Abstract

We report on a versatile method to compensate the linear attenuation in a medium, independently of its microscopic origin. The method exploits diffraction-limited Bessel beams and tailored on-axis intensity profiles, which are generated using a phase-only spatial light modulator. This technique for compensating one of the most fundamental limiting processes in linear optics is shown to be efficient for a wide range of experimental conditions (modifying the refractive index and the attenuation coefficient). Finally, we explain how this method can be advantageously exploited in applications ranging from bio-imaging light sheet microscopy to quantum memories for future quantum communication networks.

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

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References

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    [Crossref]

2018 (4)

M. Corato-Zanarella, A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Arbitrary control of polarization and intensity profiles of diffraction-attenuation-resistant beams along the propagation direction,” Phys. Rev. Appl. 9(2), 024013 (2018).
[Crossref]

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

C. Michel, O. Boughdad, M. Albert, P.-É. Larr, and M. Bellec, “Superfluid motion and drag-force cancellation in a fluid of light,” Nat. Commun. 9(1), 2108 (2018).
[Crossref]

Q. Fontaine, T. Bienaimé, S. Pigeon, E. Giacobino, A. Bramati, and Q. Glorieux, “Observation of the bogoliubov dispersion in a fluid of light,” Phys. Rev. Lett. 121(18), 183604 (2018).
[Crossref]

2016 (3)

2015 (1)

M. Zamboni-Rached and M. Mojahedi, “Shaping finite-energy diffraction- and attenuation-resistant beams through bessel-gauss–beam superposition,” Phys. Rev. A 92(4), 043839 (2015).
[Crossref]

2014 (4)

T. A. Vieira, M. Zamboni-Rached, and M. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental generation of frozen waves via holographic method,” Opt. Commun. 315, 374–380 (2014).
[Crossref]

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

I. Carusotto, “Superfluid light in bulk nonlinear media,” Proc. R. Soc. London, Ser. A 470(2169), 20140320 (2014).
[Crossref]

M. Zhao, H. Zhang, Y. Li, A. Ashok, R. Liang, W. Zhou, and L. Peng, “Cellular imaging of deep organ using two-photon bessel light-sheet nonlinear structured illumination microscopy,” Biomed. Opt. Express 5(5), 1296–1308 (2014).
[Crossref]

2013 (3)

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38(18), 3546–3549 (2013).
[Crossref]

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond bessel beams to laser ablation,” Appl. Phys. A 112(1), 29–34 (2013).
[Crossref]

2012 (5)

2011 (1)

2010 (3)

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[Crossref]

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-$\lambda$λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

2009 (3)

2008 (5)

G. Hétet, M. Hosseini, B. M. Sparkes, D. Oblak, P. K. Lam, and B. C. Buchler, “Photon echoes generated by reversing magnetic field gradients in a rubidium vapor,” Opt. Lett. 33(20), 2323–2325 (2008).
[Crossref]

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium d lines: comparison between theory and experiment,” J. Phys. B: At., Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in kerr media from pulsed bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

C. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. Stelzer, “Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy,” Science 322(5904), 1065–1069 (2008).
[Crossref]

2006 (2)

2005 (2)

M. Johns, C. A. Giller, D. C. German, and H. Liu, “Determination of reduced scattering coefficient of biological tissue from a needle-like probe,” Opt. Express 13(13), 4828–4842 (2005).
[Crossref]

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
[Crossref]

2004 (4)

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93(15), 153902 (2004).
[Crossref]

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29(1), 44–46 (2004).
[Crossref]

M. Zamboni-Rached, “Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency bessel beams: Frozen waves,” Opt. Express 12(17), 4001–4006 (2004).
[Crossref]

2003 (1)

P. Johannisson, D. Anderson, M. Lisak, and M. Marklund, “Nonlinear bessel beams,” Opt. Commun. 222(1-6), 107–115 (2003).
[Crossref]

2002 (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

1999 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

Adams, C. S.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium d lines: comparison between theory and experiment,” J. Phys. B: At., Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

Aggarwal, S.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

Albert, M.

C. Michel, O. Boughdad, M. Albert, P.-É. Larr, and M. Bellec, “Superfluid motion and drag-force cancellation in a fluid of light,” Nat. Commun. 9(1), 2108 (2018).
[Crossref]

Altin, P. A.

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

Anderson, D.

P. Johannisson, D. Anderson, M. Lisak, and M. Marklund, “Nonlinear bessel beams,” Opt. Commun. 222(1-6), 107–115 (2003).
[Crossref]

Arimondo, E.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-$\lambda$λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Ashok, A.

Bandres, M. A.

Bellec, M.

C. Michel, O. Boughdad, M. Albert, P.-É. Larr, and M. Bellec, “Superfluid motion and drag-force cancellation in a fluid of light,” Nat. Commun. 9(1), 2108 (2018).
[Crossref]

Bent, N.

Bernu, J.

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

Bhuyan, M. K.

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond bessel beams to laser ablation,” Appl. Phys. A 112(1), 29–34 (2013).
[Crossref]

Bienaimé, T.

Q. Fontaine, T. Bienaimé, S. Pigeon, E. Giacobino, A. Bramati, and Q. Glorieux, “Observation of the bogoliubov dispersion in a fluid of light,” Phys. Rev. Lett. 121(18), 183604 (2018).
[Crossref]

Boccara, A.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Bolduc, E.

Boughdad, O.

C. Michel, O. Boughdad, M. Albert, P.-É. Larr, and M. Bellec, “Superfluid motion and drag-force cancellation in a fluid of light,” Nat. Commun. 9(1), 2108 (2018).
[Crossref]

Boyd, R. W.

Boyer, V.

C. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

Bramati, A.

Q. Fontaine, T. Bienaimé, S. Pigeon, E. Giacobino, A. Bramati, and Q. Glorieux, “Observation of the bogoliubov dispersion in a fluid of light,” Phys. Rev. Lett. 121(18), 183604 (2018).
[Crossref]

Buchler, B.

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

Buchler, B. C.

Campos, J.

Carminati, R.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Carusotto, I.

I. Carusotto, “Superfluid light in bulk nonlinear media,” Proc. R. Soc. London, Ser. A 470(2169), 20140320 (2014).
[Crossref]

Chávez-Cerda, S.

Cižmár, T.

T. Čižmár and K. Dholakia, “Tunable bessel light modes: engineering the axial propagation,” Opt. Express 17(18), 15558–15570 (2009).
[Crossref]

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
[Crossref]

Clark, J. B.

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

Q. Glorieux, J. B. Clark, A. M. Marino, Z. Zhou, and P. D. Lett, “Temporally multiplexed storage of images in a gradient echo memory,” Opt. Express 20(11), 12350–12358 (2012).
[Crossref]

Corato-Zanarella, M.

M. Corato-Zanarella, A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Arbitrary control of polarization and intensity profiles of diffraction-attenuation-resistant beams along the propagation direction,” Phys. Rev. Appl. 9(2), 024013 (2018).
[Crossref]

Corzo, N. V.

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

Cottrell, D. M.

Couairon, A.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in kerr media from pulsed bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

Coudreau, T.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-$\lambda$λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Courvoisier, F.

Davis, J. A.

Del Bene, F.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[Crossref]

Dholakia, K.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

T. Čižmár and K. Dholakia, “Tunable bessel light modes: engineering the axial propagation,” Opt. Express 17(18), 15558–15570 (2009).
[Crossref]

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
[Crossref]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Di Trapani, P.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in kerr media from pulsed bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

Dorrah, A. H.

M. Corato-Zanarella, A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Arbitrary control of polarization and intensity profiles of diffraction-attenuation-resistant beams along the propagation direction,” Phys. Rev. Appl. 9(2), 024013 (2018).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

Dubessy, R.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-$\lambda$λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Dubietis, A.

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93(15), 153902 (2004).
[Crossref]

Dudley, J. M.

Dufour, P.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

Faccio, D.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in kerr media from pulsed bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93(15), 153902 (2004).
[Crossref]

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[Crossref]

Ferrier, D. E. K.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

Fink, M.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
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Fontaine, Q.

Q. Fontaine, T. Bienaimé, S. Pigeon, E. Giacobino, A. Bramati, and Q. Glorieux, “Observation of the bogoliubov dispersion in a fluid of light,” Phys. Rev. Lett. 121(18), 183604 (2018).
[Crossref]

Franco, M.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in kerr media from pulsed bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

Froehly, L.

Furfaro, L.

Garcés-Chávez, V.

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
[Crossref]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Ge, C.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium d lines: comparison between theory and experiment,” J. Phys. B: At., Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

Geng, J.

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

German, D. C.

Gesualdi, M. R.

T. A. Vieira, M. Zamboni-Rached, and M. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental generation of frozen waves via holographic method,” Opt. Commun. 315, 374–380 (2014).
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Gesualdi, M. R. R.

Giacobino, E.

Q. Fontaine, T. Bienaimé, S. Pigeon, E. Giacobino, A. Bramati, and Q. Glorieux, “Observation of the bogoliubov dispersion in a fluid of light,” Phys. Rev. Lett. 121(18), 183604 (2018).
[Crossref]

Gigan, S.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
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Giller, C. A.

Giust, R.

Glorieux, Q.

Q. Fontaine, T. Bienaimé, S. Pigeon, E. Giacobino, A. Bramati, and Q. Glorieux, “Observation of the bogoliubov dispersion in a fluid of light,” Phys. Rev. Lett. 121(18), 183604 (2018).
[Crossref]

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

Q. Glorieux, J. B. Clark, A. M. Marino, Z. Zhou, and P. D. Lett, “Temporally multiplexed storage of images in a gradient echo memory,” Opt. Express 20(11), 12350–12358 (2012).
[Crossref]

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-$\lambda$λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Golub, I.

Guibal, S.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-$\lambda$λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Guidoni, L.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-$\lambda$λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Gunn-Moore, F. J.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

Gutiérrez-Vega, J. C.

Heidmann, P.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Hétet, G.

Hosseini, M.

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

G. Hétet, M. Hosseini, B. M. Sparkes, D. Oblak, P. K. Lam, and B. C. Buchler, “Photon echoes generated by reversing magnetic field gradients in a rubidium vapor,” Opt. Lett. 33(20), 2323–2325 (2008).
[Crossref]

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P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium d lines: comparison between theory and experiment,” J. Phys. B: At., Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

Huisken, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[Crossref]

Jacquot, M.

Jasperse, M.

Johannisson, P.

P. Johannisson, D. Anderson, M. Lisak, and M. Marklund, “Nonlinear bessel beams,” Opt. Commun. 222(1-6), 107–115 (2003).
[Crossref]

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Karimi, E.

Katz, O.

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

Keller, P. J.

P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. Stelzer, “Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy,” Science 322(5904), 1065–1069 (2008).
[Crossref]

Koninck, Y. D.

Lam, P. K.

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

G. Hétet, M. Hosseini, B. M. Sparkes, D. Oblak, P. K. Lam, and B. C. Buchler, “Photon echoes generated by reversing magnetic field gradients in a rubidium vapor,” Opt. Lett. 33(20), 2323–2325 (2008).
[Crossref]

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C. Michel, O. Boughdad, M. Albert, P.-É. Larr, and M. Bellec, “Superfluid motion and drag-force cancellation in a fluid of light,” Nat. Commun. 9(1), 2108 (2018).
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S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Lett, P. D.

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

Q. Glorieux, J. B. Clark, A. M. Marino, Z. Zhou, and P. D. Lett, “Temporally multiplexed storage of images in a gradient echo memory,” Opt. Express 20(11), 12350–12358 (2012).
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C. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

Li, Y.

Liang, R.

Likforman, J.-P.

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-$\lambda$λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Lisak, M.

P. Johannisson, D. Anderson, M. Lisak, and M. Marklund, “Nonlinear bessel beams,” Opt. Commun. 222(1-6), 107–115 (2003).
[Crossref]

Liu, H.

Marino, A. M.

Q. Glorieux, J. B. Clark, A. M. Marino, Z. Zhou, and P. D. Lett, “Temporally multiplexed storage of images in a gradient echo memory,” Opt. Express 20(11), 12350–12358 (2012).
[Crossref]

C. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

Marklund, M.

P. Johannisson, D. Anderson, M. Lisak, and M. Marklund, “Nonlinear bessel beams,” Opt. Commun. 222(1-6), 107–115 (2003).
[Crossref]

Mazilu, M.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

McCarthy, N.

McCluskey, K.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

McCormick, C.

C. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

McGloin, D.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

Michel, C.

C. Michel, O. Boughdad, M. Albert, P.-É. Larr, and M. Bellec, “Superfluid motion and drag-force cancellation in a fluid of light,” Nat. Commun. 9(1), 2108 (2018).
[Crossref]

Mirtchev, T.

Mojahedi, M.

M. Corato-Zanarella, A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Arbitrary control of polarization and intensity profiles of diffraction-attenuation-resistant beams along the propagation direction,” Phys. Rev. Appl. 9(2), 024013 (2018).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

M. Zamboni-Rached and M. Mojahedi, “Shaping finite-energy diffraction- and attenuation-resistant beams through bessel-gauss–beam superposition,” Phys. Rev. A 92(4), 043839 (2015).
[Crossref]

Moreno, I.

Mugnai, D.

D. Mugnai and P. Spalla, “Electromagnetic propagation of bessel-like localized waves in the presence of absorbing media,” Opt. Commun. 282(24), 4668–4671 (2009).
[Crossref]

Nuttall, J.

Nylk, J.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

Oblak, D.

Ouadghiri-Idrissi, I.

Parola, A.

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93(15), 153902 (2004).
[Crossref]

Peng, L.

Piché, M.

Pigeon, S.

Q. Fontaine, T. Bienaimé, S. Pigeon, E. Giacobino, A. Bramati, and Q. Glorieux, “Observation of the bogoliubov dispersion in a fluid of light,” Phys. Rev. Lett. 121(18), 183604 (2018).
[Crossref]

Polesana, P.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in kerr media from pulsed bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

Popoff, S.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Porras, M. A.

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93(15), 153902 (2004).
[Crossref]

Preciado, M. A.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

Robins, N.

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[Crossref]

Santamato, E.

Schmidt, A. D.

P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. Stelzer, “Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy,” Science 322(5904), 1065–1069 (2008).
[Crossref]

Scholten, R.

Shaw, D.

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

Siddons, P.

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium d lines: comparison between theory and experiment,” J. Phys. B: At., Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[Crossref]

Spalla, P.

D. Mugnai and P. Spalla, “Electromagnetic propagation of bessel-like localized waves in the presence of absorbing media,” Opt. Commun. 282(24), 4668–4671 (2009).
[Crossref]

Sparkes, B.

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

Sparkes, B. M.

Stelzer, E. H.

P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. Stelzer, “Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy,” Science 322(5904), 1065–1069 (2008).
[Crossref]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[Crossref]

Swoger, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[Crossref]

Tello, J. A.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

Trapani, P. D.

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93(15), 153902 (2004).
[Crossref]

Turner, L.

Vieira, T. A.

T. A. Vieira, M. Zamboni-Rached, and M. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental generation of frozen waves via holographic method,” Opt. Commun. 315, 374–380 (2014).
[Crossref]

T. A. Vieira, M. R. R. Gesualdi, and M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett. 37(11), 2034–2036 (2012).
[Crossref]

Wittbrodt, J.

P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. Stelzer, “Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy,” Science 322(5904), 1065–1069 (2008).
[Crossref]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[Crossref]

Yang, Z.

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

Yzuel, M. J.

Zamboni-Rached, M.

M. Corato-Zanarella, A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Arbitrary control of polarization and intensity profiles of diffraction-attenuation-resistant beams along the propagation direction,” Phys. Rev. Appl. 9(2), 024013 (2018).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

M. Zamboni-Rached and M. Mojahedi, “Shaping finite-energy diffraction- and attenuation-resistant beams through bessel-gauss–beam superposition,” Phys. Rev. A 92(4), 043839 (2015).
[Crossref]

T. A. Vieira, M. Zamboni-Rached, and M. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental generation of frozen waves via holographic method,” Opt. Commun. 315, 374–380 (2014).
[Crossref]

T. A. Vieira, M. R. R. Gesualdi, and M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett. 37(11), 2034–2036 (2012).
[Crossref]

M. Zamboni-Rached, “Diffraction-attenuation resistant beams in absorbing media,” Opt. Express 14(5), 1804–1809 (2006).
[Crossref]

M. Zamboni-Rached, “Stationary optical wave fields with arbitrary longitudinal shape by superposing equal frequency bessel beams: Frozen waves,” Opt. Express 12(17), 4001–4006 (2004).
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Zemánek, P.

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
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Zhang, H.

Zhang, J.

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond bessel beams to laser ablation,” Appl. Phys. A 112(1), 29–34 (2013).
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Zhao, M.

Zhou, W.

Zhou, Z.

Appl. Opt. (2)

Appl. Phys. A (1)

F. Courvoisier, J. Zhang, M. K. Bhuyan, M. Jacquot, and J. M. Dudley, “Applications of femtosecond bessel beams to laser ablation,” Appl. Phys. A 112(1), 29–34 (2013).
[Crossref]

Appl. Phys. Lett. (1)

T. Čižmár, V. Garcés-Chávez, K. Dholakia, and P. Zemánek, “Optical conveyor belt for delivery of submicron objects,” Appl. Phys. Lett. 86(17), 174101 (2005).
[Crossref]

Biomed. Opt. Express (1)

J. Phys. B: At., Mol. Opt. Phys. (1)

P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium d lines: comparison between theory and experiment,” J. Phys. B: At., Mol. Opt. Phys. 41(15), 155004 (2008).
[Crossref]

Nat. Commun. (1)

C. Michel, O. Boughdad, M. Albert, P.-É. Larr, and M. Bellec, “Superfluid motion and drag-force cancellation in a fluid of light,” Nat. Commun. 9(1), 2108 (2018).
[Crossref]

Nat. Photonics (2)

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4(11), 780–785 (2010).
[Crossref]

Nature (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, “Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam,” Nature 419(6903), 145–147 (2002).
[Crossref]

New J. Phys. (2)

Q. Glorieux, J. B. Clark, N. V. Corzo, and P. D. Lett, “Generation of pulsed bipartite entanglement using four-wave mixing,” New J. Phys. 14(12), 123024 (2012).
[Crossref]

B. Sparkes, J. Bernu, M. Hosseini, J. Geng, Q. Glorieux, P. A. Altin, P. K. Lam, N. Robins, and B. Buchler, “Gradient echo memory in an ultra-high optical depth cold atomic ensemble,” New J. Phys. 15(8), 085027 (2013).
[Crossref]

Opt. Commun. (3)

D. Mugnai and P. Spalla, “Electromagnetic propagation of bessel-like localized waves in the presence of absorbing media,” Opt. Commun. 282(24), 4668–4671 (2009).
[Crossref]

P. Johannisson, D. Anderson, M. Lisak, and M. Marklund, “Nonlinear bessel beams,” Opt. Commun. 222(1-6), 107–115 (2003).
[Crossref]

T. A. Vieira, M. Zamboni-Rached, and M. R. Gesualdi, “Modeling the spatial shape of nondiffracting beams: Experimental generation of frozen waves via holographic method,” Opt. Commun. 315, 374–380 (2014).
[Crossref]

Opt. Express (7)

Opt. Lett. (9)

G. Hétet, M. Hosseini, B. M. Sparkes, D. Oblak, P. K. Lam, and B. C. Buchler, “Photon echoes generated by reversing magnetic field gradients in a rubidium vapor,” Opt. Lett. 33(20), 2323–2325 (2008).
[Crossref]

M. A. Bandres, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Parabolic nondiffracting optical wave fields,” Opt. Lett. 29(1), 44–46 (2004).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

I. Golub, T. Mirtchev, J. Nuttall, and D. Shaw, “The taming of absorption: generating a constant intensity beam in a lossy medium,” Opt. Lett. 37(13), 2556–2558 (2012).
[Crossref]

I. Golub and T. Mirtchev, “Absorption-free beam generated by a phase-engineered optical element,” Opt. Lett. 34(10), 1528–1530 (2009).
[Crossref]

T. A. Vieira, M. R. R. Gesualdi, and M. Zamboni-Rached, “Frozen waves: experimental generation,” Opt. Lett. 37(11), 2034–2036 (2012).
[Crossref]

E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38(18), 3546–3549 (2013).
[Crossref]

I. Golub, T. Mirtchev, J. Nuttall, and D. Shaw, “The taming of absorption: generating a constant intensity beam in a lossy medium,” Opt. Lett. 37(13), 2556–2558 (2012).
[Crossref]

A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Generating attenuation-resistant frozen waves in absorbing fluid,” Opt. Lett. 41(16), 3702–3705 (2016).
[Crossref]

Phys. Rev. A (4)

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in kerr media from pulsed bessel beams,” Phys. Rev. A 77(4), 043814 (2008).
[Crossref]

M. Zamboni-Rached and M. Mojahedi, “Shaping finite-energy diffraction- and attenuation-resistant beams through bessel-gauss–beam superposition,” Phys. Rev. A 92(4), 043839 (2015).
[Crossref]

C. McCormick, A. M. Marino, V. Boyer, and P. D. Lett, “Strong low-frequency quantum correlations from a four-wave-mixing amplifier,” Phys. Rev. A 78(4), 043816 (2008).
[Crossref]

Q. Glorieux, R. Dubessy, S. Guibal, L. Guidoni, J.-P. Likforman, T. Coudreau, and E. Arimondo, “Double-$\lambda$λ microscopic model for entangled light generation by four-wave mixing,” Phys. Rev. A 82(3), 033819 (2010).
[Crossref]

Phys. Rev. Appl. (1)

M. Corato-Zanarella, A. H. Dorrah, M. Zamboni-Rached, and M. Mojahedi, “Arbitrary control of polarization and intensity profiles of diffraction-attenuation-resistant beams along the propagation direction,” Phys. Rev. Appl. 9(2), 024013 (2018).
[Crossref]

Phys. Rev. Lett. (4)

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93(15), 153902 (2004).
[Crossref]

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104(10), 100601 (2010).
[Crossref]

Q. Fontaine, T. Bienaimé, S. Pigeon, E. Giacobino, A. Bramati, and Q. Glorieux, “Observation of the bogoliubov dispersion in a fluid of light,” Phys. Rev. Lett. 121(18), 183604 (2018).
[Crossref]

Proc. R. Soc. London, Ser. A (1)

I. Carusotto, “Superfluid light in bulk nonlinear media,” Proc. R. Soc. London, Ser. A 470(2169), 20140320 (2014).
[Crossref]

Sci. Adv. (1)

J. Nylk, K. McCluskey, M. A. Preciado, M. Mazilu, Z. Yang, F. J. Gunn-Moore, S. Aggarwal, J. A. Tello, D. E. K. Ferrier, and K. Dholakia, “Light-sheet microscopy with attenuation-compensated propagation-invariant beams,” Sci. Adv. 4(4), eaar4817 (2018).
[Crossref]

Science (2)

P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. Stelzer, “Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy,” Science 322(5904), 1065–1069 (2008).
[Crossref]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science 305(5686), 1007–1009 (2004).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. Numerical simulation of the longitudinal refractive stretching of the on-axis profile. When the medium refractive index $n$ is larger than 1, the calculated profile must be stretched by n to compensate for the refraction. Blue, red and grey circles are obtained by solving numerically the evolution of the Bessel beam. Blue dots are calculated for $n=1$ in air and red dots correponds to the strectched case for $n=1.33$ (without losses). To verify that we are able to compensate losses in a medium with $n>1$, we plot in gray the propagation in a lossy medium of refractive index 1.33. For red and greys data, this can be deduced from the vacuum case by stretching the z axis by a factor $n$ between $z_{1}$ and $z_{2}$. When losses are present, the on-axis intensity remains constant along the propagation (black dots) as expected.
Fig. 2.
Fig. 2. Experimental setup. $L_{1-7}$ label the different lenses. PH is a pinhole used to clean up the beam. An iris and a mask (thin metallic dot on a glass window) cut all the diffraction orders (except the first one) in the Fourier space of $L_{3}$. The mirror $M$ sets on a translation stage to adjust the $L_{4}$ focal plane position, where the Bessel beam start forming. Insets: (a) Phase mask applied on the SLM. No grating was added on top. (b) Transmission measurement setup. A wide (non-saturating) Gaussian beam splits on a (10:90) beamsplitter; the most intense part propagates through the lossy medium. The beams are focused on two photodiodes (PD) in order to monitor both the stability of the laser intensity and the material transmission. (c) Target on-axis intensity profile. The shadowed region shows where the lossy material should be positioned. (d) Transverse profile of the generated Bessel beam.
Fig. 3.
Fig. 3. Experimental characterization of the reconstructed Bessel beam. The Bessel cone angle $\theta _0$ was set to $(1/G) \times 8.5$ mrad. The white dotted lines on both sides of the central peak define the region where the Gaussian fit is performed. The 2D map is obtained by scanning slowly ($v = 2$ mm.s$^{-1}$) the microscope objective along the z axis and capturing a frame every second.
Fig. 4.
Fig. 4. Experimental profile and longitudinal intensity of the reconstructed Bessel beam in the absence of absorbing medium. (a) blue dots are experimental data of a cut at $z = 0.08$, black dashed line is the target profile calculated numerically and the red solid line is a Gaussian fit of the central region to extract the width. (b) dots are the fitted widths as function of z (blue along x an red along y) Black dashed line is the calculated target. It shows a change of less than 5% over the entire length confirming the non-diffractive nature in the transverse plane. (c) is the longitudinal intensity profile cut at $r=0$. Blue solid line is experimental data and black dashed line is the calculated target. The gray region is the region where the target is defined.
Fig. 5.
Fig. 5. Transmission T as a function of the attenuation coefficient $\alpha$. The transmission of the Bessel beam through the Rubidium vapors are plotted in blue stars ($^{87}$Rb) and orange circles ($^{85}$Rb). Data obtained with the water-milk mixture are plotted in grey diamonds. The two red lines show the transmission expected from the Beer-Lambert law for 2.5 cm and 7.5 cm long lossy materials.

Equations (17)

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E ( x , y , z = 0 ) = S ( k x , k y , z = 0 )   exp [ i ( k x x + k y y ) ] d k x d k y ,
E ( r , z = 0 ) = 1 2 π 0 S ( k , z = 0 ) J 0 ( r k ) k d k ,
E ( r = 0 , z ) = 1 π 0 S ( k 0 2 k z 2 , z = 0 )   exp [ i k z z ] k z d k z .
S ( k , z = 0 ) = 1 k z 0 I ( z ) exp [ i ( k z 0 k z ) z ] d z .
Ψ ( i , j ) = M ( i , j ) m o d [ F ( i , j ) + Φ g ( i , j ) , 2 π ] .
E 1 ( i , j , z = 0 + ) = A i n ( i , j ) s i n c [ π M ( i , j ) π ]   exp [ i ( F ( i , j ) + π M ( i , j ) ) ] ,
I ( z ) = { I 0 ( sin ( C 1 z / z 1 ) sin ( C 1 ) ) 2 i f 0 z z 1 I 0 exp [ α ( z z 1 ) ] i f z 1 z z 2 I max sin 2 [ C 2 + ( π 2 C 2 ) z z 2 z 3 z 2 ] i f z 2 z z 3 I max sin 2 [ π 2 ( 1 z z 3 z 4 z 3 ) ] i f z 3 z z 4 .
M ( i , j ) = 1 + 1 π s i n c 1 ( A ( i , j ) A i n ( i , j ) ) ,
F ( i , j ) = Φ ( i , j ) π M ( i , j ) .
m ( i ) = 1 + 1 π s i n c 1 ( A ( i , N y / 2 ) A i n ( i , N y / 2 ) ) ,
S s i n ( i , j ) = I l k z [ a i cos ( a i ) cos ( a i + b j ) a i 2 ( δ k l ) 2 i δ k sin ( a i ) e i δ k z i sin ( a i + b j ) e i δ k z j a i 2 ( δ k l ) 2 ] ,
S e x p ( i , j ) = I 2 k z e i δ k z i exp ( α l / 2 ) e i δ k z j α + 2 i δ k ,
S 1 , 2 = I 0 e i ( k z 0 k z ) z 1 n k z 0 L exp ( α z ~ 2 ) e i ( k z 0 k z ) z ~ n d z ~ = i n k z I 0 e i ( k z 0 k z ) z 1 ( k z k z 0 n ) + i α 2 ( 1 e i [ ( k z k z 0 n ) + i α 2 ] L ) .
E 1 , 2 ( r = 0 , δ z ) = I 0 e i k z 0 ( z 1 + δ z / n )   × [ i π 0 1 e i [ k z ¯ + i α 2 ] L k ¯ z + i α 2 e i k ¯ z δ z d k ¯ z ] .
I 1 ( δ z ) = i π 0 k ¯ z i α 2 k ¯ z 2 + ( α 2 ) 2 e i k ¯ z δ z d k ¯ z
I 2 ( δ z ) = i π exp ( α L 2 ) 0 k ¯ z i α 2 k ¯ z 2 + ( α 2 ) 2 e i k ¯ z ( L δ z ) d k ¯ z .
E 1 , 2 ( r = 0 , δ z ) = I 0 e i k z 0 ( z 1 + δ z / n ) × [ R e ( I 1 ) + R e ( I 2 ) ] = I 0 e i k z 0 ( z 1 + δ z / n ) exp ( α δ z 2 ) .

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