Abstract

We propose the construction of electromagnetic (or electronic) switches and beam splitters by use of chaotic two-dimensional multiport waveguides. A prototype two-port waveguide is locally deformed to produce a ternary incomplete horseshoe characteristic of mixed phase space (chaotic regions surrounding islands of stability where motion is regular). Owing to tunneling to the phase-space stability islands, quasi-bound states (QBS) appear. Then we attach transversal ports to the waveguide in the deformation region in positions where the phase-space structure is only slightly perturbed. We show how QBS can be guided out of the waveguide through the attached transversal ports, giving rise to frequency-selective switches and beam splitters.

© 2005 Optical Society of America

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References

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  1. G. B. Akguc and L. E. Reichl, Phys. Rev. E 67, 046202 (2003).
    [CrossRef]
  2. J. A. Méndez-Bermúdez, G. A. Luna-Acosta, and F. M. Izrailev, Physica E (Amsterdam) 22, 881 (2004).
    [CrossRef]
  3. J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. E 66, 046207 (2002).
    [CrossRef]
  4. A. Bäcker, A. Manze, B. Huckestein, and R. Ketzmerick, Phys. Rev. E 66, 016211 (2002).
    [CrossRef]
  5. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
    [CrossRef]
  6. A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed. (Springer-Verlag, New York, 1992).
    [CrossRef]
  7. S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  8. H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge U. Press, Cambridge, 1999).
  9. K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 246 (1940).
  10. J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. B 67, 161104(R) (2003).
    [CrossRef]

2004 (1)

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, and F. M. Izrailev, Physica E (Amsterdam) 22, 881 (2004).
[CrossRef]

2003 (2)

G. B. Akguc and L. E. Reichl, Phys. Rev. E 67, 046202 (2003).
[CrossRef]

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. B 67, 161104(R) (2003).
[CrossRef]

2002 (2)

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. E 66, 046207 (2002).
[CrossRef]

A. Bäcker, A. Manze, B. Huckestein, and R. Ketzmerick, Phys. Rev. E 66, 016211 (2002).
[CrossRef]

1940 (1)

K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 246 (1940).

Akguc, G. B.

G. B. Akguc and L. E. Reichl, Phys. Rev. E 67, 046202 (2003).
[CrossRef]

Bäcker, A.

A. Bäcker, A. Manze, B. Huckestein, and R. Ketzmerick, Phys. Rev. E 66, 016211 (2002).
[CrossRef]

Datta, S.

S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

Guckenheimer, J.

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
[CrossRef]

Holmes, P.

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
[CrossRef]

Huckestein, B.

A. Bäcker, A. Manze, B. Huckestein, and R. Ketzmerick, Phys. Rev. E 66, 016211 (2002).
[CrossRef]

Husimi, K.

K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 246 (1940).

Izrailev, F. M.

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, and F. M. Izrailev, Physica E (Amsterdam) 22, 881 (2004).
[CrossRef]

Ketzmerick, R.

A. Bäcker, A. Manze, B. Huckestein, and R. Ketzmerick, Phys. Rev. E 66, 016211 (2002).
[CrossRef]

Lichtenberg, A. J.

A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed. (Springer-Verlag, New York, 1992).
[CrossRef]

Lieberman, M. A.

A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed. (Springer-Verlag, New York, 1992).
[CrossRef]

Luna-Acosta, G. A.

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, and F. M. Izrailev, Physica E (Amsterdam) 22, 881 (2004).
[CrossRef]

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. B 67, 161104(R) (2003).
[CrossRef]

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. E 66, 046207 (2002).
[CrossRef]

Manze, A.

A. Bäcker, A. Manze, B. Huckestein, and R. Ketzmerick, Phys. Rev. E 66, 016211 (2002).
[CrossRef]

Méndez-Bermúdez, J. A.

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, and F. M. Izrailev, Physica E (Amsterdam) 22, 881 (2004).
[CrossRef]

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. B 67, 161104(R) (2003).
[CrossRef]

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. E 66, 046207 (2002).
[CrossRef]

Pichugin, K. N.

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. B 67, 161104(R) (2003).
[CrossRef]

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. E 66, 046207 (2002).
[CrossRef]

Reichl, L. E.

G. B. Akguc and L. E. Reichl, Phys. Rev. E 67, 046202 (2003).
[CrossRef]

Šeba, P.

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. B 67, 161104(R) (2003).
[CrossRef]

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. E 66, 046207 (2002).
[CrossRef]

Stöckmann, H.-J.

H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge U. Press, Cambridge, 1999).

Phys. Rev. B (1)

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. B 67, 161104(R) (2003).
[CrossRef]

Phys. Rev. E (3)

G. B. Akguc and L. E. Reichl, Phys. Rev. E 67, 046202 (2003).
[CrossRef]

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, P. Šeba, and K. N. Pichugin, Phys. Rev. E 66, 046207 (2002).
[CrossRef]

A. Bäcker, A. Manze, B. Huckestein, and R. Ketzmerick, Phys. Rev. E 66, 016211 (2002).
[CrossRef]

Physica E (Amsterdam) (1)

J. A. Méndez-Bermúdez, G. A. Luna-Acosta, and F. M. Izrailev, Physica E (Amsterdam) 22, 881 (2004).
[CrossRef]

Proc. Phys. Math. Soc. Jpn. (1)

K. Husimi, Proc. Phys. Math. Soc. Jpn. 22, 246 (1940).

Other (4)

J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
[CrossRef]

A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, 2nd ed. (Springer-Verlag, New York, 1992).
[CrossRef]

S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge U. Press, Cambridge, 1995).
[CrossRef]

H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge U. Press, Cambridge, 1999).

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Figures (5)

Fig. 1
Fig. 1

(a) Geometry of the waveguide, (b) horseshoe, and (c) transient PM with surface of section at y = 0 ; ( d , a , L ) = ( 1.0 , 0.305 , 5.55 ) . The tendrils (see Ref. [5]) of the horseshoe in (b) are plotted up to level three. The thick curves in (b) are the limits of stability islands. The transient PMs in (c) were constructed for rays entering the cavity from the left-hand port.

Fig. 2
Fig. 2

Density plots for scattering wave functions calculated at resonance energies (light and dark, minimum and maximum, respectively). (a) E = 4008.8583 , (b) E = 4027.0597 . These QBS were constructed by averaging all the M = 20 open modes. E = 2 d 2 E W M 2 π 2 , where E W is the energy of the wave and M is the largest transversal mode m beyond which the longitudinal wave vector [ 2 E W ( m π d ) 2 ] 1 2 becomes complex.

Fig. 3
Fig. 3

Transient PMs (dots) and Husimi distributions (darker and lighter, minimum and maximum, respectively) with the surface of section at y = 0 constructed for rays and waves entering the waveguides of (a), (b) Fig. 1(a) and (c), (d) Fig. 4(c) from the left-hand port. In (a) and (b) the Husimi distributions for the QBS of Figs. 2(a), 2(b), respectively, are shown. In (c) and (d) the Husimi distributions for scattering states at G LU and G LD maxima, respectively, are plotted, both at G LR minima. (c) E = 3997.34 , (d) E = 4103.4096 .

Fig. 4
Fig. 4

Examples of (a)–(c) switch and (d)–(f) beam-splitter setups.

Fig. 5
Fig. 5

Transient PMs with the surface of section at y = 0 constructed for rays entering the beam-splitter setup of Fig. 4(c) from the left-hand port. d T = (a) 0.05, (b) 0.10, (c) 0.15, (d) 0.25.

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