,” Opt. Lett. 29(15), 1772 (2004). [CrossRef] [PubMed]

] as well as A. Couairon and co-workers [9

9. G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing Multiple Femtosecond Filaments in Air,” Phys. Rev. Lett. 93, 035003 (2004). [CrossRef] [PubMed]

] addressed the question of modelling the MF in a deterministic regime and demonstrated theoretically its origin as breakup of initial beam cylindrical symmetry resulting from vectorial effect. This can be achieved experimentally modifying the characteristics of the input beam using super gaussian and elliptical spatial profiles [10

10. A. Dubietis, G. Tamos̆auskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126 (2004). [CrossRef] [PubMed]

], circular polarisation [11–13

11. G. Fibich and B. Ilan, “Multiple Filamentation of Circularly Polarized Beams,” Phys. Rev. Lett. 89(1), 013901 (2002). [CrossRef] [PubMed]

], astigmatic beams [8

8. G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamention in air,” Opt. Lett. 29(15), 1772 (2004). [CrossRef] [PubMed]

] or amplitude and phase masks [14

14. T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Circular phase mask for control and stabilization of single optical filaments,” Opt. Lett. 31(15), 2326–2328 (2006). [CrossRef] [PubMed]

, 15

15. V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B 80(2), 267–275 (2005). [CrossRef]

]. In our recent work [13

13. O. Varela, A. Zaïr, J. San Roman, B. Alonso, I. J. Sola, C. Prieto, and L. Roso, “Above-millijoule supercontinuum generation using polarisation dependent filamentation in atoms and molecules,” Opt. Express 17(5), 3630–3639 (2009). [CrossRef] [PubMed]

] we notice in linear polarisation a clear difference between the atomic and the molecular MF transverse spatial distribution. To explain the spatial distribution difference observed, we proposed an initial hypothesis based on additionnal anisotropy in the molecular compared to the atomic response. To clarify this point and to investigate a new method for deterministic spatial MF control, we present in this article a study on the MF spatial distribution controlling the concentration of mixture of gases composed of atoms (Argon) and molecules (Nitrogen) with equivalent ionisation level (Ip) to undergo the same ionisation process, different nonlinear index (n 2(N 2) = 2.3 × 10−19 cm 2/W; n 2(Ar) = 1.74 × 10−19 cm 2/W) and ionisation cross section (at 800 nm and for multiphoton ionisation K=11, σ(N 2) = 6.31 × 10−140 s −1 cm 2K WK; σ(Ar) = 6.0 × 10−140 s −1 cm 2K WK [16–18

16. A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008). [CrossRef]

]) that lead to comparable electron density ρ. This choice will allow us to identify if the nonlinearity could be responsible for the different MF distribution observed [13

13. O. Varela, A. Zaïr, J. San Roman, B. Alonso, I. J. Sola, C. Prieto, and L. Roso, “Above-millijoule supercontinuum generation using polarisation dependent filamentation in atoms and molecules,” Opt. Express 17(5), 3630–3639 (2009). [CrossRef] [PubMed]

].

In this article we demonstrate a control on double femtosecond filamentation spatial distribution providing a new manner to control deterministic MF. The measurement of super continuum from pulses propagating through each filaments channel shows the capability of deterministic MF spatial distribution controlled by gas mixture to provide source of few-cycle pulses spatially distributed. Such source could be applied to spatially encoded measurements such as SEA-SPIDER [19–21

19. A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31(12), 1914–1916 (2006). [CrossRef] [PubMed]

] and its XUV version using High-order harmonic generation, XUV-SEA-SPIDER [22

22. E. Cormier, I. A. Walmsley, E. M. Kosik, A. S. Wyatt, L. Corner, and L. F. DiMauro, “Self-referencing, spectrally, or spatially encoded spectral interferometry for the complete characterization of attosecond electromagnetic pulses,” Phys. Rev, Lett. 94(3), 033905 (2005). [CrossRef]

]. This source will also be quite useful to explore new High-order harmonic schemes such as transient gratings [23

23. Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100(14), 143903 (2008). [CrossRef] [PubMed]

] or method for cut-off frequency extension using two few-cycle laser pulses of same colour [24

24. J. A. Perez-Hernandez, D. Hoffmann, A. Zaïr, L. E. Chipperfield, L. Plaja, C. Ruiz, J. P. Marangos, and L. Roso, “Extension of the cut-off in high-harmonic generation using two delayed pulses of the same colour,” J. Phys. At. Mol. Opt. Phys. 42, 13, 134004 (2009). [CrossRef]

].

2. Experiment and results

We defined for our experiment the concentration of gas mixture composed of argon atoms and nitrogen molecules as the ratio of atomic and molecular moles in the interaction volume. For its description we considered equation of state following the Van der Waals law for both gases species (Van derWaals constants specific of each gas are used). The Van derWaals equation can be analytically inverted thus obtaining the number of moles as a function of the gas pressure of each species used. Controlling the partial pressures of each gas in our set-up allowed to control the concentration of atom versus molecule applying the Dalton’s law for the total pressure definition. The Dalton’s law is used considering that in our experiment no pressure gradient has been used [25

25. A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Express 30(19), 2657–2659 (2005).

] but static pressure in the cell target so that the total pressure is uniform over the propagation length with local thermal equilibrium. We generate filaments using a few-mJ linearly polarised 35 fs IR pulses source at a repetition rate of 10 Hz from our laser system (Amplitude Inc.) that provides average power up to the TW level. The laser beam is focused with a spherical silver mirror (Radius of Curvature ROC -3000 mm) into a gas cell of 2 m long filled with the mixture of gases and the output beam is then collimated. A set of chirped mirrors is used to compress the output pulse over the large bandwidth generated through self-phase modulation along the filament. The gas cell is filled with a mixture of two gases species: argon (atomic) and nitrogen (molecular) at different partial pressures. The concentration of the gas mixture is gradually changed from 100 % nitrogen (gas target composed only of molecules) to 100% argon (gas target without molecules). For each measurement, the cell is filled at the partial pressures needed. During all the measurement the total pressure in the cell is maintained. The cell is then pumped in between each partial pressure setting. As a reference, we first generate a SF using an input energy of 4.8 mJ and a total pressure of 980 mbar in pure argon cell target. Then, by increasing the pressure in the cell up to 1400 mbar, we induce double filaments transverse spatial distribution in pure argon cell target. In both experiments, we study the spatial profile evolution with the gas concentration. We also measured the spectral distribution and the output energy in a spatially selected child-filament, as explained below, to check that a continuum was generated and to compare energy under each configuration for a given child-filament.

Fig. 1. Dependence of single filament (a) and multi-filament (b) spatial distribution with concentration of argon/nitrogen in the cell target. The single filament case is unchanged by the target concentration and is taken as reference in this experiment. The multi-filamentation distribution exhibits a clear dependence with the concentration of gas and highlight the possibility to use this new degree of freedom for controlling the deterministic position of the child-filaments produced.
Fig. 2. Spectral distribution for the single filament (a) and for one of the child-filament within the multifilament regime (b), as a function of the gas concentration.

3. Model and discussion

In our experiment we first checked that the rotation of the linearly polarised input pulse did not change the double filament orientation neither in argon nor in nitrogen. So any asymmetries depending on the polarisation (such as ionisation or ultra-fast molecular alignment) could not explain the change on the axis between the argon experiment and the nitrogen experiment. The experiment has been performed under same laser conditions (same pulse duration, same input laser beam profile). Our hypothesis to explain the observations consists of considering that the filamentation process begins at different propagation distances for the argon than for the nitrogen due to their different nonlinearity. As we are dealing with elliptic spatial beam profiles, the spatial profile along the propagation will change which could lead, depending on the starting point of the filamentation process for each gas, to different multi-filamentation patterns. To further understand this behaviour, we have implemented numerical simulations of the multi-filamentation nonlinear propagation using a elliptical profile for the input beam. In this model, we take into account the diffraction, the instantaneous and retarded Kerr effect in the molecular case, the plasma defocusing and the multi-photon absorption. Obviously, in our experiments the Raman effect (retarded Kerr) will be only present for the molecular gas, which enlarges the nonlinear differences between both gases. Since the propagation lacks cylindrical symmetry, we have used the temporally averaged model proposed by L. Bergé, S. Skupin and co-workers, shown below, where the temporal coordinate disappears simplifying a lot the computing time [27

27. L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple Filamentation of Terawatt Laser Pulses in Air,” Phys. Rev. Lett. 92, 225002 (2004). [CrossRef] [PubMed]

].

izψ+12k02ψ+αk0n2ψ2ψγψ2Kψ+iνψ2K1ψ=0
(1)

By looking at the distribution of the child-filaments over the propagation axis (scenario described in Media 1), we notice indeed that in the argon case the MF formation appears before the geometrical focus. The model shows in this case that almost five small filaments are generated in that early stage of the nonlinear propagation region. Further away the central filament disappears, and when reaching the end of the tube, after two meters of propagation [see Fig. 3(a)], two of the four filaments keeps almost all the energy, being these aligned parallel to the elliptical spatial distribution of the beam at the focus when it is propagated linearly. In the case of nitrogen, a different behaviour is observed: the MF formation occurs around the geometrical focus, where three filaments are generated, aligned perpendicular to the linear spatial distribution of the beam at the focus. After the propagation along the two meters cell the central filament disappears giving all its energy to the other two, which are the two filaments observed at the end of the cell [see Fig. 3(b)].

Fig. 3. (Media 1) Calculated dependence of multiple filaments spatial distribution in pure (concentration of 100 %) argon (a) and nitrogen (b)target at the output of the cell target (propagation over z=2 m). The multi-filamentation distribution exhibits a clear dependence with the gas species used. The following values have been taken for the simulation: K = 11, σK = 6.31 × 10−140 s −1 cm 22 W −11, n 2 = 2.3 × 1019 cm 2/W for N 2 and σK = 6.0 × 10−140 s −1 cm 22 W −11, n 2 = 1.74 × 1019 cm 2/W for Ar, τK = 70fs, ρ = 2.5 × 1019 cm −3, ρc = 1.8 × 1021 cm −3 [16–18].

4. Conclusion

In this work, we have studied for the first time to our knowledge the implication of gas mixture with equivalent ionisation level to control deterministic multi-filamentation formation. We demonstrate this control on double femtosecond filamentation spatial distribution providing a new method for the control of deterministic MF. Our simulation shows the implication of the synthesised nonlinearity in the control process and suggest that only a difference of nonlinear propagation between the two gases used, is necessary to induce such control. The synthesised nonlinearity obtained is not only of great interest for the multi-filamentation control but it also provides new types of medium with new nonlinearities that cannot be obtained in pure medium. The measurement of supercontinuum from pulses propagating through each child-filaments offers the possibility to use this new degree of freedom for providing source of few-cycle pulses spatially distributed, useful for sources characterisation from IR to XUV [19–22

19. A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31(12), 1914–1916 (2006). [CrossRef] [PubMed]

] and secondary sources for high-order harmonic generation [23

23. Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100(14), 143903 (2008). [CrossRef] [PubMed]

, 24

24. J. A. Perez-Hernandez, D. Hoffmann, A. Zaïr, L. E. Chipperfield, L. Plaja, C. Ruiz, J. P. Marangos, and L. Roso, “Extension of the cut-off in high-harmonic generation using two delayed pulses of the same colour,” J. Phys. At. Mol. Opt. Phys. 42, 13, 134004 (2009). [CrossRef]

].

Acknowledgements

We acknowledge support from Spanish Ministerio de Ciencia e Innovación through the Consolider Program SAUUL (CSD2007-00013), Research project FIS2009-09522 and from Junta de Castilla y León through the Program for Groups of Excellence (GR27). We also acknowledge support from the Centro de Laseres Pulsados, CLPU, Salamanca, Spain. The research work of Benjamin Alonso is supported by the MICINN through the Formación de Profesorado Universitario grant program. Dr. Amelle Zaïr thanks Dr. Roland Guichard, Dr. Stefan Skupin and Dr. Luis Plaja for fruitfull discussions.

References and links

1.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear media,” JETP Lett. 3, 307 (1966).

2.

C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense carrier-envelope phase-locked few-cycle laser pulses through filamentation,” App. Phys. B 79, 673–677 (2004). [CrossRef]

3.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, “5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis,” J. Phys. At. Mol. Opt. Phys.39S257–S264 (2006). [CrossRef]

4.

A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, U. Keller, A. Couairon, M. Franco, and A. Mysyrowicz, “Spatio-temporal characterization of few-cycle pulses obtained by filamentation,” Opt. Express 15(9), 5394–5404 (2007). [CrossRef] [PubMed]

5.

O. G. Kosareva, I. N. Murtazin, N. A. Panov, A. B. Savelev, V. P. Kandidov, and S. L. Chin, “Pulse shortening due to filamentation in transparent medium,” Laser Phys. Lett. 4(2), 126–132 (2006). [CrossRef]

6.

L. Bergé, “Self-compression of 2µ m laser filaments,” Opt. Express 16(26), 21529–21543 (2008). [CrossRef] [PubMed]

7.

O. D. Mucke, S. Alisauskas, J. A. Verhoef, A. Pugzlys, A. Baltuska, V. Smilgevicius, J. Pocius, L. Giniunas, R. Danielius, and N. Forget, “Self-compression of millijoule 1.5µm pulses,” Opt. Lett. 34(16), 2498–2500 (2009). [PubMed]

8.

G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamention in air,” Opt. Lett. 29(15), 1772 (2004). [CrossRef] [PubMed]

9.

G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing Multiple Femtosecond Filaments in Air,” Phys. Rev. Lett. 93, 035003 (2004). [CrossRef] [PubMed]

10.

A. Dubietis, G. Tamos̆auskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126 (2004). [CrossRef] [PubMed]

11.

G. Fibich and B. Ilan, “Multiple Filamentation of Circularly Polarized Beams,” Phys. Rev. Lett. 89(1), 013901 (2002). [CrossRef] [PubMed]

12.

A. Trisorio and C. P. Hauri, “Control and characterization of multiple circularly polarized femtosecond filaments in argon,” Opt. Lett. 32, 1650–1652 (2007). [CrossRef] [PubMed]

13.

O. Varela, A. Zaïr, J. San Roman, B. Alonso, I. J. Sola, C. Prieto, and L. Roso, “Above-millijoule supercontinuum generation using polarisation dependent filamentation in atoms and molecules,” Opt. Express 17(5), 3630–3639 (2009). [CrossRef] [PubMed]

14.

T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Circular phase mask for control and stabilization of single optical filaments,” Opt. Lett. 31(15), 2326–2328 (2006). [CrossRef] [PubMed]

15.

V. P. Kandidov, N. Akozbek, M. Scalora, O. G. Kosareva, A. V. Nyakk, Q. Luo, S. A. Hosseini, and S. L. Chin, “Towards a control of multiple filamentation by spatial regularization of a high-power femtosecond laser pulse,” Appl. Phys. B 80(2), 267–275 (2005). [CrossRef]

16.

A. Couairon, H. S. Chakraborty, and M. B. Gaarde, “From single-cycle self-compressed filaments to isolated attosecond pulses in noble gases,” Phys. Rev. A 77, 053814 (2008). [CrossRef]

17.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2–4), 47–189 (2007). [CrossRef]

18.

J. Wu, H. Cai, H. P. Zeng, and A. Couairon, “Femtosecond filamentation and pulse compression in the wake of molecular alignment more options,” Opt. Lett. 33(22), 2593–2595 (2008). [CrossRef] [PubMed]

19.

A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31(12), 1914–1916 (2006). [CrossRef] [PubMed]

20.

T. Witting, D. R. Austin, and I. A. Walmsley, “Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization,” Opt. Lett. 34(7), 881–883 (2009). [CrossRef] [PubMed]

21.

T. Witting, D. R. Austin, and I. A. Walmsley, “Ultrashort pulse characterization by spectral shearing interferometry with spatially chirped ancillae,” Opt. Express 17(21), 18983–18994 (2009). [CrossRef]

22.

E. Cormier, I. A. Walmsley, E. M. Kosik, A. S. Wyatt, L. Corner, and L. F. DiMauro, “Self-referencing, spectrally, or spatially encoded spectral interferometry for the complete characterization of attosecond electromagnetic pulses,” Phys. Rev, Lett. 94(3), 033905 (2005). [CrossRef]

23.

Y. Mairesse, D. Zeidler, N. Dudovich, M. Spanner, J. Levesque, D. M. Villeneuve, and P. B. Corkum, “High-order harmonic transient grating spectroscopy in a molecular jet,” Phys. Rev. Lett. 100(14), 143903 (2008). [CrossRef] [PubMed]

24.

J. A. Perez-Hernandez, D. Hoffmann, A. Zaïr, L. E. Chipperfield, L. Plaja, C. Ruiz, J. P. Marangos, and L. Roso, “Extension of the cut-off in high-harmonic generation using two delayed pulses of the same colour,” J. Phys. At. Mol. Opt. Phys. 42, 13, 134004 (2009). [CrossRef]

25.

A. Couairon, M. Franco, A. Mysyrowicz, J. Biegert, and U. Keller, “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Opt. Express 30(19), 2657–2659 (2005).

26.

C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998). [CrossRef]

27.

L. Berge, S. Skupin, F. Lederer, G. Mejean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple Filamentation of Terawatt Laser Pulses in Air,” Phys. Rev. Lett. 92, 225002 (2004). [CrossRef] [PubMed]

OCIS Codes
(020.0020) Atomic and molecular physics : Atomic and molecular physics
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: June 9, 2010
Revised Manuscript: June 14, 2010
Manuscript Accepted: June 16, 2010
Published: July 7, 2010

Citation
Benjamín Alonso, Amelle Zaïr, Julio San Román, Oscar Varela, and Luis Roso, "Femtosecond multi-filamentation control by mixture of gases: towards synthesised nonlinearity," Opt. Express 18, 15467-15474 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-15467


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References

  1. V. I. Bespalov, and V. I. Talanov, “Filamentary structure of light beams in nonlinear media,” JETP Lett. 3, 307 (1966).
  2. C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79, 673–677 (2004). [CrossRef]
  3. A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, “5.1 fs pulses generated by filamentation and carrier-envelope phase stability analysis,” J. Phys. At. Mol. Opt. Phys. 39, S257–S264 (2006). [CrossRef]
  4. A. Zaïr, A. Guandalini, F. Schapper, M. Holler, J. Biegert, L. Gallmann, U. Keller, A. Couairon, M. Franco, and A. Mysyrowicz, “Spatio-temporal characterization of few-cycle pulses obtained by filamentation,” Opt. Express 15(9), 5394–5404 (2007). [CrossRef] [PubMed]
  5. O. G. Kosareva, I. N. Murtazin, N. A. Panov, A. B. Savelev, V. P. Kandidov, and S. L. Chin, “Pulse shortening due to filamentation in transparent medium,” Laser Phys. Lett. 4(2), 126–132 (2006). [CrossRef]
  6. L. Bergé, “Self-compression of 2 μm laser filaments,” Opt. Express 16(26), 21529–21543 (2008). [CrossRef] [PubMed]
  7. O. D. Mucke, S. Alisauskas, J. A. Verhoef, A. Pugzlys, A. Baltuska, V. Smilgevicius, J. Pocius, L. Giniunas, R. Danielius, and N. Forget, “Self-compression of millijoule 1.5μm pulses,” Opt. Lett. 34(16), 2498–2500 (2009). [PubMed]
  8. G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29(15), 1772 (2004). [CrossRef] [PubMed]
  9. G. Méchain, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Organizing Multiple Femtosecond Filaments in Air,” Phys. Rev. Lett. 93, 035003 (2004). [CrossRef] [PubMed]
  10. A. Dubietis, G. Tamošauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126 (2004). [CrossRef] [PubMed]
  11. G. Fibich and B. Ilan, “Multiple Filamentation of Circularly Polarized Beams,” Phys. Rev. Lett. 89 (1), 013901 (2002). [CrossRef] [PubMed]
  12. A. Trisorio, and C. P. Hauri, “Control and characterization of multiple circularly polarized femtosecond filaments in argon,” Opt. Lett. 32, 1650–1652 (2007). [CrossRef] [PubMed]
  13. O. Varela, A. Zaïr, J. San Roman, B. Alonso, I. J. Sola, C. Prieto, and L. Roso, “Above-millijoule super-continuum generation using polarisation dependent filamentation in atoms and molecules,” Opt. Express 17(5), 3630–3639 (2009). [CrossRef] [PubMed]
  14. T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Circular phase mask for control and stabilization of single optical filaments,” Opt. Lett. 31(15), 2326–2328 (2006). [CrossRef] [PubMed]
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