Abstract

We studied white-light generation in water using spatially- structured beams of femtosecond radiation. By changing the transverse spatial phase of an initial Gaussian beam with a 1D spatial light modulator to that of an Hermite-Gaussian (HGn,m) mode, we were able to generate beams exhibiting phase discontinuities and steeper intensity gradients. When the spatial phase of an initial Gaussian beam (showing no significant white-light generation) was changed to that of a HG01, or HG11 mode, significant amounts of white-light were produced. Because self-focusing is known to play an important role in white-light generation, the self-focusing lengths of the resulting transverse intensity profiles were used to qualitatively explain this production. Distributions of the laser intensity for beams having step-wise spatial phase variations were modeled using the Fresnel-Kirchhoff integral in the Fresnel approximation and found to be in good agreement with experiment.

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    [CrossRef]

2011 (1)

2007 (1)

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

2005 (2)

K. Cook, R. McGeorge, A. K. Kar, M. R. Taghizadeh, and R. A. Lamb, “Coherent array of white-light continuum filaments produced by diffractive microlenses,” Appl. Phys. Lett. 86(2), 021105 (2005).
[CrossRef]

A. Dharmadhikari, F. Rajgara, D. Mathur, H. Schroeder, and J. Liu, “Efficient broadband emission from condensed media irradiated by low-intensity, unfocused, ultrashort laser light,” Opt. Express 13(21), 8555–8564 (2005).
[CrossRef] [PubMed]

2004 (3)

2001 (1)

T. Kobayashi, T. Saito, and H. Ohtani, “Real-time spectroscopy of transition states in bacteriorhodopsin during retinal isomerization,” Nature 414(6863), 531–534 (2001).
[CrossRef] [PubMed]

2000 (2)

S. Cussat-Blanc, A. Ivanov, D. Lupinski, and E. Freysz, “KTiOPO4, KTiOAsO4, and KNbO3 crystals for mid-infrared femtosecond optical parametric amplifiers: analysis and comparison,” Appl. Phys. B 70(S1), S247–S252 (2000).
[CrossRef]

T. Kobayashi and A. Shirakawa, “Tunable visible and near-infrared pulse generator in a 5 fs regime,” Appl. Phys. B 70(S1), S239–S246 (2000).
[CrossRef]

1999 (1)

1998 (1)

A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white light continuum,” Phys. Rev. Lett. 80(20), 4406–4409 (1998).
[CrossRef]

1997 (1)

1996 (3)

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]

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

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of Pulse Splitting in Nonlinear Dispersive Media,” Phys. Rev. Lett. 77(18), 3783–3786 (1996).
[CrossRef] [PubMed]

1995 (1)

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, “Laser-induced band-gap collapse in GaAs,” Phys. Rev. B Condens. Matter 51(11), 6959–6970 (1995).
[CrossRef] [PubMed]

1993 (3)

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

1989 (1)

P. B. Corkum and C. Rolland, “Femtosecond continua produced in gases,” IEEE J. Quantum Electron. 25(12), 2634–2639 (1989).
[CrossRef]

1986 (2)

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

J. H. Glownia, J. Misewich, and P. P. Sorokin, “Ultrafast ultraviolet pump-probe apparatus,” J. Opt. Soc. Am. B 3(11), 1573–1579 (1986).
[CrossRef]

1984 (1)

1983 (1)

1977 (1)

W. Lee Smith, P. Liu, and N. Bloembergen, “Superbroadening in H2O and D2O by self-focused picosecond pulses from a YAlG: Nd laser,” Phys. Rev. A 15(6), 2396–2403 (1977).
[CrossRef]

1975 (1)

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

1973 (1)

N. Bloembergen, “The influence of electron plasma formation on superbroadening in light filaments,” Opt. Commun. 8(4), 285–288 (1973).
[CrossRef]

1970 (1)

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Bloembergen, N.

W. Lee Smith, P. Liu, and N. Bloembergen, “Superbroadening in H2O and D2O by self-focused picosecond pulses from a YAlG: Nd laser,” Phys. Rev. A 15(6), 2396–2403 (1977).
[CrossRef]

N. Bloembergen, “The influence of electron plasma formation on superbroadening in light filaments,” Opt. Commun. 8(4), 285–288 (1973).
[CrossRef]

Brodeur, A.

A. Brodeur and S. L. Chin, “Ultrafast white-light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16(4), 637–650 (1999).
[CrossRef]

A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white light continuum,” Phys. Rev. Lett. 80(20), 4406–4409 (1998).
[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]

Chen, Y.

Chin, S.

Chin, S. L.

A. Brodeur and S. L. Chin, “Ultrafast white-light continuum generation and self-focusing in transparent condensed media,” J. Opt. Soc. Am. B 16(4), 637–650 (1999).
[CrossRef]

A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white light continuum,” Phys. Rev. Lett. 80(20), 4406–4409 (1998).
[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]

V. François, F. A. Ilkov, and S. L. Chin, “Experimental study of the supercontinuum spectral width evolution in CO2 gas,” Opt. Commun. 99(3-4), 241–246 (1993).
[CrossRef]

F. A. Ilkov, L. Sh. Ilkova, and S. L. Chin, “Supercontinuum generation versus optical breakdown in CO(2) gas,” Opt. Lett. 18(9), 681–683 (1993).
[CrossRef] [PubMed]

Cook, K.

K. Cook, R. McGeorge, A. K. Kar, M. R. Taghizadeh, and R. A. Lamb, “Coherent array of white-light continuum filaments produced by diffractive microlenses,” Appl. Phys. Lett. 86(2), 021105 (2005).
[CrossRef]

Corkum, P. B.

P. B. Corkum and C. Rolland, “Femtosecond continua produced in gases,” IEEE J. Quantum Electron. 25(12), 2634–2639 (1989).
[CrossRef]

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

Couairon, A.

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

Cui, Y.

Cussat-Blanc, S.

S. Cussat-Blanc, A. Ivanov, D. Lupinski, and E. Freysz, “KTiOPO4, KTiOAsO4, and KNbO3 crystals for mid-infrared femtosecond optical parametric amplifiers: analysis and comparison,” Appl. Phys. B 70(S1), S247–S252 (2000).
[CrossRef]

de Matos, C. J. S.

Dharmadhikari, A.

Fork, R. L.

François, V.

V. François, F. A. Ilkov, and S. L. Chin, “Experimental study of the supercontinuum spectral width evolution in CO2 gas,” Opt. Commun. 99(3-4), 241–246 (1993).
[CrossRef]

Freysz, E.

E. Hugonnot, M. Somekh, D. Villate, F. Salin, and E. Freysz, “Optical parametric chirped pulse amplification and spectral shaping of a continuum generated in a photonic band gap fiber,” Opt. Express 12(11), 2397–2403 (2004).
[CrossRef] [PubMed]

S. Cussat-Blanc, A. Ivanov, D. Lupinski, and E. Freysz, “KTiOPO4, KTiOAsO4, and KNbO3 crystals for mid-infrared femtosecond optical parametric amplifiers: analysis and comparison,” Appl. Phys. B 70(S1), S247–S252 (2000).
[CrossRef]

Fujimoto, J. G.

Gaeta, A. L.

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of Pulse Splitting in Nonlinear Dispersive Media,” Phys. Rev. Lett. 77(18), 3783–3786 (1996).
[CrossRef] [PubMed]

Gapontsev, V. P.

Glezer, E. N.

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, “Laser-induced band-gap collapse in GaAs,” Phys. Rev. B Condens. Matter 51(11), 6959–6970 (1995).
[CrossRef] [PubMed]

Glownia, J. H.

Hart, N.

He, G. S.

Hirlimann, C.

Hsiung, P.-L.

Huang, L.

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, “Laser-induced band-gap collapse in GaAs,” Phys. Rev. B Condens. Matter 51(11), 6959–6970 (1995).
[CrossRef] [PubMed]

Hugonnot, E.

Ilkov, F. A.

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]

V. François, F. A. Ilkov, and S. L. Chin, “Experimental study of the supercontinuum spectral width evolution in CO2 gas,” Opt. Commun. 99(3-4), 241–246 (1993).
[CrossRef]

F. A. Ilkov, L. Sh. Ilkova, and S. L. Chin, “Supercontinuum generation versus optical breakdown in CO(2) gas,” Opt. Lett. 18(9), 681–683 (1993).
[CrossRef] [PubMed]

Ilkova, L. Sh.

Ivanov, A.

S. Cussat-Blanc, A. Ivanov, D. Lupinski, and E. Freysz, “KTiOPO4, KTiOAsO4, and KNbO3 crystals for mid-infrared femtosecond optical parametric amplifiers: analysis and comparison,” Appl. Phys. B 70(S1), S247–S252 (2000).
[CrossRef]

Kar, A. K.

K. Cook, R. McGeorge, A. K. Kar, M. R. Taghizadeh, and R. A. Lamb, “Coherent array of white-light continuum filaments produced by diffractive microlenses,” Appl. Phys. Lett. 86(2), 021105 (2005).
[CrossRef]

Kaya, G.

Kaya, N.

Ko, T. H.

Kobayashi, T.

T. Kobayashi, T. Saito, and H. Ohtani, “Real-time spectroscopy of transition states in bacteriorhodopsin during retinal isomerization,” Nature 414(6863), 531–534 (2001).
[CrossRef] [PubMed]

T. Kobayashi and A. Shirakawa, “Tunable visible and near-infrared pulse generator in a 5 fs regime,” Appl. Phys. B 70(S1), S239–S246 (2000).
[CrossRef]

Kolomenskii, A. A.

Lamb, R. A.

K. Cook, R. McGeorge, A. K. Kar, M. R. Taghizadeh, and R. A. Lamb, “Coherent array of white-light continuum filaments produced by diffractive microlenses,” Appl. Phys. Lett. 86(2), 021105 (2005).
[CrossRef]

Lee Smith, W.

W. Lee Smith, P. Liu, and N. Bloembergen, “Superbroadening in H2O and D2O by self-focused picosecond pulses from a YAlG: Nd laser,” Phys. Rev. A 15(6), 2396–2403 (1977).
[CrossRef]

Liu, J.

Liu, P.

W. Lee Smith, P. Liu, and N. Bloembergen, “Superbroadening in H2O and D2O by self-focused picosecond pulses from a YAlG: Nd laser,” Phys. Rev. A 15(6), 2396–2403 (1977).
[CrossRef]

Lupinski, D.

S. Cussat-Blanc, A. Ivanov, D. Lupinski, and E. Freysz, “KTiOPO4, KTiOAsO4, and KNbO3 crystals for mid-infrared femtosecond optical parametric amplifiers: analysis and comparison,” Appl. Phys. B 70(S1), S247–S252 (2000).
[CrossRef]

Marburger, J. H.

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

Mathur, D.

Mazur, E.

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, “Laser-induced band-gap collapse in GaAs,” Phys. Rev. B Condens. Matter 51(11), 6959–6970 (1995).
[CrossRef] [PubMed]

McGeorge, R.

K. Cook, R. McGeorge, A. K. Kar, M. R. Taghizadeh, and R. A. Lamb, “Coherent array of white-light continuum filaments produced by diffractive microlenses,” Appl. Phys. Lett. 86(2), 021105 (2005).
[CrossRef]

Misewich, J.

Mysyrowicz, A.

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

Ohtani, H.

T. Kobayashi, T. Saito, and H. Ohtani, “Real-time spectroscopy of transition states in bacteriorhodopsin during retinal isomerization,” Nature 414(6863), 531–534 (2001).
[CrossRef] [PubMed]

Paulus, G. G.

Penzkofer, A.

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

Popov, S. V.

Prasad, P. N.

Rajgara, F.

Ranka, J. K.

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of Pulse Splitting in Nonlinear Dispersive Media,” Phys. Rev. Lett. 77(18), 3783–3786 (1996).
[CrossRef] [PubMed]

Rolland, C.

P. B. Corkum and C. Rolland, “Femtosecond continua produced in gases,” IEEE J. Quantum Electron. 25(12), 2634–2639 (1989).
[CrossRef]

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

Saito, T.

T. Kobayashi, T. Saito, and H. Ohtani, “Real-time spectroscopy of transition states in bacteriorhodopsin during retinal isomerization,” Nature 414(6863), 531–534 (2001).
[CrossRef] [PubMed]

Salin, F.

Schirmer, R. W.

J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, “Observation of Pulse Splitting in Nonlinear Dispersive Media,” Phys. Rev. Lett. 77(18), 3783–3786 (1996).
[CrossRef] [PubMed]

Schroeder, H.

Schuessler, H. A.

Shank, C. V.

Shapiro, S. L.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[CrossRef]

Shen, Y. R.

Shirakawa, A.

T. Kobayashi and A. Shirakawa, “Tunable visible and near-infrared pulse generator in a 5 fs regime,” Appl. Phys. B 70(S1), S239–S246 (2000).
[CrossRef]

Siegal, Y.

E. N. Glezer, Y. Siegal, L. Huang, and E. Mazur, “Laser-induced band-gap collapse in GaAs,” Phys. Rev. B Condens. Matter 51(11), 6959–6970 (1995).
[CrossRef] [PubMed]

Somekh, M.

Sorokin, P. P.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Srinivasan-Rao, T.

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

Strohaber, J.

Taghizadeh, M. R.

K. Cook, R. McGeorge, A. K. Kar, M. R. Taghizadeh, and R. A. Lamb, “Coherent array of white-light continuum filaments produced by diffractive microlenses,” Appl. Phys. Lett. 86(2), 021105 (2005).
[CrossRef]

Taylor, J. R.

Tomlinson, W. J.

Villate, D.

Wilson, K. R.

Wittmann, M.

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

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Xu, G. C.

Yakovlev, V. V.

Yang, G.

Yen, R.

Appl. Opt. (1)

Appl. Phys. B (2)

S. Cussat-Blanc, A. Ivanov, D. Lupinski, and E. Freysz, “KTiOPO4, KTiOAsO4, and KNbO3 crystals for mid-infrared femtosecond optical parametric amplifiers: analysis and comparison,” Appl. Phys. B 70(S1), S247–S252 (2000).
[CrossRef]

T. Kobayashi and A. Shirakawa, “Tunable visible and near-infrared pulse generator in a 5 fs regime,” Appl. Phys. B 70(S1), S239–S246 (2000).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup to generate HG modes with the 1D SLM and for studies of white-light generation of HG beams in water. Laser radiation from the Ti:sapphire laser enters the setup from the left. Blue arrows (E) show the initial polarization of the beam and the changes of this polarization after the passage of the periscope P1 and a (λ/2) wave plate (WP). Other optical components used: P2-periscope to adjust the beam height, SLM - spatial light modulator, FM - folding mirror. Notice that in P1 the mirrors are rotated relative to each other in the horizontal plane by 90°, while in P2 the mirrors are parallel. The incident HG beam enters a 40mm long cuvette (C). A CCD camera for taking images is first placed at position 1 on the entrance of the cuvette to record the generated HG beam. Then the camera is placed at position 2 to record the generated white light on a frosted paper screen (FP) after the radiation of the pump beam is reflected by an 800nm dielectric mirror (DM). The colored picture of HG11 taken by a color digital camera at position 2 shows the strong white cores with colorful rings (conical emission) in the lower right inset. (a), (b), (c), and (d) present grey-scale encoded phase masks to create HG00, HG01, HG10 and HG11 beams, respectively.

Fig. 2
Fig. 2

The measured distributions of the laser intensity in the HG00, HG01, HG10 and HG11 beams. Each laser distribution has been peak normalized. HG beams in panels (a d) are created with the phase masks (a d) as shown in the inset of Fig. 1.

Fig. 3
Fig. 3

The normalized distributions of the laser intensity in the cases of HG00, HG01, HG10 and HG11 beams calculated by the integrals with appropriate phase factors (Eqs. (5,6)).

Fig. 4
Fig. 4

The measured white-light intensity distributions on the CCD for all HG modes generated at the fixed geometry. Intensities are normalized respect to max white-light generation peak in HG11.

Fig. 5
Fig. 5

The top view of the experimentally measured distributions of the laser intensity for the HG00, HG01, HG10 and HG11 beams from panels (a d) of Fig. 2. The intensity lobes used for the calculation of the critical power and self-focusing distance of HG beams (main lobes) are shown with black solid circles in panels (a d), drawn at FWHM values of the peak intensity; the dotted lines show the same for other peaks in the intensity distributions.

Equations (6)

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P crit =3.77 λ 0 2 8π n 0 n 2
L sf = 0.734π n 0 a 0 2 λ 0 [ ( P/ P crit 0.852 ) 2 0.0219 ] 1/2
E n x , m y (x,y,z)= ( 1 2 n x + m y π n x ! m y ! ) 1/2 1 w z × H n x ( 2 x w z ) H m y ( 2 y w z ) e ( r 2 / w z 2 ) ×expi[ k r 2 2 R z ( n x + m y +1) ϕ G (z)+kz ].
E(x,y,z=d) i e ikd e i k 2d ( x 2 + y 2 ) λd aperture E(x',y',z=0) e i k 2d ( x 2 + y 2 ) e i k d (xx'+yy') dx'dy'
E(x,y,z=d) i e ikd e i k 2d ( x 2 + y 2 ) λd E 0 e x 2 + y 2 w o 2 e i k 2d ( x 2 + y 2 ) e i k d (xx'+yy') e iφ( x , y ) dx'dy' .
φ( x )={ π< x <0 00< x < and φ( y )={ 0< y <0 π0< y < .

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