Abstract

Spatial Bloch oscillations of light waves of purely topological origin are theoretically shown to exist in weakly deformed slab waveguides. As the optical rays trapped in the deformed waveguide can roll freely, wave diffraction is strongly affected by the topology of the deformed surface, which can be tailored to simulate the effect of a tilted periodic refractive index.

© 2007 Optical Society of America

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References

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2007

2006

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Yu. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, Phys. Rev. Lett. 96, 053903 (2006).
[CrossRef] [PubMed]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, Opt. Lett. 31, 1489 (2006).
[CrossRef] [PubMed]

N. Chiodo, G. Della Valle, R. Osellame, S. Longhi, G. Cerullo, R. Ramponi, P. Laporta, and U. Morgner, Opt. Lett. 31, 1651 (2006).
[CrossRef] [PubMed]

S. Schwartz, M. Cozzini, C. Menotti, I. Carusotto, P. Bouyer, and S. Stringari, New J. Phys. 8, 162 (2006).
[CrossRef]

2005

A. Marchi, S. Reggiani, M. Rudan, and A. Bertoni, Phys. Rev. B 72, 035403 (2005).
[CrossRef]

2004

B. A. Usievich, V. A. Sychugov, J. Kh. Nirligareev, and K. M. Golant, Opt. Spectrosc. 97, 790 (2004).
[CrossRef]

2003

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, Phys. Rev. Lett. 91, 263902 (2003).
[CrossRef]

1999

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

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

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

1981

R. C. T. Costa, Phys. Rev. A 23, 1982 (1981).
[CrossRef]

Nature

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef] [PubMed]

New J. Phys.

S. Schwartz, M. Cozzini, C. Menotti, I. Carusotto, P. Bouyer, and S. Stringari, New J. Phys. 8, 162 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectrosc.

B. A. Usievich, V. A. Sychugov, J. Kh. Nirligareev, and K. M. Golant, Opt. Spectrosc. 97, 790 (2004).
[CrossRef]

Phys. Rev. A

R. C. T. Costa, Phys. Rev. A 23, 1982 (1981).
[CrossRef]

Phys. Rev. B

A. Marchi, S. Reggiani, M. Rudan, and A. Bertoni, Phys. Rev. B 72, 035403 (2005).
[CrossRef]

Phys. Rev. Lett.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

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

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, Phys. Rev. Lett. 91, 263902 (2003).
[CrossRef]

H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Yu. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, Phys. Rev. Lett. 96, 053903 (2006).
[CrossRef] [PubMed]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Schematic of a deformed slab waveguide and of the curvilinear coordinate system. The inset shows the refractive index profile n of the undulated slab waveguide used in numerical simulations.

Fig. 2
Fig. 2

BO in an undulating and circularly curved slab waveguide with constant thickness along the normal for R = ( a ) 10 and (b) 5 mm . The intensity cross sections of input and output beams are shown in the top and bottom pictures.

Fig. 3
Fig. 3

Same as Fig. 2 but for a guiding layer thickness uniform along the vertical y direction.

Equations (7)

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( 2 E x 2 + 2 E y 2 + 2 E z 2 ) + k 0 2 n 2 ( x , y , z ) E = 0 ,
D ψ + ( M 2 K ) ψ + k 0 2 n eff 2 ψ = 0 ,
r = x 0 ( q 1 ) u x + y 0 ( q 1 ) u y + q 2 u z ,
2 ψ q 1 2 + 2 ψ z 2 + 1 4 S 2 ( q 1 ) ψ + k 0 2 n eff 2 ψ = 0 ,
i A z = 2 2 n eff 2 A q 1 2 2 A 8 n eff S 2 ( q 1 ) ,
2 E u 2 + 2 E v 2 + exp ( 2 u R ) [ 2 E y 2 + k 0 2 n 2 ( u , y ) E ] = 0 .
i A v = 2 2 n eff 2 A q 1 2 2 A 8 n eff S 2 ( q 1 ) n s R x 0 ( q 1 ) A ,

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