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Optimal transmission through a randomly perturbed waveguide in the localization regime
1. | Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris VII, site Chevaleret, case 7012, 75205 Paris Cedex 13, France |
References:
[1] |
C. W. J. Beenakker, Random-matrix theory of quantum transport, Rev. Mod. Phys., 69 (1997), 731-808. arXiv:cond-mat/9612179">arXiv:cond-mat/9612179" target="_blank">arXiv:cond-mat/9612179 |
[2] |
R. E. Collins, "Field Theory of Guided Waves," Mac Graw-Hill, New York, 1960. |
[3] |
O. N. Dorokhov, On the coexistence of localized and extended electronic states in the metallic phase, Solid State Commun., 51 (1984), 381-384.
doi: 10.1016/0038-1098(84)90117-0. |
[4] |
J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Sølna, "Wave Propagation and Time Reversal in Randomly Layered Media," Springer, New York, 2007. |
[5] |
J. Garnier, Multi-scaled diffusion-approximation Applications to wave propagation in random media, ESAIM Probab. Statist., 1 (1997), 183-206.
doi: 10.1051/ps:1997107. |
[6] |
J. Garnier and G. Papanicolaou, Pulse propagation and time reversal in random waveguides, SIAM J. Appl. Math., 67 (2007), 1718-1739. |
[7] |
P. Gérard and E. Leichtnam, Ergodic properties of the eigenfunctions for the Dirichlet problem, Duke Math. Journal, 71 (1993), 559-607. |
[8] |
M. E. Gertsenshtein and V. B. Vasil'ev, Waveguides with random inhomogeneities and Brownian motion in the Lobachevsky plane, Theory Probab. Appl., 4 (1959), 391-398.
doi: 10.1137/1104038. |
[9] |
Y. Imry, Active transmission channels and universal conductance fluctuations, Europhys. Lett., 1 (1986), 249.
doi: 10.1209/0295-5075/1/5/008. |
[10] |
P. A. Mello, P. Pereyra and N. Kumar, Macroscopic approach to multichannel disordered conductors, Ann. Phys., 181 (1988), 290-317.
doi: 10.1016/0003-4916(88)90169-8. |
[11] |
K. A. Muttalib, Random matrix theory and the scaling theory of localization, Phys. Rev. Lett., 64 (1990), 745-747.
doi: 10.1103/PhysRevLett.65.745. |
[12] |
Y. V. Nazarov, Limits of universality in disordered conductors, Phys. Rev. Lett., 73 (1994), 134-137.
doi: 10.1103/PhysRevLett.73.134. |
[13] |
G. C. Papanicolaou, Wave propagation in a one-dimensional random medium, SIAM J. Appl. Math., 21 (1971), 13-18.
doi: 10.1137/0121002. |
[14] |
G. Papanicolaou, L. Ryzhik and K. Sølna, Statistical stability in time reversal, SIAM J. Appl. Math., 64 (2004), 1133-1155.
doi: 10.1137/S0036139902411107. |
[15] |
G. Papanicolaou, L. Ryzhik and K. Sølna, Self-averaging from lateral diversity in the Itô-Schrödinger equation, SIAM Multiscale Model. Simul., 6 (2007), 468-492 (electronic).
doi: 10.1137/060668882. |
[16] |
J. B. Pendry, A. MacKinnon and A. B. Pretre, Maximal fluctuations - a new phenomenon in disordered systems, Physica A, 168 (1990), 400-407.
doi: 10.1016/0378-4371(90)90391-5. |
[17] |
J.-L. Pichard, N. Zanon, Y. Imry and A. D. Stone, Theory of random multiplicative transfer matrices and its implications for quantum transport, J. Phys., 51 (1990), 587-609. |
[18] |
I. M. Vellekoop and A. P. Mosk, Universal optimal transmission of light through disordered materials, Phys. Rev. Lett., 101 (2008), 120601. arXiv:0804.2412v2 |
[19] |
I. M. Vellekoop and A. P. Mosk, Focusing coherent light through opaque strongly scattering media, Opt. Lett., 32 (2007), 2309-2311.
doi: 10.1364/OL.32.002309. |
[20] |
S. Zelditch and M. Zworski, Ergodicity of eigenfunctions for ergodic billiards, Commun. Math. Phys., 175 (1996), 673-682.
doi: 10.1007/BF02099513. |
show all references
References:
[1] |
C. W. J. Beenakker, Random-matrix theory of quantum transport, Rev. Mod. Phys., 69 (1997), 731-808. arXiv:cond-mat/9612179">arXiv:cond-mat/9612179" target="_blank">arXiv:cond-mat/9612179 |
[2] |
R. E. Collins, "Field Theory of Guided Waves," Mac Graw-Hill, New York, 1960. |
[3] |
O. N. Dorokhov, On the coexistence of localized and extended electronic states in the metallic phase, Solid State Commun., 51 (1984), 381-384.
doi: 10.1016/0038-1098(84)90117-0. |
[4] |
J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Sølna, "Wave Propagation and Time Reversal in Randomly Layered Media," Springer, New York, 2007. |
[5] |
J. Garnier, Multi-scaled diffusion-approximation Applications to wave propagation in random media, ESAIM Probab. Statist., 1 (1997), 183-206.
doi: 10.1051/ps:1997107. |
[6] |
J. Garnier and G. Papanicolaou, Pulse propagation and time reversal in random waveguides, SIAM J. Appl. Math., 67 (2007), 1718-1739. |
[7] |
P. Gérard and E. Leichtnam, Ergodic properties of the eigenfunctions for the Dirichlet problem, Duke Math. Journal, 71 (1993), 559-607. |
[8] |
M. E. Gertsenshtein and V. B. Vasil'ev, Waveguides with random inhomogeneities and Brownian motion in the Lobachevsky plane, Theory Probab. Appl., 4 (1959), 391-398.
doi: 10.1137/1104038. |
[9] |
Y. Imry, Active transmission channels and universal conductance fluctuations, Europhys. Lett., 1 (1986), 249.
doi: 10.1209/0295-5075/1/5/008. |
[10] |
P. A. Mello, P. Pereyra and N. Kumar, Macroscopic approach to multichannel disordered conductors, Ann. Phys., 181 (1988), 290-317.
doi: 10.1016/0003-4916(88)90169-8. |
[11] |
K. A. Muttalib, Random matrix theory and the scaling theory of localization, Phys. Rev. Lett., 64 (1990), 745-747.
doi: 10.1103/PhysRevLett.65.745. |
[12] |
Y. V. Nazarov, Limits of universality in disordered conductors, Phys. Rev. Lett., 73 (1994), 134-137.
doi: 10.1103/PhysRevLett.73.134. |
[13] |
G. C. Papanicolaou, Wave propagation in a one-dimensional random medium, SIAM J. Appl. Math., 21 (1971), 13-18.
doi: 10.1137/0121002. |
[14] |
G. Papanicolaou, L. Ryzhik and K. Sølna, Statistical stability in time reversal, SIAM J. Appl. Math., 64 (2004), 1133-1155.
doi: 10.1137/S0036139902411107. |
[15] |
G. Papanicolaou, L. Ryzhik and K. Sølna, Self-averaging from lateral diversity in the Itô-Schrödinger equation, SIAM Multiscale Model. Simul., 6 (2007), 468-492 (electronic).
doi: 10.1137/060668882. |
[16] |
J. B. Pendry, A. MacKinnon and A. B. Pretre, Maximal fluctuations - a new phenomenon in disordered systems, Physica A, 168 (1990), 400-407.
doi: 10.1016/0378-4371(90)90391-5. |
[17] |
J.-L. Pichard, N. Zanon, Y. Imry and A. D. Stone, Theory of random multiplicative transfer matrices and its implications for quantum transport, J. Phys., 51 (1990), 587-609. |
[18] |
I. M. Vellekoop and A. P. Mosk, Universal optimal transmission of light through disordered materials, Phys. Rev. Lett., 101 (2008), 120601. arXiv:0804.2412v2 |
[19] |
I. M. Vellekoop and A. P. Mosk, Focusing coherent light through opaque strongly scattering media, Opt. Lett., 32 (2007), 2309-2311.
doi: 10.1364/OL.32.002309. |
[20] |
S. Zelditch and M. Zworski, Ergodicity of eigenfunctions for ergodic billiards, Commun. Math. Phys., 175 (1996), 673-682.
doi: 10.1007/BF02099513. |
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