Abstract

We present experimental observations of exact dynamic localization of an optical beam in a periodically curved AlGaAs waveguide array. The dynamic localization of the beam is “exact” in that it is observed even when the photonic band of the array is not well described in the nearest-neighbor tight-binding approximation. We present the spatial evolution of the beam around the two-period plane in the structure, explicitly demonstrating the delocalization and subsequent relocalization of the beam. We also demonstrate the strong wavelength dependence of the beam relocalization for a four period structure.

© 2007 Optical Society of America

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  1. D. H. Dunlap and V. M. Kenkre, "Dynamic localization of a charged-particle moving under the influence of an electric-field," Phys. Rev. B 34, 3625-3633 (1986).
    [CrossRef]
  2. M. Holthaus, "Collapse of minibands in far-infrared irradiated superlattices," Phys. Rev. Lett. 69, 351-354 (1992).
    [CrossRef] [PubMed]
  3. X. G. Zhao, "Motion of Bloch electrons in time-dependent electric-fields with off-diagonal effects," Phys. Lett. A 167, 291-294 (1992).
    [CrossRef]
  4. A. W. Ghosh, A. V. Kuznetsov, and J. W. Wilkins, "Reflection of THz radiation by a superlattice," Phys. Rev. Lett. 79, 3494-3497 (1997).
    [CrossRef]
  5. W. X. Yan, S. Q. Bao, X. G. Zhao, and J. Q. Liang, "Dynamic localization versus photon-assisted transport in semiconductor superlattices driven by dc-ac fields," Phys. Rev. B 61, 7269-7272 (2000).
    [CrossRef]
  6. M. M. Dignam and C. M. de Sterke, "Conditions for Dynamic localization in generalized ac electric fields," Phys. Rev. Lett. 88, 046806-1-046806-4 (2002).
    [CrossRef] [PubMed]
  7. A. Z. Zhang, L. J. Yang, and M. M. Dignam, "Influence of excitonic effects on dynamic localization in semiconductor superlattices in combined dc and ac electric fields," Phys. Rev. B 67, 205318-1-205318-7 (2003).
    [CrossRef]
  8. F. Bloch, "Uber die Quantenmechanik der Elektronen in Kristallgittern," Z. Phys. A: Hadrons Nucl. 52, 555-600 (1928).
  9. C. Zener, "A theory of the electrical breakdown of solid dielectrics," Proc. R. Soc. London, Ser. A, Containing Papers of a Mathematical and Physical Character 145, 523-529 (1934).
    [CrossRef]
  10. H. M. James, "Electronic states in perturbed periodic systems," Phys. Rev. 76, 1611-1624 (1949).
    [CrossRef]
  11. J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
    [CrossRef]
  12. R.-B. Liu and B.-F. Zhu, "Degenerate four-wave-mixing signals from a dc- and ac-driven semiconductor superlattice," Phys. Rev. B 59, 5759-5769 (1999).
    [CrossRef]
  13. C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993).
    [CrossRef] [PubMed]
  14. K. W. Madison, M. C. Fischer, R. B. Diener, Q. Niu, and M. G. Raizen, "Dynamical Bloch band suppression in an optical lattice," Phys. Rev. Lett. 81, 5093-5096 (1998).
    [CrossRef]
  15. G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, "Dynamic localization and ac Bloch oscillations in periodic optical waveguide arrays," Opt. Commun. 218, 87-92 (2003).
    [CrossRef]
  16. J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
    [CrossRef]
  17. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901-1-243901-4 (2006).
    [CrossRef] [PubMed]
  18. T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752-4755 (1999).
    [CrossRef]
  19. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and K. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
    [CrossRef]
  20. G. Lenz, I. Talanina, and C. M. de Sterke, "Bloch oscillations in an array of curved optical waveguides," Phys. Rev. Lett. 83, 963-966 (1999).
    [CrossRef]
  21. M. Heiblum and J. H. Harris, "Analysis of curved optical-waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75-83 (1975).
    [CrossRef]
  22. K. S. Chiang, "Dual effective-index method for the analysis of rectangular dielectric wave-guides," Appl. Opt. 25, 2169-2174 (1986).
    [CrossRef] [PubMed]
  23. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902-1-053902-4 (2003).
    [CrossRef] [PubMed]
  24. J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Express 13, 1780-1796 (2005).
    [CrossRef] [PubMed]
  25. K. Drese and M. Holthaus, "Anderson localization in an ac-driven two-band model," J. Phys.: Condens. Matter 8, 1193-1206 (1996).
    [CrossRef]
  26. S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization," Phys. Rev. B 74,155116-1-11 (2006).
    [CrossRef]
  27. S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, "The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling," J. Appl. Phys. 87, 7825-7837 (2000).
    [CrossRef]
  28. P. Domachuk, C. M. de Sterke, J. Wan, and M. M. Dignam, "Dynamic localization in continuous ac electric fields," Phys. Rev. B 66, 165313-1-165313-10 (2002).
    [CrossRef]
  29. N. Chiodo, G. Della Valle, R. Osellame, S. Longhi, G. Cerullo, R. Ramponi, and U. Laporta, P. Morgner, "Imaging of Bloch oscillations in erbium-doped curved waveguide arrays," Opt. Lett. 31, 1651-1653 (2006).
    [CrossRef] [PubMed]

2006

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901-1-243901-4 (2006).
[CrossRef] [PubMed]

S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization," Phys. Rev. B 74,155116-1-11 (2006).
[CrossRef]

N. Chiodo, G. Della Valle, R. Osellame, S. Longhi, G. Cerullo, R. Ramponi, and U. Laporta, P. Morgner, "Imaging of Bloch oscillations in erbium-doped curved waveguide arrays," Opt. Lett. 31, 1651-1653 (2006).
[CrossRef] [PubMed]

2005

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Express 13, 1780-1796 (2005).
[CrossRef] [PubMed]

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

2003

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, "Dynamic localization and ac Bloch oscillations in periodic optical waveguide arrays," Opt. Commun. 218, 87-92 (2003).
[CrossRef]

A. Z. Zhang, L. J. Yang, and M. M. Dignam, "Influence of excitonic effects on dynamic localization in semiconductor superlattices in combined dc and ac electric fields," Phys. Rev. B 67, 205318-1-205318-7 (2003).
[CrossRef]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902-1-053902-4 (2003).
[CrossRef] [PubMed]

2002

P. Domachuk, C. M. de Sterke, J. Wan, and M. M. Dignam, "Dynamic localization in continuous ac electric fields," Phys. Rev. B 66, 165313-1-165313-10 (2002).
[CrossRef]

M. M. Dignam and C. M. de Sterke, "Conditions for Dynamic localization in generalized ac electric fields," Phys. Rev. Lett. 88, 046806-1-046806-4 (2002).
[CrossRef] [PubMed]

2000

W. X. Yan, S. Q. Bao, X. G. Zhao, and J. Q. Liang, "Dynamic localization versus photon-assisted transport in semiconductor superlattices driven by dc-ac fields," Phys. Rev. B 61, 7269-7272 (2000).
[CrossRef]

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, "The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling," J. Appl. Phys. 87, 7825-7837 (2000).
[CrossRef]

1999

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and K. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

G. Lenz, I. Talanina, and C. M. de Sterke, "Bloch oscillations in an array of curved optical waveguides," Phys. Rev. Lett. 83, 963-966 (1999).
[CrossRef]

R.-B. Liu and B.-F. Zhu, "Degenerate four-wave-mixing signals from a dc- and ac-driven semiconductor superlattice," Phys. Rev. B 59, 5759-5769 (1999).
[CrossRef]

1998

K. W. Madison, M. C. Fischer, R. B. Diener, Q. Niu, and M. G. Raizen, "Dynamical Bloch band suppression in an optical lattice," Phys. Rev. Lett. 81, 5093-5096 (1998).
[CrossRef]

1997

A. W. Ghosh, A. V. Kuznetsov, and J. W. Wilkins, "Reflection of THz radiation by a superlattice," Phys. Rev. Lett. 79, 3494-3497 (1997).
[CrossRef]

1996

K. Drese and M. Holthaus, "Anderson localization in an ac-driven two-band model," J. Phys.: Condens. Matter 8, 1193-1206 (1996).
[CrossRef]

1993

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993).
[CrossRef] [PubMed]

1992

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

M. Holthaus, "Collapse of minibands in far-infrared irradiated superlattices," Phys. Rev. Lett. 69, 351-354 (1992).
[CrossRef] [PubMed]

X. G. Zhao, "Motion of Bloch electrons in time-dependent electric-fields with off-diagonal effects," Phys. Lett. A 167, 291-294 (1992).
[CrossRef]

1986

D. H. Dunlap and V. M. Kenkre, "Dynamic localization of a charged-particle moving under the influence of an electric-field," Phys. Rev. B 34, 3625-3633 (1986).
[CrossRef]

K. S. Chiang, "Dual effective-index method for the analysis of rectangular dielectric wave-guides," Appl. Opt. 25, 2169-2174 (1986).
[CrossRef] [PubMed]

1975

M. Heiblum and J. H. Harris, "Analysis of curved optical-waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

1949

H. M. James, "Electronic states in perturbed periodic systems," Phys. Rev. 76, 1611-1624 (1949).
[CrossRef]

1934

C. Zener, "A theory of the electrical breakdown of solid dielectrics," Proc. R. Soc. London, Ser. A, Containing Papers of a Mathematical and Physical Character 145, 523-529 (1934).
[CrossRef]

1928

F. Bloch, "Uber die Quantenmechanik der Elektronen in Kristallgittern," Z. Phys. A: Hadrons Nucl. 52, 555-600 (1928).

Aitchison, J. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902-1-053902-4 (2003).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and K. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Bao, S. Q.

W. X. Yan, S. Q. Bao, X. G. Zhao, and J. Q. Liang, "Dynamic localization versus photon-assisted transport in semiconductor superlattices driven by dc-ac fields," Phys. Rev. B 61, 7269-7272 (2000).
[CrossRef]

Bartal, G.

Bloch, F.

F. Bloch, "Uber die Quantenmechanik der Elektronen in Kristallgittern," Z. Phys. A: Hadrons Nucl. 52, 555-600 (1928).

Brauer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

Buljan, H.

Cerullo, G.

Chiang, K. S.

Chiodo, N.

Cianci, E.

S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization," Phys. Rev. B 74,155116-1-11 (2006).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901-1-243901-4 (2006).
[CrossRef] [PubMed]

Cohen, O.

Cunningham, J. E.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

de Sterke, C. M.

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, "Dynamic localization and ac Bloch oscillations in periodic optical waveguide arrays," Opt. Commun. 218, 87-92 (2003).
[CrossRef]

M. M. Dignam and C. M. de Sterke, "Conditions for Dynamic localization in generalized ac electric fields," Phys. Rev. Lett. 88, 046806-1-046806-4 (2002).
[CrossRef] [PubMed]

P. Domachuk, C. M. de Sterke, J. Wan, and M. M. Dignam, "Dynamic localization in continuous ac electric fields," Phys. Rev. B 66, 165313-1-165313-10 (2002).
[CrossRef]

G. Lenz, I. Talanina, and C. M. de Sterke, "Bloch oscillations in an array of curved optical waveguides," Phys. Rev. Lett. 83, 963-966 (1999).
[CrossRef]

Della Valle, G.

Diener, R. B.

K. W. Madison, M. C. Fischer, R. B. Diener, Q. Niu, and M. G. Raizen, "Dynamical Bloch band suppression in an optical lattice," Phys. Rev. Lett. 81, 5093-5096 (1998).
[CrossRef]

Dignam, M. M.

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

A. Z. Zhang, L. J. Yang, and M. M. Dignam, "Influence of excitonic effects on dynamic localization in semiconductor superlattices in combined dc and ac electric fields," Phys. Rev. B 67, 205318-1-205318-7 (2003).
[CrossRef]

P. Domachuk, C. M. de Sterke, J. Wan, and M. M. Dignam, "Dynamic localization in continuous ac electric fields," Phys. Rev. B 66, 165313-1-165313-10 (2002).
[CrossRef]

M. M. Dignam and C. M. de Sterke, "Conditions for Dynamic localization in generalized ac electric fields," Phys. Rev. Lett. 88, 046806-1-046806-4 (2002).
[CrossRef] [PubMed]

Domachuk, P.

P. Domachuk, C. M. de Sterke, J. Wan, and M. M. Dignam, "Dynamic localization in continuous ac electric fields," Phys. Rev. B 66, 165313-1-165313-10 (2002).
[CrossRef]

Drese, K.

K. Drese and M. Holthaus, "Anderson localization in an ac-driven two-band model," J. Phys.: Condens. Matter 8, 1193-1206 (1996).
[CrossRef]

Dunlap, D. H.

D. H. Dunlap and V. M. Kenkre, "Dynamic localization of a charged-particle moving under the influence of an electric-field," Phys. Rev. B 34, 3625-3633 (1986).
[CrossRef]

Efremidis, N. K.

Eisenberg, H. S.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902-1-053902-4 (2003).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and K. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

Feldmann, J.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Fischer, M. C.

K. W. Madison, M. C. Fischer, R. B. Diener, Q. Niu, and M. G. Raizen, "Dynamical Bloch band suppression in an optical lattice," Phys. Rev. Lett. 81, 5093-5096 (1998).
[CrossRef]

Fleischer, J. W.

Foglietti, V.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901-1-243901-4 (2006).
[CrossRef] [PubMed]

S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization," Phys. Rev. B 74,155116-1-11 (2006).
[CrossRef]

Freedman, B.

Gehrsitz, S.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, "The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling," J. Appl. Phys. 87, 7825-7837 (2000).
[CrossRef]

Ghosh, A. W.

A. W. Ghosh, A. V. Kuznetsov, and J. W. Wilkins, "Reflection of THz radiation by a superlattice," Phys. Rev. Lett. 79, 3494-3497 (1997).
[CrossRef]

Gourgon, C.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, "The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling," J. Appl. Phys. 87, 7825-7837 (2000).
[CrossRef]

Harris, J. H.

M. Heiblum and J. H. Harris, "Analysis of curved optical-waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

Heiblum, M.

M. Heiblum and J. H. Harris, "Analysis of curved optical-waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

Herres, N.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, "The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling," J. Appl. Phys. 87, 7825-7837 (2000).
[CrossRef]

Holthaus, M.

K. Drese and M. Holthaus, "Anderson localization in an ac-driven two-band model," J. Phys.: Condens. Matter 8, 1193-1206 (1996).
[CrossRef]

M. Holthaus, "Collapse of minibands in far-infrared irradiated superlattices," Phys. Rev. Lett. 69, 351-354 (1992).
[CrossRef] [PubMed]

James, H. M.

H. M. James, "Electronic states in perturbed periodic systems," Phys. Rev. 76, 1611-1624 (1949).
[CrossRef]

Kenkre, V. M.

D. H. Dunlap and V. M. Kenkre, "Dynamic localization of a charged-particle moving under the influence of an electric-field," Phys. Rev. B 34, 3625-3633 (1986).
[CrossRef]

Kohler, K.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993).
[CrossRef] [PubMed]

Kurz, H.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993).
[CrossRef] [PubMed]

Kuznetsov, A. V.

A. W. Ghosh, A. V. Kuznetsov, and J. W. Wilkins, "Reflection of THz radiation by a superlattice," Phys. Rev. Lett. 79, 3494-3497 (1997).
[CrossRef]

Laforest, M.

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901-1-243901-4 (2006).
[CrossRef] [PubMed]

S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization," Phys. Rev. B 74,155116-1-11 (2006).
[CrossRef]

Laporta, U.

Lederer, F.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

Lenz, G.

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, "Dynamic localization and ac Bloch oscillations in periodic optical waveguide arrays," Opt. Commun. 218, 87-92 (2003).
[CrossRef]

G. Lenz, I. Talanina, and C. M. de Sterke, "Bloch oscillations in an array of curved optical waveguides," Phys. Rev. Lett. 83, 963-966 (1999).
[CrossRef]

Leo, K.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993).
[CrossRef] [PubMed]

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Liang, J. Q.

W. X. Yan, S. Q. Bao, X. G. Zhao, and J. Q. Liang, "Dynamic localization versus photon-assisted transport in semiconductor superlattices driven by dc-ac fields," Phys. Rev. B 61, 7269-7272 (2000).
[CrossRef]

Liu, R.-B.

R.-B. Liu and B.-F. Zhu, "Degenerate four-wave-mixing signals from a dc- and ac-driven semiconductor superlattice," Phys. Rev. B 59, 5759-5769 (1999).
[CrossRef]

Lobino, M.

S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization," Phys. Rev. B 74,155116-1-11 (2006).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901-1-243901-4 (2006).
[CrossRef] [PubMed]

Longhi, S.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901-1-243901-4 (2006).
[CrossRef] [PubMed]

N. Chiodo, G. Della Valle, R. Osellame, S. Longhi, G. Cerullo, R. Ramponi, and U. Laporta, P. Morgner, "Imaging of Bloch oscillations in erbium-doped curved waveguide arrays," Opt. Lett. 31, 1651-1653 (2006).
[CrossRef] [PubMed]

S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization," Phys. Rev. B 74,155116-1-11 (2006).
[CrossRef]

Madison, K. W.

K. W. Madison, M. C. Fischer, R. B. Diener, Q. Niu, and M. G. Raizen, "Dynamical Bloch band suppression in an optical lattice," Phys. Rev. Lett. 81, 5093-5096 (1998).
[CrossRef]

Mandelik, D.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902-1-053902-4 (2003).
[CrossRef] [PubMed]

Manela, O.

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901-1-243901-4 (2006).
[CrossRef] [PubMed]

S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization," Phys. Rev. B 74,155116-1-11 (2006).
[CrossRef]

Meier, T.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Miller, D. A. B.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Morandotti, R.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902-1-053902-4 (2003).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and K. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Morgner, P.

Niu, Q.

K. W. Madison, M. C. Fischer, R. B. Diener, Q. Niu, and M. G. Raizen, "Dynamical Bloch band suppression in an optical lattice," Phys. Rev. Lett. 81, 5093-5096 (1998).
[CrossRef]

Osellame, R.

Parker, R.

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, "Dynamic localization and ac Bloch oscillations in periodic optical waveguide arrays," Opt. Commun. 218, 87-92 (2003).
[CrossRef]

Pertsch, T.

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and K. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Raizen, M. G.

K. W. Madison, M. C. Fischer, R. B. Diener, Q. Niu, and M. G. Raizen, "Dynamical Bloch band suppression in an optical lattice," Phys. Rev. Lett. 81, 5093-5096 (1998).
[CrossRef]

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901-1-243901-4 (2006).
[CrossRef] [PubMed]

N. Chiodo, G. Della Valle, R. Osellame, S. Longhi, G. Cerullo, R. Ramponi, and U. Laporta, P. Morgner, "Imaging of Bloch oscillations in erbium-doped curved waveguide arrays," Opt. Lett. 31, 1651-1653 (2006).
[CrossRef] [PubMed]

S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization," Phys. Rev. B 74,155116-1-11 (2006).
[CrossRef]

Reinhart, F. K.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, "The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling," J. Appl. Phys. 87, 7825-7837 (2000).
[CrossRef]

Roskos, H. G.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993).
[CrossRef] [PubMed]

Schmitt-Rink, S.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Schulze, A.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Schwartz, T.

Schwedler, R.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993).
[CrossRef] [PubMed]

Segev, M.

Shah, J.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Sigg, H.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, "The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling," J. Appl. Phys. 87, 7825-7837 (2000).
[CrossRef]

Silberberg, K.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and K. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Silberberg, Y.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902-1-053902-4 (2003).
[CrossRef] [PubMed]

Talanina, I.

G. Lenz, I. Talanina, and C. M. de Sterke, "Bloch oscillations in an array of curved optical waveguides," Phys. Rev. Lett. 83, 963-966 (1999).
[CrossRef]

Thomas, P.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

von Plessen, G.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Vonlanthen, A.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, "The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling," J. Appl. Phys. 87, 7825-7837 (2000).
[CrossRef]

Wan, J.

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

P. Domachuk, C. M. de Sterke, J. Wan, and M. M. Dignam, "Dynamic localization in continuous ac electric fields," Phys. Rev. B 66, 165313-1-165313-10 (2002).
[CrossRef]

Wanke, M. C.

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, "Dynamic localization and ac Bloch oscillations in periodic optical waveguide arrays," Opt. Commun. 218, 87-92 (2003).
[CrossRef]

Waschke, C.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993).
[CrossRef] [PubMed]

Wilkins, J. W.

A. W. Ghosh, A. V. Kuznetsov, and J. W. Wilkins, "Reflection of THz radiation by a superlattice," Phys. Rev. Lett. 79, 3494-3497 (1997).
[CrossRef]

Yan, W. X.

W. X. Yan, S. Q. Bao, X. G. Zhao, and J. Q. Liang, "Dynamic localization versus photon-assisted transport in semiconductor superlattices driven by dc-ac fields," Phys. Rev. B 61, 7269-7272 (2000).
[CrossRef]

Yang, L. J.

A. Z. Zhang, L. J. Yang, and M. M. Dignam, "Influence of excitonic effects on dynamic localization in semiconductor superlattices in combined dc and ac electric fields," Phys. Rev. B 67, 205318-1-205318-7 (2003).
[CrossRef]

Zener, C.

C. Zener, "A theory of the electrical breakdown of solid dielectrics," Proc. R. Soc. London, Ser. A, Containing Papers of a Mathematical and Physical Character 145, 523-529 (1934).
[CrossRef]

Zhang, A. Z.

A. Z. Zhang, L. J. Yang, and M. M. Dignam, "Influence of excitonic effects on dynamic localization in semiconductor superlattices in combined dc and ac electric fields," Phys. Rev. B 67, 205318-1-205318-7 (2003).
[CrossRef]

Zhao, X. G.

W. X. Yan, S. Q. Bao, X. G. Zhao, and J. Q. Liang, "Dynamic localization versus photon-assisted transport in semiconductor superlattices driven by dc-ac fields," Phys. Rev. B 61, 7269-7272 (2000).
[CrossRef]

X. G. Zhao, "Motion of Bloch electrons in time-dependent electric-fields with off-diagonal effects," Phys. Lett. A 167, 291-294 (1992).
[CrossRef]

Zhu, B.-F.

R.-B. Liu and B.-F. Zhu, "Degenerate four-wave-mixing signals from a dc- and ac-driven semiconductor superlattice," Phys. Rev. B 59, 5759-5769 (1999).
[CrossRef]

Appl. Opt.

Containing Papers of a Mathematical and Physical Character

C. Zener, "A theory of the electrical breakdown of solid dielectrics," Proc. R. Soc. London, Ser. A, Containing Papers of a Mathematical and Physical Character 145, 523-529 (1934).
[CrossRef]

IEEE J. Quantum Electron.

M. Heiblum and J. H. Harris, "Analysis of curved optical-waveguides by conformal transformation," IEEE J. Quantum Electron. 11, 75-83 (1975).
[CrossRef]

J. Appl. Phys.

S. Gehrsitz, F. K. Reinhart, C. Gourgon, N. Herres, A. Vonlanthen, and H. Sigg, "The refractive index of AlxGa1−xAs below the band gap: Accurate determination and empirical modeling," J. Appl. Phys. 87, 7825-7837 (2000).
[CrossRef]

J. Phys.: Condens. Matter

K. Drese and M. Holthaus, "Anderson localization in an ac-driven two-band model," J. Phys.: Condens. Matter 8, 1193-1206 (1996).
[CrossRef]

Opt. Commun.

G. Lenz, R. Parker, M. C. Wanke, and C. M. de Sterke, "Dynamic localization and ac Bloch oscillations in periodic optical waveguide arrays," Opt. Commun. 218, 87-92 (2003).
[CrossRef]

J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, "Optical filters based on dynamic localization in curved coupled optical waveguides," Opt. Commun. 247, 353-365 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

X. G. Zhao, "Motion of Bloch electrons in time-dependent electric-fields with off-diagonal effects," Phys. Lett. A 167, 291-294 (1992).
[CrossRef]

Phys. Rev.

H. M. James, "Electronic states in perturbed periodic systems," Phys. Rev. 76, 1611-1624 (1949).
[CrossRef]

Phys. Rev. B

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. von Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, "Optical investigation of Bloch oscillations in a semiconductor superlattice," Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

R.-B. Liu and B.-F. Zhu, "Degenerate four-wave-mixing signals from a dc- and ac-driven semiconductor superlattice," Phys. Rev. B 59, 5759-5769 (1999).
[CrossRef]

D. H. Dunlap and V. M. Kenkre, "Dynamic localization of a charged-particle moving under the influence of an electric-field," Phys. Rev. B 34, 3625-3633 (1986).
[CrossRef]

W. X. Yan, S. Q. Bao, X. G. Zhao, and J. Q. Liang, "Dynamic localization versus photon-assisted transport in semiconductor superlattices driven by dc-ac fields," Phys. Rev. B 61, 7269-7272 (2000).
[CrossRef]

A. Z. Zhang, L. J. Yang, and M. M. Dignam, "Influence of excitonic effects on dynamic localization in semiconductor superlattices in combined dc and ac electric fields," Phys. Rev. B 67, 205318-1-205318-7 (2003).
[CrossRef]

S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Semiclassical motion of a multiband Bloch particle in a time-dependent field: Optical visualization," Phys. Rev. B 74,155116-1-11 (2006).
[CrossRef]

P. Domachuk, C. M. de Sterke, J. Wan, and M. M. Dignam, "Dynamic localization in continuous ac electric fields," Phys. Rev. B 66, 165313-1-165313-10 (2002).
[CrossRef]

Phys. Rev. Lett.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902-1-053902-4 (2003).
[CrossRef] [PubMed]

M. M. Dignam and C. M. de Sterke, "Conditions for Dynamic localization in generalized ac electric fields," Phys. Rev. Lett. 88, 046806-1-046806-4 (2002).
[CrossRef] [PubMed]

M. Holthaus, "Collapse of minibands in far-infrared irradiated superlattices," Phys. Rev. Lett. 69, 351-354 (1992).
[CrossRef] [PubMed]

A. W. Ghosh, A. V. Kuznetsov, and J. W. Wilkins, "Reflection of THz radiation by a superlattice," Phys. Rev. Lett. 79, 3494-3497 (1997).
[CrossRef]

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice," Phys. Rev. Lett. 70, 3319-3322 (1993).
[CrossRef] [PubMed]

K. W. Madison, M. C. Fischer, R. B. Diener, Q. Niu, and M. G. Raizen, "Dynamical Bloch band suppression in an optical lattice," Phys. Rev. Lett. 81, 5093-5096 (1998).
[CrossRef]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, "Observation of dynamic localization in periodically curved waveguide arrays," Phys. Rev. Lett. 96, 243901-1-243901-4 (2006).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, "Optical Bloch oscillations in temperature tuned waveguide arrays," Phys. Rev. Lett. 83, 4752-4755 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and K. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

G. Lenz, I. Talanina, and C. M. de Sterke, "Bloch oscillations in an array of curved optical waveguides," Phys. Rev. Lett. 83, 963-966 (1999).
[CrossRef]

Z. Phys. A: Hadrons Nucl.

F. Bloch, "Uber die Quantenmechanik der Elektronen in Kristallgittern," Z. Phys. A: Hadrons Nucl. 52, 555-600 (1928).

Supplementary Material (1)

» Media 1: GIF (452 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the CCOW structure. The central waveguide is highlighted, defining the origin of the coordinate system, (u,v). Note the dependence of the waveguide radius of curvature, R(v), with respect to the propagation distance, v, where R ( v ) = + R o for 1 4 Λ < v 3 4 Λ ; R ( v ) = R o for 3 4 Λ < v 5 3 Λ . Also note that u and v are not drawn to the same scale.

Fig. 2.
Fig. 2.

(a) 2D BPM simulation and (b) one-band Schrödinger model of EDL in a 4-period non-NNTB CCOW array. The beam profiles at v/Λ = 4 show excellent relocalization. Both spatial maps are plotted on a logarithmic scale, while the beam profiles are plotted on a linear scale.

Fig. 3.
Fig. 3.

One-band Schrödinger model of ADL breakdown in a 4-period non-NNTB CCOW array. The beam profile at v/Λ = 4 clearly shows DL breakdown. The spatial map is plotted on a logarithmic scale, while the beam profile is plotted on a linear scale.

Fig. 4.
Fig. 4.

Photomask layout. (a) Launch geometry of the CCOW array consisting of 51 waveguides from a single mode waveguide. (b) The 4-period EDL CCOW array, terminated on an output slab waveguide. (c) The 21 EDL CCOW experiments, each with a length of 3 DL periods, and offset by a Δz = 250 μm. The aspect ratio is 1 : 1 in all figures. Hence, the waveguide curvature is barely visible, and the individual waveguides in the CCOW arrays in figures (b) and (c) are not resolved at this zoom level.

Fig. 5.
Fig. 5.

(a) Measured and (b) simulation results of the EDL wavelength dependence at v/Λ = 4 from 1480 nm to 1600 nm. (c) Measured and one-band Schrödinger simulation at 1555 nm of the beam at v/Λ = 4. Both figures (a) and (b) are plotted on a logarithmic scale, while figure (c) is plotted on a linear scale.

Fig. 6.
Fig. 6.

Video of the EDL CCOW wavelength dependence, highlighting the correspondence of the measured beam divergence with the theoretical predictions from the one-band Schrödinger model (453 kB) [Media 1]

Fig. 7.
Fig. 7.

(a) Captured image from one of the 21 experiments (plotted on a linear scale); (b) Measured and (c) one-band Schrödinger simulations of one full period around the second EDL plane at 1550 nm. Both figures (b) and (c) are plotted on a logarithmic scale.

Equations (5)

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

t = v c , m * = h n ¯ , U ( u ) = h c δ n 2 ( u ) 2 n ¯ λ , e F ( t ) = h c n ¯ λ R ( v ) ,
β ( k u ) = 2 π n ¯ λ + p = β p e i p k u d ,
v 1 v 2 1 R ( v ) d v = Q λ R n ¯ d ,
R ( v ) = { + R o for ( m + 1 4 ) Λ < v ( m + 3 4 ) Λ R o for ( m + 3 4 ) Λ < v ( m + 5 4 ) Λ ,
R o = Λ n ¯ d 2 Q λ R .

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