Abstract

Spatial shaping of ultrashort laser beams at the focal plane is theoretically analyzed. The description of the pulse is performed by its expansion in terms of Laguerre-Gaussian orthonormal modes. This procedure gives both a comprehensive interpretation of the propagation dynamics and the required signal to encode onto a spatial light modulator for spatial shaping, without using iterative algorithms. As an example, pulses with top-hat and annular spatial profiles are designed and their dynamics analyzed. The interference of top-hat pulses is also investigated finding potential applications in high precision pump-probe experiments (without using delay lines) and for the creation of subwavelength ablation patterns. In addition, a novel class of ultrashort pulses possessing non-stationary orbital angular momentum is also proposed. These exotic pulses provide additional degrees of freedom that open up new perspectives in fields such as laser-matter interaction and micro-machining.

© 2013 OSA

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2013 (2)

R. J. Mahon and J. A. Murphy, “Diffraction of an optical pulse as an expansion in ultrashort orthogonal Gaussian beam modes,” J. Op. Soc. Am. A30, 215–226 (2013).
[CrossRef]

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett.110, 143603 (2013).
[CrossRef]

2012 (4)

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev.6, 607–621 (2012).
[CrossRef]

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mével, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B: At. Mol. Opt. Phys.45, 074018 (2012).
[CrossRef]

V. Loriot, O. Mendoza-Yero, G. Mínguez-Vega, L. Bañares, and R. de Nalda, “Experimental demonstration of the quasy-direct space-to-time pulse shaping principle,” IEEE Photon. Technol. Lett.24, 273–275 (2012).
[CrossRef]

C. T. Schmiegelow and F. Schmidt-Kaler, “Light with orbital angular momentum interacting with trapped ions,” Eur. Phys. J. D66, 157 (2012).
[CrossRef]

2011 (2)

2010 (12)

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spacio-temporal couplings in ultrashort laser pulses,” J. Opt.12, 093001 (2010).
[CrossRef]

Y.-D. Liu and C. Gao, “Study on the time-varying and propagating characteristics of ultrashort pulse Laguerre-Gaussian beam,” Opt. Express18, 12104–12110 (2010).
[CrossRef] [PubMed]

Ó. Martínez-Matos, J. A. Rodrigo, M. P. Hernández-Garay, J. G. Izquierdo, R. Weigand, M. L. Calvo, P. Cheben, P. Vaveliuk, and L. Bañares, “Generation of femtosecond paraxial beams with arbitrary spatial distributions,” Opt. Lett.35, 652–654 (2010).
[CrossRef]

E. Cagniot, M. Fromager, and K. Ait-Ameur, “Modeling the propagation of apertured high-order Laguerre-Gaussian beams by a user-friendly version of the mode expansion method,” J. Opt. Soc. Am. A27, 484–491 (2010).
[CrossRef]

H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature466, 604–607 (2010).
[CrossRef] [PubMed]

I. Marienko, V. Denisenko, V. Slusar, and M. Soskin, “Dynamic space shaping of intense ultrashort laser light with blazed-type gratings,” Opt. Express18, 25143–25150 (2010).
[CrossRef] [PubMed]

E. Abramochkin, E. Razueva, and V. Volostnikov, “General astigmatic transform of Hermite-Laguerre-Gaussian beams,” J. Opt. Soc. Am. A27, 2506–2513 (2010).
[CrossRef]

C. Hnatovsky, V. G. Shvedov, W. Krolikowski, and A. V. Rode, “Materials processing with tightly focused femtosecond vortex laser pulse,” Opt. Lett.35, 3417–3419 (2010).
[CrossRef] [PubMed]

J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express18, 2144–2151 (2010).
[CrossRef] [PubMed]

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express18, 566–574 (2010).
[CrossRef] [PubMed]

A. Picón, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express18, 3660–3671 (2010).
[CrossRef] [PubMed]

J. C. Shane, M. Mazilu, W. M. Lee, and K. Dholakia, “Effect of pulse temporal shape on optical trapping and impulse transfer using ultrashort pulsed laser,” Opt. Express18, 7554–7568, (2010).
[CrossRef] [PubMed]

2009 (1)

Y. Toda, K. Nagaoka, K. Shimatake, and R. Morita, “Generation and spatiotemporal evolution of optical vortices in femtosecond laser pulses,” Electr. Eng. JPN167, 39–46 (2009).
[CrossRef]

2008 (2)

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

A. Schwarz and W. Rudolph, “Dispersion-compensating beam shaper for femtosecond optical vortex beams,” Opt. Lett.33, 2970–2972 (2008).
[CrossRef] [PubMed]

2007 (4)

2006 (3)

2005 (3)

A. Vincote and L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett.95, 193901 (2005).
[CrossRef]

I. G. Mariyenko, J. Strohaber, and C. J. G. J. Uiterwaal, “Creation of optical vortices in femtosecond pulses,” Opt. Express19, 7599–7608 (2005).
[CrossRef]

N. Sanner, N. Huot, E. Audouard, C. Larat, J.-P. Huignard, and B. Loiseaux, “Programmable focal spot shaping of amplified femtosecond laser pulses,” Opt. Lett.30, 1479–1482 (2005).
[CrossRef] [PubMed]

2004 (1)

2002 (1)

J. T. Foley and E. Wolf, “Anomalous behavior of spectra near phase singularities,” J. Op. Soc. of Am. A19, 2510–2516 (2002).
[CrossRef]

2001 (2)

S. Feng and H. G. Winful, “Higher-order transverse modes of isodiffracting pulses,” Phys. Rev. E63, 046602 (2001).
[CrossRef]

D. E. Leaird and A. M. Weiner, “Femtosecond direct space-to-time pulse shaping,” IEEE J. Quantum Electron.37, 494–504 (2001).
[CrossRef]

1997 (1)

1996 (1)

R. Borghi, F. Gori, and M. Santarsiero, “Optimization of Laguerre-Gauss truncated series,” Opt. Commun.125, 197–203 (1996).
[CrossRef]

1992 (1)

1983 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik35, 237–246 (1972).

’ t Hooft, G. W.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’ t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett.96, 133901 (2006).
[CrossRef] [PubMed]

Abramochkin, E.

Ait-Ameur, K.

Akturk, S.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spacio-temporal couplings in ultrashort laser pulses,” J. Opt.12, 093001 (2010).
[CrossRef]

Alieva, T.

Andrews, L. C.

Arias, I.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Arnold, C. B.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev.6, 607–621 (2012).
[CrossRef]

Arrizón, V.

Atencia, J.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Audouard, E.

N. Sanner, N. Huot, E. Audouard, C. Larat, and J. -P. Huignard, “Direct ultrafast laser micro-structuring of materials using programmable beam shaping, ” Opt. Laser Eng.45, 737–741 (2007).
[CrossRef]

N. Sanner, N. Huot, E. Audouard, C. Larat, J.-P. Huignard, and B. Loiseaux, “Programmable focal spot shaping of amplified femtosecond laser pulses,” Opt. Lett.30, 1479–1482 (2005).
[CrossRef] [PubMed]

Bañares, L.

V. Loriot, O. Mendoza-Yero, G. Mínguez-Vega, L. Bañares, and R. de Nalda, “Experimental demonstration of the quasy-direct space-to-time pulse shaping principle,” IEEE Photon. Technol. Lett.24, 273–275 (2012).
[CrossRef]

Ó. Martínez-Matos, J. A. Rodrigo, M. P. Hernández-Garay, J. G. Izquierdo, R. Weigand, M. L. Calvo, P. Cheben, P. Vaveliuk, and L. Bañares, “Generation of femtosecond paraxial beams with arbitrary spatial distributions,” Opt. Lett.35, 652–654 (2010).
[CrossRef]

Bergé, L.

A. Vincote and L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett.95, 193901 (2005).
[CrossRef]

Bertrand, J. B.

H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature466, 604–607 (2010).
[CrossRef] [PubMed]

Bezuhanov, K.

Bhuyan, M. K.

Borghi, R.

R. Borghi, F. Gori, and M. Santarsiero, “Optimization of Laguerre-Gauss truncated series,” Opt. Commun.125, 197–203 (1996).
[CrossRef]

Bowlan, P.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spacio-temporal couplings in ultrashort laser pulses,” J. Opt.12, 093001 (2010).
[CrossRef]

Cagniot, E.

Calvo, G. F.

Calvo, M. L.

Cámara, A.

Carrada, R.

Cheben, P.

Chujo, K.

Collados, V.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Constant, E.

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mével, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B: At. Mol. Opt. Phys.45, 074018 (2012).
[CrossRef]

Corkum, P. B.

H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature466, 604–607 (2010).
[CrossRef] [PubMed]

Courvoisier, F.

Day, H. H.

A. Jefferey and H. H. Day, Handbook of Mathematical Formulas and Integrals (Academic Press, 2008).

de Nalda, R.

V. Loriot, O. Mendoza-Yero, G. Mínguez-Vega, L. Bañares, and R. de Nalda, “Experimental demonstration of the quasy-direct space-to-time pulse shaping principle,” IEEE Photon. Technol. Lett.24, 273–275 (2012).
[CrossRef]

Denisenko, V.

Descamps, D.

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mével, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B: At. Mol. Opt. Phys.45, 074018 (2012).
[CrossRef]

Dholakia, K.

Dreischuh, A.

Dubrouil, A.

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mével, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B: At. Mol. Opt. Phys.45, 074018 (2012).
[CrossRef]

Dudley, J. M.

Duocastella, M.

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev.6, 607–621 (2012).
[CrossRef]

Eliel, E. R.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’ t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett.96, 133901 (2006).
[CrossRef] [PubMed]

Erden, M. F.

Feng, S.

S. Feng and H. G. Winful, “Higher-order transverse modes of isodiffracting pulses,” Phys. Rev. E63, 046602 (2001).
[CrossRef]

Fibich, G.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’ t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett.96, 133901 (2006).
[CrossRef] [PubMed]

Foley, J. T.

J. T. Foley and E. Wolf, “Anomalous behavior of spectra near phase singularities,” J. Op. Soc. of Am. A19, 2510–2516 (2002).
[CrossRef]

Fromager, M.

Furfaro, L.

Gaeta, A. L.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’ t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett.96, 133901 (2006).
[CrossRef] [PubMed]

Gao, C.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik35, 237–246 (1972).

González, L. A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, 1996).

Gori, F.

R. Borghi, F. Gori, and M. Santarsiero, “Optimization of Laguerre-Gauss truncated series,” Opt. Commun.125, 197–203 (1996).
[CrossRef]

Grow, T. D.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’ t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett.96, 133901 (2006).
[CrossRef] [PubMed]

Gu, X.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spacio-temporal couplings in ultrashort laser pulses,” J. Opt.12, 093001 (2010).
[CrossRef]

Hamazaki, J.

Hansinger, P.

P. Hansinger, A. Dreischuh, and G. G. Paulus, “Vortices in ultrashort laser pulses,” Appl. Phys. B104, 561–567 (2011).
[CrossRef]

Hernández-Garay, M. P.

Hnatovsky, C.

Hort, O.

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mével, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B: At. Mol. Opt. Phys.45, 074018 (2012).
[CrossRef]

Huignard, J. -P.

N. Sanner, N. Huot, E. Audouard, C. Larat, and J. -P. Huignard, “Direct ultrafast laser micro-structuring of materials using programmable beam shaping, ” Opt. Laser Eng.45, 737–741 (2007).
[CrossRef]

Huignard, J.-P.

Huot, N.

N. Sanner, N. Huot, E. Audouard, C. Larat, and J. -P. Huignard, “Direct ultrafast laser micro-structuring of materials using programmable beam shaping, ” Opt. Laser Eng.45, 737–741 (2007).
[CrossRef]

N. Sanner, N. Huot, E. Audouard, C. Larat, J.-P. Huignard, and B. Loiseaux, “Programmable focal spot shaping of amplified femtosecond laser pulses,” Opt. Lett.30, 1479–1482 (2005).
[CrossRef] [PubMed]

Ishaaya, A.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’ t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett.96, 133901 (2006).
[CrossRef] [PubMed]

Izquierdo, J. G.

Jacquot, M.

Jefferey, A.

A. Jefferey and H. H. Day, Handbook of Mathematical Formulas and Integrals (Academic Press, 2008).

Judkins, J. B.

Kartashov, D. V.

H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature466, 604–607 (2010).
[CrossRef] [PubMed]

Kivshar, Y.

Kobayashi, Y.

Krolikowski, W.

Królikowski, W.

Lacourt, P.-A.

Lakshminarayanan, V.

V. Lakshminarayanan, M. L. Calvo, and T. Alieva, Mathematical Optics: Classical, Quantum and Computational Methods (CRC Press, 2012).
[CrossRef]

Larat, C.

N. Sanner, N. Huot, E. Audouard, C. Larat, and J. -P. Huignard, “Direct ultrafast laser micro-structuring of materials using programmable beam shaping, ” Opt. Laser Eng.45, 737–741 (2007).
[CrossRef]

N. Sanner, N. Huot, E. Audouard, C. Larat, J.-P. Huignard, and B. Loiseaux, “Programmable focal spot shaping of amplified femtosecond laser pulses,” Opt. Lett.30, 1479–1482 (2005).
[CrossRef] [PubMed]

Leaird, D. E.

D. E. Leaird and A. M. Weiner, “Femtosecond direct space-to-time pulse shaping,” IEEE J. Quantum Electron.37, 494–504 (2001).
[CrossRef]

Lee, W. M.

Liu, Y.-D.

Loiseaux, B.

Loriot, V.

V. Loriot, O. Mendoza-Yero, G. Mínguez-Vega, L. Bañares, and R. de Nalda, “Experimental demonstration of the quasy-direct space-to-time pulse shaping principle,” IEEE Photon. Technol. Lett.24, 273–275 (2012).
[CrossRef]

Mahon, R. J.

R. J. Mahon and J. A. Murphy, “Diffraction of an optical pulse as an expansion in ultrashort orthogonal Gaussian beam modes,” J. Op. Soc. Am. A30, 215–226 (2013).
[CrossRef]

Marienko, I.

Mariyenko, I. G.

I. G. Mariyenko, J. Strohaber, and C. J. G. J. Uiterwaal, “Creation of optical vortices in femtosecond pulses,” Opt. Express19, 7599–7608 (2005).
[CrossRef]

Martínez-Matos, Ó.

Mazilu, M.

Méndez, C.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Mendoza-Yero, O.

V. Loriot, O. Mendoza-Yero, G. Mínguez-Vega, L. Bañares, and R. de Nalda, “Experimental demonstration of the quasy-direct space-to-time pulse shaping principle,” IEEE Photon. Technol. Lett.24, 273–275 (2012).
[CrossRef]

Mével, E.

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mével, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B: At. Mol. Opt. Phys.45, 074018 (2012).
[CrossRef]

Mínguez-Vega, G.

V. Loriot, O. Mendoza-Yero, G. Mínguez-Vega, L. Bañares, and R. de Nalda, “Experimental demonstration of the quasy-direct space-to-time pulse shaping principle,” IEEE Photon. Technol. Lett.24, 273–275 (2012).
[CrossRef]

Miyamoto, K.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett.110, 143603 (2013).
[CrossRef]

Mompart, J.

Morita, R.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett.110, 143603 (2013).
[CrossRef]

J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express18, 2144–2151 (2010).
[CrossRef] [PubMed]

Y. Toda, K. Nagaoka, K. Shimatake, and R. Morita, “Generation and spatiotemporal evolution of optical vortices in femtosecond laser pulses,” Electr. Eng. JPN167, 39–46 (2009).
[CrossRef]

Murphy, J. A.

R. J. Mahon and J. A. Murphy, “Diffraction of an optical pulse as an expansion in ultrashort orthogonal Gaussian beam modes,” J. Op. Soc. Am. A30, 215–226 (2013).
[CrossRef]

Nagaoka, K.

Y. Toda, K. Nagaoka, K. Shimatake, and R. Morita, “Generation and spatiotemporal evolution of optical vortices in femtosecond laser pulses,” Electr. Eng. JPN167, 39–46 (2009).
[CrossRef]

Neshev, D.

Omatsu, T.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett.110, 143603 (2013).
[CrossRef]

J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express18, 2144–2151 (2010).
[CrossRef] [PubMed]

Ozaktas, H. M.

Paulus, G. G.

Petersen, C.

Petit, S.

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mével, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B: At. Mol. Opt. Phys.45, 074018 (2012).
[CrossRef]

Phillips, R. L.

Picón, A.

Plaja, L.

A. Picón, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express18, 3660–3671 (2010).
[CrossRef] [PubMed]

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Quintanilla, M.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Razueva, E.

Rode, A. V.

Rodrigo, J. A.

Roso, L.

A. Picón, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express18, 3660–3671 (2010).
[CrossRef] [PubMed]

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Rudolph, W.

Ruiz, C.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Ruiz, U.

San Román, J.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Sanner, N.

N. Sanner, N. Huot, E. Audouard, C. Larat, and J. -P. Huignard, “Direct ultrafast laser micro-structuring of materials using programmable beam shaping, ” Opt. Laser Eng.45, 737–741 (2007).
[CrossRef]

N. Sanner, N. Huot, E. Audouard, C. Larat, J.-P. Huignard, and B. Loiseaux, “Programmable focal spot shaping of amplified femtosecond laser pulses,” Opt. Lett.30, 1479–1482 (2005).
[CrossRef] [PubMed]

Santarsiero, M.

R. Borghi, F. Gori, and M. Santarsiero, “Optimization of Laguerre-Gauss truncated series,” Opt. Commun.125, 197–203 (1996).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik35, 237–246 (1972).

Scarborough, T. D.

Schätzel, M. G.

Schmidt-Kaler, F.

C. T. Schmiegelow and F. Schmidt-Kaler, “Light with orbital angular momentum interacting with trapped ions,” Eur. Phys. J. D66, 157 (2012).
[CrossRef]

Schmiegelow, C. T.

C. T. Schmiegelow and F. Schmidt-Kaler, “Light with orbital angular momentum interacting with trapped ions,” Eur. Phys. J. D66, 157 (2012).
[CrossRef]

Schwarz, A.

Shane, J. C.

Shimatake, K.

Y. Toda, K. Nagaoka, K. Shimatake, and R. Morita, “Generation and spatiotemporal evolution of optical vortices in femtosecond laser pulses,” Electr. Eng. JPN167, 39–46 (2009).
[CrossRef]

Shvedov, V. G.

Slusar, V.

Sola, I. J.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Soskin, M.

Strohaber, J.

Takahashi, F.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett.110, 143603 (2013).
[CrossRef]

Takizawa, S.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett.110, 143603 (2013).
[CrossRef]

Tanda, S.

Toda, Y.

Y. Toda, K. Nagaoka, K. Shimatake, and R. Morita, “Generation and spatiotemporal evolution of optical vortices in femtosecond laser pulses,” Electr. Eng. JPN167, 39–46 (2009).
[CrossRef]

Tokizane, Y.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett.110, 143603 (2013).
[CrossRef]

Toyoda, K.

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett.110, 143603 (2013).
[CrossRef]

Trebino, R.

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spacio-temporal couplings in ultrashort laser pulses,” J. Opt.12, 093001 (2010).
[CrossRef]

Uiterwaal, C. J. G. J.

Vaveliuk, P.

Vázquez de Aldana, J. R.

Villamarín, A.

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

Villeneuve, D. M.

H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature466, 604–607 (2010).
[CrossRef] [PubMed]

Vincote, A.

A. Vincote and L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett.95, 193901 (2005).
[CrossRef]

Volostnikov, V.

Vuong, L. T.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’ t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett.96, 133901 (2006).
[CrossRef] [PubMed]

Walther, H.

Weigand, R.

Weiner, A. M.

D. E. Leaird and A. M. Weiner, “Femtosecond direct space-to-time pulse shaping,” IEEE J. Quantum Electron.37, 494–504 (2001).
[CrossRef]

Winful, H. G.

S. Feng and H. G. Winful, “Higher-order transverse modes of isodiffracting pulses,” Phys. Rev. E63, 046602 (2001).
[CrossRef]

Withford, M. J.

Wolf, E.

J. T. Foley and E. Wolf, “Anomalous behavior of spectra near phase singularities,” J. Op. Soc. of Am. A19, 2510–2516 (2002).
[CrossRef]

Wörner, H. J.

H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature466, 604–607 (2010).
[CrossRef] [PubMed]

Ziolkowski, R. W.

Appl. Opt. (2)

Appl. Phys. B (2)

I. J. Sola, V. Collados, L. Plaja, C. Méndez, J. San Román, C. Ruiz, I. Arias, A. Villamarín, J. Atencia, M. Quintanilla, and L. Roso, “High power vortex generation with volume phase holograms and non-linear experiments in gases,” Appl. Phys. B91, 115–118 (2008).
[CrossRef]

P. Hansinger, A. Dreischuh, and G. G. Paulus, “Vortices in ultrashort laser pulses,” Appl. Phys. B104, 561–567 (2011).
[CrossRef]

Electr. Eng. JPN (1)

Y. Toda, K. Nagaoka, K. Shimatake, and R. Morita, “Generation and spatiotemporal evolution of optical vortices in femtosecond laser pulses,” Electr. Eng. JPN167, 39–46 (2009).
[CrossRef]

Eur. Phys. J. D (1)

C. T. Schmiegelow and F. Schmidt-Kaler, “Light with orbital angular momentum interacting with trapped ions,” Eur. Phys. J. D66, 157 (2012).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. E. Leaird and A. M. Weiner, “Femtosecond direct space-to-time pulse shaping,” IEEE J. Quantum Electron.37, 494–504 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

V. Loriot, O. Mendoza-Yero, G. Mínguez-Vega, L. Bañares, and R. de Nalda, “Experimental demonstration of the quasy-direct space-to-time pulse shaping principle,” IEEE Photon. Technol. Lett.24, 273–275 (2012).
[CrossRef]

J. Op. Soc. Am. A (1)

R. J. Mahon and J. A. Murphy, “Diffraction of an optical pulse as an expansion in ultrashort orthogonal Gaussian beam modes,” J. Op. Soc. Am. A30, 215–226 (2013).
[CrossRef]

J. Op. Soc. of Am. A (1)

J. T. Foley and E. Wolf, “Anomalous behavior of spectra near phase singularities,” J. Op. Soc. of Am. A19, 2510–2516 (2002).
[CrossRef]

J. Opt. (1)

S. Akturk, X. Gu, P. Bowlan, and R. Trebino, “Spacio-temporal couplings in ultrashort laser pulses,” J. Opt.12, 093001 (2010).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Opt. Soc. Am. B (2)

J. Phys. B: At. Mol. Opt. Phys. (1)

E. Constant, A. Dubrouil, O. Hort, S. Petit, D. Descamps, and E. Mével, “Spatial shaping of intense femtosecond beams for the generation of high-energy attosecond pulses,” J. Phys. B: At. Mol. Opt. Phys.45, 074018 (2012).
[CrossRef]

Laser Photonics Rev. (1)

M. Duocastella and C. B. Arnold, “Bessel and annular beams for materials processing,” Laser Photonics Rev.6, 607–621 (2012).
[CrossRef]

Nature (1)

H. J. Wörner, J. B. Bertrand, D. V. Kartashov, P. B. Corkum, and D. M. Villeneuve, “Following a chemical reaction using high-harmonic interferometry,” Nature466, 604–607 (2010).
[CrossRef] [PubMed]

Opt. Commun. (1)

R. Borghi, F. Gori, and M. Santarsiero, “Optimization of Laguerre-Gauss truncated series,” Opt. Commun.125, 197–203 (1996).
[CrossRef]

Opt. Express (8)

I. G. Mariyenko, J. Strohaber, and C. J. G. J. Uiterwaal, “Creation of optical vortices in femtosecond pulses,” Opt. Express19, 7599–7608 (2005).
[CrossRef]

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. M. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express18, 566–574 (2010).
[CrossRef] [PubMed]

J. Hamazaki, R. Morita, K. Chujo, Y. Kobayashi, S. Tanda, and T. Omatsu, “Optical-vortex laser ablation,” Opt. Express18, 2144–2151 (2010).
[CrossRef] [PubMed]

A. Picón, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express18, 3660–3671 (2010).
[CrossRef] [PubMed]

I. Marienko, V. Denisenko, V. Slusar, and M. Soskin, “Dynamic space shaping of intense ultrashort laser light with blazed-type gratings,” Opt. Express18, 25143–25150 (2010).
[CrossRef] [PubMed]

J. A. Rodrigo, T. Alieva, A. Cámara, Ó. Martínez-Matos, P. Cheben, and M. L. Calvo, “Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections,” Opt. Express19, 6064–6077 (2011).
[CrossRef] [PubMed]

J. C. Shane, M. Mazilu, W. M. Lee, and K. Dholakia, “Effect of pulse temporal shape on optical trapping and impulse transfer using ultrashort pulsed laser,” Opt. Express18, 7554–7568, (2010).
[CrossRef] [PubMed]

Y.-D. Liu and C. Gao, “Study on the time-varying and propagating characteristics of ultrashort pulse Laguerre-Gaussian beam,” Opt. Express18, 12104–12110 (2010).
[CrossRef] [PubMed]

Opt. Laser Eng. (1)

N. Sanner, N. Huot, E. Audouard, C. Larat, and J. -P. Huignard, “Direct ultrafast laser micro-structuring of materials using programmable beam shaping, ” Opt. Laser Eng.45, 737–741 (2007).
[CrossRef]

Opt. Lett. (6)

Optik (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik35, 237–246 (1972).

Phys. Rev. E (1)

S. Feng and H. G. Winful, “Higher-order transverse modes of isodiffracting pulses,” Phys. Rev. E63, 046602 (2001).
[CrossRef]

Phys. Rev. Lett. (3)

K. Toyoda, F. Takahashi, S. Takizawa, Y. Tokizane, K. Miyamoto, R. Morita, and T. Omatsu, “Transfer of light helicity to nanostructures,” Phys. Rev. Lett.110, 143603 (2013).
[CrossRef]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’ t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett.96, 133901 (2006).
[CrossRef] [PubMed]

A. Vincote and L. Bergé, “Femtosecond optical vortices in air,” Phys. Rev. Lett.95, 193901 (2005).
[CrossRef]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, 1996).

V. Lakshminarayanan, M. L. Calvo, and T. Alieva, Mathematical Optics: Classical, Quantum and Computational Methods (CRC Press, 2012).
[CrossRef]

A. Jefferey and H. H. Day, Handbook of Mathematical Formulas and Integrals (Academic Press, 2008).

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Figures (7)

Fig. 1
Fig. 1

(a) Approach to implement the encoded signal in phase-only computer generated holograms to the whole spectrum of the pulse. The imaging optical system cancels out the spatial chirp at the 2D SLM and makes the approach nondispersive. (b) Typical arrangement for laser micro-machining in which the spatial pulse shaping at the focus is desired.

Fig. 2
Fig. 2

(a) Instantaneous intensity and phase for the monochromatic case �� 5 , 3 Mon with s = f, normalized to the spatial extent in Cartesian coordinates. Intensity evolution of the wavelet �� 5 , 3 Mon (b) and the pulselet ℒ��5,3 for the arrangements (c) s = f and (d) s = 5f as a function of the normalized time and spatial extent. Arrows connect the rings in Cartesian coordinates (a) with the rings in the space-time representation (b) for the monochromatic case. Dashed lines delimits the temporal HWHM centered on the pulse peak intensity. Intensity graphs are normalized to its maximum value, while the gray-scale in the phase representation runs from −π, black, to +π, white, radians. The parameters are f = 15 cm; w0 = 150μm; τ0 = 15 fs; λ0 = 800 nm and β3 = 670μm.

Fig. 3
Fig. 3

Intensity and phase in Cartesian coordinates for the pulselet ℒ��5,3 evaluated at the snapshots indicated in the figure with (a) s = f and (b) s = 5f. It is also displayed the instantaneous intensity and phase for the monochromatic case �� 5 , 3 Mon with s = f. Intensity graphs are normalized to its maximum value, while the gray-scale in the phase representation runs from −π, black, to +π, white, radians. Parameters are the same than in Fig. 2.

Fig. 4
Fig. 4

(a) Top-hat beam profile (thick gray line) at the focal plane and the LG expansion (blue line) computed for 31 terms using the normalized coefficients Bn,0 shown in the inset. The field of the ultrashort pulse evaluated at t = 0 (red line) also shows a top-hat beam profile. (b) Signal to be encoded in the computer generated hologram obtained by Fourier Transforming the top-hat function (thick gray line) and its expansion (blue line) using the same numbers of terms. Instantaneous intensity of the pulse at the focus as computed by (8) using the coefficients of the inset for (c) s = f and (d) s = 5f. In Fig. 4(a) and Figs. 4(c)–4(d) the axial extents are shown in relation to the radius a = 1.4 mm and the parameters are the same than in Fig. 2.

Fig. 5
Fig. 5

(a) Top-hat and annular beam profile (thick gray line) at the focal plane and the LG expansion (blue line) computed for 31 terms. The field of the ultrashort pulse evaluated at t = 0 (red line) shows a similar profile. (b) Expansion of the signal to be encoded in the computer generated hologram using the same numbers of terms. Instantaneous intensity of the pulse at the focus as computed by (8) for (c) s = f and (d) s = 5f. In Fig. 5(a) and Figs. 5(c)–5(d) the axial extents are shown in relation to the radius a = 350 μm and the parameters are the same than in Fig. 2.

Fig. 6
Fig. 6

Temporal evolution of the intensity as a interference of two spatial top-hat ultrafast beams with (a) a = 1.4 mm and (b) a = 70μm, for the case s = f and b = ±1.4 mm. The axial extents are shown in relation to the radius a. The parameters are the same than in Fig. 2.

Fig. 7
Fig. 7

(a) Temporal evolution of the intensity at the focal plane by using a signal composed by the superposition of LG0,5 and LG0,−5 modes with w0 = 50 and 400μm, respectively. Transverse intensity evaluated at the snapshots t = −4τ0 (b) and t = 0 (c). The topological charge jumps from m = 5 to m = −5 as the pulse evolves in time.

Equations (22)

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E 0 ( ω , r 0 , ϕ 0 , z = 0 ) = S ( ω ) exp ( r 0 2 β 2 ) R ( r 0 , ϕ 0 ) ,
E 0 ( ω , r 0 , ϕ 0 , z = 0 ) = S ( ω ) R ( r 0 , ϕ 0 ) ,
E ( r , ϕ , s + f ; ω ) = P ( r ; ω ) F T [ E 0 ( r 0 , ϕ 0 , z = 0 ; ω ) ] ,
P ( r ; ω ) = i ω 2 π c f exp [ i ω c ( s + f ) ] exp [ i ω 2 f c ( 1 s f ) r 2 ]
( t , r , ϕ , s + f ) = 1 2 π E ( r , ϕ , s + f ; ω ) exp ( i ω t ) d ω .
R ( r 0 , ϕ 0 ) = n , m = 0 A n , m LG n , m ( r 0 , ϕ 0 ; w 0 ) ,
LG n , m ( r 0 , ϕ 0 ; w 0 ) = 2 | m | + 1 n ! π ( n + | m | ) ! exp ( i m ϕ 0 ) w 0 | m | + 1 r 0 | m | L n ( | m | ) ( 2 r 0 2 w 0 2 ) exp ( r 0 2 w 0 2 ) .
( t , r , ϕ , s + f ) = n , m = 0 A n , m 𝒢 n , m ( t , r , ϕ , s + f ) ,
𝒢 n , m ( t , r , ϕ , s + f ) = 1 2 π S ( ω ) P ( r ; ω ) T F [ LG n , m ( r 0 , ϕ 0 ; w 0 ) ] exp ( i ω t ) d ω .
A n , m = 0 2 π ( 0 R ( r 0 , ϕ 0 ) LG n , m * ( r 0 , ϕ 0 ; w 0 ) r 0 d r 0 ) d ϕ 0 .
T F [ LG n , m ( r 0 , ϕ 0 ; w 0 ) ] = ( i ) 2 n + | m | 2 π c f ω LG n , m ( r , ϕ ; w ) ,
𝒢 n , m ( t , r , ϕ , s + f ) = ( i ) 2 n + | m | c f S ( ω ) ω P ( r ; ω ) LG n , m ( r , ϕ ; w ) exp ( i ω t ) d ω .
𝒢 n , m Mon ( t , r , ϕ , s + f ) = ( i ) 2 n + | m | + 1 ( 2 π ) 1 exp ( i ω 0 t p ) LG n , m ( r , ϕ ; w 1 ) ,
t p = t s + f c 1 2 f c ( 1 s f ) r 2
s ( t ) = exp ( t 2 τ 0 2 ) exp ( i ω 0 t ) ,
𝒢 n , m ( t , t , ϕ , s + f ) = ( 1 ) n + | m | + 1 n ! 2 π ( n + | m | ) ! 1 ρ 0 ( τ 0 τ 1 ) 2 × exp [ ( τ 0 τ 1 ) 2 r 2 w 1 2 ] exp ( i m ϕ ) exp ( i ω 1 t p ) exp ( t p 2 τ 1 2 ) × p = 0 n ( n + | m | p + | m | ) 1 p ! [ ( τ 0 τ 1 ) 2 r 2 ρ 0 ] 2 p + | m | H 2 p + | m | + 1 ( t p + i ω 0 2 τ 0 2 τ 1 ) ,
τ 1 = τ 0 1 + ( r ρ 0 ) 2 ,
f ( r , ϕ ) = n , m B n , m L G n , m ( r , ϕ ; w 1 ) ,
Mon ( 0 , r , ϕ , s + f ) exp [ i ω 0 2 f c ( 1 s f ) r 2 ] n , m A n , m ( i ) 2 n + | m | + 1 LG n , m ( r , ϕ ; 2 f c w 0 ω 0 ) ,
A n , m ( i ) 2 n | m | 1 B n , m exp [ i ω 0 2 f c ( 1 s f ) r 2 ] ,
ε M = 1 1 U 2 n , m M B n , m 2 ,
t p ± ( t , r ) = t s + f c 1 2 f c ( 1 s f ) r 2 ± b f c x .

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