Abstract

By employing the pseudospectral time-domain (PSTD) simulation technique, we analyze the propagation of monochromatic light through a macroscopic scattering medium. Simulation results show that, monochromatic light can be directed through a scattering medium and focus into a narrow peak; a range of wavelengths has been simulated. Furthermore, we compare: i) focusing monochromatic light through a macroscopic scattering medium, and, ii) focusing monochromatic light through vacuum. Based upon numerical solutions of Maxwell’s equations, we demonstrate: with a fully-surrounding wavefront of specific amplitude and phase, sub-diffraction focusing can be achieved with monochromatic light, with or without the presence of a scattering medium.

© 2015 Optical Society of America

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References

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  1. G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315(5815), 1120–1122 (2007).
    [Crossref] [PubMed]
  2. I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010).
    [Crossref]
  3. X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
    [Crossref] [PubMed]
  4. Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
    [Crossref] [PubMed]
  5. R. Fiolka, K. Si, and M. Cui, “Parallel wavefront measurements in ultrasound pulse guided digital phase conjugation,” Opt. Express 20(22), 24827–24834 (2012).
    [Crossref] [PubMed]
  6. J. W. Tay, P. X. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
    [Crossref] [PubMed]
  7. A. Edelman and N. R. Rao, “Random matrix theory,” Acta Numer. 14, 233–297 (1999).
    [Crossref]
  8. M. Kim, W. Choi, C. Yoon, G. H. Kim, and W. Choi, “Relation between transmission eigenchannels and single-channel optimizing modes in a disordered medium,” Opt. Lett. 38(16), 2994–2996 (2013).
    [Crossref] [PubMed]
  9. W. Choi, A. P. Mosk, Q.-H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
    [Crossref]
  10. A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
    [Crossref]
  11. J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
    [Crossref]
  12. M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
    [Crossref]
  13. T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
    [Crossref] [PubMed]
  14. H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
    [Crossref] [PubMed]
  15. J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt. 18(2), 025004 (2013).
    [Crossref] [PubMed]
  16. Q. H. Liu, “Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm,” IEEE Trans. Geosci. Rem. Sens. 37(2), 917–926 (1999).
    [Crossref]
  17. S. H. Tseng, W. L. Ting, and S. J. Wang, “2-D PSTD Simulation of the time-reversed ultrasound-encoded deep-tissue imaging technique,” Biomed. Opt. Express 5(3), 882–894 (2014).
    [Crossref] [PubMed]
  18. P. R. T. Munro, D. Engelke, and D. D. Sampson, “A compact source condition for modelling focused fields using the pseudospectral time-domain method,” Opt. Express 22(5), 5599–5613 (2014).
    [Crossref] [PubMed]
  19. S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
    [Crossref]
  20. R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A 87(4), 041801 (2013).
    [Crossref]
  21. Y. Huang, C. Tsai, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” (in review).
  22. S. H. Choi and Y. L. Kim, “Hybridized/coupled multiple resonances in nacre,” Phys. Rev. B 89(3), 035115 (2014).
    [Crossref]
  23. J. de Rosny and M. Fink, “Overcoming the Diffraction Limit In Wave Physics Using a Time-Reversal Mirror and a Novel Acoustic Sink,” Phys. Rev. Lett. 89(12), 124301 (2002).
    [Crossref] [PubMed]
  24. Y. Huang, Y. Hung, and S. H. Tseng, “An optical Target to eliminate impinging light in a light scattering simulation,” Comput. Phys. Commun. 185(10), 2504–2509 (2014).
    [Crossref]
  25. M. J. Steel, B. Marks, and A. Rahmani, “Properties of sub-diffraction limited focusing by optical phase conjugation,” Opt. Express 18(2), 1487–1500 (2010).
    [Crossref] [PubMed]

2014 (5)

J. W. Tay, P. X. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
[Crossref] [PubMed]

S. H. Tseng, W. L. Ting, and S. J. Wang, “2-D PSTD Simulation of the time-reversed ultrasound-encoded deep-tissue imaging technique,” Biomed. Opt. Express 5(3), 882–894 (2014).
[Crossref] [PubMed]

P. R. T. Munro, D. Engelke, and D. D. Sampson, “A compact source condition for modelling focused fields using the pseudospectral time-domain method,” Opt. Express 22(5), 5599–5613 (2014).
[Crossref] [PubMed]

S. H. Choi and Y. L. Kim, “Hybridized/coupled multiple resonances in nacre,” Phys. Rev. B 89(3), 035115 (2014).
[Crossref]

Y. Huang, Y. Hung, and S. H. Tseng, “An optical Target to eliminate impinging light in a light scattering simulation,” Comput. Phys. Commun. 185(10), 2504–2509 (2014).
[Crossref]

2013 (6)

R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A 87(4), 041801 (2013).
[Crossref]

M. Kim, W. Choi, C. Yoon, G. H. Kim, and W. Choi, “Relation between transmission eigenchannels and single-channel optimizing modes in a disordered medium,” Opt. Lett. 38(16), 2994–2996 (2013).
[Crossref] [PubMed]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt. 18(2), 025004 (2013).
[Crossref] [PubMed]

2012 (4)

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref] [PubMed]

R. Fiolka, K. Si, and M. Cui, “Parallel wavefront measurements in ultrasound pulse guided digital phase conjugation,” Opt. Express 20(22), 24827–24834 (2012).
[Crossref] [PubMed]

2011 (2)

W. Choi, A. P. Mosk, Q.-H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[Crossref] [PubMed]

2010 (2)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010).
[Crossref]

M. J. Steel, B. Marks, and A. Rahmani, “Properties of sub-diffraction limited focusing by optical phase conjugation,” Opt. Express 18(2), 1487–1500 (2010).
[Crossref] [PubMed]

2007 (1)

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315(5815), 1120–1122 (2007).
[Crossref] [PubMed]

2002 (1)

J. de Rosny and M. Fink, “Overcoming the Diffraction Limit In Wave Physics Using a Time-Reversal Mirror and a Novel Acoustic Sink,” Phys. Rev. Lett. 89(12), 124301 (2002).
[Crossref] [PubMed]

1999 (2)

A. Edelman and N. R. Rao, “Random matrix theory,” Acta Numer. 14, 233–297 (1999).
[Crossref]

Q. H. Liu, “Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm,” IEEE Trans. Geosci. Rem. Sens. 37(2), 917–926 (1999).
[Crossref]

1996 (1)

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[Crossref]

Carminati, R.

R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A 87(4), 041801 (2013).
[Crossref]

Cho, Y.-H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

Choi, S. H.

S. H. Choi and Y. L. Kim, “Hybridized/coupled multiple resonances in nacre,” Phys. Rev. B 89(3), 035115 (2014).
[Crossref]

Choi, W.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

M. Kim, W. Choi, C. Yoon, G. H. Kim, and W. Choi, “Relation between transmission eigenchannels and single-channel optimizing modes in a disordered medium,” Opt. Lett. 38(16), 2994–2996 (2013).
[Crossref] [PubMed]

M. Kim, W. Choi, C. Yoon, G. H. Kim, and W. Choi, “Relation between transmission eigenchannels and single-channel optimizing modes in a disordered medium,” Opt. Lett. 38(16), 2994–2996 (2013).
[Crossref] [PubMed]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

W. Choi, A. P. Mosk, Q.-H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

W. Choi, A. P. Mosk, Q.-H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

Choi, Y.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Cui, M.

Dasari, R. R.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

de Rosny, J.

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315(5815), 1120–1122 (2007).
[Crossref] [PubMed]

J. de Rosny and M. Fink, “Overcoming the Diffraction Limit In Wave Physics Using a Time-Reversal Mirror and a Novel Acoustic Sink,” Phys. Rev. Lett. 89(12), 124301 (2002).
[Crossref] [PubMed]

DiMarzio, C. A.

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt. 18(2), 025004 (2013).
[Crossref] [PubMed]

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref] [PubMed]

Edelman, A.

A. Edelman and N. R. Rao, “Random matrix theory,” Acta Numer. 14, 233–297 (1999).
[Crossref]

Engelke, D.

Feld, M. S.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

Fink, M.

R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A 87(4), 041801 (2013).
[Crossref]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315(5815), 1120–1122 (2007).
[Crossref] [PubMed]

J. de Rosny and M. Fink, “Overcoming the Diffraction Limit In Wave Physics Using a Time-Reversal Mirror and a Novel Acoustic Sink,” Phys. Rev. Lett. 89(12), 124301 (2002).
[Crossref] [PubMed]

Fiolka, R.

Gedney, S. D.

S. D. Gedney, “An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,” IEEE Trans. Antenn. Propag. 44(12), 1630–1639 (1996).
[Crossref]

Han, S.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

Hillman, T. R.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

Hollmann, J. L.

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt. 18(2), 025004 (2013).
[Crossref] [PubMed]

Horstmeyer, R.

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt. 18(2), 025004 (2013).
[Crossref] [PubMed]

Huang, Y.

Y. Huang, Y. Hung, and S. H. Tseng, “An optical Target to eliminate impinging light in a light scattering simulation,” Comput. Phys. Commun. 185(10), 2504–2509 (2014).
[Crossref]

Y. Huang, C. Tsai, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” (in review).

Hung, Y.

Y. Huang, Y. Hung, and S. H. Tseng, “An optical Target to eliminate impinging light in a light scattering simulation,” Comput. Phys. Commun. 185(10), 2504–2509 (2014).
[Crossref]

Judkewitz, B.

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref] [PubMed]

Kim, G. H.

Kim, J.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Kim, M.

M. Kim, W. Choi, C. Yoon, G. H. Kim, and W. Choi, “Relation between transmission eigenchannels and single-channel optimizing modes in a disordered medium,” Opt. Lett. 38(16), 2994–2996 (2013).
[Crossref] [PubMed]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Kim, Y. L.

S. H. Choi and Y. L. Kim, “Hybridized/coupled multiple resonances in nacre,” Phys. Rev. B 89(3), 035115 (2014).
[Crossref]

Ko, S. H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

Lagendijk, A.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010).
[Crossref]

Lai, P. X.

J. W. Tay, P. X. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
[Crossref] [PubMed]

Lee, J. O.

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

Lerosey, G.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315(5815), 1120–1122 (2007).
[Crossref] [PubMed]

Liu, H.

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[Crossref] [PubMed]

Liu, Q. H.

Q. H. Liu, “Large-scale simulations of electromagnetic and acoustic measurements using the pseudospectral time-domain (PSTD) algorithm,” IEEE Trans. Geosci. Rem. Sens. 37(2), 917–926 (1999).
[Crossref]

Marks, B.

Mosk, A. P.

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

W. Choi, A. P. Mosk, Q.-H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010).
[Crossref]

Munro, P. R. T.

Nam, K. T.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

Park, C.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

Park, J.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

Park, J.-H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

Park, Q. H.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Park, Q.-H.

W. Choi, A. P. Mosk, Q.-H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

Park, Y.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

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Steel, M. J.

Suzuki, Y.

J. W. Tay, P. X. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
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Tay, J. W.

J. W. Tay, P. X. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
[Crossref] [PubMed]

Ting, W. L.

Tourin, A.

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315(5815), 1120–1122 (2007).
[Crossref] [PubMed]

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Y. Huang, C. Tsai, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” (in review).

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Y. Huang, Y. Hung, and S. H. Tseng, “An optical Target to eliminate impinging light in a light scattering simulation,” Comput. Phys. Commun. 185(10), 2504–2509 (2014).
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S. H. Tseng, W. L. Ting, and S. J. Wang, “2-D PSTD Simulation of the time-reversed ultrasound-encoded deep-tissue imaging technique,” Biomed. Opt. Express 5(3), 882–894 (2014).
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Y. Huang, C. Tsai, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” (in review).

Vandenbem, C.

R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A 87(4), 041801 (2013).
[Crossref]

Vellekoop, I. M.

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010).
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J. W. Tay, P. X. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
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Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
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X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[Crossref] [PubMed]

Yamauchi, T.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

Yang, C.

J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt. 18(2), 025004 (2013).
[Crossref] [PubMed]

Yang, C. H.

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref] [PubMed]

Yaqoob, Z.

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
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Yu, H.

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
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A. Edelman and N. R. Rao, “Random matrix theory,” Acta Numer. 14, 233–297 (1999).
[Crossref]

Biomed. Opt. Express (1)

Comput. Phys. Commun. (1)

Y. Huang, Y. Hung, and S. H. Tseng, “An optical Target to eliminate impinging light in a light scattering simulation,” Comput. Phys. Commun. 185(10), 2504–2509 (2014).
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J. L. Hollmann, R. Horstmeyer, C. Yang, and C. A. DiMarzio, “Analysis and modeling of an ultrasound-modulated guide star to increase the depth of focusing in a turbid medium,” J. Biomed. Opt. 18(2), 025004 (2013).
[Crossref] [PubMed]

Nat. Commun. (1)

Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. H. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012).
[Crossref] [PubMed]

Nat. Photonics (5)

I. M. Vellekoop, A. Lagendijk, and A. P. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4(5), 320–322 (2010).
[Crossref]

X. Xu, H. Liu, and L. V. Wang, “Time-reversed ultrasonically encoded optical focusing into scattering media,” Nat. Photonics 5(3), 154–157 (2011).
[Crossref] [PubMed]

A. P. Mosk, A. Lagendijk, G. Lerosey, and M. Fink, “Controlling waves in space and time for imaging and focusing in complex media,” Nat. Photonics 6(5), 283–292 (2012).
[Crossref]

J.-H. Park, C. Park, H. Yu, J. Park, S. Han, J. Shin, S. H. Ko, K. T. Nam, Y.-H. Cho, and Y. Park, “Subwavelength light focusing using random nanoparticles,” Nat. Photonics 7(6), 454–459 (2013).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q. H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6(9), 583–585 (2012).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (1)

R. Pierrat, C. Vandenbem, M. Fink, and R. Carminati, “Subwavelength focusing inside an open disordered medium by time reversal at a single point antenna,” Phys. Rev. A 87(4), 041801 (2013).
[Crossref]

Phys. Rev. B (2)

S. H. Choi and Y. L. Kim, “Hybridized/coupled multiple resonances in nacre,” Phys. Rev. B 89(3), 035115 (2014).
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W. Choi, A. P. Mosk, Q.-H. Park, and W. Choi, “Transmission eigenchannels in a disordered medium,” Phys. Rev. B 83(13), 134207 (2011).
[Crossref]

Phys. Rev. Lett. (2)

H. Yu, T. R. Hillman, W. Choi, J. O. Lee, M. S. Feld, R. R. Dasari, and Y. Park, “Measuring large optical transmission matrices of disordered media,” Phys. Rev. Lett. 111(15), 153902 (2013).
[Crossref] [PubMed]

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Sci. Rep. (2)

J. W. Tay, P. X. Lai, Y. Suzuki, and L. V. Wang, “Ultrasonically encoded wavefront shaping for focusing into random media,” Sci. Rep. 4, 3918 (2014).
[Crossref] [PubMed]

T. R. Hillman, T. Yamauchi, W. Choi, R. R. Dasari, M. S. Feld, Y. Park, and Z. Yaqoob, “Digital optical phase conjugation for delivering two-dimensional images through turbid media,” Sci. Rep. 3, 1909 (2013).
[Crossref] [PubMed]

Science (1)

G. Lerosey, J. de Rosny, A. Tourin, and M. Fink, “Focusing beyond the diffraction limit with far-field time reversal,” Science 315(5815), 1120–1122 (2007).
[Crossref] [PubMed]

Other (1)

Y. Huang, C. Tsai, and S. H. Tseng, “PSTD simulation of the continuous-wave optical phase conjugation phenomenon,” (in review).

Supplementary Material (3)

» Media 1: MOV (851 KB)     
» Media 2: MOV (3773 KB)     
» Media 3: MOV (1750 KB)     

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Figures (9)

Fig. 1
Fig. 1 (a) Light propagation through vacuum. (b) Light propagation through a scattering medium exhibits a sinuous, complex pattern resembling a network of branching water channels.
Fig. 2
Fig. 2 Schematics of light propagation through a scattering medium. Light propagating from A to B along different routes (e.g. green path and red path) would in general be out-of-phase due to the difference in optical path length.
Fig. 3
Fig. 3 Propagation of OPC light is modeled in two stages: (a) Forward scenario: a CW light source embedded at the center of a 40-μm-diameter empty region centered inside a scattering medium consisting of 630 randomly-positioned (minimum edge-to-edge spacing of 0.5 μm), 10-μm-diameter dielectric (n = 1.6) cylinders. (b) Playback scenario: amplitude and phase of the CW outgoing wave is recorded and phase-conjugated to form a circular wavefront converging through the scattering medium.
Fig. 4
Fig. 4 (Media 1) Simulating CW, fully-surrounding, phase-conjugated light impinging upon a scattering medium. The scattering medium consists of 22,222 non-absorbing, randomly-positioned, 5-μm-diameter dielectric cylinders closely packed within a circular region of 1160 μm diameter; the scattering mean free path is 6.86 μm, the optical thickness is 169, and the strength of disorder is 0.0619. The λ = 1 μm CW light is generated with the phase-conjugated, CW amplitude and phase of outgoing light recorded in the forward scenario. a) A ring-shaped, CW wavefront of light is generated periodically. b) At t = 1 ps, light propagates through the scattering medium via multiple scattering, c) At t = 1.5 ps, light converges at the center and then diverges outward. (d) A soft sink technique is employed to eliminate the outgoing light, leaving only the incoming light component. A zoomed-in view of (d) is shown in (e).
Fig. 5
Fig. 5 Simulation of light (λ = 4 μm) back-propagated through a scattering medium consisting of 1600 6-μm-diameter dielectric cylinders, each with a refractive index (a) n = 1.05, (b) n = 1.2, (c) n = 1.3, respectively. Inset-figures: Regardless of n, the back-propagated light converges coherently and reconstructs the original light profile (FWHM peak width ~4 μm as measured along the white dashed line at the center).
Fig. 6
Fig. 6 Simulation of light (λ = 4 μm) back-propagated through a 560-μm-diameter scattering medium consisting of N 2.4-μm-diameter dielectric (n = 1.2) cylinders, where (a) N = 3000, (b) N = 9000, and (c) N = 16356, respectively. Inset-figures: Regardless of N, the back-propagated light converges coherently and reconstructs the original light profile (FWHM peak width ~4 μm as measured along the white dashed line at the center).
Fig. 7
Fig. 7 (Media 2) Simulation of light back-propagated through a scattering medium to a narrow peak. The scattering medium consists of 1600 randomly positioned, 6-μm-diameter dielectric (n = 1.2) cylinders. A 4-μm-wide plane-wave light source (wavelength λ) is embedded at the center of the scattering medium. From top to bottom: (a) λ = 1 μm, (b) λ = 4 μm, (c) λ = 16 μm, (d) λ = 64 μm, (e) λ = 256 μm, respectively. In each subplot, the forward propagation light profile (gray dashed line) is compared to the back-propagated light (blue line) and the back-propagated light with a soft sink to eliminate the outgoing light component (black line). A zoomed-in view is shown in each inset-figure. Before eliminating the outgoing field component the root-mean-square error is: (a) 9.5%, (b) 4.97%, (c) 15.5%, (d) 29.5%, and, (e) 46.7%, respectively; after eliminating the outgoing light component, the root-mean-square error is: (a) 3.05%, (b) 0.58%, (c) 0.40%, (d) 0.24%, and, (e) 0.19%, respectively. The peak width at FWHM is: (a) 1.7 μm, (b) 3.0 μm, (c) 4.1μm, (d) 3.7 μm, (e) 3.0 μm, respectively. It is clear that the peak width of the forward light and back-propagated light profiles are identical.
Fig. 8
Fig. 8 (Media 3) Simulation of light back-propagated through vacuum to a narrow peak. A 4-μm-wide plane-wave light source (wavelength λ) is embedded at the center of the simulation. From top to bottom: (a) λ = 1 μm, (b) λ = 4 μm, (c) λ = 16 μm, (d) λ = 64 μm, (e) λ = 256 μm, respectively. In each subplot, the forward propagation light profile (gray dashed line) is compared to the back-propagated light (blue line) and the back-propagated light with a soft sink to eliminate the outgoing light component (black line). A zoomed-in view is shown in each inset-figure. Before eliminating the outgoing field component the root-mean-square error is: (a) 0.23%, (b) 1.84%, (c) 9.32%, (d) 30.29%, and, (e) 65.68%, respectively; after eliminating the outgoing light component, the root-mean-square error is: (a) 0.17%, (b) 0.089%, (c) 0.20%, (d) 0.208, and, (e) 0.17%, respectively. The FWHM is: (a) 1.8 μm, (b) 3.3 μm, (c) 5 μm, (d) 3.6 μm, (e) 3.1 μm, respectively. It is clear that the peak width of the forward light and back-propagated light profiles are identical.
Fig. 9
Fig. 9 Convergence analyses of the simulation. With a soft sink to eliminate the outgoing light component, the impinging light profile reconstructed from back-propagated light is compared to the original outgoing light in the forward scenario. The accuracy of the simulation increases with: (a) increased number of simulation time-steps (CW steady state), and, (b) increased distance between the OPC region and the scattering medium, where outgoing light impinges the OPC region at near normal incidence.

Equations (1)

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{ E x | i }= F 1 { j k x F{ E i } },

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