Abstract

Space-time (ST) wave packets are pulsed beams in which the spatial frequencies and wavelengths are tightly correlated. Proper design of the functional form of these correlations results in diffraction-free and dispersion-free axial propagation; that is, propagation invariance in free space. To date, observed propagation distances of such ST wave packets has been on the order of a few centimeters. Here we synthesize an ST wave packet in the form of a pulsed optical sheet of transverse spatial width ∼200 μm and spectral bandwidth of ∼2 nm, and observe its diffraction-free propagation for approximately 6 meters. For such ST wave packets, we identify the spectral uncertainty – the precision in associating the spatial and temporal frequencies – as a critical parameter in determining the propagation-invariant distance. We present a design strategy and an experimental methodology that enables further increase in the diffraction-free length.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (4)

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

M. A. Porras, “Nature, diffraction-free propagation via space-time correlations, and nonlinear generation of time-diffracting light beams,” Phys. Rev. A 97, 063803 (2018).
[Crossref]

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

H. E. Kondakci, M. Yessenov, M. Meem, D. Reyes, D. Thul, S. Rostami 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] [PubMed]

2017 (7)

C. Okoro, H. E. Kondakci, A. F. Abouraddy, and K. C. Toussaint, “Demonstration of an optical-coherence converter,” Optica 4, 1052–1058 (2017).
[Crossref]

A. Sainte-Marie, O. Gobert, and F. Quere, “Controlling the velocity of ultrashort light pulses in vacuum through spatio-temporal couplings,” Optica 4, 1298–1304 (2017).
[Crossref]

M. A. Porras, “Gaussian beams diffracting in time,” Opt. Lett. 42, 4679–4682 (2017).
[Crossref] [PubMed]

L. J. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).
[Crossref]

L. J. Wong and I. Kaminer, “Ultrashort tilted-pulse-front pulses and nonparaxial tilted-phase-front beams,” ACS Photon. 4, 2257–2264 (2017).
[Crossref]

N. K. Efremidis, “Spatiotemporal diffraction-free pulsed beams in free-space of the Airy and Bessel type,” Opt. Lett. 23, 5038–5041 (2017).
[Crossref]

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

2016 (4)

2015 (3)

S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, and C. Marquardt, “Classically entangled optical beams for high-speed kinematic sensing,” Optica 2, 864–868 (2015).
[Crossref]

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Rep. 5, 15333 (2015).
[Crossref] [PubMed]

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Quantum-like nonseparable structures in optical beams,” New J. Phys. 17, 043024 (2015).
[Crossref]

2013 (1)

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photon. 7, 72–78 (2013).
[Crossref]

2011 (3)

2010 (4)

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

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).
[Crossref]

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

B. M. Rodríguez-Lara, “Normalization of optical Weber waves and Weber-Gauss beams,” J. Opt. Soc. Am. A 27, 327–332 (2010).
[Crossref]

2009 (1)

A. Luis, “Coherence, polarization, and entanglement for classical light fields,” Opt. Commun. 282, 3665–3670 (2009).
[Crossref]

2008 (1)

B. J. Sussman, R. Lausten, and A. Stolow, “Focusing of light following a 4 − f pulse shaper: Considerations for quantum control,” Phys. Rev. A 77, 043416 (2008).
[Crossref]

2007 (1)

2005 (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

2004 (4)

2003 (1)

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] [PubMed]

2002 (2)

2000 (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[Crossref]

1998 (2)

R. M. Koehl, T. Hattori, and K. A. Nelson, “Automated spatial and temporal shaping of femtosecond pulses,” Opt. Commun. 157, 57–61 (1998).
[Crossref]

R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[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]

1992 (1)

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves–exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelec. Freq. Control 39, 19–31 (1992).
[Crossref]

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

1983 (1)

J. N. Brittingham, “Focus wave modes in homogeneous Maxwell’s equations: Transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[Crossref]

1978 (1)

L. Mackinnon, “A nondispersive de Broglie wave packet,” Found. Phys. 8, 157–176 (1978).
[Crossref]

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. Rostami 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] [PubMed]

C. Okoro, H. E. Kondakci, A. F. Abouraddy, and K. C. Toussaint, “Demonstration of an optical-coherence converter,” Optica 4, 1052–1058 (2017).
[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] [PubMed]

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Rep. 5, 15333 (2015).
[Crossref] [PubMed]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photon. 7, 72–78 (2013).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Self-healing of space-time light sheets,” Opt. Lett.43, in press (2018).

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

Aiello, A.

Alonso, M. A.

Bandres, M. A.

Banzer, P.

Berg-Johansen, S.

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Bhaduri, B.

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

Borges, C. V. S.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

Brittingham, J. N.

J. N. Brittingham, “Focus wave modes in homogeneous Maxwell’s equations: Transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[Crossref]

Chávez-Cerda, S.

Christodoulides, D. N.

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] [PubMed]

Derevyanko, S.

U. Levy, S. Derevyanko, and Y. Silberberg, “Light modes of free space,” Prog. Opt. 61, 237–281 (2016).
[Crossref]

Dholakia, K.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).
[Crossref]

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

Di Giuseppe, G.

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photon. 7, 72–78 (2013).
[Crossref]

Di Trapani, P.

D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, “Bessel X waves in two- and three-dimensional bidispersive optical systems,” Opt. Lett. 29, 1446–1448 (2004).
[Crossref] [PubMed]

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] [PubMed]

Dudley, A.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

X.-F. Qian and J. H. Eberly, “Entanglement and classical polarization states,” Opt. Lett. 36, 4110–4112 (2011).
[Crossref] [PubMed]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Efremidis, N. K.

N. K. Efremidis, “Spatiotemporal diffraction-free pulsed beams in free-space of the Airy and Bessel type,” Opt. Lett. 23, 5038–5041 (2017).
[Crossref]

D. N. Christodoulides, N. K. Efremidis, P. Di Trapani, and B. A. Malomed, “Bessel X waves in two- and three-dimensional bidispersive optical systems,” Opt. Lett. 29, 1446–1448 (2004).
[Crossref] [PubMed]

Feurer, T.

Forbes, A.

Friberg, A. T.

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

Gabriel, C.

Giacobino, E.

Gobert, O.

Greenleaf, J. F.

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves–exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelec. Freq. Control 39, 19–31 (1992).
[Crossref]

Gunn-Moore, F.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).
[Crossref]

Gutiérrez-Vega, J. C.

Hattori, T.

R. M. Koehl, T. Hattori, and K. A. Nelson, “Automated spatial and temporal shaping of femtosecond pulses,” Opt. Commun. 157, 57–61 (1998).
[Crossref]

Holleczek, A.

Hor-Meyll, M.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

Huguenin, J. A. O.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

Jedrkiewicz, O.

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] [PubMed]

Jesacher, A.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Kagalwala, K. H.

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Rep. 5, 15333 (2015).
[Crossref] [PubMed]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photon. 7, 72–78 (2013).
[Crossref]

Kaminer, I.

L. J. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).
[Crossref]

L. J. Wong and I. Kaminer, “Ultrashort tilted-pulse-front pulses and nonparaxial tilted-phase-front beams,” ACS Photon. 4, 2257–2264 (2017).
[Crossref]

Khoury, A. Z.

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

Koehl, R. M.

T. Feurer, J. C. Vaughan, R. M. Koehl, and K. A. Nelson, “Multidimensional control of femtosecond pulses by use of a programmable liquid-crystal matrix,” Opt. Lett. 27, 652–654 (2002).
[Crossref]

R. M. Koehl, T. Hattori, and K. A. Nelson, “Automated spatial and temporal shaping of femtosecond pulses,” Opt. Commun. 157, 57–61 (1998).
[Crossref]

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. Rostami 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] [PubMed]

C. Okoro, H. E. Kondakci, A. F. Abouraddy, and K. C. Toussaint, “Demonstration of an optical-coherence converter,” Optica 4, 1052–1058 (2017).
[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] [PubMed]

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Rep. 5, 15333 (2015).
[Crossref] [PubMed]

H. E. Kondakci and A. F. Abouraddy, “Self-healing of space-time light sheets,” Opt. Lett.43, in press (2018).

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

Lausten, R.

B. J. Sussman, R. Lausten, and A. Stolow, “Focusing of light following a 4 − f pulse shaper: Considerations for quantum control,” Phys. Rev. A 77, 043416 (2008).
[Crossref]

Leuchs, G.

Levy, U.

U. Levy, S. Derevyanko, and Y. Silberberg, “Light modes of free space,” Prog. Opt. 61, 237–281 (2016).
[Crossref]

Longhi, S.

Lu, J.-Y.

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves–exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelec. Freq. Control 39, 19–31 (1992).
[Crossref]

Luis, A.

A. Luis, “Coherence, polarization, and entanglement for classical light fields,” Opt. Commun. 282, 3665–3670 (2009).
[Crossref]

Mackinnon, L.

L. Mackinnon, “A nondispersive de Broglie wave packet,” Found. Phys. 8, 157–176 (1978).
[Crossref]

Malomed, B. A.

Marquardt, C.

Maurer, C.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Mazilu, M.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).
[Crossref]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

McLaren, M.

Meem, M.

Menon, R.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Nelson, K. A.

T. Feurer, J. C. Vaughan, R. M. Koehl, and K. A. Nelson, “Multidimensional control of femtosecond pulses by use of a programmable liquid-crystal matrix,” Opt. Lett. 27, 652–654 (2002).
[Crossref]

R. M. Koehl, T. Hattori, and K. A. Nelson, “Automated spatial and temporal shaping of femtosecond pulses,” Opt. Commun. 157, 57–61 (1998).
[Crossref]

Okoro, C.

Ornigotti, M.

Parker, K. J.

Piskarskas, A.

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] [PubMed]

Porras, M. A.

M. A. Porras, “Nature, diffraction-free propagation via space-time correlations, and nonlinear generation of time-diffracting light beams,” Phys. Rev. A 97, 063803 (2018).
[Crossref]

M. A. Porras, “Gaussian beams diffracting in time,” Opt. Lett. 42, 4679–4682 (2017).
[Crossref] [PubMed]

M. A. Porras, “Self-trapped pulsed beams with finite power in Kerr media excited by time-diffracting, space-time beams,” arXiv:1805.07985 (2018).

Qian, X.-F.

Quere, F.

Reivelt, K.

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

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

Reyes, D.

Richardson, M.

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Rodríguez-Lara, B. M.

Rostami Fairchild, S.

Saari, P.

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

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

Sainte-Marie, A.

Saleh, B. E. A.

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Rep. 5, 15333 (2015).
[Crossref] [PubMed]

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photon. 7, 72–78 (2013).
[Crossref]

Sheppard, C. J. R.

Silberberg, Y.

U. Levy, S. Derevyanko, and Y. Silberberg, “Light modes of free space,” Prog. Opt. 61, 237–281 (2016).
[Crossref]

Siviloglou, G. A.

Spreeuw, R. J. C.

R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[Crossref]

Stevenson, D. J.

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).
[Crossref]

Stiller, B.

Stolow, A.

B. J. Sussman, R. Lausten, and A. Stolow, “Focusing of light following a 4 − f pulse shaper: Considerations for quantum control,” Phys. Rev. A 77, 043416 (2008).
[Crossref]

Sussman, B. J.

B. J. Sussman, R. Lausten, and A. Stolow, “Focusing of light following a 4 − f pulse shaper: Considerations for quantum control,” Phys. Rev. A 77, 043416 (2008).
[Crossref]

Thul, D.

Töppel, F.

Toussaint, K. C.

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).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Turunen, J.

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

Valiulis, G.

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] [PubMed]

Vaughan, J. C.

Weiner, A. M.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[Crossref]

A. M. Weiner, Ultrafast Optics (Wiley, 2009).
[Crossref]

Wong, L. J.

L. J. Wong and I. Kaminer, “Ultrashort tilted-pulse-front pulses and nonparaxial tilted-phase-front beams,” ACS Photon. 4, 2257–2264 (2017).
[Crossref]

L. J. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).
[Crossref]

Yessenov, M.

ACS Photon. (2)

L. J. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photon. 4, 1131–1137 (2017).
[Crossref]

L. J. Wong and I. Kaminer, “Ultrashort tilted-pulse-front pulses and nonparaxial tilted-phase-front beams,” ACS Photon. 4, 2257–2264 (2017).
[Crossref]

Adv. Opt. Photon. (1)

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

Found. Phys. (2)

L. Mackinnon, “A nondispersive de Broglie wave packet,” Found. Phys. 8, 157–176 (1978).
[Crossref]

R. J. C. Spreeuw, “A classical analogy of entanglement,” Found. Phys. 28, 361–374 (1998).
[Crossref]

IEEE Trans. Ultrason. Ferroelec. Freq. Control (1)

J.-Y. Lu and J. F. Greenleaf, “Nondiffracting X waves–exact solutions to free-space scalar wave equation and their finite aperture realizations,” IEEE Trans. Ultrason. Ferroelec. Freq. Control 39, 19–31 (1992).
[Crossref]

J. Appl. Phys. (1)

J. N. Brittingham, “Focus wave modes in homogeneous Maxwell’s equations: Transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[Crossref]

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

Laser Photon. Rev. (2)

M. Mazilu, D. J. Stevenson, F. Gunn-Moore, and K. Dholakia, “Light beats the spread: ‘non-diffracting’ beams,” Laser Photon. Rev. 4, 529–547 (2010).
[Crossref]

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photon. Rev. 5, 81–101 (2011).
[Crossref]

Nat. Photon. (1)

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photon. 7, 72–78 (2013).
[Crossref]

Nat. Photonics (1)

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

New J. Phys. (1)

A. Aiello, F. Töppel, C. Marquardt, E. Giacobino, and G. Leuchs, “Quantum-like nonseparable structures in optical beams,” New J. Phys. 17, 043024 (2015).
[Crossref]

Opt. Commun. (2)

A. Luis, “Coherence, polarization, and entanglement for classical light fields,” Opt. Commun. 282, 3665–3670 (2009).
[Crossref]

R. M. Koehl, T. Hattori, and K. A. Nelson, “Automated spatial and temporal shaping of femtosecond pulses,” Opt. Commun. 157, 57–61 (1998).
[Crossref]

Opt. Express (5)

Opt. Lett. (7)

Optica (3)

Phys. Rev. A (4)

C. V. S. Borges, M. Hor-Meyll, J. A. O. Huguenin, and A. Z. Khoury, “Bell-like inequality for the spin-orbit separability of a laser beam,” Phys. Rev. A 82, 033833 (2010).
[Crossref]

M. A. Porras, “Nature, diffraction-free propagation via space-time correlations, and nonlinear generation of time-diffracting light beams,” Phys. Rev. A 97, 063803 (2018).
[Crossref]

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

B. J. Sussman, R. Lausten, and A. Stolow, “Focusing of light following a 4 − f pulse shaper: Considerations for quantum control,” Phys. Rev. A 77, 043416 (2008).
[Crossref]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (4)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

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

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

Prog. Opt. (2)

U. Levy, S. Derevyanko, and Y. Silberberg, “Light modes of free space,” Prog. Opt. 61, 237–281 (2016).
[Crossref]

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

Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[Crossref]

Sci. Rep. (1)

K. H. Kagalwala, H. E. Kondakci, A. F. Abouraddy, and B. E. A. Saleh, “Optical coherency matrix tomography,” Sci. Rep. 5, 15333 (2015).
[Crossref] [PubMed]

Other (5)

A. M. Weiner, Ultrafast Optics (Wiley, 2009).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Self-healing of space-time light sheets,” Opt. Lett.43, in press (2018).

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

M. A. Porras, “Self-trapped pulsed beams with finite power in Kerr media excited by time-diffracting, space-time beams,” arXiv:1805.07985 (2018).

H. E. Hernández-Figueroa, E. Recami, and M. Zamboni-Rached, eds., Non-diffracting Waves (Wiley, 2014).

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Figures (6)

Fig. 1
Fig. 1 Concept of a ST light sheet. (a) Geometric representation of the free-space light-cone k x 2 + k z 2 = ( ω / c ) 2. The spectral locus of an ST wave packet lies at the intersection of the light-cone with a spectral hyperplane that is tilted an angle θ with respect to the (kx, kz)-plane, is parallel to the kx-axis, and passes through the point ( k x , k z , ω c ) = ( 0 , k o , k o ). This spectral hyperplane intersects with the (kz, ω c)-plane in a straight line. (b) Calculated projection of a section of the spatio-temporal spectral curve in (a) onto the (kx, λ)-plane. The spatio-temporal spectrum has the form of a product of two Gaussian functions, one in kx and the other in λ whose width is δλ; the temporal bandwidth is Δλ =1 nm (FWHM), the spatial bandwidth is Δkx = 250 rad/mm (HWHM), and θ = π 3. The spectral hyperplane intersects with the light-cone in a hyperbola, a section of which is shown here. Note that shorter wavelengths (higher temporal frequencies) are associated with higher spatial frequencies because θ >45°, in contrast with θ <45° (the spectral hyperplane intersects with the light-cone in an ellipse) as used in our experiment, whereupon the association between spatial and temporal frequencies is reversed.
Fig. 2
Fig. 2 Calculated diffraction-free (or propagation-invariant) distance for ST light-sheets as a function of spatial bandwidth Δkx and the spectral uncertainty δλ. The tilt angle of the spectral hyperplane with respect to the light-cone is θ =44.98° and the central wavelength is λo =800.5 nm, which are the values used in our experiment. The spatio-temporal correlations introduced in the ST wave packet entails that the temporal bandwidth Δλ varies with Δkx when θ is held fixed. The transverse spatial beam width is x0 = πkx.
Fig. 3
Fig. 3 Schematic depiction of the optical setup for synthesizing ST light sheets. BE: Beam expander; BS1, BS2: beam splitters; L1−y: cylindrical lens; L2−s: spherical lens; G: diffraction grating; CCD1, CCD2: CCD cameras; SLM: spatial light modulator. The focal lengths of the lenses L1−y and L2−s are 50 cm and 7.5 cm, respectively.
Fig. 4
Fig. 4 Selection of the parameters of the ST light sheet. (a) Dependence of the temporal bandwidth Δλ on the spatial bandwidth Δkx for 5 different tilt angles θ in the range 44° ≤ θ < 45°. (b) Phase patterns displayed on the SLM for three tilt angles from (a). The point at kx = 15 rad/mm for θ = 44.98° is the operating point in the experiment. (c) The relationship between the incidence angle φi and output angle φo of the second diffraction order m =2 for the diffraction grating G in Fig. 3. The dotted lines identify the selected parameters in our experiment. (d) The spatial distribution along the y-direction of the wavelengths at the SLM plane for an incidence angle of φi =69° on the grating, as highlighted in (c).
Fig. 5
Fig. 5 Synthesis of ST light sheets. (a) The phase distribution Φ(x, y) imparted by the SLM onto the impinging spatially spread spectrum to produce the target ST light sheet. (b) Measured spatio-temporal spectrum |(kx, λ)|2 obtained by CCD2. The inset shows the spectral intensity of the initial femtosecond Ti:Sa pulses.
Fig. 6
Fig. 6 (a) Measured spatial profiles I(x, y; z) at selected axial positions z (provided above each panel) extending up to 6 m. The scale bar represents 1 mm along both x and y directions. (b) Evolution of the transverse FWHM of I(x, z) and (b) the peak intensity I(0, z) along the axial direction z.

Equations (5)

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E ( x , z ; t ) = e i ( k o z ω o t ) d k x d ω ψ ˜ ( k x , ω ω o ) e i { k x x + ( k z ( k x , ω ) k o ) z ( ω ω o ) t } ,
E ( x , z ; t ) = e i ( k o z ω o t ) d k x ψ ˜ ( k x ) e i { k x x + [ k z ( | k x | ) k o ] z [ ω ( | k x | ) ω o ] t } ,
E ( x , z ; t ) = e i ( k o z ω o t ) d k x ψ ˜ ( k x ) e i { k x x + [ k z ( | k x | ) k o ] [ z c t tan θ ] } e i ( k o z ω o t ) ψ ( x , z c t tan θ ; 0 ) ;
1 k 1 2 ( ω c k 2 ) 2 + k x 2 k 3 2 = 1 ,
E ( x , z ; t ) = d k x d ω ψ ˜ ( k x ) g ( ω ω ( | k x | ) ) e i ( k x x + k z ( ω , k x ) z ω t ) ,

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