Abstract

Can an optical pulse traverse a non-dispersive material at the speed of light in vacuum? Because traditional approaches for controlling the group velocity of light manipulate either the material or structural resonances, an absence of dispersion altogether appears to exclude such a prospect. Here we demonstrate theoretically and experimentally that “space–time” wave packets—pulsed beams in which the spatial and temporal degrees of freedom are tightly intertwined—can indeed traverse a non-dispersive transparent optical material at the speed of light in vacuum. We synthesize wave packets whose spatio-temporal spectra lie along the intersection of the material’s light-cone with a spectral hyperplane tilted to coincide with the vacuum light-line. By measuring the group delay interferometrically with respect to a generic reference pulse, we confirm that the wave packet group velocity in a variety of materials (including water, glass, and sapphire) is the speed of light in vacuum.

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

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References

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2018 (5)

2017 (2)

K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358, eaan5196 (2017).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Diffraction-free space-time beams,” Nat. Photonics 11, 733–740 (2017).
[Crossref]

2016 (3)

2014 (2)

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

R. Jedamzik, S. Reichel, and P. Hartmann, “Optical glass with tightest refractive index and dispersion tolerances for high-end optical designs,” Proc. SPIE 8982, 89821F (2014).
[Crossref]

2013 (1)

2012 (1)

2011 (1)

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

2010 (2)

2009 (5)

2008 (3)

2007 (1)

2006 (2)

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96, 193901 (2006).
[Crossref]

C. J. Zapata-Rodríguez and M. A. Porras, “X-wave bullets with negative group velocity in vacuum,” Opt. Lett. 31, 3532–3534 (2006).
[Crossref]

2005 (2)

2004 (2)

S. Longhi, “Gaussian pulsed beams with arbitrary speed,” Opt. Express 12, 935–940 (2004).
[Crossref]

P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).
[Crossref]

2003 (2)

M. A. Porras, G. Valiulis, and P. Di Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016613 (2003).
[Crossref]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[Crossref]

2002 (2)

I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
[Crossref]

J. Hebling, G. Almási, I. Z. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large-area THz-pulse generation,” Opt. Express 10, 1161–1166 (2002).
[Crossref]

2000 (2)

K. Reivelt and P. Saari, “Optical generation of focus wave modes,” J. Opt. Soc. Am. A 17, 1785–1790 (2000).
[Crossref]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref]

1999 (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 m per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

1997 (1)

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
[Crossref]

1996 (3)

1993 (1)

R. Donnelly and R. Ziolkowski, “Designing localized waves,” Proc. R. Soc. Lond. A 440, 541–565 (1993).
[Crossref]

1984 (1)

1973 (1)

1965 (1)

1962 (1)

Abouraddy, A. F.

H. E. Kondakci and A. F. Abouraddy, “Airy wavepackets accelerating in space-time,” Phys. Rev. Lett. 120, 163901 (2018).
[Crossref]

H. E. Kondakci, M. Yessenov, M. Meem, D. Reyes, D. Thul, S. R. Fairchild, M. Richardson, R. Menon, and A. F. Abouraddy, “Synthesizing broadband propagation-invariant space-time wave packets using transmissive phase plates,” Opt. Express 26, 13628–13638 (2018).
[Crossref]

B. Bhaduri, M. Yessenov, and A. F. Abouraddy, “Meters-long propagation of diffraction-free space-time light sheets,” Opt. Express 26, 20111–20121 (2018).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Self-healing of space-time light sheets,” Opt. Lett. 43, 3830–3833 (2018).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Diffraction-free space-time beams,” Nat. Photonics 11, 733–740 (2017).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Diffraction-free pulsed optical beams via space-time correlations,” Opt. Express 24, 28659–28668 (2016).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Optical space-time wave packets of arbitrary group velocity in free space,” arXiv:1810.08893 (2018).

M. Yessenov, B. Bhaduri, H. E. Kondakci, and A. F. Abouraddy, “Classification of propagation-invariant space-time light-sheets in free space: Theory and experiments,” arXiv:1809.08375 (2018).

Alexeev, I.

I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
[Crossref]

Almási, G.

Alonso, M. A.

Andreoni, A.

Averchi, A.

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008).
[Crossref]

Bartal, B.

Behroozi, C.

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 m per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Betsis, S. C.

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

Bhaduri, B.

B. Bhaduri, M. Yessenov, and A. F. Abouraddy, “Meters-long propagation of diffraction-free space-time light sheets,” Opt. Express 26, 20111–20121 (2018).
[Crossref]

M. Yessenov, B. Bhaduri, H. E. Kondakci, and A. F. Abouraddy, “Classification of propagation-invariant space-time light-sheets in free space: Theory and experiments,” arXiv:1809.08375 (2018).

Biegert, J.

Bonaretti, F.

Bowlan, P.

Boyd, R. W.

K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358, eaan5196 (2017).
[Crossref]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
[Crossref]

Bragheri, F.

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96, 193901 (2006).
[Crossref]

Braverman, B.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[Crossref]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Cirloganu, C. M.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Clerici, M.

Conti, C.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[Crossref]

Couairon, A.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, “Spatio-temporal reshaping and X wave dynamics in optical filaments,” Opt. Express 15, 13077–13095 (2007).
[Crossref]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96, 193901 (2006).
[Crossref]

Dallaire, M.

Danielius, R.

Di Trapani, P.

O. Jedrkiewicz, Y.-D. Wang, G. Valiulis, and P. Di Trapani, “One dimensional spatial localization of polychromatic stationary wave-packets in normally dispersive media,” Opt. Express 21, 25000–25009 (2013).
[Crossref]

F. Bonaretti, D. Faccio, M. Clerici, J. Biegert, and P. Di Trapani, “Spatiotemporal amplitude and phase retrieval of Bessel-X pulses using a Hartmann-Shack sensor,” Opt. Express 17, 9804–9809 (2009).
[Crossref]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, “Spatio-temporal reshaping and X wave dynamics in optical filaments,” Opt. Express 15, 13077–13095 (2007).
[Crossref]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96, 193901 (2006).
[Crossref]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[Crossref]

M. A. Porras, G. Valiulis, and P. Di Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016613 (2003).
[Crossref]

R. Danielius, A. Piskarskas, P. Di Trapani, A. Andreoni, C. Solcia, and P. Foggi, “Matching of group velocities by spatial walk-off in collinear three-wave interaction with tilted pulses,” Opt. Lett. 21, 973–975 (1996).
[Crossref]

Dodge, M. J.

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref]

Donnelly, R.

R. Donnelly and R. Ziolkowski, “Designing localized waves,” Proc. R. Soc. Lond. A 440, 541–565 (1993).
[Crossref]

Dubietis, A.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, “Spatio-temporal reshaping and X wave dynamics in optical filaments,” Opt. Express 15, 13077–13095 (2007).
[Crossref]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96, 193901 (2006).
[Crossref]

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 m per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Faccio, D.

Fairchild, S. R.

Feuerhake, M.

Fishman, D. A.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Foggi, P.

Friberg, A. T.

J. Turunen and A. T. Friberg, “Propagation-invariant optical fields,” Prog. Opt. 54, 1–88 (2010).
[Crossref]

Fülöp, J. A.

J. A. Fülöp and J. Hebling, “Applications of tilted-pulse-front excitation,” in Recent Optical and Photonic Technologies, K. Y. Kim, ed. (InTech, 2010).

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
[Crossref]

Giessen, H.

Gissibl, T.

Hagan, D.

M. Reichert, A. Smirl, G. Salamo, D. Hagan, and E. Van Stryland, “Observation of nondegenerate two-photon gain in GaAs,” Phys. Rev. Lett. 117, 073602 (2016).
[Crossref]

Hagan, D. J.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

Hale, G. M.

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 m per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Hartmann, P.

R. Jedamzik, S. Reichel, and P. Hartmann, “Optical glass with tightest refractive index and dispersion tolerances for high-end optical designs,” Proc. SPIE 8982, 89821F (2014).
[Crossref]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 m per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

Hebling, J.

Hendrych, M.

Herráez, M. G.

Hess, O.

K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358, eaan5196 (2017).
[Crossref]

Hloupis, G.

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

Hoffmann, M. C.

Jedamzik, R.

R. Jedamzik, S. Reichel, and P. Hartmann, “Optical glass with tightest refractive index and dispersion tolerances for high-end optical designs,” Proc. SPIE 8982, 89821F (2014).
[Crossref]

Jedrkiewicz, O.

Kedenburg, S.

Kim, K. Y.

I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
[Crossref]

Kolesik, M.

Kondakci, H. E.

H. E. Kondakci and A. F. Abouraddy, “Airy wavepackets accelerating in space-time,” Phys. Rev. Lett. 120, 163901 (2018).
[Crossref]

H. E. Kondakci, M. Yessenov, M. Meem, D. Reyes, D. Thul, S. R. Fairchild, M. Richardson, R. Menon, and A. F. Abouraddy, “Synthesizing broadband propagation-invariant space-time wave packets using transmissive phase plates,” Opt. Express 26, 13628–13638 (2018).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Self-healing of space-time light sheets,” Opt. Lett. 43, 3830–3833 (2018).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Diffraction-free space-time beams,” Nat. Photonics 11, 733–740 (2017).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Diffraction-free pulsed optical beams via space-time correlations,” Opt. Express 24, 28659–28668 (2016).
[Crossref]

M. Yessenov, B. Bhaduri, H. E. Kondakci, and A. F. Abouraddy, “Classification of propagation-invariant space-time light-sheets in free space: Theory and experiments,” arXiv:1809.08375 (2018).

H. E. Kondakci and A. F. Abouraddy, “Optical space-time wave packets of arbitrary group velocity in free space,” arXiv:1810.08893 (2018).

Kozma, I. Z.

Krok, P.

Kuhl, J.

Kuntz, K. B.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[Crossref]

Kuzmich, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref]

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K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
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Longhi, S.

Lotti, A.

Lvovsky, A. I.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
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McCarthy, N.

Meem, M.

Menon, R.

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I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
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Monroe, M.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
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K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
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Padilha, L. A.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
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K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
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Pessina, E. M.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
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R. Jedamzik, S. Reichel, and P. Hartmann, “Optical glass with tightest refractive index and dispersion tolerances for high-end optical designs,” Proc. SPIE 8982, 89821F (2014).
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M. Reichert, A. Smirl, G. Salamo, D. Hagan, and E. Van Stryland, “Observation of nondegenerate two-photon gain in GaAs,” Phys. Rev. Lett. 117, 073602 (2016).
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P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).
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M. Reichert, A. Smirl, G. Salamo, D. Hagan, and E. Van Stryland, “Observation of nondegenerate two-photon gain in GaAs,” Phys. Rev. Lett. 117, 073602 (2016).
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Sõnajalg, H.

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K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
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Tamosauskas, G.

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K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
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Trillo, S.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
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Trull, J.

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
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K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358, eaan5196 (2017).
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J. Turunen and A. T. Friberg, “Propagation-invariant optical fields,” Prog. Opt. 54, 1–88 (2010).
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O. Jedrkiewicz, Y.-D. Wang, G. Valiulis, and P. Di Trapani, “One dimensional spatial localization of polychromatic stationary wave-packets in normally dispersive media,” Opt. Express 21, 25000–25009 (2013).
[Crossref]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[Crossref]

M. A. Porras, G. Valiulis, and P. Di Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016613 (2003).
[Crossref]

Valtna-Lukner, H.

Van Stryland, E.

M. Reichert, A. Smirl, G. Salamo, D. Hagan, and E. Van Stryland, “Observation of nondegenerate two-photon gain in GaAs,” Phys. Rev. Lett. 117, 073602 (2016).
[Crossref]

Van Stryland, E. W.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
[Crossref]

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Wang, L. J.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
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Wang, Y.-D.

Webster, S.

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
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Yessenov, M.

Youn, S. H.

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
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Zhang, X.

K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358, eaan5196 (2017).
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R. Donnelly and R. Ziolkowski, “Designing localized waves,” Proc. R. Soc. Lond. A 440, 541–565 (1993).
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Adv. Opt. Photon. (1)

Appl. Opt. (2)

Appl. Phys. B (1)

K. Moutzouris, M. Papamichael, S. C. Betsis, I. Stavrakas, G. Hloupis, and D. Triantis, “Refractive, dispersive and thermo-optic properties of twelve organic solvents in the visible and near-infrared,” Appl. Phys. B 116, 617–622 (2014).
[Crossref]

J. Opt. Soc. Am. (2)

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

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

Nat. Photonics (3)

D. A. Fishman, C. M. Cirloganu, S. Webster, L. A. Padilha, M. Monroe, D. J. Hagan, and E. W. Van Stryland, “Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption,” Nat. Photonics 5, 561–565 (2011).
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H. E. Kondakci and A. F. Abouraddy, “Diffraction-free space-time beams,” Nat. Photonics 11, 733–740 (2017).
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T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2, 465–473 (2008).
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Nature (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. Behroozi, “Light speed reduction to 17 m per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[Crossref]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[Crossref]

Opt. Express (12)

K. Y. Song, M. G. Herráez, and L. Thévenaz, “Gain-assisted pulse advancement using single and double Brillouin gain peaks in optical fibers,” Opt. Express 13, 9758–9765 (2005).
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S. Longhi, “Gaussian pulsed beams with arbitrary speed,” Opt. Express 12, 935–940 (2004).
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H. E. Kondakci and A. F. Abouraddy, “Diffraction-free pulsed optical beams via space-time correlations,” Opt. Express 24, 28659–28668 (2016).
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K. J. Parker and M. A. Alonso, “The longitudinal iso-phase condition and needle pulses,” Opt. Express 24, 28669–28677 (2016).
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D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, “Spatio-temporal reshaping and X wave dynamics in optical filaments,” Opt. Express 15, 13077–13095 (2007).
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M. Dallaire, N. McCarthy, and M. Piché, “Spatiotemporal Bessel beams: theory and experiments,” Opt. Express 17, 18148–18164 (2009).
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O. Jedrkiewicz, Y.-D. Wang, G. Valiulis, and P. Di Trapani, “One dimensional spatial localization of polychromatic stationary wave-packets in normally dispersive media,” Opt. Express 21, 25000–25009 (2013).
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J. Hebling, G. Almási, I. Z. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large-area THz-pulse generation,” Opt. Express 10, 1161–1166 (2002).
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F. Bonaretti, D. Faccio, M. Clerici, J. Biegert, and P. Di Trapani, “Spatiotemporal amplitude and phase retrieval of Bessel-X pulses using a Hartmann-Shack sensor,” Opt. Express 17, 9804–9809 (2009).
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B. Bhaduri, M. Yessenov, and A. F. Abouraddy, “Meters-long propagation of diffraction-free space-time light sheets,” Opt. Express 26, 20111–20121 (2018).
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H. E. Kondakci, M. Yessenov, M. Meem, D. Reyes, D. Thul, S. R. Fairchild, M. Richardson, R. Menon, and A. F. Abouraddy, “Synthesizing broadband propagation-invariant space-time wave packets using transmissive phase plates,” Opt. Express 26, 13628–13638 (2018).
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M. Clerici, D. Faccio, A. Lotti, E. Rubino, O. Jedrkiewicz, J. Biegert, and P. D. Trapani, “Finite-energy, accelerating Bessel pulses,” Opt. Express 16, 19807–19811 (2008).
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Opt. Lett. (6)

Opt. Mater. Express (1)

Phys. Rev. A (2)

P. Saari, “Reexamination of group velocities of structured light pulses,” Phys. Rev. A 97, 063824 (2018).
[Crossref]

K. B. Kuntz, B. Braverman, S. H. Youn, M. Lobino, E. M. Pessina, and A. I. Lvovsky, “Spatial and temporal characterization of a Bessel beam produced using a conical mirror,” Phys. Rev. A 79, 043802 (2009).
[Crossref]

Phys. Rev. E (2)

P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).
[Crossref]

M. A. Porras, G. Valiulis, and P. Di Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016613 (2003).
[Crossref]

Phys. Rev. Lett. (6)

H. E. Kondakci and A. F. Abouraddy, “Airy wavepackets accelerating in space-time,” Phys. Rev. Lett. 120, 163901 (2018).
[Crossref]

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
[Crossref]

I. Alexeev, K. Y. Kim, and H. M. Milchberg, “Measurement of the superluminal group velocity of an ultrashort Bessel beam pulse,” Phys. Rev. Lett. 88, 073901 (2002).
[Crossref]

P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, C. Conti, and S. Trillo, “Spontaneously generated X-shaped light bullets,” Phys. Rev. Lett. 91, 093904 (2003).
[Crossref]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, “Conical emission, pulse splitting, and X-wave parametric amplification in nonlinear dynamics of ultrashort light pulses,” Phys. Rev. Lett. 96, 193901 (2006).
[Crossref]

M. Reichert, A. Smirl, G. Salamo, D. Hagan, and E. Van Stryland, “Observation of nondegenerate two-photon gain in GaAs,” Phys. Rev. Lett. 117, 073602 (2016).
[Crossref]

Proc. R. Soc. Lond. A (1)

R. Donnelly and R. Ziolkowski, “Designing localized waves,” Proc. R. Soc. Lond. A 440, 541–565 (1993).
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Proc. SPIE (1)

R. Jedamzik, S. Reichel, and P. Hartmann, “Optical glass with tightest refractive index and dispersion tolerances for high-end optical designs,” Proc. SPIE 8982, 89821F (2014).
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Prog. Opt. (1)

J. Turunen and A. T. Friberg, “Propagation-invariant optical fields,” Prog. Opt. 54, 1–88 (2010).
[Crossref]

Science (2)

K. L. Tsakmakidis, O. Hess, R. W. Boyd, and X. Zhang, “Ultraslow waves on the nanoscale,” Science 358, eaan5196 (2017).
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R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
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H. E. Kondakci and A. F. Abouraddy, “Optical space-time wave packets of arbitrary group velocity in free space,” arXiv:1810.08893 (2018).

M. Yessenov, B. Bhaduri, H. E. Kondakci, and A. F. Abouraddy, “Classification of propagation-invariant space-time light-sheets in free space: Theory and experiments,” arXiv:1809.08375 (2018).

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Figures (5)

Fig. 1.
Fig. 1. Controlling the group velocity of a ST wave packet in a non-dispersive optical material. (a) The spatio-temporal spectrum of the ST wave packet in a material of refractive index n lies at the intersection of the light-cone kx2+kz2=(nωc)2, having an apex angle of tan1n, with a plane P(θm); we assume n>1 throughout. The intersection here (black curve) is a hyperbola on the surface of the light-cone. The projection of this spatio-temporal spectrum onto the (kz,ωc)-plane is a straight line that makes an angle θm with respect to the kz-axis. The group velocity in the medium is vg=ctanθm, and is independent of the refractive index. Our goal is to synthesize ST wave packets in any given material with θm=45° such that vg=c in the material. (b) The projection of the spatio-temporal spectrum in (a) onto the (kx,ωc)-plane, which is invariant upon traversing the planar boundary between different materials at normal incidence. (c) The projection in (b) is consistent with the intersection of the free-space light-cone kx2+kz2=(ωc)2 with a non-planar surface. The projection of this surface on the (kz,ωc)-plane is a conic section (solid curve), but it can be approximated for narrow bandwidths as a straight line (dotted line) making an angle θa with the kz-axis.
Fig. 2.
Fig. 2. Schematic of the setup used to synthesize and characterize ST wave packets traveling in a medium at the speed of light in vacuum. BS, beam splitter; Lx, Ly, cylindrical lenses along the x- and y-axes, respectively; Ls, spherical lens; A, aperture; SLM, spatial light modulator; G, diffraction grating; CCD, charge coupled device camera. Inset is the two-dimensional phase pattern imparted by the SLM to the impinging spatially resolved input-pulse spectrum.
Fig. 3.
Fig. 3. (a) Measured spatio-temporal spectrum |E˜(kx,λ)|2 for a ST wave packet having θa=77.1° (the value corresponding to propagation at c in BK7, n1.51). (b) The spatio-temporal spectrum projected onto the (kz,ωc)-plane after normalizing both axes with respect to ko=2π/λo, where λo=797nm. The dotted red line corresponds to the light-line in vacuum θ=45°. The ST wave packet synthesized in free space is confirmed to have a spectral tilt angle of θ=77.1°, as illustrated in the inset, which is required for propagation at c in BK7 glass. (c) Spatial evolution of the time-averaged intensity I(x,z) along the optical axis, showing a diffraction-free length of 70mm. Here θa=60.6° (the value corresponding to propagation at c in distilled water, n1.33). Also shown on the same axial scale is the Rayleigh range zR=0.7mm of a traditional beam of the same transverse width of the ST wave packet. (d) Measured spatio-temporal intensity profile I(x,0,τ) of the ST wave packet after traversing a BK7 glass sample of length L=48mm, which is almost identical to the profile in absence of the sample. (e) Normalized pulse profile I(x=0,0,t) at the center of the transverse profile in (d) before and after inserting the BK7 sample (the pulses have been smoothed using median filtering). Here, z=0 corresponds to the location of the beam splitter BS4 in Fig. 2. The plotted delay is τd=41.4ps, which corresponds to a group delay of τm=160.11ps for the ST wave packet traversing a BK7 sample of length L=48mm.
Fig. 4.
Fig. 4. (a) Measured normalized group delay τm/τo (and normalized group velocity vg/c in the material) after traversing a length L=50mm in distilled water (n1.33) and L=48mm in BK7 glass (n1.51) versus the spectral tilt angle θa of ST wave packets synthesized in air. The points are experimental data and the continuous curves are the theoretical expectation, Eq. (5). (b) Measured delay length Δ and normalized group delay for BK7 glass while increasing the sample length L. The points are experimental results, and the continuous line is the theoretical expectation. Inset shows the group delay in the material τm normalized with respect to the delay in free space τo.
Fig. 5.
Fig. 5. Measured delay length Δ normalized with respect to the sample length L for ST wave packets traversing a variety of optical materials at c. The points are data, and the continuous curve is the theoretical expectation [Eq. (6)]. Errors in estimating the group delays used to obtain the group velocity correspond to 40 μm of delay in free space (133 fs, the minimum detectable shift in the pulse peak). This represents an accuracy of 1.43% error with respect to a pulse width of 9.3 ps.

Tables (1)

Tables Icon

Table 1. List of the Materials Utilized and Their Relevant Parameters: The Measured Refractive Index n, the Corresponding Spectral Tilt Angle θa of the ST Wave Packet in Air, and Length of the Sample La

Equations (13)

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ψ(x,z,t)=dkxψ˜(kx)eikxxei(ωωo)(tzccotθ)=ψ(x,0,tzvg),
tanθa=tanθmn(n21)tanθm.
tanθa=11+nn2.
ϕ=1+521.618.
τmτo=n+τa+τdτoτo,
ΔL=τdτo=(n1)2,
(1+ntanθ)2n2ko2tan2θ(ωcko1+ntanθ)2kx2n2ko2ntanθ+1ntanθ1=1,
(kzko)2=12Ω{n21ntanθm}Ω2{n211tan2θm},
ωωo=1+kx22ko2tanθatanθa1,ωωo=1+kx22n2ko2ntanθmntanθm1.
tanθa=tanθmn(n21)tanθm,tanθm=ntanθa(n21)tanθa+1.
kzko+n(n21)tanθmtanθm(ωcko),
ωc=ko+tanθmn(n21)tanθm(kzko)=ko+(kzko)tanθa,
ΔL=(11n)(11tanθa).

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