Abstract

We have studied the propagation and Zener tunneling of light in a binary parabolic optical waveguide array (BPOWA), which consists of two evanescently coupled dissimilar optical waveguides. Because of Bragg reflections, the BPOWA attains two minibands separated by a minigap at the zone boundary. Various coherent superpositions of optical oscillations and Zener tunneling occur for different parameters on the phase diagram. In particular, Bloch–Zener oscillation and a different type of Bloch–dipole–Zener oscillation are obtained by field-evolution analysis. The results may have potential applications in optical splitting and waveguiding devices and may shed light on the coherent phenomena in optical lattices.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  9. R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2010 (4)

2009 (2)

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef] [PubMed]

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

2008 (1)

S. Longhi, “Optical Bloch oscillations and Zener tunneling with nonclassical light,” Phys. Rev. Lett. 101, 193902 (2008).
[CrossRef] [PubMed]

2007 (5)

W. Lin and G. P. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91, 143121 (2007).
[CrossRef]

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sanchez-Dehesa, “Acoustic analogue of electronic Bloch oscillations and resonant Zener tunneling in ultrasonic superlattices,” Phys. Rev. Lett. 98, 134301 (2007).
[CrossRef] [PubMed]

B. M. Breid, D. Witthaut, and H. J. Korsch, “Manipulation of matter waves using Bloch and Bloch-Zener oscillations,” New J. Phys. 9, 62 (2007).
[CrossRef]

A. Fratalocchi, K. A. Rutkowska, M. A. Karpierz, and G. Assanto, “Light induced angular steering via Floquet-Bloch band-tunnelling in one-dimensional liquid crystalline photonic lattices,” Opto-Electron. Rev. 15, 210–214 (2007).
[CrossRef]

2006 (5)

B. M. Breid, D. Witthaut, and H. J. Korsch, “Bloch-Zener oscillations,” New J. Phys. 8, 110 (2006).
[CrossRef]

S. Longhi, “Optical Zener-Bloch oscillations in binary waveguide arrays,” Europhys. Lett. 76, 416–421 (2006).
[CrossRef]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, and A. Brauer, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

A. V. Ponomarev and A. R. Kolovsky, “Dipole and Bloch oscillations of cold atoms in a parabolic lattice,” Laser Phys. 16, 367–370 (2006).
[CrossRef]

2004 (1)

2003 (2)

C. Menotti, A. Smerzi, and A. Trombettoni, “Superfluid dynamics of a Bose-Einstein condensate in a periodic potential,” New J. Phys. 5, 112 (2003).
[CrossRef]

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[CrossRef]

1999 (2)

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 Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756–4759(1999).
[CrossRef]

1998 (1)

1994 (1)

T. Dekorsy, P. Leisching, K. Khler, and H. Kurz, “Electro-optic detection of Bloch oscillations,” Phys. Rev. B 50, 8106–8109(1994).
[CrossRef]

1934 (1)

C. Zener, “A theory of electrical breakdown of solid dielectrics,” Proc. R. Soc. London Series A 145, 523–529 (1934).
[CrossRef]

1928 (1)

F. Bloch, “Quantum mechanics of electrons in crystals,” Z. Phys. 52, 555–600 (1928).
[CrossRef]

Aitchison, J. S.

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

Assanto, G.

A. Fratalocchi, K. A. Rutkowska, M. A. Karpierz, and G. Assanto, “Light induced angular steering via Floquet-Bloch band-tunnelling in one-dimensional liquid crystalline photonic lattices,” Opto-Electron. Rev. 15, 210–214 (2007).
[CrossRef]

Bloch, F.

F. Bloch, “Quantum mechanics of electrons in crystals,” Z. Phys. 52, 555–600 (1928).
[CrossRef]

Brauer, A.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, and A. Brauer, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (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]

Breid, B. M.

B. M. Breid, D. Witthaut, and H. J. Korsch, “Manipulation of matter waves using Bloch and Bloch-Zener oscillations,” New J. Phys. 9, 62 (2007).
[CrossRef]

B. M. Breid, D. Witthaut, and H. J. Korsch, “Bloch-Zener oscillations,” New J. Phys. 8, 110 (2006).
[CrossRef]

Chan, C. T.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

Chan, Y. S.

Christodoulides, D. N.

Costantino, P.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[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]

Davoyan, A. R.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Dekorsy, T.

T. Dekorsy, P. Leisching, K. Khler, and H. Kurz, “Electro-optic detection of Bloch oscillations,” Phys. Rev. B 50, 8106–8109(1994).
[CrossRef]

Desyatnikov, A. S.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

Dreisow, F.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef] [PubMed]

Efremidis, N. K.

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. 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]

Fratalocchi, A.

A. Fratalocchi, K. A. Rutkowska, M. A. Karpierz, and G. Assanto, “Light induced angular steering via Floquet-Bloch band-tunnelling in one-dimensional liquid crystalline photonic lattices,” Opto-Electron. Rev. 15, 210–214 (2007).
[CrossRef]

Ghulinyan, M.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[CrossRef]

Heinrich, M.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef] [PubMed]

Karpierz, M. A.

A. Fratalocchi, K. A. Rutkowska, M. A. Karpierz, and G. Assanto, “Light induced angular steering via Floquet-Bloch band-tunnelling in one-dimensional liquid crystalline photonic lattices,” Opto-Electron. Rev. 15, 210–214 (2007).
[CrossRef]

Khler, K.

T. Dekorsy, P. Leisching, K. Khler, and H. Kurz, “Electro-optic detection of Bloch oscillations,” Phys. Rev. B 50, 8106–8109(1994).
[CrossRef]

Kivshar, Y. S.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

Kolovsky, A. R.

A. V. Ponomarev and A. R. Kolovsky, “Dipole and Bloch oscillations of cold atoms in a parabolic lattice,” Laser Phys. 16, 367–370 (2006).
[CrossRef]

Korsch, H. J.

B. M. Breid, D. Witthaut, and H. J. Korsch, “Manipulation of matter waves using Bloch and Bloch-Zener oscillations,” New J. Phys. 9, 62 (2007).
[CrossRef]

B. M. Breid, D. Witthaut, and H. J. Korsch, “Bloch-Zener oscillations,” New J. Phys. 8, 110 (2006).
[CrossRef]

Kosevich, Y. A.

H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sanchez-Dehesa, “Acoustic analogue of electronic Bloch oscillations and resonant Zener tunneling in ultrasonic superlattices,” Phys. Rev. Lett. 98, 134301 (2007).
[CrossRef] [PubMed]

Krolikowski, W.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

Kurz, H.

T. Dekorsy, P. Leisching, K. Khler, and H. Kurz, “Electro-optic detection of Bloch oscillations,” Phys. Rev. B 50, 8106–8109(1994).
[CrossRef]

Lederer, F.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, and A. Brauer, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (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]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701–1703(1998).
[CrossRef]

Leisching, P.

T. Dekorsy, P. Leisching, K. Khler, and H. Kurz, “Electro-optic detection of Bloch oscillations,” Phys. Rev. B 50, 8106–8109(1994).
[CrossRef]

Lin, W.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

W. Lin and G. P. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91, 143121 (2007).
[CrossRef]

Longhi, S.

S. Longhi, “Bloch oscillations in tight-binding lattices with defects,” Phys. Rev. B 81, 195118 (2010).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef] [PubMed]

S. Longhi, “Optical Bloch oscillations and Zener tunneling with nonclassical light,” Phys. Rev. Lett. 101, 193902 (2008).
[CrossRef] [PubMed]

S. Longhi, “Optical Zener-Bloch oscillations in binary waveguide arrays,” Europhys. Lett. 76, 416–421 (2006).
[CrossRef]

Menotti, C.

C. Menotti, A. Smerzi, and A. Trombettoni, “Superfluid dynamics of a Bose-Einstein condensate in a periodic potential,” New J. Phys. 5, 112 (2003).
[CrossRef]

Michaelis, D.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, and A. Brauer, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Morandotti, R.

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

Neshev, D. N.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

Nolte, S.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef] [PubMed]

Oton, C. J.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[CrossRef]

Pavesi, L.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[CrossRef]

Pertsch, T.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef] [PubMed]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, and A. Brauer, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (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]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701–1703(1998).
[CrossRef]

Peschel, U.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

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

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701–1703(1998).
[CrossRef]

Ponomarev, A. V.

A. V. Ponomarev and A. R. Kolovsky, “Dipole and Bloch oscillations of cold atoms in a parabolic lattice,” Laser Phys. 16, 367–370 (2006).
[CrossRef]

Rutkowska, K. A.

A. Fratalocchi, K. A. Rutkowska, M. A. Karpierz, and G. Assanto, “Light induced angular steering via Floquet-Bloch band-tunnelling in one-dimensional liquid crystalline photonic lattices,” Opto-Electron. Rev. 15, 210–214 (2007).
[CrossRef]

Sanchez-Dehesa, J.

H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sanchez-Dehesa, “Acoustic analogue of electronic Bloch oscillations and resonant Zener tunneling in ultrasonic superlattices,” Phys. Rev. Lett. 98, 134301 (2007).
[CrossRef] [PubMed]

Sanchis-Alepuz, H.

H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sanchez-Dehesa, “Acoustic analogue of electronic Bloch oscillations and resonant Zener tunneling in ultrasonic superlattices,” Phys. Rev. Lett. 98, 134301 (2007).
[CrossRef] [PubMed]

Sapienza, R.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[CrossRef]

Shadrivov, I. V.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Silberberg, Y.

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

Smerzi, A.

C. Menotti, A. Smerzi, and A. Trombettoni, “Superfluid dynamics of a Bose-Einstein condensate in a periodic potential,” New J. Phys. 5, 112 (2003).
[CrossRef]

Streppel, U.

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, and A. Brauer, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Sukhorukov, A. A.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

Szameit, A.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef] [PubMed]

Trombettoni, A.

C. Menotti, A. Smerzi, and A. Trombettoni, “Superfluid dynamics of a Bose-Einstein condensate in a periodic potential,” New J. Phys. 5, 112 (2003).
[CrossRef]

Trompeter, H.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, and A. Brauer, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Tunnermann, A.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef] [PubMed]

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Wang, G. P.

W. Lin and G. P. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91, 143121 (2007).
[CrossRef]

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

Wiersma, D.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[CrossRef]

Witthaut, D.

B. M. Breid, D. Witthaut, and H. J. Korsch, “Manipulation of matter waves using Bloch and Bloch-Zener oscillations,” New J. Phys. 9, 62 (2007).
[CrossRef]

B. M. Breid, D. Witthaut, and H. J. Korsch, “Bloch-Zener oscillations,” New J. Phys. 8, 110 (2006).
[CrossRef]

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M. J. Zheng, J. J. Xiao, and K. W. Yu, “Controllable optical Bloch oscillation in planar graded optical waveguide arrays,” Phys. Rev. A 81, 033829 (2010).
[CrossRef]

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Zener, C.

C. Zener, “A theory of electrical breakdown of solid dielectrics,” Proc. R. Soc. London Series A 145, 523–529 (1934).
[CrossRef]

Zheng, M. J.

Zhou, X.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

Appl. Phys. Lett. (3)

W. Lin and G. P. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91, 143121 (2007).
[CrossRef]

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91, 243113 (2007).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94, 161105 (2009).
[CrossRef]

Europhys. Lett. (1)

S. Longhi, “Optical Zener-Bloch oscillations in binary waveguide arrays,” Europhys. Lett. 76, 416–421 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

Laser Phys. (1)

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[CrossRef]

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C. Menotti, A. Smerzi, and A. Trombettoni, “Superfluid dynamics of a Bose-Einstein condensate in a periodic potential,” New J. Phys. 5, 112 (2003).
[CrossRef]

B. M. Breid, D. Witthaut, and H. J. Korsch, “Manipulation of matter waves using Bloch and Bloch-Zener oscillations,” New J. Phys. 9, 62 (2007).
[CrossRef]

B. M. Breid, D. Witthaut, and H. J. Korsch, “Bloch-Zener oscillations,” New J. Phys. 8, 110 (2006).
[CrossRef]

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[CrossRef]

Phys. Rev. A (1)

M. J. Zheng, J. J. Xiao, and K. W. Yu, “Controllable optical Bloch oscillation in planar graded optical waveguide arrays,” Phys. Rev. A 81, 033829 (2010).
[CrossRef]

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S. Longhi, “Bloch oscillations in tight-binding lattices with defects,” Phys. Rev. B 81, 195118 (2010).
[CrossRef]

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[CrossRef]

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R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91, 263902 (2003).
[CrossRef]

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[CrossRef]

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[CrossRef]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

S. Longhi, “Optical Bloch oscillations and Zener tunneling with nonclassical light,” Phys. Rev. Lett. 101, 193902 (2008).
[CrossRef] [PubMed]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, and A. Brauer, “Visual observation of Zener tunneling,” Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tunnermann, and S. Longhi, “Bloch-Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic diagram of a BPOWA. (b) Dispersion relation of unitary POWA (dotted curves) and binary POWA (solid curves). The parameters are N = 101 , α = 2.0 , κ = 1.0 , and δ V = 0.5 .

Fig. 2
Fig. 2

Phase diagram of a BPOWA. There are two bands whose boundaries are β ( x , 0 ) , β ( x , π / 2 ) , β + ( x , π / 2 ) , and β + ( x , 0 ) . Separated by three critical lines β ( 0 , π / 2 ) , β + ( 0 , π / 2 ) , and β + ( 0 , 0 ) , 10 regions are formed. The correspondences among these regions and different optical oscillations are as follows: DO, regions 2 and 4; left BO (LBO), regions 1, 5, 7, and 9; right BO (RBO), regions 3, 6, 8, and 10. The parameters are N = 101 , n 0 = 20 , k 0 = π , σ = 1 , α = 2.0 , κ = 1.0 , and δ V = 0.5 .

Fig. 3
Fig. 3

Band structures with components of input Gaussian beams, contour plots of | ψ ( x , z ) | 2 and | ϕ ( k , z ) | 2 for three cases: (a)–(c)  δ V = 0.0 , (d)–(f)  δ V = 0.5 , and (g)–(i)  δ V = 1.0 . The other parameters are N = 101 , n 0 = 20 , k 0 = 0 , σ = 1 , α = 2.0 , and κ = 1.0 .

Fig. 4
Fig. 4

Band structures with components of input Gaussian beams, contour plots of | ψ ( x , z ) | 2 and | ϕ ( k , z ) | 2 for three cases: (a)–(c)  δ V = 0.0 , (d)–(f)  δ V = 0.5 , and (g)–(i)  δ V = 1.0 . The other parameters are the same as those in Fig. 3 except k 0 = π .

Fig. 5
Fig. 5

(a) Visual demonstration of band structure through spatial evolution of a light beam (LBO) in a BPOWA. The parameters are the same as those in Fig. 3e. (b) Comparison of the field-evolution analysis result and Hamiltonian optics result of BDZO. The parameters are the same as those in Fig. 4e.

Equations (8)

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[ i d d z + V ( x n ) δ V 2 ] a n ( z ) + κ [ b n 1 ( z ) + b n ( z ) ] = 0 , [ i d d z + V ( x n ) + δ V 2 ] b n ( z ) + κ [ a n ( z ) + a n + 1 ( z ) ] = 0 ,
H ( u v ) = β ( u v ) ,
β ± ( x , k ) = V ( x ) ± 2 κ 2 ( 1 + cos 2 k d ) + δ V 2 4 .
ψ ( n , 0 ) = 1 ( 2 π σ 2 ) 1 / 4 e ( n n 0 ) 2 4 σ 2 e i k 0 ( n n 0 ) ,
| ψ ( n , 0 ) = m A m | m ,
| ψ ( n , z ) = m A m e i β m z | m .
| ϕ ( k , z ) = F [ | ψ ( x , z ) ] .
d x d z = β ( x , k ) k , d k d z = β ( x , k ) x .

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