Abstract

We numerically study the propagation of a Laguerre-Gaussian beam through polar molecular media via the exact solution of full-wave Maxwell-Bloch equations where the rotating-wave and slowly-varying-envelope approximations are not included. It is found that beyond the coexistence of odd-order and even-order vortex harmonics due to inversion asymmetry of the system, the light propagation effect results in the intensity enhancement of a high-order vortex harmonics. Moreover, the orbital momentum successfully transfers from the fundamental laser driver to the vortex harmonics which topological charger number is directly proportional to its order.

© 2017 Optical Society of America

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References

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  1. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
    [Crossref] [PubMed]
  2. A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12(8), 083053 (2010).
    [Crossref]
  3. M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8(10), 743–746 (2012).
    [Crossref]
  4. L. Rego, J. S. Román, A. Picón, L. Plaja, and C. Hernández-García, “Nonperturbative twist in the generation of extreme-ultraviolet vortex beams,” Phys. Rev. Lett. 117(16), 163202 (2016).
    [Crossref] [PubMed]
  5. T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
    [Crossref]
  6. G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
    [Crossref] [PubMed]
  7. X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
    [Crossref] [PubMed]
  8. C. Hernández-García, A. Picón, J. San Román, and L. Plaja, “Attosecond extreme ultraviolet vortices from high-order harmonic generation,” Phys. Rev. Lett. 111(8), 083602 (2013).
    [Crossref] [PubMed]
  9. Y. Y. Chen, X. L. Feng, and C. Liu, “Generation of nonlinear vortex precursors,” Phys. Rev. Lett. 117(2), 023901 (2016).
    [Crossref] [PubMed]
  10. W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007).
    [Crossref] [PubMed]
  11. A. Brown and W. J. Meath, “On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules,” J. Chem. Phys. 109(21), 9351–9365 (1998).
    [Crossref]
  12. V. P. Kalosha and J. Herrmann, “Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,” Phys. Rev. Lett. 83(3), 544–547 (1999).
    [Crossref]
  13. C. Liu, M. C. Kohler, K. Z. Hatsagortsyan, C. Müller, and C. H. Keitel, “Laser-guided relativistic quantum dynamics,” New J. Phys. 11(10), 105045 (2009).
    [Crossref]
  14. Y. I. Salaminm, “Accurate fields of a radially polarized Gaussian laser beam,” New J. Phys. 8(8), 133 (2006).
    [Crossref]
  15. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
    [Crossref]
  16. R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995).
    [Crossref] [PubMed]
  17. C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation,” Phys. Rev. Lett. 92(4), 047402 (2004).
    [Crossref] [PubMed]
  18. C. Zhang, J. Yao, J. Ni, and F. A. Umran, “Enhanced harmonic emission from a polar molecule medium driven by few-cycle laser pulses,” Opt. Express 20(24), 26521–26527 (2012).
    [Crossref] [PubMed]
  19. C. Zhang, C. Liu, and Z. Xu, “Control of higher spectral components by spatially inhomogeneous fields in quantum wells,” Phys. Rev. A 88(3), 035805 (2013).
    [Crossref]
  20. S. Hughes, “Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,” Phys. Rev. Lett. 81(16), 3363–3366 (1998).
    [Crossref]
  21. Y. Xiao, D. N. Maywar, and G. P. Agrawal, “Propagation of few-cycle pulses in nonlinear Kerr media: harmonic generation,” Opt. Lett. 38(5), 724–726 (2013).
    [Crossref] [PubMed]
  22. F. I. Gauthey, B. M. Garraway, and P. L. Knight, “High harmonic generation and periodic level crossings,” Phys. Rev. A 56(4), 3093–3096 (1997).
    [Crossref]
  23. C. Liu, S. Gong, R. Li, and Z. Xu, “Coherent control in the generation of harmonics and hyper-Raman lines from a strongly driven two-level atom,” Phys. Rev. A 69(2), 023406 (2004).
    [Crossref]

2016 (2)

L. Rego, J. S. Román, A. Picón, L. Plaja, and C. Hernández-García, “Nonperturbative twist in the generation of extreme-ultraviolet vortex beams,” Phys. Rev. Lett. 117(16), 163202 (2016).
[Crossref] [PubMed]

Y. Y. Chen, X. L. Feng, and C. Liu, “Generation of nonlinear vortex precursors,” Phys. Rev. Lett. 117(2), 023901 (2016).
[Crossref] [PubMed]

2015 (1)

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

2014 (1)

G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
[Crossref] [PubMed]

2013 (3)

C. Hernández-García, A. Picón, J. San Román, and L. Plaja, “Attosecond extreme ultraviolet vortices from high-order harmonic generation,” Phys. Rev. Lett. 111(8), 083602 (2013).
[Crossref] [PubMed]

C. Zhang, C. Liu, and Z. Xu, “Control of higher spectral components by spatially inhomogeneous fields in quantum wells,” Phys. Rev. A 88(3), 035805 (2013).
[Crossref]

Y. Xiao, D. N. Maywar, and G. P. Agrawal, “Propagation of few-cycle pulses in nonlinear Kerr media: harmonic generation,” Opt. Lett. 38(5), 724–726 (2013).
[Crossref] [PubMed]

2012 (2)

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8(10), 743–746 (2012).
[Crossref]

C. Zhang, J. Yao, J. Ni, and F. A. Umran, “Enhanced harmonic emission from a polar molecule medium driven by few-cycle laser pulses,” Opt. Express 20(24), 26521–26527 (2012).
[Crossref] [PubMed]

2010 (1)

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12(8), 083053 (2010).
[Crossref]

2009 (1)

C. Liu, M. C. Kohler, K. Z. Hatsagortsyan, C. Müller, and C. H. Keitel, “Laser-guided relativistic quantum dynamics,” New J. Phys. 11(10), 105045 (2009).
[Crossref]

2007 (1)

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007).
[Crossref] [PubMed]

2006 (1)

Y. I. Salaminm, “Accurate fields of a radially polarized Gaussian laser beam,” New J. Phys. 8(8), 133 (2006).
[Crossref]

2004 (2)

C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation,” Phys. Rev. Lett. 92(4), 047402 (2004).
[Crossref] [PubMed]

C. Liu, S. Gong, R. Li, and Z. Xu, “Coherent control in the generation of harmonics and hyper-Raman lines from a strongly driven two-level atom,” Phys. Rev. A 69(2), 023406 (2004).
[Crossref]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

2000 (1)

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[Crossref]

1999 (1)

V. P. Kalosha and J. Herrmann, “Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,” Phys. Rev. Lett. 83(3), 544–547 (1999).
[Crossref]

1998 (2)

A. Brown and W. J. Meath, “On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules,” J. Chem. Phys. 109(21), 9351–9365 (1998).
[Crossref]

S. Hughes, “Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,” Phys. Rev. Lett. 81(16), 3363–3366 (1998).
[Crossref]

1997 (1)

F. I. Gauthey, B. M. Garraway, and P. L. Knight, “High harmonic generation and periodic level crossings,” Phys. Rev. A 56(4), 3093–3096 (1997).
[Crossref]

1995 (1)

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995).
[Crossref] [PubMed]

1966 (1)

K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966).
[Crossref]

Agrawal, G. P.

Arnold, J. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995).
[Crossref] [PubMed]

Benseny, A.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12(8), 083053 (2010).
[Crossref]

Boyd, R. W.

G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
[Crossref] [PubMed]

Brabec, T.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[Crossref]

Brown, A.

A. Brown and W. J. Meath, “On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules,” J. Chem. Phys. 109(21), 9351–9365 (1998).
[Crossref]

Calvo, G. F.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12(8), 083053 (2010).
[Crossref]

Chen, Y. Y.

Y. Y. Chen, X. L. Feng, and C. Liu, “Generation of nonlinear vortex precursors,” Phys. Rev. Lett. 117(2), 023901 (2016).
[Crossref] [PubMed]

Cheng, Y.

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007).
[Crossref] [PubMed]

Corkum, P. B.

G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
[Crossref] [PubMed]

Dreischuh, A.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8(10), 743–746 (2012).
[Crossref]

Elsaesser, T.

C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation,” Phys. Rev. Lett. 92(4), 047402 (2004).
[Crossref] [PubMed]

Feng, X. L.

Y. Y. Chen, X. L. Feng, and C. Liu, “Generation of nonlinear vortex precursors,” Phys. Rev. Lett. 117(2), 023901 (2016).
[Crossref] [PubMed]

Frumker, E.

G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
[Crossref] [PubMed]

Gariepy, G.

G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
[Crossref] [PubMed]

Garraway, B. M.

F. I. Gauthey, B. M. Garraway, and P. L. Knight, “High harmonic generation and periodic level crossings,” Phys. Rev. A 56(4), 3093–3096 (1997).
[Crossref]

Gauthey, F. I.

F. I. Gauthey, B. M. Garraway, and P. L. Knight, “High harmonic generation and periodic level crossings,” Phys. Rev. A 56(4), 3093–3096 (1997).
[Crossref]

Gogny, D. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, “Ultrafast pulse interactions with two-level atoms,” Phys. Rev. A 52(4), 3082–3094 (1995).
[Crossref] [PubMed]

Gong, S.

W. Yang, X. Song, S. Gong, Y. Cheng, and Z. Xu, “Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium,” Phys. Rev. Lett. 99(13), 133602 (2007).
[Crossref] [PubMed]

C. Liu, S. Gong, R. Li, and Z. Xu, “Coherent control in the generation of harmonics and hyper-Raman lines from a strongly driven two-level atom,” Phys. Rev. A 69(2), 023406 (2004).
[Crossref]

Hammond, T. J.

G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
[Crossref] [PubMed]

Hansinger, P.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8(10), 743–746 (2012).
[Crossref]

Hatsagortsyan, K. Z.

C. Liu, M. C. Kohler, K. Z. Hatsagortsyan, C. Müller, and C. H. Keitel, “Laser-guided relativistic quantum dynamics,” New J. Phys. 11(10), 105045 (2009).
[Crossref]

Hernández-García, C.

L. Rego, J. S. Román, A. Picón, L. Plaja, and C. Hernández-García, “Nonperturbative twist in the generation of extreme-ultraviolet vortex beams,” Phys. Rev. Lett. 117(16), 163202 (2016).
[Crossref] [PubMed]

C. Hernández-García, A. Picón, J. San Román, and L. Plaja, “Attosecond extreme ultraviolet vortices from high-order harmonic generation,” Phys. Rev. Lett. 111(8), 083602 (2013).
[Crossref] [PubMed]

Herrmann, J.

V. P. Kalosha and J. Herrmann, “Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,” Phys. Rev. Lett. 83(3), 544–547 (1999).
[Crossref]

Hey, R.

C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation,” Phys. Rev. Lett. 92(4), 047402 (2004).
[Crossref] [PubMed]

Hughes, S.

S. Hughes, “Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses,” Phys. Rev. Lett. 81(16), 3363–3366 (1998).
[Crossref]

Kalosha, V. P.

V. P. Kalosha and J. Herrmann, “Formation of optical subcycle pulses and full Maxwell-Bloch solitary waves by coherent propagation effects,” Phys. Rev. Lett. 83(3), 544–547 (1999).
[Crossref]

Keitel, C. H.

C. Liu, M. C. Kohler, K. Z. Hatsagortsyan, C. Müller, and C. H. Keitel, “Laser-guided relativistic quantum dynamics,” New J. Phys. 11(10), 105045 (2009).
[Crossref]

Kern, C.

M. Zürch, C. Kern, P. Hansinger, A. Dreischuh, and C. Spielmann, “Strong-field physics with singular light beams,” Nat. Phys. 8(10), 743–746 (2012).
[Crossref]

Kim, K. T.

G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
[Crossref] [PubMed]

Knight, P. L.

F. I. Gauthey, B. M. Garraway, and P. L. Knight, “High harmonic generation and periodic level crossings,” Phys. Rev. A 56(4), 3093–3096 (1997).
[Crossref]

Kohler, M. C.

C. Liu, M. C. Kohler, K. Z. Hatsagortsyan, C. Müller, and C. H. Keitel, “Laser-guided relativistic quantum dynamics,” New J. Phys. 11(10), 105045 (2009).
[Crossref]

Krausz, F.

T. Brabec and F. Krausz, “Intense few-cycle laser fields: Frontiers of nonlinear optics,” Rev. Mod. Phys. 72(2), 545–591 (2000).
[Crossref]

Leach, J.

G. Gariepy, J. Leach, K. T. Kim, T. J. Hammond, E. Frumker, R. W. Boyd, and P. B. Corkum, “Creating high-harmonic beams with controlled orbital angular momentum,” Phys. Rev. Lett. 113(15), 153901 (2014).
[Crossref] [PubMed]

Li, R.

C. Liu, S. Gong, R. Li, and Z. Xu, “Coherent control in the generation of harmonics and hyper-Raman lines from a strongly driven two-level atom,” Phys. Rev. A 69(2), 023406 (2004).
[Crossref]

Liu, C.

Y. Y. Chen, X. L. Feng, and C. Liu, “Generation of nonlinear vortex precursors,” Phys. Rev. Lett. 117(2), 023901 (2016).
[Crossref] [PubMed]

C. Zhang, C. Liu, and Z. Xu, “Control of higher spectral components by spatially inhomogeneous fields in quantum wells,” Phys. Rev. A 88(3), 035805 (2013).
[Crossref]

C. Liu, M. C. Kohler, K. Z. Hatsagortsyan, C. Müller, and C. H. Keitel, “Laser-guided relativistic quantum dynamics,” New J. Phys. 11(10), 105045 (2009).
[Crossref]

C. Liu, S. Gong, R. Li, and Z. Xu, “Coherent control in the generation of harmonics and hyper-Raman lines from a strongly driven two-level atom,” Phys. Rev. A 69(2), 023406 (2004).
[Crossref]

Luo, C. W.

C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation,” Phys. Rev. Lett. 92(4), 047402 (2004).
[Crossref] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[Crossref] [PubMed]

Maywar, D. N.

Meath, W. J.

A. Brown and W. J. Meath, “On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules,” J. Chem. Phys. 109(21), 9351–9365 (1998).
[Crossref]

Mompart, J.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12(8), 083053 (2010).
[Crossref]

Müller, C.

C. Liu, M. C. Kohler, K. Z. Hatsagortsyan, C. Müller, and C. H. Keitel, “Laser-guided relativistic quantum dynamics,” New J. Phys. 11(10), 105045 (2009).
[Crossref]

Ni, J.

Picón, A.

L. Rego, J. S. Román, A. Picón, L. Plaja, and C. Hernández-García, “Nonperturbative twist in the generation of extreme-ultraviolet vortex beams,” Phys. Rev. Lett. 117(16), 163202 (2016).
[Crossref] [PubMed]

C. Hernández-García, A. Picón, J. San Román, and L. Plaja, “Attosecond extreme ultraviolet vortices from high-order harmonic generation,” Phys. Rev. Lett. 111(8), 083602 (2013).
[Crossref] [PubMed]

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12(8), 083053 (2010).
[Crossref]

Plaja, L.

L. Rego, J. S. Román, A. Picón, L. Plaja, and C. Hernández-García, “Nonperturbative twist in the generation of extreme-ultraviolet vortex beams,” Phys. Rev. Lett. 117(16), 163202 (2016).
[Crossref] [PubMed]

C. Hernández-García, A. Picón, J. San Román, and L. Plaja, “Attosecond extreme ultraviolet vortices from high-order harmonic generation,” Phys. Rev. Lett. 111(8), 083602 (2013).
[Crossref] [PubMed]

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12(8), 083053 (2010).
[Crossref]

Ploog, K. H.

C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation,” Phys. Rev. Lett. 92(4), 047402 (2004).
[Crossref] [PubMed]

Rego, L.

L. Rego, J. S. Román, A. Picón, L. Plaja, and C. Hernández-García, “Nonperturbative twist in the generation of extreme-ultraviolet vortex beams,” Phys. Rev. Lett. 117(16), 163202 (2016).
[Crossref] [PubMed]

Reimann, K.

C. W. Luo, K. Reimann, M. Woerner, T. Elsaesser, R. Hey, and K. H. Ploog, “Phase-resolved nonlinear response of a two-dimensional electron gas under femtosecond intersubband excitation,” Phys. Rev. Lett. 92(4), 047402 (2004).
[Crossref] [PubMed]

Román, J. S.

L. Rego, J. S. Román, A. Picón, L. Plaja, and C. Hernández-García, “Nonperturbative twist in the generation of extreme-ultraviolet vortex beams,” Phys. Rev. Lett. 117(16), 163202 (2016).
[Crossref] [PubMed]

Roso, L.

A. Picón, A. Benseny, J. Mompart, J. R. Vázquez de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Transferring orbital and spin angular momenta of light to atoms,” New J. Phys. 12(8), 083053 (2010).
[Crossref]

Salaminm, Y. I.

Y. I. Salaminm, “Accurate fields of a radially polarized Gaussian laser beam,” New J. Phys. 8(8), 133 (2006).
[Crossref]

San Román, J.

C. Hernández-García, A. Picón, J. San Román, and L. Plaja, “Attosecond extreme ultraviolet vortices from high-order harmonic generation,” Phys. Rev. Lett. 111(8), 083602 (2013).
[Crossref] [PubMed]

Shen, B.

X. Zhang, B. Shen, Y. Shi, X. Wang, L. Zhang, W. Wang, J. Xu, L. Yi, and Z. Xu, “Generation of intense high-order vortex harmonics,” Phys. Rev. Lett. 114(17), 173901 (2015).
[Crossref] [PubMed]

Shi, Y.

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Figures (5)

Fig. 1
Fig. 1 Temporal and spatial evolution of laser pulses at propagation distance of (a) 2 µm and (b) 8 µm. (c) The corresponding spectra of laser pulses at different propagation distances. (d) The amplified spectra around the third-order harmonic region.
Fig. 2
Fig. 2 Transverse field distribution of the (a) second, (b) third, (c) fourth, (d) fifth, (e) sixth and (f) seventh harmonics in the x-y plane at propagation distance of 2 µm.
Fig. 3
Fig. 3 Same as in Fig. 2, but for the propagation distance of 8 µm.
Fig. 4
Fig. 4 Fourth-order harmonic of transverse field distributions at beam waist (a) a0 = 7µm, (b) a0 = 11 µm and (c) a0 = 15µm. Fifth-order harmonic of transverse field distributions at beam waist (d) a0 = 7µm, (e) a0 = 11 µm and (f) a0 = 15µm.
Fig. 5
Fig. 5 Same as in Fig. 2, but for meeting ω12 = 3.2ω0.

Equations (4)

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E (t=0,z)= E lp sech[ 1.76( z z 0 )/( c τ 0 ) ]cos[ ω 0 ( z z 0 )/c ] E lp (t=0,r,ϕ,z)= E 0 ( 1+ z ˜ 2 / z R 2 ) 1/2 ( r a( z ˜ ) ) | l | L p | l | ( 2 r 2 a 2 ( z ˜ ) )exp( r 2 a 2 ( z ˜ ) )
×exp( ik r 2 z ˜ 2( z ˜ 2 + z R 2 ) )exp( ilϕ )exp( i( 2p+| l |+1 ) tan 1 z ˜ z R ),
H t = 1 μ 0 × E , E t = 1 ε 0 × H 1 ε 0 P t ,
ρ 12 t =i( ω 12 ρ 12 + E un E d ρ 12 ) 1 τ 1 ρ 12 , n t =i 2u E( ρ 12 ρ 12 * ) 1 τ 2 n.

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