Abstract

Light propagating through random media produces characteristic speckle patterns, directly related to the large multitude of scattering events. These complex dynamics remarkably display robustness to perturbation of the incoming light parameters, maintaining correlation in the scattered wavefront. This behavior is known as the optical memory effect. Here we unveil the properties of the nonlinear optical memory effect, which occurs when an optothermal nonlinearity perturbs the random material. The effect is characterized through a series of pump and probe experiments in silica aerogel, in the visible range. This additional degree of freedom further generalizes the memory effect, opening the road to applications based on the nonlinear response of random media.

© 2019 Optical Society of America

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References

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2019 (1)

A. Fleming, C. Conti, and A. Di Falco, Ann. Phys. 531, 1900091 (2019).
[Crossref]

2017 (1)

2016 (1)

M. C. Braidotti, S. Gentilini, A. Fleming, M. C. Samuels, A. Di Falco, and C. Conti, Appl. Phys. Lett. 109, 041104 (2016).
[Crossref]

2015 (4)

2014 (5)

S. Gentilini, F. Ghajeri, N. Ghofraniha, A. Di Falco, and C. Conti, Opt. Express 22, 1667 (2014).
[Crossref]

O. Katz, E. Small, Y. Guan, and Y. Silberberg, Optica 1, 170 (2014).
[Crossref]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

T. Strudley, R. Bruck, B. Mills, and O. L. Muskens, Light Sci. Appl. 3, e207 (2014).
[Crossref]

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, IEEE J. Sel. Top. Quantum Electron. 20, 242 (2014).
[Crossref]

2013 (1)

B. Redding, S. F. Liew, R. Sarma, and H. Cao, Nat. Photonics 7, 746 (2013).
[Crossref]

2012 (2)

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, Opt. Express 20, 4840 (2012).
[Crossref]

2011 (4)

L. Xiao and T. A. Birks, Opt. Lett. 36, 3275 (2011).
[Crossref]

E. Van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[Crossref]

M. Abb, E. P. Bakkers, and O. L. Muskens, Phys. Rev. Lett. 106, 143902 (2011).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, New J. Phys. 13, 123021 (2011).
[Crossref]

2010 (3)

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, Science 330, 1368 (2010).
[Crossref]

T. W. Kohlgraf-Owens and A. Dogariu, Opt. Lett. 35, 2236 (2010).
[Crossref]

2009 (1)

S. Faez, P. Johnson, and A. Lagendijk, Phys. Rev. Lett. 103, 053903 (2009).
[Crossref]

2007 (1)

2002 (1)

C. W. Connor and K. Hynynen, Phys. Med. Biol. 47, 1911 (2002).
[Crossref]

2001 (1)

1999 (1)

1996 (1)

1988 (3)

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. Tan, IEEE J. Quantum Electron. 24, 693 (1988).
[Crossref]

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[Crossref]

Abb, M.

M. Abb, E. P. Bakkers, and O. L. Muskens, Phys. Rev. Lett. 106, 143902 (2011).
[Crossref]

Aegerter, M. A.

M. A. Aegerter, N. Leventis, and M. M. Koebel, Aerogels Handbook (Springer, 2011).

Akbulut, D.

E. Van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[Crossref]

Bakkers, E. P.

M. Abb, E. P. Bakkers, and O. L. Muskens, Phys. Rev. Lett. 106, 143902 (2011).
[Crossref]

Ben-Yakar, A.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, IEEE J. Sel. Top. Quantum Electron. 20, 242 (2014).
[Crossref]

Bertolotti, J.

S. Schott, J. Bertolotti, J.-F. Léger, L. Bourdieu, and S. Gigan, Opt. Express 23, 13505 (2015).
[Crossref]

E. Van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[Crossref]

Birks, T. A.

L. Xiao and T. A. Birks, Opt. Lett. 36, 3275 (2011).
[Crossref]

M. D. Grogan, M. D. Rollings, L. Xiao, W. J. Wadsworth, R. England, S. Maier, and T. A. Birks, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2010), paper JThE21.

Boccara, A.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Boccara, A. C.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, New J. Phys. 13, 123021 (2011).
[Crossref]

Bossy, E.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

Bourdieu, L.

Braidotti, M. C.

M. C. Braidotti, S. Gentilini, A. Fleming, M. C. Samuels, A. Di Falco, and C. Conti, Appl. Phys. Lett. 109, 041104 (2016).
[Crossref]

Brown, A. N.

Bruck, R.

T. Strudley, R. Bruck, B. Mills, and O. L. Muskens, Light Sci. Appl. 3, e207 (2014).
[Crossref]

Cao, H.

B. Redding, S. F. Liew, R. Sarma, and H. Cao, Nat. Photonics 7, 746 (2013).
[Crossref]

Caravaca-Aguirre, A. M.

Carminati, R.

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Chaigne, T.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

Chan, K. M. C.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, IEEE J. Sel. Top. Quantum Electron. 20, 242 (2014).
[Crossref]

Cheong, W.-F.

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. Tan, IEEE J. Quantum Electron. 24, 693 (1988).
[Crossref]

Conkey, D. B.

Connor, C. W.

C. W. Connor and K. Hynynen, Phys. Med. Biol. 47, 1911 (2002).
[Crossref]

Conti, C.

A. Fleming, C. Conti, and A. Di Falco, Ann. Phys. 531, 1900091 (2019).
[Crossref]

M. C. Braidotti, S. Gentilini, A. Fleming, M. C. Samuels, A. Di Falco, and C. Conti, Appl. Phys. Lett. 109, 041104 (2016).
[Crossref]

S. Gentilini, F. Ghajeri, N. Ghofraniha, A. Di Falco, and C. Conti, Opt. Express 22, 1667 (2014).
[Crossref]

Derevyanko, S.

H. Frostig, E. Small, S. Derevyanko, and Y. Silberberg, “Focusing coherent light through a nonlinear scattering medium,” arXiv:1607.08105 (2016).

Di Falco, A.

A. Fleming, C. Conti, and A. Di Falco, Ann. Phys. 531, 1900091 (2019).
[Crossref]

M. C. Braidotti, S. Gentilini, A. Fleming, M. C. Samuels, A. Di Falco, and C. Conti, Appl. Phys. Lett. 109, 041104 (2016).
[Crossref]

S. Gentilini, F. Ghajeri, N. Ghofraniha, A. Di Falco, and C. Conti, Opt. Express 22, 1667 (2014).
[Crossref]

Dogariu, A.

England, R.

M. D. Grogan, M. D. Rollings, L. Xiao, W. J. Wadsworth, R. England, S. Maier, and T. A. Birks, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2010), paper JThE21.

Faez, S.

S. Faez, P. Johnson, and A. Lagendijk, Phys. Rev. Lett. 103, 053903 (2009).
[Crossref]

Feng, S.

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[Crossref]

Ferhanoglu, O.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, IEEE J. Sel. Top. Quantum Electron. 20, 242 (2014).
[Crossref]

Fink, M.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, New J. Phys. 13, 123021 (2011).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Fleming, A.

A. Fleming, C. Conti, and A. Di Falco, Ann. Phys. 531, 1900091 (2019).
[Crossref]

M. C. Braidotti, S. Gentilini, A. Fleming, M. C. Samuels, A. Di Falco, and C. Conti, Appl. Phys. Lett. 109, 041104 (2016).
[Crossref]

Frenz, M.

Freudiger, C. W.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, Science 330, 1368 (2010).
[Crossref]

Freund, I.

I. Freund, M. Rosenbluh, and S. Feng, Phys. Rev. Lett. 61, 2328 (1988).
[Crossref]

Frostig, H.

H. Frostig, E. Small, S. Derevyanko, and Y. Silberberg, “Focusing coherent light through a nonlinear scattering medium,” arXiv:1607.08105 (2016).

Gentilini, S.

M. C. Braidotti, S. Gentilini, A. Fleming, M. C. Samuels, A. Di Falco, and C. Conti, Appl. Phys. Lett. 109, 041104 (2016).
[Crossref]

S. Gentilini, F. Ghajeri, N. Ghofraniha, A. Di Falco, and C. Conti, Opt. Express 22, 1667 (2014).
[Crossref]

Ghaffari, S. A.

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. Tan, IEEE J. Quantum Electron. 24, 693 (1988).
[Crossref]

Ghajeri, F.

Ghofraniha, N.

Gigan, S.

S. Schott, J. Bertolotti, J.-F. Léger, L. Bourdieu, and S. Gigan, Opt. Express 23, 13505 (2015).
[Crossref]

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, New J. Phys. 13, 123021 (2011).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Grogan, M. D.

M. D. Grogan, M. D. Rollings, L. Xiao, W. J. Wadsworth, R. England, S. Maier, and T. A. Birks, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2010), paper JThE21.

Guan, Y.

Holtom, G. R.

B. G. Saar, C. W. Freudiger, J. Reichman, C. M. Stanley, G. R. Holtom, and X. S. Xie, Science 330, 1368 (2010).
[Crossref]

Horstmeyer, R.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, Optica 4, 886 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, Nat. Phys. 11, 684 (2015).
[Crossref]

Hoy, C. L.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, IEEE J. Sel. Top. Quantum Electron. 20, 242 (2014).
[Crossref]

Hynynen, K.

C. W. Connor and K. Hynynen, Phys. Med. Biol. 47, 1911 (2002).
[Crossref]

Ith, M.

Johnson, P.

S. Faez, P. Johnson, and A. Lagendijk, Phys. Rev. Lett. 103, 053903 (2009).
[Crossref]

Judkewitz, B.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, Optica 4, 886 (2017).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, Nat. Phys. 11, 684 (2015).
[Crossref]

Kane, C.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[Crossref]

Karajanagi, S. S.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, IEEE J. Sel. Top. Quantum Electron. 20, 242 (2014).
[Crossref]

Katz, O.

T. Chaigne, O. Katz, A. C. Boccara, M. Fink, E. Bossy, and S. Gigan, Nat. Photonics 8, 58 (2014).
[Crossref]

O. Katz, E. Small, Y. Guan, and Y. Silberberg, Optica 1, 170 (2014).
[Crossref]

Kim, K. H.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, IEEE J. Sel. Top. Quantum Electron. 20, 242 (2014).
[Crossref]

Kobler, J. B.

C. L. Hoy, O. Ferhanoglu, M. Yildirim, K. H. Kim, S. S. Karajanagi, K. M. C. Chan, J. B. Kobler, S. M. Zeitels, and A. Ben-Yakar, IEEE J. Sel. Top. Quantum Electron. 20, 242 (2014).
[Crossref]

Koebel, M. M.

M. A. Aegerter, N. Leventis, and M. M. Koebel, Aerogels Handbook (Springer, 2011).

Kohlgraf-Owens, T. W.

Korotkova, O.

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

E. Van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[Crossref]

S. Faez, P. Johnson, and A. Lagendijk, Phys. Rev. Lett. 103, 053903 (2009).
[Crossref]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, and A. D. Stone, Phys. Rev. Lett. 61, 834 (1988).
[Crossref]

Léger, J.-F.

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, and S. Gigan, New J. Phys. 13, 123021 (2011).
[Crossref]

S. Popoff, G. Lerosey, R. Carminati, M. Fink, A. Boccara, and S. Gigan, Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Leventis, N.

M. A. Aegerter, N. Leventis, and M. M. Koebel, Aerogels Handbook (Springer, 2011).

Liew, S. F.

B. Redding, S. F. Liew, R. Sarma, and H. Cao, Nat. Photonics 7, 746 (2013).
[Crossref]

Lin, W.-C.

Maier, S.

M. D. Grogan, M. D. Rollings, L. Xiao, W. J. Wadsworth, R. England, S. Maier, and T. A. Birks, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2010), paper JThE21.

Mills, B.

T. Strudley, R. Bruck, B. Mills, and O. L. Muskens, Light Sci. Appl. 3, e207 (2014).
[Crossref]

Mosk, A.

E. Van Putten, D. Akbulut, J. Bertolotti, W. L. Vos, A. Lagendijk, and A. Mosk, Phys. Rev. Lett. 106, 193905 (2011).
[Crossref]

I. M. Vellekoop and A. Mosk, Opt. Lett. 32, 2309 (2007).
[Crossref]

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, Nat. Photonics 6, 283 (2012).
[Crossref]

Motamedi, M.

W.-C. Lin, M. Motamedi, and A. J. Welch, Appl. Opt. 35, 3413 (1996).
[Crossref]

M. Motamedi, A. J. Welch, W.-F. Cheong, S. A. Ghaffari, and O. Tan, IEEE J. Quantum Electron. 24, 693 (1988).
[Crossref]

Muskens, O. L.

T. Strudley, R. Bruck, B. Mills, and O. L. Muskens, Light Sci. Appl. 3, e207 (2014).
[Crossref]

M. Abb, E. P. Bakkers, and O. L. Muskens, Phys. Rev. Lett. 106, 143902 (2011).
[Crossref]

Osnabrugge, G.

Papadopoulos, I. N.

G. Osnabrugge, R. Horstmeyer, I. N. Papadopoulos, B. Judkewitz, and I. M. Vellekoop, Optica 4, 886 (2017).
[Crossref]

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H. Frostig, E. Small, S. Derevyanko, and Y. Silberberg, “Focusing coherent light through a nonlinear scattering medium,” arXiv:1607.08105 (2016).

M. D. Grogan, M. D. Rollings, L. Xiao, W. J. Wadsworth, R. England, S. Maier, and T. A. Birks, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2010), paper JThE21.

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Figures (4)

Fig. 1.
Fig. 1. Optical setup used for manipulation of the measurement of the NL-OMEM. The probe is sub-mW 532 nm CW source. This probe is collimated to overfill an SLM, which patterns the wavefront that then passes through a 4 - f system, selecting the first order. A 10 × objective focuses the beam within the aerogel, which is then collected by a 50 × objective. The pump was a Toptica i-BeamSmart 200 mW 488 nm CW laser, expanded and collimated to fill the back focal lens of the 50 × objective. The scattered transmission was recorded continuously by a Basler 1920ac CCD camera. LPF, long-pass filters at 500 nm cutoff are used to block the pump beam from key pieces of apparatus and prevent diffusely scattered light from reaching the camera. DM, a 505 nm long-pass dichroic mirror. LP, linear polarizers, with polarization axis noted by a black arrow. Curved arrow, represent optics that are on adjustable mounts.
Fig. 2.
Fig. 2. Schematic showing the geometry of the pump–probe experiments. The white box indicates the imaging area. The large red diffuse spot represents the thermal radial profile. Each of the four pairs of white points indicates different positions at which the output is optimized. Using pairs of focus points, it is possible to identify both shifts and distortions in the scattered wavefront, through both the relative intensity, position, and separation of the focus points. The yellow inset shows the effect of the pump on an individual pair of focus points. The direction of shift in the focus points is indicated by the red arrow, along with a representation of that shift. To evaluate the effect of the perturbation, a ROI around the spots in their initial state (OFF), represented by the white shaded region, is correlated with the surrounding area of the scattered state during pumping (ON).
Fig. 3.
Fig. 3. Example of the NL-OMEM through nonlinear perturbation. Using a pump power of 150 mW at a distance of 0.53 mm from the pump. Left, original wavefront. Right, perturbed wavefront exhibiting the NL-OMEM.
Fig. 4.
Fig. 4. Correlation of the area surrounding the ROI with respect to its shift by memory effects. The colored lines refer to changes in correlation due to NL-OMEM. The thick black line refers to changes in correlation due to the shift–shift memory effect. (a) The pump beam acting 1250 pixels/0.78 mm vertically displaced from the ROI. (b) 1050 pixels/0.65 mm. (c) 850 pixels/0.53 mm. (d) 750 pixels/0.47 mm. In every case, the system was pumped for 1 min. The thin black line highlights the linear trend in the final correlation of the perturbed system with pump power.

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