Abstract

Space-time wave packets are a class of pulsed optical beams that are diffraction-free and dispersion-free in free space by virtue of introducing a tight correlation between the spatial and temporal degrees of freedom of the field. Such wave packets have been recently synthesized in a novel configuration that makes use of a spatial light modulator to realize the required spatio-temporal correlations. This arrangement combines pulse-modulation and beam-shaping to assign one spatial frequency to each wavelength according to a prescribed correlation function. Relying on a spatial light modulator results in several limitations by virtue of their pixelation, small area, and low energy-handling capability. Here we demonstrate the synthesis of space-time wave packets with one spatial dimension kept uniform – that is, light sheets – using transparent transmissive phase plates produced by a gray-scale lithography process. We confirm the diffraction-free behavior of wave packets having a bandwidth of 0.25 nm (filtered from a typical femtosecond Ti:sapphire laser) and 30 nm (a multi-terawatt femtosecond laser). This work paves the way for developing versatile high-energy light bullets for applications in nonlinear optics and laser machining.

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

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References

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2018 (1)

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

2017 (8)

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

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

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

N. Mohammad, M. Meem, X. Wan, and R. Menon, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics,” Sci. Rep. 7, 5789 (2017).
[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]

2016 (4)

2015 (1)

P. Wang, J. A. Dominguez-Caballero, D. J. Friedman, and R. Menon, “A new class of multi-bandgap high-efficiency photovoltaics enabled by broadband diffractive optics,” Prog. Photovolt. 23, 1073–1079 (2015).
[Crossref]

2014 (1)

N. Barbieri, Z. Hosseinimakarem, K. Lim, M. Durand, M. Baudelet, E. Johnson, and M. Richardson, “Helical filaments,” Appl. Phys. Lett. 104, 261109 (2014).
[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 (2)

2010 (2)

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

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)

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 (1)

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

1984 (1)

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

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 pulsed optical beams via space-time correlations,” Opt. Express 24, 28659–28668 (2016).
[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]

Alonso, M. A.

Bandres, M. A.

Barbieri, N.

Baudelet, M.

N. Barbieri, Z. Hosseinimakarem, K. Lim, M. Durand, M. Baudelet, E. Johnson, and M. Richardson, “Helical filaments,” Appl. Phys. Lett. 104, 261109 (2014).
[Crossref]

N. Barbieri, M. Weidman, G. Katona, M. Baudelet, Z. Roth, E. Johnson, G. Siviloglou, D. Christodoulides, and M. Richardson, “Double helical laser beams based on interfering first-order Bessel beams,” J. Opt. Soc. Am. A 28, 1462–1469 (2011).
[Crossref]

B. Webb, J. Bradford, K. Lim, N. Bodnar, A. Vaupel, E. McKee, M. Baudelet, M. M. Durand, L. Shah, and M. Richardson, “Compact 10 TW laser to generate multi-filament arrays,” CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper SM1F.6.

Bélanger, P. A.

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]

Bodnar, N.

B. Webb, J. Bradford, K. Lim, N. Bodnar, A. Vaupel, E. McKee, M. Baudelet, M. M. Durand, L. Shah, and M. Richardson, “Compact 10 TW laser to generate multi-filament arrays,” CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper SM1F.6.

Bradford, J.

B. Webb, J. Bradford, K. Lim, N. Bodnar, A. Vaupel, E. McKee, M. Baudelet, M. M. Durand, L. Shah, and M. Richardson, “Compact 10 TW laser to generate multi-filament arrays,” CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper SM1F.6.

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.

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]

Crain, M.

C. McKenna, K. Walsh, M. Crain, and J. Lake, “Maskless direct write grayscale lithography for MEMS applications,” in Micro/Nano Symposium (UGIM), 2010 18th Biennial University/Government/Industry, pp. 1–4. IEEE (2010).

Derevyanko, S.

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

Dominguez-Caballero, J. A.

P. Wang, J. A. Dominguez-Caballero, D. J. Friedman, and R. Menon, “A new class of multi-bandgap high-efficiency photovoltaics enabled by broadband diffractive optics,” Prog. Photovolt. 23, 1073–1079 (2015).
[Crossref]

Dudley, A.

Durand, M.

N. Barbieri, Z. Hosseinimakarem, K. Lim, M. Durand, M. Baudelet, E. Johnson, and M. Richardson, “Helical filaments,” Appl. Phys. Lett. 104, 261109 (2014).
[Crossref]

Durand, M. M.

B. Webb, J. Bradford, K. Lim, N. Bodnar, A. Vaupel, E. McKee, M. Baudelet, M. M. Durand, L. Shah, and M. Richardson, “Compact 10 TW laser to generate multi-filament arrays,” CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper SM1F.6.

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.

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]

Friedman, D. J.

P. Wang, J. A. Dominguez-Caballero, D. J. Friedman, and R. Menon, “A new class of multi-bandgap high-efficiency photovoltaics enabled by broadband diffractive optics,” Prog. Photovolt. 23, 1073–1079 (2015).
[Crossref]

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]

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]

Hernández-Figueroa, H. E.

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

Hosseinimakarem, Z.

N. Barbieri, Z. Hosseinimakarem, K. Lim, M. Durand, M. Baudelet, E. Johnson, and M. Richardson, “Helical filaments,” Appl. Phys. Lett. 104, 261109 (2014).
[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]

Johnson, E.

Kagalwala, K. H.

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]

Katona, G.

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

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 pulsed optical beams via space-time correlations,” Opt. Express 24, 28659–28668 (2016).
[Crossref] [PubMed]

Lake, J.

C. McKenna, K. Walsh, M. Crain, and J. Lake, “Maskless direct write grayscale lithography for MEMS applications,” in Micro/Nano Symposium (UGIM), 2010 18th Biennial University/Government/Industry, pp. 1–4. IEEE (2010).

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]

Levy, U.

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

Lim, K.

N. Barbieri, Z. Hosseinimakarem, K. Lim, M. Durand, M. Baudelet, E. Johnson, and M. Richardson, “Helical filaments,” Appl. Phys. Lett. 104, 261109 (2014).
[Crossref]

B. Webb, J. Bradford, K. Lim, N. Bodnar, A. Vaupel, E. McKee, M. Baudelet, M. M. Durand, L. Shah, and M. Richardson, “Compact 10 TW laser to generate multi-filament arrays,” CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper SM1F.6.

Longhi, S.

Lu, J.-Y.

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Meem, M.

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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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N. Barbieri, M. Weidman, G. Katona, M. Baudelet, Z. Roth, E. Johnson, G. Siviloglou, D. Christodoulides, and M. Richardson, “Double helical laser beams based on interfering first-order Bessel beams,” J. Opt. Soc. Am. A 28, 1462–1469 (2011).
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B. Webb, J. Bradford, K. Lim, N. Bodnar, A. Vaupel, E. McKee, M. Baudelet, M. M. Durand, L. Shah, and M. Richardson, “Compact 10 TW laser to generate multi-filament arrays,” CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper SM1F.6.

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).
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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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Wan, X.

N. Mohammad, M. Meem, X. Wan, and R. Menon, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics,” Sci. Rep. 7, 5789 (2017).
[Crossref] [PubMed]

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Webb, B.

B. Webb, J. Bradford, K. Lim, N. Bodnar, A. Vaupel, E. McKee, M. Baudelet, M. M. Durand, L. Shah, and M. Richardson, “Compact 10 TW laser to generate multi-filament arrays,” CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper SM1F.6.

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

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)

Appl. Phys. Lett. (1)

N. Barbieri, Z. Hosseinimakarem, K. Lim, M. Durand, M. Baudelet, E. Johnson, and M. Richardson, “Helical filaments,” Appl. Phys. Lett. 104, 261109 (2014).
[Crossref]

Found. Phys. (1)

L. Mackinnon, “A nondispersive de Broglie wave packet,” Found. Phys. 8, 157–176 (1978).
[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).
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J. Opt. Soc. Am. A (4)

Laser Photon. Rev. (1)

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]

Opt. Commun. (1)

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 (3)

Opt. Lett. (6)

Optica (2)

Phys. Rev. A (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]

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 (1)

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

Phys. Rev. Lett. (3)

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]

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]

Prog. Photovolt. (1)

P. Wang, J. A. Dominguez-Caballero, D. J. Friedman, and R. Menon, “A new class of multi-bandgap high-efficiency photovoltaics enabled by broadband diffractive optics,” Prog. Photovolt. 23, 1073–1079 (2015).
[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)

N. Mohammad, M. Meem, X. Wan, and R. Menon, “Full-color, large area, transmissive holograms enabled by multi-level diffractive optics,” Sci. Rep. 7, 5789 (2017).
[Crossref] [PubMed]

Other (9)

Data sheet of Heidelberg μ PG 101: http://www.himt.de/index.php/upg-101.html

Data sheet of AZ developer: http://www.microchemicals.com/micro/az_developer.pdf

B. Webb, J. Bradford, K. Lim, N. Bodnar, A. Vaupel, E. McKee, M. Baudelet, M. M. Durand, L. Shah, and M. Richardson, “Compact 10 TW laser to generate multi-filament arrays,” CLEO: 2014, OSA Technical Digest (Optical Society of America, 2014), paper SM1F.6.

B. Webb, “Design and Engineering of Ultrafast Amplification Systems,” Ph.D. thesis, University of Central Florida (2016).

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

C. McKenna, K. Walsh, M. Crain, and J. Lake, “Maskless direct write grayscale lithography for MEMS applications,” in Micro/Nano Symposium (UGIM), 2010 18th Biennial University/Government/Industry, pp. 1–4. IEEE (2010).

Data sheet of Shipley 1813 photoresist: http://www.microchem.com/PDFs_Dow/S1800.pdf

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

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

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Figures (6)

Fig. 1
Fig. 1 Concept of space-time (ST) pulsed beams or wave-packets. (a) The surface of the light-cone k x 2 + k z 2 = ( ω / c ) 2 in the (kx, kz, ω) domain is the locus of all propagating plane waves. The intersection of the light-cone with a spectral plane orthogonal to the (kz, ω)-plane is the spectral locus of a family of diffraction-free and dispersion-free ST wave packets for each value of the tilt angle φ the plane makes with respect to the kz-axis. (b) The ST pulsed beam is synthesized such that each spatial frequency kx is associated with one temporal frequency ω. In the specific case depicted here, higher temporal frequencies (smaller wavelengths) are associated with higher magnitude spatial frequencies (depicted here as a colored sinusoid), while kx = 0 (depicted as a straight line) is associated with the lowest temporal frequency (largest wavelength). (c) Calculated ST intensity profile |E (x, 0, τ)|2, where τ corresponds to time in the traveling frame of the pulse. In principle, the profile is invariant along the axial coordinate z. We set φ=90° and make use of a Gaussian spectral profile in the calculation.
Fig. 2
Fig. 2 Schematic of the optical setup for synthesizing ST wave packets (pulsed beams) using transmissive phase plates. The same overall setup is utilized in synthesizing two ST wave packets having bandwidths of Δλ =0.25 nm and 30 nm. Top inset: Definitions of the symbols used to identify the optical components in the setup. Middle inset: Values of the distances and focal lengths utilized to synthesize ST wave packets with Δλ =0.25 nm; bottom inset: corresponding values for Δλ =30 nm.
Fig. 3
Fig. 3 (a) Measured FROG trace obtained via a GRENOUILLE 8-50 (Swamp Optics) of the pulses from the Ti:Sa laser (Tsunami, Spectra Physics). Although the laser bandwidth is ∼ 8 nm, we spectrally filter a bandwidth Δλ ∼ 0.25 nm from it for our ST wave packet synthesis experiment. (b) The spectral intensity and phase of the pulses obtained from the FROG trace. (c) The corresponding pulse intensity and phase in the time domain obtained from the FROG trace.
Fig. 4
Fig. 4 (a) Measured spatio-temporal spectrum |(kx, λ)|2 for synthesized ST wave packets with bandwidth Δλ ~ 0:25 nm. (b) Optical micrograph of the phase plate used. Inset shows magnified (4×) optical micrograph of the section enclosed in the rectangle). (c) Measured time-averaged intensity profile I(x, z) = ∫dt |E(x, z, t)|2 obtained with CCD1 in Fig. 2 that is scanned axially along z.
Fig. 5
Fig. 5 (a) Measured FROG trace obtained via a GRENOUILLE 8-50 (Swamp Optics) of the pulses from a Ti:Sa-based multi-terawatt femstosecond laser; Δλ ∼30 nm. (b) The spectral intensity and phase of the pulses obtained from the FROG trace. (c) The corresponding pulse intensity and phase in the time domain obtained from the FROG trace.
Fig. 6
Fig. 6 Measured spatio-temporal spectrum |(kx, λ)|2 for synthesized ST wave packets with bandwidth Δλ ∼30 nm. (b) Optical micrograph of the phase plate used. (c) Measured time-averaged intensity profile I(x, z) = ∫dt |E(x, z, t)|2 obtained with CCD1 in Fig. 2 that is scanned axially along.

Equations (2)

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E ( x , y , z ) = d k x d ω E ˜ ( k x , ω ) e i ( k x x + k z z ω t ) .
E ( x , y , z ) = d k x ψ ˜ ( k x ) e i k x x e i k z ( z v o t ) e i ω o t = ψ ( x , z v g t ) e i ( k o z ω o t ) .

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