Abstract

We show that classical analogs to quantum coherent and displaced Fock states can emerge in one-dimensional semi-infinite photonic lattices having a square root law for the coupling coefficients. Beam dynamics in these fully integrable structures is described in closed form, irrespective of the site of excitation. The trajectories of these beams are closely examined, and pertinent examples are provided for their realization.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2010 (1)

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, Phys. Rev. A. 81, 023834 (2010).
[CrossRef]

2009 (2)

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Cristodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef] [PubMed]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, Phys. Rev. Lett. 102, 253904 (2009).
[CrossRef] [PubMed]

2008 (1)

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (2)

H. Trompeter, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

K. G. Makris and D. N. Christodoulides, Phys. Rev. E 73, 036616 (2006).
[CrossRef]

2005 (1)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

1990 (1)

F. A. M. de Oliveira, M. S. Kim, and P. L. Knight, Phys. Rev. A 41, 2645 (1990).
[CrossRef] [PubMed]

1965 (1)

1963 (1)

R. G. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

Arfken, G.

G. Arfken, Mathematical Methods for Physicists(Academic, 1985).

Avidan, A.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef] [PubMed]

Bromberg, Y.

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, Phys. Rev. Lett. 102, 253904 (2009).
[CrossRef] [PubMed]

Christodoulides, D. N.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef] [PubMed]

K. G. Makris and D. N. Christodoulides, Phys. Rev. E 73, 036616 (2006).
[CrossRef]

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Cristodoulides, D. N.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Cristodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef] [PubMed]

de Oliveira, F. A. M.

F. A. M. de Oliveira, M. S. Kim, and P. L. Knight, Phys. Rev. A 41, 2645 (1990).
[CrossRef] [PubMed]

Dreisow, F.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, Phys. Rev. A. 81, 023834 (2010).
[CrossRef]

A. Szameit, F. Dreisow, T. Pertschi, S. Nolte, and A. Tunnermann, Opt. Express 15, 1579 (2007).
[CrossRef] [PubMed]

Glauber, R. G.

R. G. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

Heinrich, M.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, Phys. Rev. A. 81, 023834 (2010).
[CrossRef]

Iwanow, R.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Jones, A. L.

Keil, R.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, Phys. Rev. A. 81, 023834 (2010).
[CrossRef]

Kim, M. S.

F. A. M. de Oliveira, M. S. Kim, and P. L. Knight, Phys. Rev. A 41, 2645 (1990).
[CrossRef] [PubMed]

Kip, D.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Cristodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef] [PubMed]

Knight, P. L.

F. A. M. de Oliveira, M. S. Kim, and P. L. Knight, Phys. Rev. A 41, 2645 (1990).
[CrossRef] [PubMed]

Lahini, Y.

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, Phys. Rev. Lett. 102, 253904 (2009).
[CrossRef] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef] [PubMed]

Lederer, F.

H. Trompeter, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Louisell, W. H.

W. H. Louisell, Quantum and Statistical Properties of Radiation (Wiley, 1973).

Makris, K. G.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Cristodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef] [PubMed]

K. G. Makris and D. N. Christodoulides, Phys. Rev. E 73, 036616 (2006).
[CrossRef]

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Morandotti, R.

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, Phys. Rev. Lett. 102, 253904 (2009).
[CrossRef] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef] [PubMed]

Nolte, S.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, Phys. Rev. A. 81, 023834 (2010).
[CrossRef]

A. Szameit, F. Dreisow, T. Pertschi, S. Nolte, and A. Tunnermann, Opt. Express 15, 1579 (2007).
[CrossRef] [PubMed]

Peleg, O.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Cristodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef] [PubMed]

Pertsch, T.

H. Trompeter, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Pertschi, T.

Pozzi, F.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef] [PubMed]

Rüter, C. E.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Cristodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef] [PubMed]

Segev, M.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Cristodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef] [PubMed]

Shandarova, K.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Cristodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef] [PubMed]

Silberberg, Y.

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, Phys. Rev. Lett. 102, 253904 (2009).
[CrossRef] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef] [PubMed]

Sorel, M.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef] [PubMed]

Stegeman, G. I.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Szameit, A.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, Phys. Rev. A. 81, 023834 (2010).
[CrossRef]

A. Szameit, F. Dreisow, T. Pertschi, S. Nolte, and A. Tunnermann, Opt. Express 15, 1579 (2007).
[CrossRef] [PubMed]

Trompeter, H.

H. Trompeter, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

Tunnermann, A.

Tünnermann, A.

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, Phys. Rev. A. 81, 023834 (2010).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford U. Press, 2007).

Yeh, P.

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford U. Press, 2007).

J. Opt. Soc. Am. (1)

Opt. Express (1)

Phys. Rev. (1)

R. G. Glauber, Phys. Rev. 131, 2766 (1963).
[CrossRef]

Phys. Rev. A (1)

F. A. M. de Oliveira, M. S. Kim, and P. L. Knight, Phys. Rev. A 41, 2645 (1990).
[CrossRef] [PubMed]

Phys. Rev. A. (1)

R. Keil, A. Szameit, F. Dreisow, M. Heinrich, S. Nolte, and A. Tünnermann, Phys. Rev. A. 81, 023834 (2010).
[CrossRef]

Phys. Rev. E (1)

K. G. Makris and D. N. Christodoulides, Phys. Rev. E 73, 036616 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

H. Trompeter, T. Pertsch, and F. Lederer, Phys. Rev. Lett. 96, 023901 (2006).
[CrossRef] [PubMed]

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Cristodoulides, O. Peleg, and M. Segev, Phys. Rev. Lett. 102, 123905 (2009).
[CrossRef] [PubMed]

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef] [PubMed]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef] [PubMed]

Y. Bromberg, Y. Lahini, R. Morandotti, and Y. Silberberg, Phys. Rev. Lett. 102, 253904 (2009).
[CrossRef] [PubMed]

Other (3)

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford U. Press, 2007).

G. Arfken, Mathematical Methods for Physicists(Academic, 1985).

W. H. Louisell, Quantum and Statistical Properties of Radiation (Wiley, 1973).

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Figures (3)

Fig. 1
Fig. 1

Propagation dynamics when the first waveguide site is excited. The dashed curve indicates the trajectory where the energy is highest during propagation. The inset depicts a semi-infinite waveguide array where n is the corresponding coupling constant.

Fig. 2
Fig. 2

(a) Intensity evolution of the twentieth classical displaced state and (b) its corresponding output intensity profile at Z = 3 .

Fig. 3
Fig. 3

(a) Intensity evolution of the classical coherent state and (b) its corresponding output intensity distribution at Z = 3 . Similarly, for the (c) first classical displaced state and (d) its intensity profile at Z = 3 .

Equations (12)

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

i d E n d Z + n + 1 E n + 1 + n E n 1 = 0 ,
n + 1 a n + 1 + μ a n n a n 1 = 0.
i d ψ ( x , Z ) d Z = ( a + a ) ψ ( x , Z ) ,
ψ ( x , Z ) = n = 0 E n ( Z ) ψ n ( x ) .
i n = 0 d E n ( Z ) d Z | n = n = 0 ( n E n ( Z ) | n 1 + n + 1 E n ( Z ) | n + 1 ) .
| ψ ( Z ) = exp ( i Z ( a + a ) ) | ψ ( 0 ) .
E m = exp ( Z 2 / 2 ) m | exp ( i Z a ) exp ( i Z a ) | k .
E k + s ( Z ) = exp ( Z 2 / 2 ) ( i Z ) s k ! ( k + s ) ! L k s ( Z 2 ) ,
E k s ( Z ) = exp ( Z 2 / 2 ) ( i Z ) s ( k s ) ! k ! L k s s ( Z 2 ) .
E m ( Z ) = exp ( Z 2 / 2 ) ( i Z ) m m ! .
| α = i Z = exp ( | α | 2 2 ) n = 0 ( α ) n n ! | n ,
Z = f ( n ) = exp ( 1 2 [ γ + k = 1 n 1 k ] ) ,

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