Abstract

Joint structuring of the spatio-temporal spectrum of a pulsed optical beam can lead to a host of unusual properties, such as diffraction-free propagation and tunable group velocities in free space. Such ‘space-time’ wave packets have been synthesized exclusively in the visible and near-infrared spectral regions. Here we synthesize the first space-time wave packet in the mid-infrared exploiting a transmissive phase plate fabricated via gray-scale lithography. A mid-infrared wave packet having a bandwidth of ∼60 nm at a wavelength of 2.35 μm is synthesized such that its transverse width is ∼300 μm and is monitored for a propagation distance of 7 m, corresponding to 80 × the Rayleigh range of a Gaussian beam at the same wavelength and having the same initial transverse spatial width. The experimental methodology presented here and the reported results will help appropriate spatio-temporally structured light in the mid-infrared for a wide variety of applications including imaging, sensing, and metrology.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (14)

Z. Du, S. Zhang, J. Li, N. Gao, and K. Tong, “Mid-infrared tunable laser-based broadband fingerprint absorption spectroscopy for trace gas sensing: A review,” Appl. Sci. 9(2), 338 (2019).
[Crossref]

B. Bhaduri, M. Yessenov, D. Reyes, J. Pena, M. Meem, S. R. Fairchild, R. Menon, M. C. Richardson, and A. F. Abouraddy, “Broadband space-time wave packets propagating for 70 m,” Opt. Lett. 44(8), 2073–2076 (2019).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Optical space-time wave packets of arbitrary group velocity in free space,” Nat. Commun. 10(1), 929 (2019).
[Crossref]

B. Bhaduri, M. Yessenov, and A. F. Abouraddy, “Space-time wave packets that travel in optical materials at the speed of light in vacuum,” Optica 6(2), 139–146 (2019).
[Crossref]

M. Yessenov, B. Bhaduri, H. E. Kondakci, and A. F. Abouraddy, “Weaving the rainbow: Space-time optical wave packets,” Opt. Photonics News 30(5), 34–41 (2019).
[Crossref]

P. Saari, O. Rebane, and I. Besieris, “Reexamination of energy flow velocities of non-diffracting localized waves,” Phys. Rev. A 100(1), 013849 (2019).
[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,” Phys. Rev. A 99(2), 023856 (2019).
[Crossref]

A. Forbes, A. Aiello, and B. Ndagano, “Classically entangled light,” Prog. Opt. 64, 99–153 (2019).
[Crossref]

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11(1), 67–134 (2019).
[Crossref]

N. Korolkova and G. Leuchs, “Quantum correlations in separable multi-mode states and in classically entangled light,” Rep. Prog. Phys. 82(5), 056001 (2019).
[Crossref]

H. E. Kondakci, M. A. Alonso, and A. F. Abouraddy, “Classical entanglement underpins the invariant propagation of space-time wave packets,” Opt. Lett. 44(11), 2645–2648 (2019).
[Crossref]

M. Yessenov, B. Bhaduri, L. Mach, D. Mardani, H. E. Kondakci, M. A. Alonso, G. A. Atia, and A. F. Abouraddy, “What is the maximum differential group delay achievable by a space-time wave packet in free space?” Opt. Express 27(9), 12443–12457 (2019).
[Crossref]

M. Yessenov, B. Bhaduri, H. E. Kondakci, M. Meem, R. Menon, and A. F. Abouraddy, “Non-diffracting broadband incoherent space-time fields,” Optica 6(5), 598–607 (2019).
[Crossref]

M. Yessenov and A. F. Abouraddy, “Changing the speed of optical coherence in free space,” Opt. Lett. 44(21), 5125–5128 (2019).
[Crossref]

2018 (7)

P. Saari, “Reexamination of group velocities of structured light pulses,” Phys. Rev. A 97(6), 063824 (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(6), 063803 (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(10), 13628–13638 (2018).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Self-healing of space-time light sheets,” Opt. Lett. 43(16), 3830–3833 (2018).
[Crossref]

B. Bhaduri, M. Yessenov, and A. F. Abouraddy, “Meters-long propagation of diffraction-free space-time light sheets,” Opt. Express 26(16), 20111–20121 (2018).
[Crossref]

B. Henderson, A. Khodabakhsh, M. Metsälä, I. Ventrillard, F. M. Schmidt, D. Romanini, G. A. D. Ritchie, S. te Lintel Hekkert, R. Briot, T. Risby, N. Marczin, F. J. M. Harren, and S. M. Cristescu, “Laser spectroscopy for breath analysis: towards clinical implementation,” Appl. Phys. B 124(8), 161 (2018).
[Crossref]

R. Bogue, “Remote chemical sensing: a review of techniques and recent developments,” Sens. Rev. 38(4), 453–457 (2018).
[Crossref]

2017 (9)

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K.-H. Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11(4), 222–226 (2017).
[Crossref]

A. Aadhi, V. Sharma, R. P. Singh, and G. K. Samanta, “Continuous-wave, singly resonant parametric oscillator-based mid-infrared optical vortex source,” Opt. Lett. 42(18), 3674–3677 (2017).
[Crossref]

A. Camper, H. Park, Y. H. Lai, H. Kageyama, S. Li, B. K. Talbert, C. I. Blaga, P. Agostini, T. Ruchon, and L. F. DiMauro, “Tunable mid-infrared source of light carrying orbital angular momentum in the femtosecond regime,” Opt. Lett. 42(19), 3769–3772 (2017).
[Crossref]

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

M. A. Porras, “Gaussian beams diffracting in time,” Opt. Lett. 42(22), 4679–4682 (2017).
[Crossref]

N. K. Efremidis, “Spatiotemporal diffraction-free pulsed beams in free-space of the Airy and Bessel type,” Opt. Lett. 42(23), 5038–5041 (2017).
[Crossref]

L. J. Wong and I. Kaminer, “Abruptly focusing and defocusing needles of light and closed-form electromagnetic wavepackets,” ACS Photonics 4(5), 1131–1137 (2017).
[Crossref]

L. J. Wong and I. Kaminer, “Ultrashort tilted-pulsefront pulses and nonparaxial tilted-phase-front beams,” ACS Photonics 4(9), 2257–2264 (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(1), 5789 (2017).
[Crossref]

2015 (2)

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. Photovoltaics 23(9), 1073–1079 (2015).
[Crossref]

S. B. Mirov, V. V. Fedorov, D. Martyshkin, I. S. Moskalev, M. Mirov, and S. Vasilyev, “Progress in mid-IR lasers based on Cr and Fe-doped II–VI chalcogenides,” IEEE J. Sel. Top. Quantum Electron. 21(1), 292–310 (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. Photonics 7(1), 72–78 (2013).
[Crossref]

2011 (1)

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
[Crossref]

2010 (2)

2009 (1)

D. B. Strasfeld, S.-H. Shim, and M. T. Zanni, “New advances in mid-ir pulse shaping and its application to 2d ir spectroscopy and ground-state coherent control,” Adv. Chem. Phys. 141, 1–28 (2009).
[Crossref]

2007 (2)

2002 (1)

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E 66(5), 056611 (2002).
[Crossref]

1997 (1)

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79(21), 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., Ferroelect., Freq. Contr. 39(1), 19–31 (1992).
[Crossref]

1983 (1)

J. N. Brittingham, “Focus wave modes in homogeneous Maxwell’s equations: Transverse electric mode,” J. Appl. Phys. 54(3), 1179–1189 (1983).
[Crossref]

Aadhi, A.

Abouraddy, A. F.

B. Bhaduri, M. Yessenov, D. Reyes, J. Pena, M. Meem, S. R. Fairchild, R. Menon, M. C. Richardson, and A. F. Abouraddy, “Broadband space-time wave packets propagating for 70 m,” Opt. Lett. 44(8), 2073–2076 (2019).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Optical space-time wave packets of arbitrary group velocity in free space,” Nat. Commun. 10(1), 929 (2019).
[Crossref]

B. Bhaduri, M. Yessenov, and A. F. Abouraddy, “Space-time wave packets that travel in optical materials at the speed of light in vacuum,” Optica 6(2), 139–146 (2019).
[Crossref]

M. Yessenov, B. Bhaduri, H. E. Kondakci, and A. F. Abouraddy, “Weaving the rainbow: Space-time optical wave packets,” Opt. Photonics News 30(5), 34–41 (2019).
[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,” Phys. Rev. A 99(2), 023856 (2019).
[Crossref]

H. E. Kondakci, M. A. Alonso, and A. F. Abouraddy, “Classical entanglement underpins the invariant propagation of space-time wave packets,” Opt. Lett. 44(11), 2645–2648 (2019).
[Crossref]

M. Yessenov, B. Bhaduri, L. Mach, D. Mardani, H. E. Kondakci, M. A. Alonso, G. A. Atia, and A. F. Abouraddy, “What is the maximum differential group delay achievable by a space-time wave packet in free space?” Opt. Express 27(9), 12443–12457 (2019).
[Crossref]

M. Yessenov, B. Bhaduri, H. E. Kondakci, M. Meem, R. Menon, and A. F. Abouraddy, “Non-diffracting broadband incoherent space-time fields,” Optica 6(5), 598–607 (2019).
[Crossref]

M. Yessenov and A. F. Abouraddy, “Changing the speed of optical coherence in free space,” Opt. Lett. 44(21), 5125–5128 (2019).
[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(10), 13628–13638 (2018).
[Crossref]

H. E. Kondakci and A. F. Abouraddy, “Self-healing of space-time light sheets,” Opt. Lett. 43(16), 3830–3833 (2018).
[Crossref]

B. Bhaduri, M. Yessenov, and A. F. Abouraddy, “Meters-long propagation of diffraction-free space-time light sheets,” Opt. Express 26(16), 20111–20121 (2018).
[Crossref]

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

K. H. Kagalwala, G. Di Giuseppe, A. F. Abouraddy, and B. E. A. Saleh, “Bell’s measure in classical optical coherence,” Nat. Photonics 7(1), 72–78 (2013).
[Crossref]

B. Bhaduri, M. Yessenov, and A. F. Abouraddy, “Anomalous refraction of optical space-time wave packets,” arXiv:1912.13341 (2019).

Agostini, P.

Aiello, A.

A. Forbes, A. Aiello, and B. Ndagano, “Classically entangled light,” Prog. Opt. 64, 99–153 (2019).
[Crossref]

Alonso, M. A.

Ambrosio, A.

E. Toninelli, B. Ndagano, A. Vallés, B. Sephton, I. Nape, A. Ambrosio, F. Capasso, M. J. Padgett, and A. Forbes, “Concepts in quantum state tomography and classical implementation with intense light: a tutorial,” Adv. Opt. Photonics 11(1), 67–134 (2019).
[Crossref]

Atia, G. A.

Averchi, A.

Bernet, S.

C. Maurer, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “What spatial light modulators can do for optical microscopy,” Laser Photonics Rev. 5(1), 81–101 (2011).
[Crossref]

Besieris, I.

P. Saari, O. Rebane, and I. Besieris, “Reexamination of energy flow velocities of non-diffracting localized waves,” Phys. Rev. A 100(1), 013849 (2019).
[Crossref]

Bhaduri, B.

M. Yessenov, B. Bhaduri, H. E. Kondakci, and A. F. Abouraddy, “Weaving the rainbow: Space-time optical wave packets,” Opt. Photonics News 30(5), 34–41 (2019).
[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,” Phys. Rev. A 99(2), 023856 (2019).
[Crossref]

B. Bhaduri, M. Yessenov, and A. F. Abouraddy, “Space-time wave packets that travel in optical materials at the speed of light in vacuum,” Optica 6(2), 139–146 (2019).
[Crossref]

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[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Concept of space-time wave packets. (a) A plane-wave pulse having uniform intensity profile (left) undergoes spatio-temporal spectral phase modulation to produce a ST wave packet having the form of a light-sheet (right). The intensity profiles are both measured. (b) Spectral representation of a plane-wave pulse on the surface of the light-cone in $(k_{x},k_{z},\tfrac {\omega }{c})$-space, corresponding to the field on the left in (a). The spatio-temporal locus lies along the tangent to the light-cone at $k_{x}\!=\!0$. (c) Spectral representation of a ST wave packet on the surface of the light-cone in $(k_{x},k_{z},\tfrac {\omega }{c})$-space, corresponding to the field on the right in (a). The spatio-temporal locus is again one-dimensional, but now lies at the intersection of the light-cone with a tilted spectral plane.
Fig. 2.
Fig. 2. Schematic of the optical setup for synthesis and characterization of ST wave packets, consisting of four major sections: (i) A field synthesis section that introduces the spatio-temporal correlations into the input field, thereby producing MIR diffraction-free ST wave packets. (ii) Spatio-temporal spectral analysis section to characterize the ST beam in Fourier space $(k_{x}$, $\lambda )$. (iii) Beam analysis section to observe the ST field in physical space by capturing the transverse time-averaged intensity along the propagation axis $z$. (iv) Spectral analysis of ST wave packets. For consistency with our previous work, the direction vertical to the optical table is denoted as the $x$-axis; consequently, the horizontal direction is the $y$-axis. In the bottom right corner we plot the two-dimensional phase distribution implemented on the phase plate.
Fig. 3.
Fig. 3. (a) Measured spectrum of the input beam from the Cr$^{2+}$:ZnS laser with $\Delta \lambda \approx 90$ nm. (b) Measured transmission spectrum of the phase plate in the wavelength range of interest. The inset shows the location on the phase plate where the transmission measurement was performed. (c) Measured spectrum of the synthesized MIR ST wave packet.
Fig. 4.
Fig. 4. (a) Spatio-temporal spectral intensity $|\tilde {\psi }(k_x,\lambda )|^2$ measured by Camera-1, where $\delta \lambda \approx 150$ pm, $\Delta \lambda \approx 60$ nm, $\Delta k_x\approx 8$ rad/mm and the red dotted line corresponds to a theoretical plot of the spatio-temporal spectral trajectory of the ST wave packet when $\theta =45.005^{\circ }$. (b) The measured spatio-temporal spectral intensity plot projected onto the $(k_z,\tfrac {\omega }{c})$-plane. The blue dashed line represents the light line $k_z\!=\!\tfrac {\omega }{c}$. Because of the very small deviation between the spectral tilt angle $\theta =45.005^{\circ }$ and the light-line (tilted at $45^{\circ }$), they appear to coincide. (c) Same plot as (b) but in a rotated coordinate system ($k^{+},k^{-}$) to bring out the deviation of the spatio-temporal spectrum from the light-line (dashed blue line). The dark-red dotted line corresponds to the theoretical expectations.
Fig. 5.
Fig. 5. Measured time-averaged transverse intensity profiles $I(x,y)$ of the ST wave packet along the propagation direction at axial positions $z\approx$1, 2.4, 3, 4, 5, 6, and 7 meters.
Fig. 6.
Fig. 6. (a) Measured normalized on-axis peak intensity $I_{p}(x=0,z)$ with propagation distance $z$. The data is compared to the decay of a Gaussian beam (dotted curve) of the same width and at the same wavelength. (b) Change in beam width (FWHM) with propagation distance $z$. Inset shows the increase in width for the corresponding Gaussian beam.

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L m a x c δ ω 1 | 1 cot θ | .

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