Abstract

Spectral anomalies of femtosecond pulses with orbital angular momentum were studied in the vicinity of singularities. Bessel-Gauss (BG) beams were generated with mode-locked Ti:sapphire oscillators and dispersion-compensated diffractive axicons acting as spiral phase plates (SPPs). High-resolution two-dimensional spectral mapping was performed with a scanning fiber probe. Progressive rotation of the most pronounced features, known as “spectral eyes”, in the maps of spectral moments was found at increasing propagation distance. The phenomenon is explained by a wavelength-dependent Gouy phase shift of interfering spectral components in the twisted wavefront. Spatial “spectral switching” was detected for few-cycle pulses. Possible improvements of selectivity are proposed.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (2)

F. Schlaepfer, A. Ludwig, M. Lucchini, L. Kasmi, M. Volkov, L. Gallmann, and U. Keller, “Gouy phase shift for annular beam profiles in attosecond experiments,” Opt. Express 25(4), 3646–3655 (2017).
[PubMed]

D. Hoff, M. Krüger, L. Maisenbacher, A. M. Sayler, G. G. Paulus, and P. Hommelhoff, “Tracing the phase of focused broadband laser pulses,” Nat. Phys. 13, 4185 (2017).

2016 (2)

M. Bock and R. Grunwald, “Mapping the spectral twist of few cycle vortex pulses,” Proc. SPIE 9764, 97640O (2016).

J. D. Rodrigues, L. G. Marcassa, and J. T. Mendoca, “Excitation of high orbital momentum Rydberg states with Laguerre-Gauss beams,” J. Phys. At. Mol. Opt. Phys. 49, 074007 (2016).

2014 (3)

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[PubMed]

M. Musigmann, J. Jahns, M. Bock, and R. Grunwald, “Refractive-diffractive dispersion compensation for optical vortex beams with ultrashort pulse durations,” Appl. Opt. 53(31), 7304–7311 (2014).
[PubMed]

R. Grunwald, T. Elsaesser, and M. Bock, “Spatio-temporal coherence mapping of few-cycle vortex pulses,” Sci. Rep. 4, 7148 (2014).
[PubMed]

2013 (4)

M. Bock, J. Brunne, A. Treffer, S. König, U. Wallrabe, and R. Grunwald, “Sub-3-cycle vortex pulses of tunable topological charge,” Opt. Lett. 38(18), 3642–3645 (2013).
[PubMed]

B. S. Davis and L. Kaplan, “Transverse phase variation of a Gaussian beam,” J. Opt. 15, 075706 (2013).

P. Vaveliuk, O. M. Matos, and G. Torchia, “Features of the Gouy phase of nondiffracting beams,” Prog. Electromagnetics Res. 140, 599–611 (2013).

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

2012 (7)

2011 (4)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: Origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).

X. Pang, T. D. Visser, and E. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun. 284(24), 5517–5522 (2011).

2010 (5)

2009 (3)

2008 (3)

2007 (1)

2006 (4)

L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257(1), 1–8 (2006).

C. J. Zapata-Rodríguez, “Analytical characterization of spectral anomalies in polychromatic aperture beams,” Opt. Commun. 257(1), 9–15 (2006).

X. Hu and J. Pu, “Spectral anomalies of focused high order Bessel beams in the neighborhood of focus,” Opt. Commun. 266, 413–418 (2006).

J. Hamazaki, Y. Mineta, K. Oka, and R. Morita, “Direct observation of Gouy phase shift in a propagating optical vortex,” Opt. Express 14(18), 8382–8392 (2006).
[PubMed]

2005 (1)

2004 (3)

2003 (1)

2002 (5)

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89(14), 143601 (2002).
[PubMed]

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88(1), 013901 (2002).
[PubMed]

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88(18), 183902 (2002).
[PubMed]

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66 (2002).

M. V. Berry, “Exploring the colours of dark light,” New J. Phys. 4, 74 (2002).

2001 (3)

T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189, 5–14 (2001).

S. Feng and H. G. Winful, “Physical origin of the Gouy phase shift,” Opt. Lett. 26(8), 485–487 (2001).
[PubMed]

G. A. Swartzlander., “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26(8), 497–499 (2001).
[PubMed]

1998 (2)

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(5), 4064–4075 (1997).

1996 (1)

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt. 43(2), 219–221 (1996).

1995 (1)

H. He, M. E. H. 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(5), 826–829 (1995).
[PubMed]

1992 (2)

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39(8), 985–990 (1992).

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).
[PubMed]

1980 (1)

1956 (1)

E. H. Linfoot and E. Wolf, “Phase Distribution near Focus in an Aberration-free Diffraction Image,” Proc. Phys. Soc. B 69, 823 (1956).

1938 (1)

A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev. 54(11), 931–936 (1938).

1890 (1)

L. G. Gouy, “Sur une propriete nouvelle des ondes lumineuses,” C. R. Acad. Sci. Paris 110, 1251–1253 (1890).

Ackemann, T.

T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189, 5–14 (2001).

Alfano, R. R.

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).
[PubMed]

Andrews, D. L.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89(14), 143601 (2002).
[PubMed]

Angelsky, O. V.

Anzolin, G.

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).

Assafrao, Ada. C.

Babiker, M.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89(14), 143601 (2002).
[PubMed]

Baltuška, A.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Barnett, S.

Baumann, S. M.

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39(8), 985–990 (1992).

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).
[PubMed]

Bennett, C. R.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89(14), 143601 (2002).
[PubMed]

Berry, M. V.

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66 (2002).

M. V. Berry, “Exploring the colours of dark light,” New J. Phys. 4, 74 (2002).

Bezuhanov, K.

Bliokh, K. Y.

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

Bock, M.

Börner, P.

Bowman, R.

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).

Boyd, R. W.

Bretner, I.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Whirling plasmons: angular momentum selection rule,” Opt. Photonics News 20(12), 26 (2009).

Brunne, J.

Calvo, G. F.

Chen, J.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. A, Pure Appl. Opt. 14, 055707 (2012).

Courtial, J.

Cui, H. X.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. A, Pure Appl. Opt. 14, 055707 (2012).

Das, S. K.

Dávila Romero, L. C.

M. Babiker, C. R. Bennett, D. L. Andrews, and L. C. Dávila Romero, “Orbital angular momentum exchange in the interaction of twisted light with molecules,” Phys. Rev. Lett. 89(14), 143601 (2002).
[PubMed]

Davis, B. S.

B. S. Davis and L. Kaplan, “Transverse phase variation of a Gaussian beam,” J. Opt. 15, 075706 (2013).

de Aldana, J. R.

Diehl, M.

Ding, C.

Dogariu, A.

G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88(18), 183902 (2002).
[PubMed]

Dreischuh, A.

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

K. Bezuhanov, A. Dreischuh, G. G. Paulus, M. G. Schätzel, and H. Walther, “Vortices in femtosecond laser fields,” Opt. Lett. 29(16), 1942–1944 (2004).
[PubMed]

Elsaesser, T.

R. Grunwald, T. Elsaesser, and M. Bock, “Spatio-temporal coherence mapping of few-cycle vortex pulses,” Sci. Rep. 4, 7148 (2014).
[PubMed]

Feng, S.

Fickler, R.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[PubMed]

Fischer, C.

Franke-Arnold, S.

Friese, M. E. H.

H. He, M. E. H. 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(5), 826–829 (1995).
[PubMed]

Gallmann, L.

Galvez, E. J.

Gatto, A.

Gbur, G.

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88(1), 013901 (2002).
[PubMed]

Gibson, G.

Gomez, V.

Gorodetski, Y.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Whirling plasmons: angular momentum selection rule,” Opt. Photonics News 20(12), 26 (2009).

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(5), 4064–4075 (1997).

Goulielmakis, E.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Gouy, L. G.

L. G. Gouy, “Sur une propriete nouvelle des ondes lumineuses,” C. R. Acad. Sci. Paris 110, 1251–1253 (1890).

Griebner, U.

Grosse-Nobis, W.

T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189, 5–14 (2001).

Grunwald, R.

Gu, B.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. A, Pure Appl. Opt. 14, 055707 (2012).

Guzzinati, G.

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

Hamazaki, J.

Hansinger, P.

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

Hanson, S. G.

Hariharan, P.

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt. 43(2), 219–221 (1996).

Hasman, E.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Whirling plasmons: angular momentum selection rule,” Opt. Photonics News 20(12), 26 (2009).

He, H.

H. He, M. E. H. 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(5), 826–829 (1995).
[PubMed]

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(5), 4064–4075 (1997).

H. He, M. E. H. 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(5), 826–829 (1995).
[PubMed]

Hellwarth, R. W.

Helseth, L. E.

L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257(1), 1–8 (2006).

Herzig, H. P.

Hnatovsky, C.

Hoff, D.

D. Hoff, M. Krüger, L. Maisenbacher, A. M. Sayler, G. G. Paulus, and P. Hommelhoff, “Tracing the phase of focused broadband laser pulses,” Nat. Phys. 13, 4185 (2017).

Hommelhoff, P.

D. Hoff, M. Krüger, L. Maisenbacher, A. M. Sayler, G. G. Paulus, and P. Hommelhoff, “Tracing the phase of focused broadband laser pulses,” Nat. Phys. 13, 4185 (2017).

Hu, X.

X. Hu and J. Pu, “Spectral anomalies of focused high order Bessel beams in the neighborhood of focus,” Opt. Commun. 266, 413–418 (2006).

Huber, M.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[PubMed]

Huferath, S.

Jahns, J.

Jankowska, E.

Kalb, D. M.

Kaplan, L.

B. S. Davis and L. Kaplan, “Transverse phase variation of a Gaussian beam,” J. Opt. 15, 075706 (2013).

Kartazaev, V.

Kärtner, F. X.

Kasmi, L.

Kebbel, V.

Keller, U.

Kern, C.

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

Kim, M.-S.

Kleiner, V.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Whirling plasmons: angular momentum selection rule,” Opt. Photonics News 20(12), 26 (2009).

König, S.

Krausz, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Krolikowski, W.

Krüger, M.

D. Hoff, M. Krüger, L. Maisenbacher, A. M. Sayler, G. G. Paulus, and P. Hommelhoff, “Tracing the phase of focused broadband laser pulses,” Nat. Phys. 13, 4185 (2017).

Lapkiewicz, R.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[PubMed]

Lavery, M. P. J.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[PubMed]

Le, T.

Leniec, M.

Lezius, M.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Li, Y. N.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. A, Pure Appl. Opt. 14, 055707 (2012).

Lindner, F.

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Linfoot, E. H.

E. H. Linfoot and E. Wolf, “Phase Distribution near Focus in an Aberration-free Diffraction Image,” Proc. Phys. Soc. B 69, 823 (1956).

Lippi, G. L.

T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189, 5–14 (2001).

Lü, B.

Lucchini, M.

Ludwig, A.

MacMillan, L. H.

Maisenbacher, L.

D. Hoff, M. Krüger, L. Maisenbacher, A. M. Sayler, G. G. Paulus, and P. Hommelhoff, “Tracing the phase of focused broadband laser pulses,” Nat. Phys. 13, 4185 (2017).

Maksimyak, A. P.

Maksimyak, P. P.

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(5), 4064–4075 (1997).

Marcassa, L. G.

J. D. Rodrigues, L. G. Marcassa, and J. T. Mendoca, “Excitation of high orbital momentum Rydberg states with Laguerre-Gauss beams,” J. Phys. At. Mol. Opt. Phys. 49, 074007 (2016).

Martelli, P.

Martinelli, M.

Masajada, J.

Matos, O. M.

P. Vaveliuk, O. M. Matos, and G. Torchia, “Features of the Gouy phase of nondiffracting beams,” Prog. Electromagnetics Res. 140, 599–611 (2013).

Mendoca, J. T.

J. D. Rodrigues, L. G. Marcassa, and J. T. Mendoca, “Excitation of high orbital momentum Rydberg states with Laguerre-Gauss beams,” J. Phys. At. Mol. Opt. Phys. 49, 074007 (2016).

Mineta, Y.

Molina-Terriza, G.

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).

Mompart, J.

Moneta, G.

Morita, R.

Musigmann, M.

Néron, J.-L.

Neumann, U.

Nori, F.

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

Oka, K.

Ottevaere, H.

Padgett, M.

Padgett, M. J.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[PubMed]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: Origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).

Pan, L.

Pang, X.

X. Pang, T. D. Visser, and E. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun. 284(24), 5517–5522 (2011).

Pas’ko, V.

Paulus, G. G.

D. Hoff, M. Krüger, L. Maisenbacher, A. M. Sayler, G. G. Paulus, and P. Hommelhoff, “Tracing the phase of focused broadband laser pulses,” Nat. Phys. 13, 4185 (2017).

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

K. Bezuhanov, A. Dreischuh, G. G. Paulus, M. G. Schätzel, and H. Walther, “Vortices in femtosecond laser fields,” Opt. Lett. 29(16), 1942–1944 (2004).
[PubMed]

Pereira, S. F.

Piché, M.

Picón, A.

Plaja, L.

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G. Popescu and A. Dogariu, “Spectral anomalies at wave-front dislocations,” Phys. Rev. Lett. 88(18), 183902 (2002).
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Pu, J.

X. Hu and J. Pu, “Spectral anomalies of focused high order Bessel beams in the neighborhood of focus,” Opt. Commun. 266, 413–418 (2006).

Putnam, W. P.

Reimann, K.

Roberts, A.

Robinson, P. A.

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt. 43(2), 219–221 (1996).

Rockstuhl, C.

Rode, A. V.

Rodrigues, J. D.

J. D. Rodrigues, L. G. Marcassa, and J. T. Mendoca, “Excitation of high orbital momentum Rydberg states with Laguerre-Gauss beams,” J. Phys. At. Mol. Opt. Phys. 49, 074007 (2016).

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Rubinowicz, A.

A. Rubinowicz, “On the anomalous propagation of phase in the focus,” Phys. Rev. 54(11), 931–936 (1938).

Rubinsztein-Dunlop, H.

H. He, M. E. H. 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(5), 826–829 (1995).
[PubMed]

Rudolph, W.

Sandhu, A.

Sayler, A. M.

D. Hoff, M. Krüger, L. Maisenbacher, A. M. Sayler, G. G. Paulus, and P. Hommelhoff, “Tracing the phase of focused broadband laser pulses,” Nat. Phys. 13, 4185 (2017).

Scharf, T.

Schattschneider, P.

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

Schätzel, M. G.

Schimpf, D. N.

Schlaepfer, F.

Schulte, J.

Schwarz, A.

Shitrit, N.

Y. Gorodetski, N. Shitrit, I. Bretner, V. Kleiner, and E. Hasman, “Whirling plasmons: angular momentum selection rule,” Opt. Photonics News 20(12), 26 (2009).

Shivaram, N.

Shvedov, V. G.

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(5), 4064–4075 (1997).

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39(8), 985–990 (1992).

Spielmann, Ch.

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

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).
[PubMed]

Steinmeyer, G.

Stibenz, G.

Swartzlander, G. A.

Sztul, H. I.

Tacca, M.

Tamburini, F.

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).

Thidé, B.

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).

Thienpont, H.

Toda, Y.

Torchia, G.

P. Vaveliuk, O. M. Matos, and G. Torchia, “Features of the Gouy phase of nondiffracting beams,” Prog. Electromagnetics Res. 140, 599–611 (2013).

Treffer, A.

Urbach, H. P.

Vasnetsov, M.

Vasnetsov, M. V.

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(5), 4064–4075 (1997).

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39(8), 985–990 (1992).

Vaveliuk, P.

P. Vaveliuk, O. M. Matos, and G. Torchia, “Features of the Gouy phase of nondiffracting beams,” Prog. Electromagnetics Res. 140, 599–611 (2013).

Verbeeck, J.

G. Guzzinati, P. Schattschneider, K. Y. Bliokh, F. Nori, and J. Verbeeck, “Observation of the Larmor and Gouy rotations with electron vortex beams,” Phys. Rev. Lett. 110(9), 093601 (2013).
[PubMed]

Visser, T. D.

X. Pang, T. D. Visser, and E. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun. 284(24), 5517–5522 (2011).

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283, 3371–3375 (2010).

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88(1), 013901 (2002).
[PubMed]

Volkov, M.

Wallrabe, U.

Walther, H.

K. Bezuhanov, A. Dreischuh, G. G. Paulus, M. G. Schätzel, and H. Walther, “Vortices in femtosecond laser fields,” Opt. Lett. 29(16), 1942–1944 (2004).
[PubMed]

F. Lindner, G. G. Paulus, H. Walther, A. Baltuška, E. Goulielmakis, M. Lezius, and F. Krausz, “Gouy phase shift for few-cycle laser pulses,” Phys. Rev. Lett. 92(11), 113001 (2004).
[PubMed]

Wang, H. T.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. A, Pure Appl. Opt. 14, 055707 (2012).

Wang, X. L.

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. A, Pure Appl. Opt. 14, 055707 (2012).

Winful, H. G.

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).
[PubMed]

Wolf, E.

X. Pang, T. D. Visser, and E. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun. 284(24), 5517–5522 (2011).

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283, 3371–3375 (2010).

G. Gbur, T. D. Visser, and E. Wolf, “Anomalous behavior of spectra near phase singularities of focused waves,” Phys. Rev. Lett. 88(1), 013901 (2002).
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E. H. Linfoot and E. Wolf, “Phase Distribution near Focus in an Aberration-free Diffraction Image,” Proc. Phys. Soc. B 69, 823 (1956).

Xu, L.

Yamane, K.

Yao, A. M.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: Origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).

Zapata-Rodríguez, C. J.

C. J. Zapata-Rodríguez, “Analytical characterization of spectral anomalies in polychromatic aperture beams,” Opt. Commun. 257(1), 9–15 (2006).

Zeilinger, A.

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[PubMed]

Zeylikovich, I.

Zürch, M.

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

Adv. Opt. Photonics (1)

A. M. Yao and M. J. Padgett, “Orbital angular momentum: Origins, behavior and applications,” Adv. Opt. Photonics 3(2), 161–204 (2011).

Appl. Opt. (2)

C. R. Acad. Sci. Paris (1)

L. G. Gouy, “Sur une propriete nouvelle des ondes lumineuses,” C. R. Acad. Sci. Paris 110, 1251–1253 (1890).

J. Mod. Opt. (2)

P. Hariharan and P. A. Robinson, “The Gouy phase shift as a geometrical quantum effect,” J. Mod. Opt. 43(2), 219–221 (1996).

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39(8), 985–990 (1992).

J. Opt. (1)

B. S. Davis and L. Kaplan, “Transverse phase variation of a Gaussian beam,” J. Opt. 15, 075706 (2013).

J. Opt. A, Pure Appl. Opt. (1)

H. X. Cui, X. L. Wang, B. Gu, Y. N. Li, J. Chen, and H. T. Wang, “Angular diffraction of an optical vortex induced by the Gouy phase,” J. Opt. A, Pure Appl. Opt. 14, 055707 (2012).

J. Opt. Soc. Am. (1)

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

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

J. D. Rodrigues, L. G. Marcassa, and J. T. Mendoca, “Excitation of high orbital momentum Rydberg states with Laguerre-Gauss beams,” J. Phys. At. Mol. Opt. Phys. 49, 074007 (2016).

Nat. Commun. (1)

R. Fickler, R. Lapkiewicz, M. Huber, M. P. J. Lavery, M. J. Padgett, and A. Zeilinger, “Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information,” Nat. Commun. 5, 4502 (2014).
[PubMed]

Nat. Photonics (1)

M. Padgett and R. Bowman, “Tweezers with a twist,” Nat. Photonics 5, 343–348 (2011).

Nat. Phys. (3)

F. Tamburini, B. Thidé, G. Molina-Terriza, and G. Anzolin, “Twisting of light around rotating black holes,” Nat. Phys. 7, 195–197 (2011).

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

D. Hoff, M. Krüger, L. Maisenbacher, A. M. Sayler, G. G. Paulus, and P. Hommelhoff, “Tracing the phase of focused broadband laser pulses,” Nat. Phys. 13, 4185 (2017).

New J. Phys. (2)

M. V. Berry, “Coloured phase singularities,” New J. Phys. 4, 66 (2002).

M. V. Berry, “Exploring the colours of dark light,” New J. Phys. 4, 74 (2002).

Opt. Commun. (6)

C. J. Zapata-Rodríguez, “Analytical characterization of spectral anomalies in polychromatic aperture beams,” Opt. Commun. 257(1), 9–15 (2006).

X. Hu and J. Pu, “Spectral anomalies of focused high order Bessel beams in the neighborhood of focus,” Opt. Commun. 266, 413–418 (2006).

X. Pang, T. D. Visser, and E. Wolf, “Phase anomaly and phase singularities of the field in the focal region of high-numerical aperture systems,” Opt. Commun. 284(24), 5517–5522 (2011).

T. D. Visser and E. Wolf, “The origin of the Gouy phase anomaly and its generalization to astigmatic wavefields,” Opt. Commun. 283, 3371–3375 (2010).

T. Ackemann, W. Grosse-Nobis, and G. L. Lippi, “The Gouy phase shift, the average phase lag of Fourier components of Hermite-Gaussian modes and their application to resonance conditions in optical cavities,” Opt. Commun. 189, 5–14 (2001).

L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257(1), 1–8 (2006).

Opt. Express (11)

J. Masajada, M. Leniec, E. Jankowska, H. Thienpont, H. Ottevaere, and V. Gomez, “Deep microstructure topography characterization with optical vortex interferometer,” Opt. Express 16(23), 19179–19191 (2008).
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K. Yamane, Y. Toda, and R. Morita, “Ultrashort optical-vortex pulse generation in few-cycle regime,” Opt. Express 20(17), 18986–18993 (2012).
[PubMed]

A. Picón, J. Mompart, J. R. de Aldana, L. Plaja, G. F. Calvo, and L. Roso, “Photoionization with orbital angular momentum beams,” Opt. Express 18(4), 3660–3671 (2010).
[PubMed]

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Supplementary Material (1)

NameDescription
» Visualization 1       Visualization 1

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Figures (8)

Fig. 1
Fig. 1

Schematic setup for spatio-spectral mapping of femtosecond OAM pulses based on a scanning fiber probe. Light sources: Ti:sapphire laser oscillators, FWHM spectral widths 10-70 nm, pulse durations 11-120 fs; beam shapers: refractive-diffractive spiral phase plates (SPP), dispersion compensated for 800 nm, x-y positioning stage: 100 nm minimum resolution; z-stage: 10 µm minimum step width; aperture diameter at the fiber entrance face: 10 µm; spectrometer: < 0.7 nm resolution. Inset: SPP, magnifying microscope and fiber probe.

Fig. 2
Fig. 2

Trade-off of spectral bandwidth (BWi) and modulation depth (MDi) (schematically). In this idealized picture, B, R are symmetric parts of the redistributed spectrum with centers of gravity at the blue and red side which correspond to separated peaks in the spatial maps. MDi is defined as the signal intensity at the crossing point of the spectra and increases from larger bandwidth (a) towards a smaller one (b). It becomes obvious that for the demonstration of Gouy rotation in spectral domain via COGs, a larger spectral contrast should be advantageous because of enhanced selectivity. Yellow bars stand for the products BWi x MDi where BWi, for reasons of simplicity, corresponds to the total extension of the spectra (here: measured between the intensity zeros).

Fig. 3
Fig. 3

Intensity map detected with an EMCCD camera at a distance of 5 mm from the SPP axicon (femtosecond illumination, central wavelength 795 nm, FWHM spectral width 10 nm, camera exposure time 5 ms, image artificially colorized). The highlighted region (white rectangular box) shows the area of interest for the spectral mapping experiments (2.8 x 3.2 µm2).

Fig. 4
Fig. 4

Spectral profiles of the femtosecond lasers used in the experiments: (a) Spectrum for the detection of the complete Gouy rotation in spectral domain (Tsunami) (central wavelength 795 nm, FWHM spectral width 10 nm, 10% width > 20 nm, corrected with respect to the spectral transfer and sensitivity of the detection system); (b) Spectrum of the few-cycle Ti:sapphire laser oscillator (FemtoSource) (central wavelength 820 nm, FWHM spectral width 71 nm, 10% width > 150 nm, corrected with respect to the spectral transfer and sensitivity of the detection system).

Fig. 5
Fig. 5

Spectral Gouy rotation in the distributions of 1st moments (COG) for a femtosecond LG-pulse (pulse duration 120 fs, FWHM spectral width 10 nm, topological charge = 1, propagation from left to right) detected by two-dimensional spectral mapping with the scanning fiber probe (step widths in x- and y-directions: 162 µm and 181 µm, respectively, axial steps 10 µm). The rotation angle ϕ covers the ranges (a) 0 το π, (b) π to 2π. This complete rotation cycle is part of multiple subsequent cycles (see Fig. 7). To optimize the displayed spectral maps, the spectral intervals for the presentation were adapted for maximum color contrast (see Fig. 6). The grey sinusoidal lines connect the COGs of both “spectral eyes” (see Visualization 1).

Fig. 6
Fig. 6

Spectral intervals corresponding to the visualization of Gouy rotation in the rotating spectral maps shown in Fig. 5 (min = minimum wavelength, max = maximum wavelength).

Fig. 7
Fig. 7

(a) Rotation angle ϕ of the connecting axis of the “spectral eyes” of the anomaly for distances between 4 and 5 mm. An axial period of about 200 µm was found for 5 rotation cycles. (b) Concatenated rotation curves for continuously increasing rotation angle ϕ. A linear slope is superimposed by weak oscillations.

Fig. 8
Fig. 8

Spectral FWHM bandwidth maps of focused few-cycle pulses (pulse duration 11 fs) with two different topological charges, (a) = 1, and (b) = 2. One recognizes a “single spectral tornado” in (a) and a “double spectral tornado” in (b), resembling the “eye” shaped spatio-spectral patterns known from polychromatic vortices. The spatial chirp is characterized by a bandwidth reversal which is clearly more symmetric in case (a) compared to case (b).

Equations (9)

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 Δ ψ G (λ)=arctan( z z R (λ) ).
U( r,z,ϕ )~ 2p! π( p+| l | )! 1 w(z) [ r 2 w(z) ] | l | × P 1 × P 2 × P 3 .
P 1 =exp[ r 2 w 2 (z) ] L p | l | ( 2 r 2 w 2 (z) ),
P 2 =exp[ ilϕ ]exp[ ik r 2 z 2( z 2 + z R 2 (λ) ) ],
P 3 =exp[ i(2p+| l |+1) ψ G (λ) ].
U( r,z,ϕ )~A( ω ) J n ( r )exp(i nϕ)exp(iβz).
 Δ ψ B ( λ )=( kβ )z
M 1 (x,y,z)= i=1 n [ λ i I(x,y,z, λ i )Δ λ i ] i=1 n [ I(x,y,z, λ i )Δ λ i ] ,
M 2 (x,y,z)= i=1 n [ ( λ i M 1 ) 2 I(x,y,z, λ i )Δ λ i ] i=1 n [ I(x,y,z, λ i )Δ λ i ] ,