Abstract

Spatiotemporal optical vortices (STOVs) are a new type of optical orbital angular momentum (OAM) with optical phase circulation in space–time. In prior work [Phys. Rev. X. 6, 031037 (2016) [CrossRef]  ], we demonstrated that a STOV is a universal structure emerging from the arrest of self-focusing collapse leading to nonlinear self-guiding in material media. Here, we demonstrate linear generation and propagation in free space of STOV-carrying pulses. Our measurements and simulations demonstrate STOV mediation of space–time energy flow within the pulse and conservation of OAM in space–time. Single-shot amplitude and phase images of STOVs are taken using a new diagnostic, transient grating single-shot supercontinuum spectral interferometry.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  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, 8185–8189 (1992).
    [Crossref]
  2. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
    [Crossref]
  3. B. M. Heffernan, S. A. Meyer, D. Restrepo, M. E. Siemens, E. A. Gibson, and J. T. Gopinath, “A fiber-coupled stimulated emission depletion microscope for bend-insensitive through-fiber imaging,” Sci. Rep. 9, 11137 (2019).
    [Crossref]
  4. G. A. Tyler and R. W. Boyd, “Influence of atmospheric turbulence on the propagation of quantum states of light carrying orbital angular momentum,” Opt. Lett. 34, 142–144 (2009).
    [Crossref]
  5. T. Doster and A. T. Watnik, “Laguerre–Gauss and Bessel–Gauss beams propagation through turbulence: analysis of channel efficiency,” Appl. Opt. 55, 10239–10246 (2016).
    [Crossref]
  6. G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2004).
    [Crossref]
  7. K. O’Holleran, M. J. Padgett, and M. R. Dennis, “Topology of optical vortex lines formed by the interference of three, four, and five plane waves,” Opt. Express 14, 3039–3044 (2006).
    [Crossref]
  8. V. Denisenko, V. Shvedov, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, A. Volyar, M. Soskin, and Y. S. Kivshar, “Determination of topological charges of polychromatic optical vortices,” Opt. Express 17, 23374–23379 (2009).
    [Crossref]
  9. A. Richter, M. Bock, J. Jahns, and R. Grunwald, “Orbital angular momentum experiments with broadband few cycle pulses,” Proc. SPIE 7613, 761308 (2010).
    [Crossref]
  10. M. A. Porras, “Upper bound to the orbital angular momentum carried by an ultrashort pulse,” Phys. Rev. Lett. 122, 123904 (2019).
    [Crossref]
  11. K. Y. Bliokh and F. Nori, “Spatiotemporal vortex beams and angular momentum,” Phys. Rev. A 86, 033824 (2012).
    [Crossref]
  12. N. Jhajj, I. Larkin, E. W. Rosenthal, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Spatiotemporal optical vortices,” Phys. Rev. X 6, 031037 (2016).
    [Crossref]
  13. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
    [Crossref]
  14. F. Salehi, A. J. Goers, G. A. Hine, L. Feder, D. Kuk, B. Miao, D. Woodbury, K. Y. Kim, and H. M. Milchberg, “MeV electron acceleration at 1  kHz with <10  mJ laser pulses,” Opt. Lett. 42, 215–218 (2017).
    [Crossref]
  15. J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
    [Crossref]
  16. N. Jhajj, “Hydrodynamic and electrodynamic implications of optical femtosecond filamentation,” Ph.D.dissertation (University of Maryland, 2017), https://drum.lib.umd.edu/handle/1903/19973 , Chap. 5.
  17. S. Zahedpour, S. W. Hancock, and H. M. Milchberg, “Direct measurement of linearly imposed spatiotemporal optical vortices (STOVs),” in Frontiers in Optics + Laser Science APS/DLS, OSA Technical Digest (Optical Society of America, 2019), paper FW5F.5.
  18. D. Faccio, A. Lotti, A. Matijosius, F. Bragheri, V. Degiorgio, A. Couairon, and P. Di Trapani, “Experimental energy-density flux characterization of ultrashort laser pulse filaments,” Opt. Express 17, 8193–8200 (2009).
    [Crossref]
  19. K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 81, 4124–4126 (2002).
    [Crossref]
  20. J. K. Wahlstrand, S. Zahedpour, and H. M. Milchberg, “Optimizing the time resolution of supercontinuum spectral interferometry,” J. Opt. Soc. Am. B 33, 1476–1481 (2016).
    [Crossref]
  21. S. Zahedpour, S. W. Hancock, and H. M. Milchberg, “Ultrashort infrared 2.5–11  µm pulses: spatiotemporal profiles and absolute nonlinear response of air constituents,” Opt. Lett. 44, 843–846 (2019).
    [Crossref]
  22. S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurement of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
    [Crossref]
  23. M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
    [Crossref]
  24. D. Jang, R. M. Schwartz, D. Woodbury, J. Griff-McMahon, A. H. Younis, H. M. Milchberg, and K.-Y. Kim, “Efficient terahertz and Brunel harmonic generation from air plasma via mid-infrared coherent control,” Optica 6, 1338–1341 (2019).
    [Crossref]
  25. A. Lotti, A. Couairon, D. Faccio, and P. Di Trapani, “Energy-flux characterization of conical and space-time coupled wave packets,” Phys. Rev. A 81, 023810 (2010).
    [Crossref]
  26. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
    [Crossref]

2019 (4)

B. M. Heffernan, S. A. Meyer, D. Restrepo, M. E. Siemens, E. A. Gibson, and J. T. Gopinath, “A fiber-coupled stimulated emission depletion microscope for bend-insensitive through-fiber imaging,” Sci. Rep. 9, 11137 (2019).
[Crossref]

M. A. Porras, “Upper bound to the orbital angular momentum carried by an ultrashort pulse,” Phys. Rev. Lett. 122, 123904 (2019).
[Crossref]

S. Zahedpour, S. W. Hancock, and H. M. Milchberg, “Ultrashort infrared 2.5–11  µm pulses: spatiotemporal profiles and absolute nonlinear response of air constituents,” Opt. Lett. 44, 843–846 (2019).
[Crossref]

D. Jang, R. M. Schwartz, D. Woodbury, J. Griff-McMahon, A. H. Younis, H. M. Milchberg, and K.-Y. Kim, “Efficient terahertz and Brunel harmonic generation from air plasma via mid-infrared coherent control,” Optica 6, 1338–1341 (2019).
[Crossref]

2017 (1)

2016 (3)

2015 (1)

2012 (2)

K. Y. Bliokh and F. Nori, “Spatiotemporal vortex beams and angular momentum,” Phys. Rev. A 86, 033824 (2012).
[Crossref]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

2010 (2)

A. Richter, M. Bock, J. Jahns, and R. Grunwald, “Orbital angular momentum experiments with broadband few cycle pulses,” Proc. SPIE 7613, 761308 (2010).
[Crossref]

A. Lotti, A. Couairon, D. Faccio, and P. Di Trapani, “Energy-flux characterization of conical and space-time coupled wave packets,” Phys. Rev. A 81, 023810 (2010).
[Crossref]

2009 (3)

2007 (1)

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

2006 (1)

2004 (2)

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2004).
[Crossref]

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[Crossref]

2002 (1)

K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 81, 4124–4126 (2002).
[Crossref]

1997 (1)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[Crossref]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

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, 8185–8189 (1992).
[Crossref]

Alexeev, I.

K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 81, 4124–4126 (2002).
[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, 8185–8189 (1992).
[Crossref]

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, 8185–8189 (1992).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh and F. Nori, “Spatiotemporal vortex beams and angular momentum,” Phys. Rev. A 86, 033824 (2012).
[Crossref]

Bock, M.

A. Richter, M. Bock, J. Jahns, and R. Grunwald, “Orbital angular momentum experiments with broadband few cycle pulses,” Proc. SPIE 7613, 761308 (2010).
[Crossref]

Boyd, R. W.

Bragheri, F.

Cheng, Y.-H.

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

Couairon, A.

A. Lotti, A. Couairon, D. Faccio, and P. Di Trapani, “Energy-flux characterization of conical and space-time coupled wave packets,” Phys. Rev. A 81, 023810 (2010).
[Crossref]

D. Faccio, A. Lotti, A. Matijosius, F. Bragheri, V. Degiorgio, A. Couairon, and P. Di Trapani, “Experimental energy-density flux characterization of ultrashort laser pulse filaments,” Opt. Express 17, 8193–8200 (2009).
[Crossref]

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

D’Ambrosio, V.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2004).
[Crossref]

Degiorgio, V.

Denisenko, V.

Dennis, M. R.

Desyatnikov, A. S.

Di Trapani, P.

A. Lotti, A. Couairon, D. Faccio, and P. Di Trapani, “Energy-flux characterization of conical and space-time coupled wave packets,” Phys. Rev. A 81, 023810 (2010).
[Crossref]

D. Faccio, A. Lotti, A. Matijosius, F. Bragheri, V. Degiorgio, A. Couairon, and P. Di Trapani, “Experimental energy-density flux characterization of ultrashort laser pulse filaments,” Opt. Express 17, 8193–8200 (2009).
[Crossref]

Doster, T.

Faccio, D.

A. Lotti, A. Couairon, D. Faccio, and P. Di Trapani, “Energy-flux characterization of conical and space-time coupled wave packets,” Phys. Rev. A 81, 023810 (2010).
[Crossref]

D. Faccio, A. Lotti, A. Matijosius, F. Bragheri, V. Degiorgio, A. Couairon, and P. Di Trapani, “Experimental energy-density flux characterization of ultrashort laser pulse filaments,” Opt. Express 17, 8193–8200 (2009).
[Crossref]

Feder, L.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

Gibson, E. A.

B. M. Heffernan, S. A. Meyer, D. Restrepo, M. E. Siemens, E. A. Gibson, and J. T. Gopinath, “A fiber-coupled stimulated emission depletion microscope for bend-insensitive through-fiber imaging,” Sci. Rep. 9, 11137 (2019).
[Crossref]

Goers, A. J.

Gopinath, J. T.

B. M. Heffernan, S. A. Meyer, D. Restrepo, M. E. Siemens, E. A. Gibson, and J. T. Gopinath, “A fiber-coupled stimulated emission depletion microscope for bend-insensitive through-fiber imaging,” Sci. Rep. 9, 11137 (2019).
[Crossref]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[Crossref]

Griff-McMahon, J.

Grunwald, R.

A. Richter, M. Bock, J. Jahns, and R. Grunwald, “Orbital angular momentum experiments with broadband few cycle pulses,” Proc. SPIE 7613, 761308 (2010).
[Crossref]

Hancock, S. W.

S. Zahedpour, S. W. Hancock, and H. M. Milchberg, “Ultrashort infrared 2.5–11  µm pulses: spatiotemporal profiles and absolute nonlinear response of air constituents,” Opt. Lett. 44, 843–846 (2019).
[Crossref]

S. Zahedpour, S. W. Hancock, and H. M. Milchberg, “Direct measurement of linearly imposed spatiotemporal optical vortices (STOVs),” in Frontiers in Optics + Laser Science APS/DLS, OSA Technical Digest (Optical Society of America, 2019), paper FW5F.5.

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[Crossref]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

Heffernan, B. M.

B. M. Heffernan, S. A. Meyer, D. Restrepo, M. E. Siemens, E. A. Gibson, and J. T. Gopinath, “A fiber-coupled stimulated emission depletion microscope for bend-insensitive through-fiber imaging,” Sci. Rep. 9, 11137 (2019).
[Crossref]

Hine, G. A.

Jahns, J.

A. Richter, M. Bock, J. Jahns, and R. Grunwald, “Orbital angular momentum experiments with broadband few cycle pulses,” Proc. SPIE 7613, 761308 (2010).
[Crossref]

Jang, D.

Jhajj, N.

N. Jhajj, I. Larkin, E. W. Rosenthal, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Spatiotemporal optical vortices,” Phys. Rev. X 6, 031037 (2016).
[Crossref]

N. Jhajj, “Hydrodynamic and electrodynamic implications of optical femtosecond filamentation,” Ph.D.dissertation (University of Maryland, 2017), https://drum.lib.umd.edu/handle/1903/19973 , Chap. 5.

Kim, K. Y.

Kim, K.-Y.

Kivshar, Y. S.

Kolesik, M.

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[Crossref]

Krolikowski, W.

Kuk, D.

Larkin, I.

N. Jhajj, I. Larkin, E. W. Rosenthal, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Spatiotemporal optical vortices,” Phys. Rev. X 6, 031037 (2016).
[Crossref]

Lotti, A.

A. Lotti, A. Couairon, D. Faccio, and P. Di Trapani, “Energy-flux characterization of conical and space-time coupled wave packets,” Phys. Rev. A 81, 023810 (2010).
[Crossref]

D. Faccio, A. Lotti, A. Matijosius, F. Bragheri, V. Degiorgio, A. Couairon, and P. Di Trapani, “Experimental energy-density flux characterization of ultrashort laser pulse filaments,” Opt. Express 17, 8193–8200 (2009).
[Crossref]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[Crossref]

Marrucci, L.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2004).
[Crossref]

Matijosius, A.

Meyer, S. A.

B. M. Heffernan, S. A. Meyer, D. Restrepo, M. E. Siemens, E. A. Gibson, and J. T. Gopinath, “A fiber-coupled stimulated emission depletion microscope for bend-insensitive through-fiber imaging,” Sci. Rep. 9, 11137 (2019).
[Crossref]

Miao, B.

Milchberg, H. M.

S. Zahedpour, S. W. Hancock, and H. M. Milchberg, “Ultrashort infrared 2.5–11  µm pulses: spatiotemporal profiles and absolute nonlinear response of air constituents,” Opt. Lett. 44, 843–846 (2019).
[Crossref]

D. Jang, R. M. Schwartz, D. Woodbury, J. Griff-McMahon, A. H. Younis, H. M. Milchberg, and K.-Y. Kim, “Efficient terahertz and Brunel harmonic generation from air plasma via mid-infrared coherent control,” Optica 6, 1338–1341 (2019).
[Crossref]

F. Salehi, A. J. Goers, G. A. Hine, L. Feder, D. Kuk, B. Miao, D. Woodbury, K. Y. Kim, and H. M. Milchberg, “MeV electron acceleration at 1  kHz with <10  mJ laser pulses,” Opt. Lett. 42, 215–218 (2017).
[Crossref]

N. Jhajj, I. Larkin, E. W. Rosenthal, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Spatiotemporal optical vortices,” Phys. Rev. X 6, 031037 (2016).
[Crossref]

J. K. Wahlstrand, S. Zahedpour, and H. M. Milchberg, “Optimizing the time resolution of supercontinuum spectral interferometry,” J. Opt. Soc. Am. B 33, 1476–1481 (2016).
[Crossref]

S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Measurement of the nonlinear refractive index of air constituents at mid-infrared wavelengths,” Opt. Lett. 40, 5794–5797 (2015).
[Crossref]

J. K. Wahlstrand, Y.-H. Cheng, and H. M. Milchberg, “Absolute measurement of the transient optical nonlinearity in N2, O2, N2O, and Ar,” Phys. Rev. A 85, 043820 (2012).
[Crossref]

K. Y. Kim, I. Alexeev, and H. M. Milchberg, “Single-shot supercontinuum spectral interferometry,” Appl. Phys. Lett. 81, 4124–4126 (2002).
[Crossref]

S. Zahedpour, S. W. Hancock, and H. M. Milchberg, “Direct measurement of linearly imposed spatiotemporal optical vortices (STOVs),” in Frontiers in Optics + Laser Science APS/DLS, OSA Technical Digest (Optical Society of America, 2019), paper FW5F.5.

Moloney, J. V.

M. Kolesik and J. V. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[Crossref]

Mysyrowicz, A.

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

Neshev, D. N.

Nori, F.

K. Y. Bliokh and F. Nori, “Spatiotemporal vortex beams and angular momentum,” Phys. Rev. A 86, 033824 (2012).
[Crossref]

O’Holleran, K.

Padgett, M. J.

Porras, M. A.

M. A. Porras, “Upper bound to the orbital angular momentum carried by an ultrashort pulse,” Phys. Rev. Lett. 122, 123904 (2019).
[Crossref]

Restrepo, D.

B. M. Heffernan, S. A. Meyer, D. Restrepo, M. E. Siemens, E. A. Gibson, and J. T. Gopinath, “A fiber-coupled stimulated emission depletion microscope for bend-insensitive through-fiber imaging,” Sci. Rep. 9, 11137 (2019).
[Crossref]

Richter, A.

A. Richter, M. Bock, J. Jahns, and R. Grunwald, “Orbital angular momentum experiments with broadband few cycle pulses,” Proc. SPIE 7613, 761308 (2010).
[Crossref]

Rosenthal, E. W.

N. Jhajj, I. Larkin, E. W. Rosenthal, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Spatiotemporal optical vortices,” Phys. Rev. X 6, 031037 (2016).
[Crossref]

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995).
[Crossref]

Salehi, F.

Schwartz, R. M.

Sciarrino, F.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2004).
[Crossref]

Shvedov, V.

Siemens, M. E.

B. M. Heffernan, S. A. Meyer, D. Restrepo, M. E. Siemens, E. A. Gibson, and J. T. Gopinath, “A fiber-coupled stimulated emission depletion microscope for bend-insensitive through-fiber imaging,” Sci. Rep. 9, 11137 (2019).
[Crossref]

Slussarenko, S.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2004).
[Crossref]

Soskin, M.

Soskin, M. S.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[Crossref]

Sponselli, A.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2004).
[Crossref]

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, 8185–8189 (1992).
[Crossref]

Tyler, G. A.

Vallone, G.

G. Vallone, V. D’Ambrosio, A. Sponselli, S. Slussarenko, L. Marrucci, F. Sciarrino, and P. Villoresi, “Free-space quantum key distribution by rotation-invariant twisted photons,” Phys. Rev. Lett. 113, 060503 (2004).
[Crossref]

Vasnetsov, M. V.

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Phys. Rev. X (1)

N. Jhajj, I. Larkin, E. W. Rosenthal, S. Zahedpour, J. K. Wahlstrand, and H. M. Milchberg, “Spatiotemporal optical vortices,” Phys. Rev. X 6, 031037 (2016).
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Figures (5)

Fig. 1.
Fig. 1. Top, setup for TG-SSSI. The STOV-carrying pump pulse (center wavelength ${\lambda _0} = 800\,\,\text{nm}$) at the output of a $4f$ pulse shaper is focused (${\sim\!{1.5}\;\unicode{x00B5} \text{J}}$) or imaged ($\sim\!{20}\;\unicode{x00B5} \text{J}$) into a 500 µm thick fused silica witness plate. The pump pulse energy is kept sufficiently low so that the STOV pulse propagates nearly linearly in the plate. A probe pulse ${\varepsilon _i}$ (${\lambda _0} = 795\,\,\text{nm}$, 2 nm bandwidth) crosses the STOV pulse direction at angle $\theta = 6^\circ $, forming a transient grating with modulations $ \propto \cos( {kx\sin \theta + \Delta \Phi ( {x,\tau } )} )$, where the symbols are defined in the main text and reference coordinates are shown next to the witness plate. The transient grating is probed by SSSI [19,20], which uses $\sim\!{1.5}\;\text{ps}$ long chirped SC reference and probe pulses ${E_{{\text{ref}}}}$ and ${E_{\text{pr}}}$ (${\lambda _0}\sim 575\,\,\text{nm}$). The result is single-shot time- and space-resolved images of amplitude and phase of STOV-carrying pulses. Bottom left, cylindrical lens-based $4f$ pulse shaper [16,17] for imposing a line-STOV on a 45 fs, $\lambda = {800}\;\text{nm}$ input pulse. A phase mask is inserted in the Fourier plane at the common focus of the cylindrical lenses. For the current experiment, we use spiral phase masks ($l = 1,l = - 1,$ and $l = 8$) and a $\pi $-step mask, all etched on fused silica, where the $\pi $-step angle $\alpha $ and the spiral orientation (for $l = - 1$) are also shown. Both the $l = 1$ and $l = 8$ plates have 16 levels (steps) every 2 $\pi $. Shaper gratings: 1200 line/mm; cylindrical lenses: focal length 20 cm.
Fig. 2.
Fig. 2. (a) Output of pulse shaper with no phase plate. The 50 fs input pulse, with a weakly parabolic temporal phase, is recovered. (b, c) Intensity and phase of pulse in far field of pulse shaper with $l = 1$ and $l = - 1$ spiral phase plates; white-bordered insets, pulse shaper near-field intensity images. The red arrows show the direction of phase circulation. Headings of each column are described in the text. In all panels, the temporal leading edge of the pulse is on the left ($\tau \lt 0$), so propagation is right to left. The pulse energy for the three far-field cases above is $\sim\!{1}\;{ \unicode{x00B5} \text{J}}$. For the near field cases (insets), the pulse energy is increased to $\sim\!{20}\;\unicode{x00B5}\text{J}$ to offset the reduced signal due to magnification.
Fig. 3.
Fig. 3. (a) Flying donut near-field intensity and phase from π-step pulse shaper (${\alpha _{\text{step}}} = + 25^\circ ,l = 1$), obtained from imaging shaper output into witness plate. (b, c) Offset lobe far-field intensity and phase, obtained by focusing shaper output into witness plate for step orientations ${\alpha _{\text{step}}} = \pm 25^\circ ( {l = \pm 1} )$; (d) simulation for ${\alpha _{\text{step}}} = - 25^\circ $ of far-field intensity and phase for (d) no dispersion; (e) group dispersion delay ($\text{GDD} = {100}\;{\text{fs}^2}$). The addition of parabolic temporal phase to the spatiotemporal phase step of (d) explains the phase pattern in (b, c). Headings of each column are described in the text. The pulse energy in panel (a) is $\sim\!{20}\;\unicode{x00B5}\text{J}$ and $\sim\!{1}\;\unicode{x00B5}\text{J}$ in panels (b) and (c). Propagation is right to left.
Fig. 4.
Fig. 4. 3D+time UPPE simulation of STOV-carrying pulse launched from a pulse shaper with a $l = + 1$ spatiospectral spiral phase factor ${e^{i\Delta \varphi ( {x,\omega } )}} = {\mathbb Z}/| {\mathbb Z} |$ corresponding to our experiment (see text). Near field is right after a 3 m lens at the pulse shaper output; far field is at the lens focus. Rayleigh range is ${z_R} = 2.3\,\,\text{m}$. The propagation direction within each panel is right to left. Top row, intensity profiles ${I_S}( {x,\tau } )$; bottom row, phase profiles $\Delta \Phi ( {x,\tau } )$ with red arrows showing phase increase direction; bottom row white-bordered insets, intensity profiles simulated using $l = + 1$ spatiospectral spiral phase factor ${\mathbb Z}$.
Fig. 5.
Fig. 5. Results from pulse shaper with $l = 8$ spiral phase plate. Pulse propagation is right to left. Left column, intensity profiles ${I_S}( {x,\tau } )$; right column, phase profiles $\Delta {\Phi }( {x,\tau } )$. All profiles are spatially rescaled for comparison. (a) Near-field intensity and phase of shaper output, obtained from imaging exit grating onto witness plate. The $l = 8$ vortex appears as eight $\pi $-step phase jumps (only six visible owing to underfilling of image by probe SC pulse). Laser pulse energy $\sim\!{20}\;\unicode{x00B5}\text{J}$; (b) far-field intensity and phase obtained by focusing shaper output onto witness plate. Here, eight $l = 1$ STOVs are seen in the phase plot (here, the SC reference pulse profile overfills the smaller spot). Laser pulse energy $\sim\!{2}\;\unicode{x00B5}\text{J}$; (c, d) Fourier transform simulation of near-field and far-field intensity and phase where the ($x,\omega $) spatial profile of the pulse in the shaper is not matched to the phase mask; (e, f) Fourier transform simulation of near-field and far-field intensity and phase where the ($x,\omega $) pulse profile in the shaper is matched to the phase plate.

Equations (1)

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E ( r , z , τ ) = a ( τ / τ s + i sgn ( l ) x / x s ) | l | E 0 ( r , z , τ ) = A ( x , τ ) e i l Φ s t E 0 ( r , z , τ ) ,

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