Abstract

We present an analytical proof of the existence of unidirectional optical Bloch oscillations in a waveguide array system. It is shown that the presence of nonreciprocity in the system allows for a complete normal-mode dephasing in one of the propagation directions, resulting in a unidirectional breakdown in Bloch oscillations. A model system consisting of an array of transversely magnetized asymmetric Si/SiO2 waveguides with a magneto-optic cover layer is presented. Large index contrasts between film and cover are critical for practical realizations.

© 2011 Optical Society of America

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2011 (1)

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

2010 (2)

2009 (1)

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef] [PubMed]

2004 (2)

1999 (1)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

1998 (1)

1996 (1)

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

1993 (1)

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

1960 (1)

A. G. Chynoweth, G. H. Wannier, R. A. Logan, and D. E. Thomas, Phys. Rev. Lett. 5, 57 (1960).
[CrossRef]

1934 (1)

C. Zener, Proc. R. Soc. A 145, 523 (1934).
[CrossRef]

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Ben Dahan, M.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

Castin, Y.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

Chen, R.

Chynoweth, A. G.

A. G. Chynoweth, G. H. Wannier, R. A. Logan, and D. E. Thomas, Phys. Rev. Lett. 5, 57 (1960).
[CrossRef]

Dötsch, H.

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Espinola, R. L.

Hao, Y.

Huang, W.-P.

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

Izuhara, T.

Jiang, G.

Jiang, X.

Kohler, K.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Kumar, P.

Kurz, H.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Lederer, F.

Leo, K.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Levy, M.

Logan, R. A.

A. G. Chynoweth, G. H. Wannier, R. A. Logan, and D. E. Thomas, Phys. Rev. Lett. 5, 57 (1960).
[CrossRef]

Longhi, S.

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef] [PubMed]

Mizumoto, T.

H. Yokoi, Y. Shoji, and T. Mizumoto, Jpn. J. Appl. Phys. 43, 5871 (2004).
[CrossRef]

Morandotti, R.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Mu, J.-W.

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

Osgood, R. M.

Peik, E.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

Pertsch, T.

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Reichel, J.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

Roskos, H. G.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Salomon, C.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

Schwedler, R.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Shoji, Y.

H. Yokoi, Y. Shoji, and T. Mizumoto, Jpn. J. Appl. Phys. 43, 5871 (2004).
[CrossRef]

Silberberg, Y.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Thomas, D. E.

A. G. Chynoweth, G. H. Wannier, R. A. Logan, and D. E. Thomas, Phys. Rev. Lett. 5, 57 (1960).
[CrossRef]

Tsai, M.-C.

Wang, M.

Wannier, G. H.

A. G. Chynoweth, G. H. Wannier, R. A. Logan, and D. E. Thomas, Phys. Rev. Lett. 5, 57 (1960).
[CrossRef]

Waschke, C.

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

Yang, J.

Yokoi, H.

H. Yokoi, Y. Shoji, and T. Mizumoto, Jpn. J. Appl. Phys. 43, 5871 (2004).
[CrossRef]

Zener, C.

C. Zener, Proc. R. Soc. A 145, 523 (1934).
[CrossRef]

Zhang, W.

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

Zhao, W.

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

W. Zhang, J.-W. Mu, W.-P. Huang, and W. Zhao, Appl. Phys. Lett. 98, 171109 (2011).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Yokoi, Y. Shoji, and T. Mizumoto, Jpn. J. Appl. Phys. 43, 5871 (2004).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (5)

A. G. Chynoweth, G. H. Wannier, R. A. Logan, and D. E. Thomas, Phys. Rev. Lett. 5, 57 (1960).
[CrossRef]

C. Waschke, H. G. Roskos, R. Schwedler, K. Leo, H. Kurz, and K. Kohler, Phys. Rev. Lett. 70, 3319 (1993).
[CrossRef] [PubMed]

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
[CrossRef] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

S. Longhi, Phys. Rev. Lett. 103, 123601 (2009).
[CrossRef] [PubMed]

Proc. R. Soc. A (1)

C. Zener, Proc. R. Soc. A 145, 523 (1934).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) Waveguide array (widths are scaled up and separations scaled down 4 × to fit in the sketch), (b) plot showing nearly equally spaced NRPS Δ β n r and propagation constant β for adjacent normal modes; a typical forward normal mode of the array showing (c) constant amplitude and width in the FW direction and (d) diffractive spread in the BW direction.

Fig. 2
Fig. 2

(a) Beam evolution for single guide excitation in the FW direction, showing BO motion, and (b) the BW direction, showing diffractive beam spread; (c) a 6 μm wide beam excitation in the FW direction, showing BO motion with the beam mostly confined to the high index side; (d) diffractive beam spread in the BW direction.

Equations (5)

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

i d a n f , b d z + δ β f , b n a n f , b + κ f , b ( a n 1 f , b + a n + 1 f , b ) = 0 ,
ε ^ = ( ε 0 i g 0 ε 0 i g 0 ε ) ,
k x · d = tan 1 [ ε f k x ( γ eff ε eff + β g ε ε eff ) ] + tan 1 [ ε f k x ( γ s ε s ) ] ,
Δ β n r = 2 Re d x d y ( x H y ) H y * ( i g / ε 2 ) d x d y | H y | 2 ε 1 .
δ β m + 1 , m f δ β m + 1 , m b = β m + 1 f β m f ( β m + 1 b β m b ) = Δ β m + 1 n r Δ β m n r = Δ ( Δ β n r ) m + 1 , m .

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