Abstract

We show that the multiple scattering events taking place inside a highly scattering medium, in conjunction with wavefront shaping, can be used to control the state of polarization of the light transmitted through a highly scattering medium. This control is achieved by using the intensity, phase, and polarization changing behavior of a scattering medium captured by a vector transmission matrix (VTM). We use a single beam incident upon a scattering medium to measure the absolute value of the VTM elements, in contrast to the multiple beams required in our previously reported approach. Further, the phase-only spatial light modulator based on a low-cost (< US$600) deformable micro-mirror array used in our work will make similar experiments accessible to other researchers.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2011).
    [CrossRef]
  2. I. M. Vellekoop, A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
    [CrossRef] [PubMed]
  3. I. M. Vellekoop, E. G. van Putten, A. Lagendijk, A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
    [CrossRef] [PubMed]
  4. I. M. Vellekoop, A. Lagendijk, A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
    [CrossRef]
  5. S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
    [CrossRef] [PubMed]
  6. D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
    [CrossRef] [PubMed]
  7. S. Tripathi, R. Paxman, T. Bifano, K. C. Toussaint, “Vector transmission matrix for the polarization behavior of light propagation in highly scattering media,” Opt. Express 20, 16067–16076 (2012).
    [CrossRef] [PubMed]
  8. Y. Guan, O. Katz, E. Small, J. Zhou, Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37, 4663–4665 (2012).
    [CrossRef] [PubMed]
  9. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, 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, 100601 (2010).
    [CrossRef] [PubMed]
  10. O. Katz, E. Small, Y. Bromberg, Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
    [CrossRef]
  11. L. Novotny, B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
    [CrossRef]
  12. S. Tripathi, K. C. Toussaint, “Versatile generation of optical vector fields and vector beams using a non-interferometric approach,” Opt. Express 20, 10788–10795 (2012).
    [CrossRef] [PubMed]
  13. Q. Zhan, “Cylindrical vector beams: From mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
    [CrossRef]
  14. S. Tripathi, B. J. Davis, K. C. Toussaint, P. S. Carney, “Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy,” J. Phys. B At. Mol. Opt. Phys. 44, 015401 (2011).
    [CrossRef]
  15. S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234–2239 (1990).
    [CrossRef] [PubMed]
  16. S. Tripathi, K. C. Toussaint, “Rapid Mueller matrix polarimetry based on parallelized polarization state generation and detection,” Opt. Express 17, 21396–21407 (2009).
    [CrossRef] [PubMed]
  17. Texas Instruments, DLP®LightCrafterTM Evaluation Module (EVM): User’s Guide(2013).
  18. S. Tripathi, K. C. Toussaint, “Quantitative control over the intensity and phase of light transmitted through highly scattering media,” Opt. Express 21, 25890–25900 (2013).
    [CrossRef] [PubMed]
  19. W. H. Lee, “Binary synthetic holograms,” Appl. Opt. 13, 1677–1682 (1974).
    [CrossRef] [PubMed]
  20. B. Schaefer, E. Collett, R. Smyth, D. Barrett, B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
    [CrossRef]
  21. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (John Wiley, 2007).
  22. R. C. Gonzalez, R. E. Woods, Digital Image Processing (Prentice Hall, 2007).
  23. R. H. Byrd, J. Nocedal, R. A. Waltz, “KNITRO: An integrated package for nonlinear optimization,” in Large Scale Nonlinear Optimization, G. D. Pillo, F. Giannessi, eds. (Springer, 2006), pp. 35–59.
    [CrossRef]

2013 (1)

2012 (3)

2011 (4)

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2011).
[CrossRef]

S. Tripathi, B. J. Davis, K. C. Toussaint, P. S. Carney, “Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy,” J. Phys. B At. Mol. Opt. Phys. 44, 015401 (2011).
[CrossRef]

O. Katz, E. Small, Y. Bromberg, Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

2010 (3)

I. M. Vellekoop, A. Lagendijk, A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[CrossRef]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, 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, 100601 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (1)

2007 (2)

I. M. Vellekoop, A. P. Mosk, “Focusing coherent light through opaque strongly scattering media,” Opt. Lett. 32, 2309–2311 (2007).
[CrossRef] [PubMed]

B. Schaefer, E. Collett, R. Smyth, D. Barrett, B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[CrossRef]

1990 (1)

1974 (1)

Austin, D. R.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Barrett, D.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[CrossRef]

Bifano, T.

Boccara, A. C.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, 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, 100601 (2010).
[CrossRef] [PubMed]

Bondareff, P.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Bromberg, Y.

O. Katz, E. Small, Y. Bromberg, Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

Byrd, R. H.

R. H. Byrd, J. Nocedal, R. A. Waltz, “KNITRO: An integrated package for nonlinear optimization,” in Large Scale Nonlinear Optimization, G. D. Pillo, F. Giannessi, eds. (Springer, 2006), pp. 35–59.
[CrossRef]

Carminati, R.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, 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, 100601 (2010).
[CrossRef] [PubMed]

Carney, P. S.

S. Tripathi, B. J. Davis, K. C. Toussaint, P. S. Carney, “Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy,” J. Phys. B At. Mol. Opt. Phys. 44, 015401 (2011).
[CrossRef]

Chatel, B.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Collett, E.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[CrossRef]

Davis, B. J.

S. Tripathi, B. J. Davis, K. C. Toussaint, P. S. Carney, “Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy,” J. Phys. B At. Mol. Opt. Phys. 44, 015401 (2011).
[CrossRef]

Fink, M.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, 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, 100601 (2010).
[CrossRef] [PubMed]

Ford, D. H.

Fraher, B.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[CrossRef]

Gigan, S.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, 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, 100601 (2010).
[CrossRef] [PubMed]

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Prentice Hall, 2007).

Guan, Y.

Hecht, B.

L. Novotny, B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
[CrossRef]

Katz, O.

Y. Guan, O. Katz, E. Small, J. Zhou, Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37, 4663–4665 (2012).
[CrossRef] [PubMed]

O. Katz, E. Small, Y. Bromberg, Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

Kimura, W. D.

Lagendijk, A.

I. M. Vellekoop, A. Lagendijk, A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[CrossRef]

I. M. Vellekoop, E. G. van Putten, A. Lagendijk, A. P. Mosk, “Demixing light paths inside disordered metamaterials,” Opt. Express 16, 67–80 (2008).
[CrossRef] [PubMed]

Lee, W. H.

Lerosey, G.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef] [PubMed]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, 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, 100601 (2010).
[CrossRef] [PubMed]

McCabe, D. J.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Mosk, A. P.

Nocedal, J.

R. H. Byrd, J. Nocedal, R. A. Waltz, “KNITRO: An integrated package for nonlinear optimization,” in Large Scale Nonlinear Optimization, G. D. Pillo, F. Giannessi, eds. (Springer, 2006), pp. 35–59.
[CrossRef]

Novotny, L.

L. Novotny, B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
[CrossRef]

Paxman, R.

Popoff, S.

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef] [PubMed]

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, 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, 100601 (2010).
[CrossRef] [PubMed]

Saleh, B. E. A.

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

Schaefer, B.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[CrossRef]

Silberberg, Y.

Y. Guan, O. Katz, E. Small, J. Zhou, Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37, 4663–4665 (2012).
[CrossRef] [PubMed]

O. Katz, E. Small, Y. Bromberg, Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

Small, E.

Y. Guan, O. Katz, E. Small, J. Zhou, Y. Silberberg, “Polarization control of multiply scattered light through random media by wavefront shaping,” Opt. Lett. 37, 4663–4665 (2012).
[CrossRef] [PubMed]

O. Katz, E. Small, Y. Bromberg, Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

Smyth, R.

B. Schaefer, E. Collett, R. Smyth, D. Barrett, B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[CrossRef]

Tajalli, A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Teich, M. C.

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

Tidwell, S. C.

Toussaint, K. C.

Tripathi, S.

van Putten, E. G.

Vellekoop, I. M.

Walmsley, I. A.

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Waltz, R. A.

R. H. Byrd, J. Nocedal, R. A. Waltz, “KNITRO: An integrated package for nonlinear optimization,” in Large Scale Nonlinear Optimization, G. D. Pillo, F. Giannessi, eds. (Springer, 2006), pp. 35–59.
[CrossRef]

Wiersma, D. S.

D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2011).
[CrossRef]

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Prentice Hall, 2007).

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: From mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
[CrossRef]

Zhou, J.

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: From mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
[CrossRef]

Am. J. Phys. (1)

B. Schaefer, E. Collett, R. Smyth, D. Barrett, B. Fraher, “Measuring the Stokes polarization parameters,” Am. J. Phys. 75, 163–168 (2007).
[CrossRef]

Appl. Opt. (2)

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

S. Tripathi, B. J. Davis, K. C. Toussaint, P. S. Carney, “Determination of the second-order nonlinear susceptibility elements of a single nanoparticle using coherent optical microscopy,” J. Phys. B At. Mol. Opt. Phys. 44, 015401 (2011).
[CrossRef]

Nat. Commun. (2)

S. Popoff, G. Lerosey, M. Fink, A. C. Boccara, S. Gigan, “Image transmission through an opaque material,” Nat. Commun. 1, 81 (2010).
[CrossRef] [PubMed]

D. J. McCabe, A. Tajalli, D. R. Austin, P. Bondareff, I. A. Walmsley, S. Gigan, B. Chatel, “Spatio-temporal focusing of an ultrafast pulse through a multiply scattering medium,” Nat. Commun. 2, 447 (2011).
[CrossRef] [PubMed]

Nat. Photonics (3)

D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7, 188–196 (2011).
[CrossRef]

I. M. Vellekoop, A. Lagendijk, A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
[CrossRef]

O. Katz, E. Small, Y. Bromberg, Y. Silberberg, “Focusing and compression of ultrashort pulses through scattering media,” Nat. Photonics 5, 372–377 (2011).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, 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, 100601 (2010).
[CrossRef] [PubMed]

Other (5)

Texas Instruments, DLP®LightCrafterTM Evaluation Module (EVM): User’s Guide(2013).

L. Novotny, B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
[CrossRef]

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

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Prentice Hall, 2007).

R. H. Byrd, J. Nocedal, R. A. Waltz, “KNITRO: An integrated package for nonlinear optimization,” in Large Scale Nonlinear Optimization, G. D. Pillo, F. Giannessi, eds. (Springer, 2006), pp. 35–59.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Schematic of the experimental setup.See text for details.

Fig. 2
Fig. 2

(a) and (b) show the X- and Y -polarized components, respectively, of the speckle pattern at the output of the scattering sample. The square box shown demarcates an ROI. The amplitude of the VTM elements governing the X- and Y -polarized optical field at the ROI are shown in (c) and (d), respectively. Similarly, the phase of the VTM elements governing the X- and Y -polarized optical field at the ROI are shown in (e) and (f), respectively.

Fig. 3
Fig. 3

Demonstration of polarization control. The left column shows the polarization ellipses corresponding to five targeted (red) and experimentally measured (blue) SOPs at the ROI shown in Fig. 2. The right column shows the corresponding expected (red) and experimentally measured (blue) intensities using the rotating quarter-waveplate technique of measuring the Stokes vector components.

Fig. 4
Fig. 4

A Poincaré sphere showing targeted SOPs is shown in (a). Experimentally observed parameters are shown in (b)–(d). See text for details.

Fig. 5
Fig. 5

Intensity profile at the observation plane measured as a function of the quarter wave-plate orientation corresponding to an input optical field designed to generate the SOP shown in Fig. 3(a) at the ROI (red square). The ROI is demarcated by a red box.

Fig. 6
Fig. 6

Experimentally measured polarization distribution over the observation plane corresponding to an input optical field designed to generate the SOP shown in Fig. 3(a) at the ROI. The ROI is demarcated by a white box.

Tables (1)

Tables Icon

Table 1 The parameters of the SOPs generated.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

f ( x , y ) = { 1 if cos { g ( x , y ) + 2 π x T } > cos ( π q ) 0 Otherwise ,
T n , m k Y = | g n m | k I n , m R k I n , m S k e i Δ ϕ n , k ,
I ( θ ) = 1 2 { S 0 R , n + S 1 R , n cos 2 ( 2 θ ) + S 2 R , n cos ( 2 θ ) sin ( 2 θ ) S 3 R , n sin ( 2 θ ) } ,
φ n = 1 2 ( S 2 R , n + i S 3 R , n ) .
T n , m X Y = | g n m | X I n , m S , X e i Δ ϕ n , X
T n , m Y Y = | g n m | Y I n , m S , Y e i ( Δ ϕ n , Y + φ n ) .
I n , m k = I n , m S , k + I n , m R , k + 2 I n , m S , k I n , m R , k | g n m | k cos ( φ n , m k + α ) ,
Minimize φ m ( I n P I n D ) 2 subject to { | R 2 | u n Y ( P ) | 2 | u n X ( P ) | 2 | < ε r ( ϕ u n X ( P ) + u n Y ( P ) ) mod 2 π < ε p ,
u n k ( P ) = m t k , m k Y e i ϕ m ,
I n P = | u n X ( P ) | 2 + | u n Y ( P ) | 2 .

Metrics