Abstract

We investigated the variations in generated white-light when crossing two femtosecond laser beams in a Kerr medium. By changing the relative delay of two interacting intense femtosecond laser pulses, we show that white-light generation can be enhanced or suppressed. With a decrease of the relative delay an enhancement of the white-light output was observed, which at even smaller delays was reverted to a suppression of white-light generation. Under choosen conditions, the level of suppression resulted in a white-light output lower than the initial level corresponding to large delays, when the pulses do not overlap in time. The enhancement of the white-light generation takes place in the pulse that is lagging. We found that the effect of the interaction of the beams depends on their relative orientation of polarization and increases when the polarizations are changed from perpendicular to parallel. The observed effects are explained by noting that at intermediate delays, the perturbations introduced in the path of the lagging beam lead to a shortening of the length of filament formation and enhancement of the white-light generation, whereas at small delays the stronger interaction and mutual rescattering reduces the intensity in the central part of the beams, suppressing filamentation and white-light generation.

© 2016 Optical Society of America

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References

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2014 (1)

Y. B. Deng, X. Q. Fu, C. Tan, H. Yang, S. G. Deng, C. X. Xiong, and G. F. Zhang, “Experimental investigation of spatiotemporal evolution of femtosecond laser pulses during small-scale self-focusing,” Appl. Phys. B 114(3), 449–454 (2014).
[Crossref]

2012 (4)

2010 (1)

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

2009 (2)

J. Darginavičius, G. Tamošauskas, G. Valiulis, and A. Dubietis, “Broadband four-wave optical parametric amplification in bulk isotropic media in the ultraviolet,” Opt. Commun. 282(14), 2995–2999 (2009).
[Crossref]

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett. 102(12), 123902 (2009).
[Crossref] [PubMed]

2008 (2)

L. M. Sanchez-Brea and F. J. Salgado-Remacha, “Three-dimensional diffraction of a thin metallic cylinder illuminated in conical incidence: application to diameter estimation,” Appl. Opt. 47(26), 4804–4811 (2008).
[Crossref] [PubMed]

A. Dubietis, G. Tamošauskas, G. Valiulis, and A. Piskarskas, “Ultrafast four-wave optical parametric amplification in transparent condensed bulk media,” Laser Chem. 9, 534951 (2008).

2007 (3)

2006 (2)

2005 (1)

Q. Yang, J. T. Seo, B. Tabibi, and H. Wang, “Slow light and superluminality in Kerr media without a pump,” Phys. Rev. Lett. 95(6), 063902 (2005).
[Crossref] [PubMed]

2004 (4)

H. Schroeder, J. Liu, and S. Chin, “From random to controlled small-scale filamentation in water,” Opt. Express 12(20), 4768–4774 (2004).
[Crossref] [PubMed]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, 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(22), 225002 (2004).
[Crossref] [PubMed]

H. Schroeder and S. L. Chin, “Visualization of the evolution of multiple filaments in methanol,” Opt. Commun. 234(1-6), 399–406 (2004).
[Crossref]

R. Nakamura and Y. Kanematsu, “Femtosecond spectral snapshots based on electronic optical Kerr effect,” Rev. Sci. Instrum. 75(3), 636–644 (2004).
[Crossref]

2003 (1)

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media (or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

2002 (2)

J. M. Harbold, F. O. Ilday, F. W. Wise, and B. G. Aitken, “Highly nonlinear Ge-As-Se and Ge-As-S-Se glasses for all-optical switching,” IEEE Photonics Technol. Lett. 14(6), 822–824 (2002).
[Crossref]

S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19(4), 753–764 (2002).
[Crossref]

2001 (1)

L. M. Sanchez-Brea and E. Bernabeu, “Diffraction by cylinders illuminated in oblique, off-axis incidence,” Optik 112(4), 169–174 (2001).
[Crossref]

2000 (2)

1999 (1)

1997 (2)

1996 (3)

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21(1), 62–65 (1996).
[Crossref] [PubMed]

M. Wittmann and A. Penzkofer, “Spectral superbroadening of femtosecond laser pulses,” Opt. Commun. 126(4-6), 308–317 (1996).
[Crossref]

A. Brodeur, F. A. Ilkov, and S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129(3-4), 193–198 (1996).
[Crossref]

1995 (1)

V. K. Tikhomirov and S. R. Elliott, “The anisotropic photorefractive effect in bulk As2S3 glass induced by polarized subgap laser light,” J. Phys. Condens. Matter 7(8), 1737–1747 (1995).
[Crossref]

1993 (2)

1992 (1)

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4(4), 362–365 (1992).
[Crossref]

1986 (2)

C. V. Shank, “Investigation of ultrafast phenomena in the femtosecond time domain,” Science 233(4770), 1276–1280 (1986).
[Crossref] [PubMed]

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57(18), 2268–2271 (1986).
[Crossref] [PubMed]

1984 (2)

1982 (1)

Y. Silberberg and I. Bar-Joseph, “Instabilities, self-oscillation and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48(22), 1541–1543 (1982).
[Crossref]

1975 (4)

Y. R. Shen, “Self-focusing: experimental,” Prog. Quantum Electron. 4, 1–34 (1975).
[Crossref]

J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
[Crossref]

A. Penzkofer, A. Seilmeier, and W. Kaiser, “Parametric four-photon generation of picosecond light at high conversion efficiency,” Opt. Commun. 14(3), 363–367 (1975).
[Crossref]

J. H. Marburger, “Self-focusing: theory,” Prog. Quantum Electron. 4, 35–110 (1975).
[Crossref]

1973 (1)

J. Reintjes, R. L. Carman, and F. Shimizu, “Study of self-focusing and self-phase-modulation in the picosecond-time regime,” Phys. Rev. A 8(3), 1486–1503 (1973).
[Crossref]

1971 (1)

1970 (1)

R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970).
[Crossref]

1967 (2)

F. Shimizu, “Frequency broadening in liquids by a short light pulse,” Phys. Rev. Lett. 19(19), 1097–1100 (1967).
[Crossref]

F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley, “Self-steepening of light pulses,” Phys. Rev. 164(2), 312–323 (1967).
[Crossref]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

Aber, J. E.

Aggarwal, I. D.

Aitken, B. G.

J. M. Harbold, F. O. Ilday, F. W. Wise, and B. G. Aitken, “Highly nonlinear Ge-As-Se and Ge-As-S-Se glasses for all-optical switching,” IEEE Photonics Technol. Lett. 14(6), 822–824 (2002).
[Crossref]

Akozbek, N.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media (or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, “Observation of self-phase modulation and small-scale filaments in crystals and glasses,” Phys. Rev. Lett. 24(11), 592–594 (1970).
[Crossref]

Asobe, M.

M. Asobe, T. Kanamori, and K. Kubodera, “Ultrafast all-optical switching using highly nonlinear chalcogenide glass fiber,” IEEE Photonics Technol. Lett. 4(4), 362–365 (1992).
[Crossref]

Bar-Joseph, I.

Y. Silberberg and I. Bar-Joseph, “Optical instabilities in a nonlinear Kerr medium,” J. Opt. Soc. Am. B 1(4), 662–670 (1984).
[Crossref]

Y. Silberberg and I. Bar-Joseph, “Instabilities, self-oscillation and chaos in a simple nonlinear optical interaction,” Phys. Rev. Lett. 48(22), 1541–1543 (1982).
[Crossref]

Becker, A.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media (or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

Bergé, L.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, 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(22), 225002 (2004).
[Crossref] [PubMed]

Bernabeu, E.

L. M. Sanchez-Brea and E. Bernabeu, “Diffraction by cylinders illuminated in oblique, off-axis incidence,” Optik 112(4), 169–174 (2001).
[Crossref]

Bernstein, A. C.

A. C. Bernstein, M. McCormick, G. M. Dyer, J. C. Sanders, and T. Ditmire, “Two-beam coupling between filament-forming beams in air,” Phys. Rev. Lett. 102(12), 123902 (2009).
[Crossref] [PubMed]

Bourayou, R.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, 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(22), 225002 (2004).
[Crossref] [PubMed]

Bowden, C. M.

V. P. Kandidov, O. G. Kosareva, I. S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C. M. Bowden, and S. L. Chin, “Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media (or supercontinuum generation),” Appl. Phys. B 77(2-3), 149–165 (2003).
[Crossref]

Brodeur, A.

A. Brodeur, C. Y. Chien, F. A. Ilkov, S. L. Chin, O. G. Kosareva, and V. P. Kandidov, “Moving focus in the propagation of ultrashort laser pulses in air,” Opt. Lett. 22(5), 304–306 (1997).
[Crossref] [PubMed]

A. Brodeur, F. A. Ilkov, and S. L. Chin, “Beam filamentation and the white light continuum divergence,” Opt. Commun. 129(3-4), 193–198 (1996).
[Crossref]

Carman, R. L.

J. Reintjes, R. L. Carman, and F. Shimizu, “Study of self-focusing and self-phase-modulation in the picosecond-time regime,” Phys. Rev. A 8(3), 1486–1503 (1973).
[Crossref]

Chau, A. H. L.

Chen, F.

T. Chen, J.-H. Si, X. Liu, F. Chen, and X. Hou, “The influence of coherent transient energy transfer on femtosecond time-resolved Z-scan measurements,” Chin. Phys. Lett. 29(10), 104211 (2012).
[Crossref]

Chen, S.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[Crossref] [PubMed]

Chen, T.

T. Chen, J.-H. Si, X. Liu, F. Chen, and X. Hou, “The influence of coherent transient energy transfer on femtosecond time-resolved Z-scan measurements,” Chin. Phys. Lett. 29(10), 104211 (2012).
[Crossref]

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M. Wittmann and A. Penzkofer, “Spectral superbroadening of femtosecond laser pulses,” Opt. Commun. 126(4-6), 308–317 (1996).
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Figures (10)

Fig. 1
Fig. 1

Experimental setup: the delay between pulses in two optical arms is changed with a translation stage. Shown are: CM -curved mirror, BS - beam splitter, TS - translation stage, M1- M6 fast silver mirrors, DM - dielectric mirror. The first incoming mirror (CM) is curved with the focal length 2.5 m. The dielectric mirror (DM, its measured reflection, R and transmission, T are shown in the graph on the right) separates as shown in the insets an IR radiation around 800 nm and the generated white-light, which were measured by a power meter or imaged on a CCD camera at various delays between the optical paths in two arms.

Fig. 2
Fig. 2

Images of beam cross-sections with filaments taken at 6.6 fs intervals of the time delay between the two arms increasing from top to bottom and from left to right: left panel shows the whole series of images; the right panel shows a magnified view of the area in the red rectangle, where light produced by separate filaments can be discerned. In each box the upper colored light spot shows filaments in the movable arm and the lower spot corresponds to the fixed arm.

Fig. 3
Fig. 3

Variations of the white-light vs. relative delay of two beams: the upper trace (blue) is the total amount of white light measured in both arms, the black trace is the power measured in the fixed arm, and the red trace is the power measured in the movable arm.

Fig. 4
Fig. 4

Spectral observation of white-light enhancement and suppression: the upper graph shows in false colors a plot of the spectral distribution of the two beams in the range 400-700 nm after their interaction in the sample as a function of the relative delay; the lower graph depicts the total (integrated) amount of white light vs. delay. An enhancement of the spectral components at small negative (from −80fs to −30 fs) and small positive (from 30fs to 80fs) delays and a strong suppression of the spectrum in the vicinity of zero delay can be clearly seen, which result also in the respective variations of the integrated white-light (lower graph).

Fig. 5
Fig. 5

Variations of the IR beams during the interaction: left top panel shows the dependence of the beam power vs. delay in fixed (red), movable (green) and in a larger area around movable arm (blue); the curves shifted up for better viewing; the power was measured in the respective circled areas (right top panel) showing the cross sections of beams on the CCD camera in the movable arm (top) and in the fixed arm (bottom) at zero delay, where arc-shaped wings of the intensity distribution are clearly visible. The bottom panel shows images of the beam cross sections taken at: large delays (−300fs) and 300fs (1 and 5), delays corresponding to maximal white-light output ~(−100fs) and ~100fs (2, 4) and zero delay (3). The starting points of arrows indicate respective delays on the time scale.

Fig. 6
Fig. 6

The dependence of the IR power on delay and images of the IR beams with the central parts blocked taken at: large delays (1, 5), at delays corresponding to maximal white-light output (2, 4) and zero delay (3). The starting points of arrows indicate respective delays on the time scale.

Fig. 7
Fig. 7

Variations of the IR radiation in the central spot of the fixed arm for different angles between polarizations of the beams in the two arms. The plots are shifted vertically for better viewing.

Fig. 8
Fig. 8

Results on white-light suppression at different angles: (a). The total amount of white light of both beams measured vs. delay at the crossing angle of 1.1 deg is shown. The quantities used in Eq. (1) are also shown. (b). The dependence of the relative suppression, ξ , of the white-light generation on the angle. The solid line connecting data points is a guide for the eye.

Fig. 9
Fig. 9

The calculated intensity distribution of two crossing beams in the yz-plane for crossing angles θ = 0.66 (a), θ = 0.99 () and θ = 1.27 (c).

Fig. 10
Fig. 10

Wave-vector diagram showing four-wave interaction: k 1,2- pump pulses, k’ 1,2-amplified waves; the circle is perpendicular to the symmetry axis OO’, the ends of all vectors of equal length satisfying phase matching conditions for four-wave interaction lie on a circle.

Equations (2)

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ξ = ( P 0 P m i n ) / P 0 ,
( I ( x , y ) / I 0 ) = |c τ ( 2 π 1 / 2 z ) 1 0 d k ( k exp [ ( k k 0 ) 2 c 2 τ 2 / 4 ] d y ' d x ' exp [ i k ( ( x x ' ) 2 + ( y y ' ) 2 ) / ( 2 z ) ] × × { exp [ ( x ' 2 + ( r y ' ) 2 ) ( 1 / a 2 i k / ( 2 f ) ) + i k ( ( r y ' ) sin ( θ / 2 ) + z cos ( θ / 2 ) ) ] + exp [ ( x ' 2 + ( r + y ' ) 2 ) ( 1 / a 2 i k / ( 2 f ) ) + i k ( ( r + y ' ) sin ( θ / 2 ) + z cos ( θ / 2 ) ) ] } | 2 ,

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