Abstract

We report the nonreciprocal behavior of an optical coupler consisting of two straight waveguides forming a small angle. An optical diode action is theoretically demonstrated when light is launched along opposite directions. The switching power is lower than the case of parallel waveguides with a constant coupling coefficient.

© 2012 Optical Society of America

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References

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  1. G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic, 2008).
  2. S. M. Jensen, IEEE J. Quantum Electron., QE-18, 1580 (1982).
    [CrossRef]
  3. S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, Opt. Lett. 13, 904 (1988).
    [CrossRef]
  4. Y. Silberberg and B. G. Sfez, Opt. Lett. 13, 1132 (1988).
    [CrossRef]
  5. J. P. Sabini, N. Finlayson, and G. I. Stegeman, Appl. Phys. Lett. 55, 1176 (1989).
    [CrossRef]
  6. A. Salandrino, K. Makris, D. N. Christodoulides, Y. Lahini, Y. Silberberg, and R. Morandotti, Opt. Commun. 282, 4524 (2009).
    [CrossRef]
  7. V. Leutheuser, U. Langbein, and F. Lederer, Opt. Commun. 75, 251 (1990).
    [CrossRef]
  8. C. Wang, Q. Li, G. Liu, G. Jin, and X. Xu, IEEE Photon. Technol. Lett. 16, 2248 (2004).
    [CrossRef]
  9. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
  10. R. Tewari and K. Thyagarajan, J. Lightwave Technol. 4, 386 (1986).
    [CrossRef]
  11. M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
    [CrossRef]

2009 (1)

A. Salandrino, K. Makris, D. N. Christodoulides, Y. Lahini, Y. Silberberg, and R. Morandotti, Opt. Commun. 282, 4524 (2009).
[CrossRef]

2008 (1)

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

2004 (1)

C. Wang, Q. Li, G. Liu, G. Jin, and X. Xu, IEEE Photon. Technol. Lett. 16, 2248 (2004).
[CrossRef]

1990 (1)

V. Leutheuser, U. Langbein, and F. Lederer, Opt. Commun. 75, 251 (1990).
[CrossRef]

1989 (1)

J. P. Sabini, N. Finlayson, and G. I. Stegeman, Appl. Phys. Lett. 55, 1176 (1989).
[CrossRef]

1988 (2)

1986 (1)

R. Tewari and K. Thyagarajan, J. Lightwave Technol. 4, 386 (1986).
[CrossRef]

1982 (1)

S. M. Jensen, IEEE J. Quantum Electron., QE-18, 1580 (1982).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic, 2008).

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

Christodoulides, D. N.

A. Salandrino, K. Makris, D. N. Christodoulides, Y. Lahini, Y. Silberberg, and R. Morandotti, Opt. Commun. 282, 4524 (2009).
[CrossRef]

Chu, S.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Duchesne, D.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Ferrera, M.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Finlayson, N.

J. P. Sabini, N. Finlayson, and G. I. Stegeman, Appl. Phys. Lett. 55, 1176 (1989).
[CrossRef]

Friberg, S. R.

Jensen, S. M.

S. M. Jensen, IEEE J. Quantum Electron., QE-18, 1580 (1982).
[CrossRef]

Jin, G.

C. Wang, Q. Li, G. Liu, G. Jin, and X. Xu, IEEE Photon. Technol. Lett. 16, 2248 (2004).
[CrossRef]

Lahini, Y.

A. Salandrino, K. Makris, D. N. Christodoulides, Y. Lahini, Y. Silberberg, and R. Morandotti, Opt. Commun. 282, 4524 (2009).
[CrossRef]

Langbein, U.

V. Leutheuser, U. Langbein, and F. Lederer, Opt. Commun. 75, 251 (1990).
[CrossRef]

Lederer, F.

V. Leutheuser, U. Langbein, and F. Lederer, Opt. Commun. 75, 251 (1990).
[CrossRef]

Leutheuser, V.

V. Leutheuser, U. Langbein, and F. Lederer, Opt. Commun. 75, 251 (1990).
[CrossRef]

Li, Q.

C. Wang, Q. Li, G. Liu, G. Jin, and X. Xu, IEEE Photon. Technol. Lett. 16, 2248 (2004).
[CrossRef]

Liscidini, M.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Little, B. E.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Liu, G.

C. Wang, Q. Li, G. Liu, G. Jin, and X. Xu, IEEE Photon. Technol. Lett. 16, 2248 (2004).
[CrossRef]

Makris, K.

A. Salandrino, K. Makris, D. N. Christodoulides, Y. Lahini, Y. Silberberg, and R. Morandotti, Opt. Commun. 282, 4524 (2009).
[CrossRef]

Morandotti, R.

A. Salandrino, K. Makris, D. N. Christodoulides, Y. Lahini, Y. Silberberg, and R. Morandotti, Opt. Commun. 282, 4524 (2009).
[CrossRef]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Moss, D. J.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Razzari, L.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Sabini, J. P.

J. P. Sabini, N. Finlayson, and G. I. Stegeman, Appl. Phys. Lett. 55, 1176 (1989).
[CrossRef]

Salandrino, A.

A. Salandrino, K. Makris, D. N. Christodoulides, Y. Lahini, Y. Silberberg, and R. Morandotti, Opt. Commun. 282, 4524 (2009).
[CrossRef]

Sfez, B. G.

Silberberg, Y.

A. Salandrino, K. Makris, D. N. Christodoulides, Y. Lahini, Y. Silberberg, and R. Morandotti, Opt. Commun. 282, 4524 (2009).
[CrossRef]

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, Opt. Lett. 13, 904 (1988).
[CrossRef]

Y. Silberberg and B. G. Sfez, Opt. Lett. 13, 1132 (1988).
[CrossRef]

Sipe, J. E.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Smith, P. S.

Stegeman, G. I.

J. P. Sabini, N. Finlayson, and G. I. Stegeman, Appl. Phys. Lett. 55, 1176 (1989).
[CrossRef]

Tewari, R.

R. Tewari and K. Thyagarajan, J. Lightwave Technol. 4, 386 (1986).
[CrossRef]

Thyagarajan, K.

R. Tewari and K. Thyagarajan, J. Lightwave Technol. 4, 386 (1986).
[CrossRef]

Wang, C.

C. Wang, Q. Li, G. Liu, G. Jin, and X. Xu, IEEE Photon. Technol. Lett. 16, 2248 (2004).
[CrossRef]

Weiner, A. M.

Xu, X.

C. Wang, Q. Li, G. Liu, G. Jin, and X. Xu, IEEE Photon. Technol. Lett. 16, 2248 (2004).
[CrossRef]

Yang, Z.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

J. P. Sabini, N. Finlayson, and G. I. Stegeman, Appl. Phys. Lett. 55, 1176 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. M. Jensen, IEEE J. Quantum Electron., QE-18, 1580 (1982).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. Wang, Q. Li, G. Liu, G. Jin, and X. Xu, IEEE Photon. Technol. Lett. 16, 2248 (2004).
[CrossRef]

J. Lightwave Technol. (1)

R. Tewari and K. Thyagarajan, J. Lightwave Technol. 4, 386 (1986).
[CrossRef]

Nat. Photon. (1)

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, Nat. Photon. 2, 737 (2008).
[CrossRef]

Opt. Commun. (2)

A. Salandrino, K. Makris, D. N. Christodoulides, Y. Lahini, Y. Silberberg, and R. Morandotti, Opt. Commun. 282, 4524 (2009).
[CrossRef]

V. Leutheuser, U. Langbein, and F. Lederer, Opt. Commun. 75, 251 (1990).
[CrossRef]

Opt. Lett. (2)

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic, 2008).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic illustration of a waveguide coupler with two cores forming a nonzero angle θ. (b) Relative output power (Pij) as a function of normalized input peak power (p=N2/Pc) in quasi-CW regime (TFWHM=0.88ps). Red dashed curve and black solid curve: light is launched from port 1, then collected at port 2 and vice versa, respectively. Blue dotted curve and green dashed–dotted curve: light is launched from port 1, then collected at port 4 and vice versa, respectively.

Fig. 2.
Fig. 2.

Results for sech-shaped input pulse with TFWHM=35.13fs. (a) Relative output power (Pij) as a function of normalized input peak power p=N2/Pc. (b) Intensity profiles for the input pulse and output pulses when p=0.45. The cyan solid curve represents the sech-shaped input pulse; all other curves represent various propagation directions as in Fig. 1(b).

Fig. 3.
Fig. 3.

Pulse propagation. (a) and (c) Light is launched from port 1, then collected at port 2 and vice versa, respectively. (b) and (d) Light is launched from port 1, then collected at port 4 and vice versa, respectively.

Equations (6)

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izA1+D(iT)A1+κ(z)A2+γ(1+iω0T)×A1(z,T)0R(t)|A1(z,Tt)|2dt=0,
izA2+D(iT)A2+κ(z)A1+γ(1+iω0T)×A2(z,T)0R(t)|A2(z,Tt)|2dt=0,
κ=k022β(n˜2n22)F1*(x,y)F2(x,y)dxdy,
κ(z)=πnco2ncl22ancoexp[(c0+c1d¯(z)+c2d¯2(z))],
iξu+z0LDD(iτ)u+vexp(α1z0ξα2z02ξ2)+(1+iω0T0τ)u0r(τ)|u(ξ,ττ)|2dτ=0,
iξv+z0LDD(iτ)v+uexp(α1z0ξα2z02ξ2)+(1+iω0T0τ)v0r(τ)|v(ξ,ττ)|2dτ=0,

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