Abstract

We show a PT-symmetric coupler having an arm with a tunable gain and a no-loss arm when appropriately de signed to possess reciprocal behavior, unlike its rivals having a fixed gain/loss arm, can perform as a tunable 2×2 spatial optical switch. The degree of the tunability equals the ratio of the coupler’s length to the total coupling length.

© 2011 Optical Society of America

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References

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  1. C. M. Bender and S. Böttcher, Phys. Rev. Lett. 80, 5243(1998).
    [CrossRef]
  2. C. M. Bender, S. Böttcher, and P. N. Meisinger, J. Math. Phys. (N.Y.) 40, 2201 (1999).
    [CrossRef]
  3. A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
    [CrossRef] [PubMed]
  4. C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodooulides, M. Segev, and D. Kip, Nat. Phys. 6, 192(2010).
    [CrossRef]
  5. K. G. Makris, R. El-Ganainy, D. N. Christodooulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
    [CrossRef] [PubMed]
  6. Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. Lett. 100, 030402 (2008).
    [CrossRef] [PubMed]
  7. H. Wang and J. Wang, Opt. Express 19, 4030 (2011).
    [CrossRef] [PubMed]
  8. R. El-Ganainy, K. G. Makris, D. N. Christodooulides, and Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).
    [CrossRef] [PubMed]
  9. H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. A 82, 043803 (2010).
    [CrossRef]
  10. T. Tamir, Integrated Optics (Springer-Verlag, New York, 1975).

2011

2010

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. A 82, 043803 (2010).
[CrossRef]

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodooulides, M. Segev, and D. Kip, Nat. Phys. 6, 192(2010).
[CrossRef]

2009

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

2008

K. G. Makris, R. El-Ganainy, D. N. Christodooulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

2007

1999

C. M. Bender, S. Böttcher, and P. N. Meisinger, J. Math. Phys. (N.Y.) 40, 2201 (1999).
[CrossRef]

1998

C. M. Bender and S. Böttcher, Phys. Rev. Lett. 80, 5243(1998).
[CrossRef]

Aimez, V.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Bender, C. M.

C. M. Bender, S. Böttcher, and P. N. Meisinger, J. Math. Phys. (N.Y.) 40, 2201 (1999).
[CrossRef]

C. M. Bender and S. Böttcher, Phys. Rev. Lett. 80, 5243(1998).
[CrossRef]

Böttcher, S.

C. M. Bender, S. Böttcher, and P. N. Meisinger, J. Math. Phys. (N.Y.) 40, 2201 (1999).
[CrossRef]

C. M. Bender and S. Böttcher, Phys. Rev. Lett. 80, 5243(1998).
[CrossRef]

Christodooulides, D. N.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodooulides, M. Segev, and D. Kip, Nat. Phys. 6, 192(2010).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. A 82, 043803 (2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodooulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodooulides, and Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).
[CrossRef] [PubMed]

Christodoulides, D. N.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Duchesne, D.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

El-Ganainy, R.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodooulides, M. Segev, and D. Kip, Nat. Phys. 6, 192(2010).
[CrossRef]

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. A 82, 043803 (2010).
[CrossRef]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

K. G. Makris, R. El-Ganainy, D. N. Christodooulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodooulides, and Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).
[CrossRef] [PubMed]

Guo, A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Kip, D.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodooulides, M. Segev, and D. Kip, Nat. Phys. 6, 192(2010).
[CrossRef]

Kottos, T.

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. A 82, 043803 (2010).
[CrossRef]

Makris, K. G.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodooulides, M. Segev, and D. Kip, Nat. Phys. 6, 192(2010).
[CrossRef]

K. G. Makris, R. El-Ganainy, D. N. Christodooulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodooulides, and Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).
[CrossRef] [PubMed]

Meisinger, P. N.

C. M. Bender, S. Böttcher, and P. N. Meisinger, J. Math. Phys. (N.Y.) 40, 2201 (1999).
[CrossRef]

Morandotti, R.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Musslimani, Z. H.

K. G. Makris, R. El-Ganainy, D. N. Christodooulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

R. El-Ganainy, K. G. Makris, D. N. Christodooulides, and Z. H. Musslimani, Opt. Lett. 32, 2632 (2007).
[CrossRef] [PubMed]

Ramezani, H.

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. A 82, 043803 (2010).
[CrossRef]

Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodooulides, M. Segev, and D. Kip, Nat. Phys. 6, 192(2010).
[CrossRef]

Salamo, G. J.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodooulides, M. Segev, and D. Kip, Nat. Phys. 6, 192(2010).
[CrossRef]

Siviloglou, G. A.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Tamir, T.

T. Tamir, Integrated Optics (Springer-Verlag, New York, 1975).

Volatier-Ravat, M.

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

Wang, H.

Wang, J.

J. Math. Phys. (N.Y.)

C. M. Bender, S. Böttcher, and P. N. Meisinger, J. Math. Phys. (N.Y.) 40, 2201 (1999).
[CrossRef]

Nat. Phys.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodooulides, M. Segev, and D. Kip, Nat. Phys. 6, 192(2010).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

H. Ramezani, T. Kottos, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. A 82, 043803 (2010).
[CrossRef]

Phys. Rev. Lett.

K. G. Makris, R. El-Ganainy, D. N. Christodooulides, and Z. H. Musslimani, Phys. Rev. Lett. 100, 103904 (2008).
[CrossRef] [PubMed]

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodooulides, Phys. Rev. Lett. 100, 030402 (2008).
[CrossRef] [PubMed]

A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, Phys. Rev. Lett. 103, 093902 (2009).
[CrossRef] [PubMed]

C. M. Bender and S. Böttcher, Phys. Rev. Lett. 80, 5243(1998).
[CrossRef]

Other

T. Tamir, Integrated Optics (Springer-Verlag, New York, 1975).

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Figures (4)

Fig. 1
Fig. 1

A schematic representation of (a) a conventional coupler and (b) the proposed 2 × 2 all optical PTS spatial switch.

Fig. 2
Fig. 2

Normalized intensity of an optical signal transmitting across the spatial switch of Fig. 1b with L = 24.8 mm , when the external pump is off ( γ = 0 ). (a) 3D and (b) 2D profiles for route 1 4 and (c) 3D and (d) 2D profiles for route 2 3 .

Fig. 3
Fig. 3

Normalized intensity of an optical signal transmitting across the spatial switch of Fig. 1b with L = 24.8 mm , when the external pump is on, providing ( γ 5.66 cm 1 ). (a) 3D and (b) 2D profiles for route 1 3 and (c) 3D and (d) 2D profiles for route 2 4 .

Fig. 4
Fig. 4

3D Profiles of normalized intensities of an optical signal propagating across the spatial switch of Fig. 1b with L = 11 × L C 90.94 mm ( N = 5 ) , when the pump is off ( γ = 0 ) via route 2 3 (a) and via route 2 4 when the pump is on and tuned for (b)  γ = 3.166 cm 1 , (c)  γ = 5.216 cm 1 , (d)  γ = 6.37 cm 1 , (e)  γ = 7.08 cm 1 , and (f)  γ = 7.473 cm 1 .

Equations (8)

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i U / z + ( 2 k 0 n 0 ) 1 2 U / x 2 + k 0 [ n R ( x ) + i n I ( x ) ] U = 0 ,
i d d z [ U 1 U 2 ] = [ 0 κ κ 0 ] [ U 1 U 2 ] ,
i d d z [ V 1 V 2 ] = [ + i γ / 4 κ κ i γ / 4 ] [ V 1 V 2 ] ,
[ V 1 ( x , z ) V 2 ( x , z ) ] = [ T ] [ V 1 ( x , 0 ) V 2 ( x , 0 ) ] ,
T 11 = cos [ ξ z ] + γ sin [ ξ z ] / 4 ξ ,
T 12 = T 21 = i κ sin [ ξ z ] / ξ ,
T 22 = cos [ ξ z ] + γ sin [ ξ z ] / 4 ξ .
γ = 4 κ ( 2 N 2 j + 1 ) ( 2 N + 2 j + 3 ) / ( 2 N + 1 ) .

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