Abstract

We study the scalar wave scattering off the spherical cavity resonator with two finite-length conical channels attached. We use the boundary wall method to explore the response of the system to changes in control parameters, such as the size of the structure and the angular width of the input and output channels, as well as their relative angular position. We found that the system is more sensitive to changes in the input channel, and a standing wave phase distribution occurs within the cavity for nontransmitting values of the incident wave number. We also saw that an optical vortex can travel unaffected through the system with aligned channels.

© 2014 Optical Society of America

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  1. M. V. Berry, “Regularity and chaos in classical mechanics, illustrated by three deformations of a circular ‘billiard’,” Eur. J. Phys. 2, 91–102 (1981).
    [CrossRef]
  2. R. W. Robinett, “Visualizing classical periodic orbits from the quantum energy spectrum via the Fourier transform: simple infinite well examples,” Am. J. Phys. 65, 1167 (1997).
    [CrossRef]
  3. R. L. Liboff and J. Greenberg, “The hexagon quantum billiard,” J. Stat. Phys. 105, 389–402 (2001).
    [CrossRef]
  4. H. Waalkens, J. Wiersig, and H. R. Dullin, “Elliptic quantum billiard,” Ann. Phys. 260, 50–90 (1997).
    [CrossRef]
  5. J. C. Gutiérrez-Vega, S. Chávez-Cerda, and R. M. Rodríguez-Dagnino, “Probability distributions in classical and quantum elliptic billiards,” Rev. Mex. Fis. 47, 480–488 (2001).
  6. M. A. Bandres and J. C. Gutiérrez-Vega, “Classical solutions for a free particle in a confocal elliptic billiard,” Am. J. Phys. 72, 810 (2004).
    [CrossRef]
  7. R. J. Noriega-Manez and J. C. Gutiérrez-Vega, “Mode structure and attenuation characteristics of hollow parabolic waveguides,” J. Opt. Soc. Am. B 24, 2273–2278 (2007).
    [CrossRef]
  8. T. Prosen, “Quantization of a generic chaotic 3D billiard with smooth boundary. I. Energy level statistics,” Phys. Lett. A 233, 323–331 (1997).
    [CrossRef]
  9. T. Prosen, “Quantization of generic chaotic 3D billiard with smooth boundary. II. Structure of high-lying eigenstates,” Phys. Lett. A 233, 332–342 (1997).
    [CrossRef]
  10. İ. M. Erhan and H. Taşeli, “A model for the computation of quantum billiards with arbitrary shapes,” J. Comput. Appl. Math. 194, 227–244 (2006).
    [CrossRef]
  11. T. Papenbrock, “Numerical study of a three-dimensional generalized stadium billiard,” Phys. Rev. E 61, 4626–4628 (2000).
    [CrossRef]
  12. R. L. Liboff, “Conical quantum billiard,” Lett. Math. Phys. 42, 389–391 (1997).
    [CrossRef]
  13. İ. M. Erhan, “Eigenvalue computation of prolate spheroidal quantum billiard,” Int. J. Math. Comput. Sci. 6, 108–113 (2010).
  14. H. Waalkens, J. Wiersig, and H. R. Dullin, “Triaxial ellipsoidal quantum billiards,” Ann. Phys. 276, 64–110 (1999).
    [CrossRef]
  15. H. Primack and U. Smilansky, “Quantization of the three-dimensional Sinai billiard,” Phys. Rev. Lett. 74, 4831–4834 (1995).
    [CrossRef]
  16. K. Na and L. E. Reichl, “Electron conductance and lifetimes in a ballistic electron waveguide,” J. Stat. Phys. 92, 519–542 (1998).
    [CrossRef]
  17. M. G. A. Crawford and P. W. Brouwer, “Density of proper delay times in chaotic and integrable quantum billiards,” Phys. Rev. E 65, 026221 (2002).
    [CrossRef]
  18. C. D. Schwieters, J. A. Alford, and J. B. Delos, “Semiclassical scattering in a circular semiconductor microstructure,” Phys. Rev. B 54, 10652–10668 (1996).
    [CrossRef]
  19. S. Ree and L. E. Reichl, “Aharonov–Bohm effect and resonances in the circular quantum billiard with two leads,” Phys. Rev. B 59, 8163–8169 (1999).
    [CrossRef]
  20. K. Fuchss, S. Ree, and L. E. Reichl, “Scattering properties of a cut-circle billiard waveguide with two conical leads,” Phys. Rev. E 63, 016214 (2000).
    [CrossRef]
  21. I. Březinová, L. Wirtz, S. Rotter, C. Stampfer, and J. Burgdörfer, “Transport through open quantum dots: making semiclassics quantitative,” Phys. Rev. B 81, 125308 (2010).
    [CrossRef]
  22. H. Ishio, “Quantum transport and classical dynamics in open billiards,” J. Stat. Phys. 83, 203–214 (1996).
    [CrossRef]
  23. C. P. Dettmann and O. Georgiou, “Transmission and reflection in the stadium billiard: time-dependent asymmetric transport,” Phys. Rev. E 83, 036212 (2011).
    [CrossRef]
  24. H. Garcia-Gracia and J. C. Gutiérrez-Vega, “Tunneling phenomena in the open elliptic quantum billiard,” Phys. Rev. E 86, 016210 (2012).
    [CrossRef]
  25. M. G. E. da Luz, A. S. Lupu-Sax, and E. J. Heller, “Quantum scattering from arbitrary boundaries,” Phys. Rev. E 56, 2496–2507 (1997).
    [CrossRef]
  26. F. M. Zanetti, E. Vicentini, and M. G. E. da Luz, “Eigenstates and scattering solutions for billiard problems: a boundary wall approach,” Ann. Phys. 323, 1644–1676 (2008).
    [CrossRef]
  27. F. M. Zanetti, M. L. Lyra, F. A. B. F. de Moura, and M. G. E. da Luz, “Resonant scattering states in 2D nanostructured waveguides: a boundary wall approach,” J. Phys. B At. Mol. Opt. Phys. 42, 025402 (2009).
    [CrossRef]

2012 (1)

H. Garcia-Gracia and J. C. Gutiérrez-Vega, “Tunneling phenomena in the open elliptic quantum billiard,” Phys. Rev. E 86, 016210 (2012).
[CrossRef]

2011 (1)

C. P. Dettmann and O. Georgiou, “Transmission and reflection in the stadium billiard: time-dependent asymmetric transport,” Phys. Rev. E 83, 036212 (2011).
[CrossRef]

2010 (2)

I. Březinová, L. Wirtz, S. Rotter, C. Stampfer, and J. Burgdörfer, “Transport through open quantum dots: making semiclassics quantitative,” Phys. Rev. B 81, 125308 (2010).
[CrossRef]

İ. M. Erhan, “Eigenvalue computation of prolate spheroidal quantum billiard,” Int. J. Math. Comput. Sci. 6, 108–113 (2010).

2009 (1)

F. M. Zanetti, M. L. Lyra, F. A. B. F. de Moura, and M. G. E. da Luz, “Resonant scattering states in 2D nanostructured waveguides: a boundary wall approach,” J. Phys. B At. Mol. Opt. Phys. 42, 025402 (2009).
[CrossRef]

2008 (1)

F. M. Zanetti, E. Vicentini, and M. G. E. da Luz, “Eigenstates and scattering solutions for billiard problems: a boundary wall approach,” Ann. Phys. 323, 1644–1676 (2008).
[CrossRef]

2007 (1)

2006 (1)

İ. M. Erhan and H. Taşeli, “A model for the computation of quantum billiards with arbitrary shapes,” J. Comput. Appl. Math. 194, 227–244 (2006).
[CrossRef]

2004 (1)

M. A. Bandres and J. C. Gutiérrez-Vega, “Classical solutions for a free particle in a confocal elliptic billiard,” Am. J. Phys. 72, 810 (2004).
[CrossRef]

2002 (1)

M. G. A. Crawford and P. W. Brouwer, “Density of proper delay times in chaotic and integrable quantum billiards,” Phys. Rev. E 65, 026221 (2002).
[CrossRef]

2001 (2)

J. C. Gutiérrez-Vega, S. Chávez-Cerda, and R. M. Rodríguez-Dagnino, “Probability distributions in classical and quantum elliptic billiards,” Rev. Mex. Fis. 47, 480–488 (2001).

R. L. Liboff and J. Greenberg, “The hexagon quantum billiard,” J. Stat. Phys. 105, 389–402 (2001).
[CrossRef]

2000 (2)

T. Papenbrock, “Numerical study of a three-dimensional generalized stadium billiard,” Phys. Rev. E 61, 4626–4628 (2000).
[CrossRef]

K. Fuchss, S. Ree, and L. E. Reichl, “Scattering properties of a cut-circle billiard waveguide with two conical leads,” Phys. Rev. E 63, 016214 (2000).
[CrossRef]

1999 (2)

S. Ree and L. E. Reichl, “Aharonov–Bohm effect and resonances in the circular quantum billiard with two leads,” Phys. Rev. B 59, 8163–8169 (1999).
[CrossRef]

H. Waalkens, J. Wiersig, and H. R. Dullin, “Triaxial ellipsoidal quantum billiards,” Ann. Phys. 276, 64–110 (1999).
[CrossRef]

1998 (1)

K. Na and L. E. Reichl, “Electron conductance and lifetimes in a ballistic electron waveguide,” J. Stat. Phys. 92, 519–542 (1998).
[CrossRef]

1997 (6)

M. G. E. da Luz, A. S. Lupu-Sax, and E. J. Heller, “Quantum scattering from arbitrary boundaries,” Phys. Rev. E 56, 2496–2507 (1997).
[CrossRef]

R. L. Liboff, “Conical quantum billiard,” Lett. Math. Phys. 42, 389–391 (1997).
[CrossRef]

T. Prosen, “Quantization of a generic chaotic 3D billiard with smooth boundary. I. Energy level statistics,” Phys. Lett. A 233, 323–331 (1997).
[CrossRef]

T. Prosen, “Quantization of generic chaotic 3D billiard with smooth boundary. II. Structure of high-lying eigenstates,” Phys. Lett. A 233, 332–342 (1997).
[CrossRef]

H. Waalkens, J. Wiersig, and H. R. Dullin, “Elliptic quantum billiard,” Ann. Phys. 260, 50–90 (1997).
[CrossRef]

R. W. Robinett, “Visualizing classical periodic orbits from the quantum energy spectrum via the Fourier transform: simple infinite well examples,” Am. J. Phys. 65, 1167 (1997).
[CrossRef]

1996 (2)

C. D. Schwieters, J. A. Alford, and J. B. Delos, “Semiclassical scattering in a circular semiconductor microstructure,” Phys. Rev. B 54, 10652–10668 (1996).
[CrossRef]

H. Ishio, “Quantum transport and classical dynamics in open billiards,” J. Stat. Phys. 83, 203–214 (1996).
[CrossRef]

1995 (1)

H. Primack and U. Smilansky, “Quantization of the three-dimensional Sinai billiard,” Phys. Rev. Lett. 74, 4831–4834 (1995).
[CrossRef]

1981 (1)

M. V. Berry, “Regularity and chaos in classical mechanics, illustrated by three deformations of a circular ‘billiard’,” Eur. J. Phys. 2, 91–102 (1981).
[CrossRef]

Alford, J. A.

C. D. Schwieters, J. A. Alford, and J. B. Delos, “Semiclassical scattering in a circular semiconductor microstructure,” Phys. Rev. B 54, 10652–10668 (1996).
[CrossRef]

Bandres, M. A.

M. A. Bandres and J. C. Gutiérrez-Vega, “Classical solutions for a free particle in a confocal elliptic billiard,” Am. J. Phys. 72, 810 (2004).
[CrossRef]

Berry, M. V.

M. V. Berry, “Regularity and chaos in classical mechanics, illustrated by three deformations of a circular ‘billiard’,” Eur. J. Phys. 2, 91–102 (1981).
[CrossRef]

Brezinová, I.

I. Březinová, L. Wirtz, S. Rotter, C. Stampfer, and J. Burgdörfer, “Transport through open quantum dots: making semiclassics quantitative,” Phys. Rev. B 81, 125308 (2010).
[CrossRef]

Brouwer, P. W.

M. G. A. Crawford and P. W. Brouwer, “Density of proper delay times in chaotic and integrable quantum billiards,” Phys. Rev. E 65, 026221 (2002).
[CrossRef]

Burgdörfer, J.

I. Březinová, L. Wirtz, S. Rotter, C. Stampfer, and J. Burgdörfer, “Transport through open quantum dots: making semiclassics quantitative,” Phys. Rev. B 81, 125308 (2010).
[CrossRef]

Chávez-Cerda, S.

J. C. Gutiérrez-Vega, S. Chávez-Cerda, and R. M. Rodríguez-Dagnino, “Probability distributions in classical and quantum elliptic billiards,” Rev. Mex. Fis. 47, 480–488 (2001).

Crawford, M. G. A.

M. G. A. Crawford and P. W. Brouwer, “Density of proper delay times in chaotic and integrable quantum billiards,” Phys. Rev. E 65, 026221 (2002).
[CrossRef]

da Luz, M. G. E.

F. M. Zanetti, M. L. Lyra, F. A. B. F. de Moura, and M. G. E. da Luz, “Resonant scattering states in 2D nanostructured waveguides: a boundary wall approach,” J. Phys. B At. Mol. Opt. Phys. 42, 025402 (2009).
[CrossRef]

F. M. Zanetti, E. Vicentini, and M. G. E. da Luz, “Eigenstates and scattering solutions for billiard problems: a boundary wall approach,” Ann. Phys. 323, 1644–1676 (2008).
[CrossRef]

M. G. E. da Luz, A. S. Lupu-Sax, and E. J. Heller, “Quantum scattering from arbitrary boundaries,” Phys. Rev. E 56, 2496–2507 (1997).
[CrossRef]

de Moura, F. A. B. F.

F. M. Zanetti, M. L. Lyra, F. A. B. F. de Moura, and M. G. E. da Luz, “Resonant scattering states in 2D nanostructured waveguides: a boundary wall approach,” J. Phys. B At. Mol. Opt. Phys. 42, 025402 (2009).
[CrossRef]

Delos, J. B.

C. D. Schwieters, J. A. Alford, and J. B. Delos, “Semiclassical scattering in a circular semiconductor microstructure,” Phys. Rev. B 54, 10652–10668 (1996).
[CrossRef]

Dettmann, C. P.

C. P. Dettmann and O. Georgiou, “Transmission and reflection in the stadium billiard: time-dependent asymmetric transport,” Phys. Rev. E 83, 036212 (2011).
[CrossRef]

Dullin, H. R.

H. Waalkens, J. Wiersig, and H. R. Dullin, “Triaxial ellipsoidal quantum billiards,” Ann. Phys. 276, 64–110 (1999).
[CrossRef]

H. Waalkens, J. Wiersig, and H. R. Dullin, “Elliptic quantum billiard,” Ann. Phys. 260, 50–90 (1997).
[CrossRef]

Erhan, I. M.

İ. M. Erhan, “Eigenvalue computation of prolate spheroidal quantum billiard,” Int. J. Math. Comput. Sci. 6, 108–113 (2010).

İ. M. Erhan and H. Taşeli, “A model for the computation of quantum billiards with arbitrary shapes,” J. Comput. Appl. Math. 194, 227–244 (2006).
[CrossRef]

Fuchss, K.

K. Fuchss, S. Ree, and L. E. Reichl, “Scattering properties of a cut-circle billiard waveguide with two conical leads,” Phys. Rev. E 63, 016214 (2000).
[CrossRef]

Garcia-Gracia, H.

H. Garcia-Gracia and J. C. Gutiérrez-Vega, “Tunneling phenomena in the open elliptic quantum billiard,” Phys. Rev. E 86, 016210 (2012).
[CrossRef]

Georgiou, O.

C. P. Dettmann and O. Georgiou, “Transmission and reflection in the stadium billiard: time-dependent asymmetric transport,” Phys. Rev. E 83, 036212 (2011).
[CrossRef]

Greenberg, J.

R. L. Liboff and J. Greenberg, “The hexagon quantum billiard,” J. Stat. Phys. 105, 389–402 (2001).
[CrossRef]

Gutiérrez-Vega, J. C.

H. Garcia-Gracia and J. C. Gutiérrez-Vega, “Tunneling phenomena in the open elliptic quantum billiard,” Phys. Rev. E 86, 016210 (2012).
[CrossRef]

R. J. Noriega-Manez and J. C. Gutiérrez-Vega, “Mode structure and attenuation characteristics of hollow parabolic waveguides,” J. Opt. Soc. Am. B 24, 2273–2278 (2007).
[CrossRef]

M. A. Bandres and J. C. Gutiérrez-Vega, “Classical solutions for a free particle in a confocal elliptic billiard,” Am. J. Phys. 72, 810 (2004).
[CrossRef]

J. C. Gutiérrez-Vega, S. Chávez-Cerda, and R. M. Rodríguez-Dagnino, “Probability distributions in classical and quantum elliptic billiards,” Rev. Mex. Fis. 47, 480–488 (2001).

Heller, E. J.

M. G. E. da Luz, A. S. Lupu-Sax, and E. J. Heller, “Quantum scattering from arbitrary boundaries,” Phys. Rev. E 56, 2496–2507 (1997).
[CrossRef]

Ishio, H.

H. Ishio, “Quantum transport and classical dynamics in open billiards,” J. Stat. Phys. 83, 203–214 (1996).
[CrossRef]

Liboff, R. L.

R. L. Liboff and J. Greenberg, “The hexagon quantum billiard,” J. Stat. Phys. 105, 389–402 (2001).
[CrossRef]

R. L. Liboff, “Conical quantum billiard,” Lett. Math. Phys. 42, 389–391 (1997).
[CrossRef]

Lupu-Sax, A. S.

M. G. E. da Luz, A. S. Lupu-Sax, and E. J. Heller, “Quantum scattering from arbitrary boundaries,” Phys. Rev. E 56, 2496–2507 (1997).
[CrossRef]

Lyra, M. L.

F. M. Zanetti, M. L. Lyra, F. A. B. F. de Moura, and M. G. E. da Luz, “Resonant scattering states in 2D nanostructured waveguides: a boundary wall approach,” J. Phys. B At. Mol. Opt. Phys. 42, 025402 (2009).
[CrossRef]

Na, K.

K. Na and L. E. Reichl, “Electron conductance and lifetimes in a ballistic electron waveguide,” J. Stat. Phys. 92, 519–542 (1998).
[CrossRef]

Noriega-Manez, R. J.

Papenbrock, T.

T. Papenbrock, “Numerical study of a three-dimensional generalized stadium billiard,” Phys. Rev. E 61, 4626–4628 (2000).
[CrossRef]

Primack, H.

H. Primack and U. Smilansky, “Quantization of the three-dimensional Sinai billiard,” Phys. Rev. Lett. 74, 4831–4834 (1995).
[CrossRef]

Prosen, T.

T. Prosen, “Quantization of a generic chaotic 3D billiard with smooth boundary. I. Energy level statistics,” Phys. Lett. A 233, 323–331 (1997).
[CrossRef]

T. Prosen, “Quantization of generic chaotic 3D billiard with smooth boundary. II. Structure of high-lying eigenstates,” Phys. Lett. A 233, 332–342 (1997).
[CrossRef]

Ree, S.

K. Fuchss, S. Ree, and L. E. Reichl, “Scattering properties of a cut-circle billiard waveguide with two conical leads,” Phys. Rev. E 63, 016214 (2000).
[CrossRef]

S. Ree and L. E. Reichl, “Aharonov–Bohm effect and resonances in the circular quantum billiard with two leads,” Phys. Rev. B 59, 8163–8169 (1999).
[CrossRef]

Reichl, L. E.

K. Fuchss, S. Ree, and L. E. Reichl, “Scattering properties of a cut-circle billiard waveguide with two conical leads,” Phys. Rev. E 63, 016214 (2000).
[CrossRef]

S. Ree and L. E. Reichl, “Aharonov–Bohm effect and resonances in the circular quantum billiard with two leads,” Phys. Rev. B 59, 8163–8169 (1999).
[CrossRef]

K. Na and L. E. Reichl, “Electron conductance and lifetimes in a ballistic electron waveguide,” J. Stat. Phys. 92, 519–542 (1998).
[CrossRef]

Robinett, R. W.

R. W. Robinett, “Visualizing classical periodic orbits from the quantum energy spectrum via the Fourier transform: simple infinite well examples,” Am. J. Phys. 65, 1167 (1997).
[CrossRef]

Rodríguez-Dagnino, R. M.

J. C. Gutiérrez-Vega, S. Chávez-Cerda, and R. M. Rodríguez-Dagnino, “Probability distributions in classical and quantum elliptic billiards,” Rev. Mex. Fis. 47, 480–488 (2001).

Rotter, S.

I. Březinová, L. Wirtz, S. Rotter, C. Stampfer, and J. Burgdörfer, “Transport through open quantum dots: making semiclassics quantitative,” Phys. Rev. B 81, 125308 (2010).
[CrossRef]

Schwieters, C. D.

C. D. Schwieters, J. A. Alford, and J. B. Delos, “Semiclassical scattering in a circular semiconductor microstructure,” Phys. Rev. B 54, 10652–10668 (1996).
[CrossRef]

Smilansky, U.

H. Primack and U. Smilansky, “Quantization of the three-dimensional Sinai billiard,” Phys. Rev. Lett. 74, 4831–4834 (1995).
[CrossRef]

Stampfer, C.

I. Březinová, L. Wirtz, S. Rotter, C. Stampfer, and J. Burgdörfer, “Transport through open quantum dots: making semiclassics quantitative,” Phys. Rev. B 81, 125308 (2010).
[CrossRef]

Taseli, H.

İ. M. Erhan and H. Taşeli, “A model for the computation of quantum billiards with arbitrary shapes,” J. Comput. Appl. Math. 194, 227–244 (2006).
[CrossRef]

Vicentini, E.

F. M. Zanetti, E. Vicentini, and M. G. E. da Luz, “Eigenstates and scattering solutions for billiard problems: a boundary wall approach,” Ann. Phys. 323, 1644–1676 (2008).
[CrossRef]

Waalkens, H.

H. Waalkens, J. Wiersig, and H. R. Dullin, “Triaxial ellipsoidal quantum billiards,” Ann. Phys. 276, 64–110 (1999).
[CrossRef]

H. Waalkens, J. Wiersig, and H. R. Dullin, “Elliptic quantum billiard,” Ann. Phys. 260, 50–90 (1997).
[CrossRef]

Wiersig, J.

H. Waalkens, J. Wiersig, and H. R. Dullin, “Triaxial ellipsoidal quantum billiards,” Ann. Phys. 276, 64–110 (1999).
[CrossRef]

H. Waalkens, J. Wiersig, and H. R. Dullin, “Elliptic quantum billiard,” Ann. Phys. 260, 50–90 (1997).
[CrossRef]

Wirtz, L.

I. Březinová, L. Wirtz, S. Rotter, C. Stampfer, and J. Burgdörfer, “Transport through open quantum dots: making semiclassics quantitative,” Phys. Rev. B 81, 125308 (2010).
[CrossRef]

Zanetti, F. M.

F. M. Zanetti, M. L. Lyra, F. A. B. F. de Moura, and M. G. E. da Luz, “Resonant scattering states in 2D nanostructured waveguides: a boundary wall approach,” J. Phys. B At. Mol. Opt. Phys. 42, 025402 (2009).
[CrossRef]

F. M. Zanetti, E. Vicentini, and M. G. E. da Luz, “Eigenstates and scattering solutions for billiard problems: a boundary wall approach,” Ann. Phys. 323, 1644–1676 (2008).
[CrossRef]

Am. J. Phys. (2)

R. W. Robinett, “Visualizing classical periodic orbits from the quantum energy spectrum via the Fourier transform: simple infinite well examples,” Am. J. Phys. 65, 1167 (1997).
[CrossRef]

M. A. Bandres and J. C. Gutiérrez-Vega, “Classical solutions for a free particle in a confocal elliptic billiard,” Am. J. Phys. 72, 810 (2004).
[CrossRef]

Ann. Phys. (3)

H. Waalkens, J. Wiersig, and H. R. Dullin, “Elliptic quantum billiard,” Ann. Phys. 260, 50–90 (1997).
[CrossRef]

F. M. Zanetti, E. Vicentini, and M. G. E. da Luz, “Eigenstates and scattering solutions for billiard problems: a boundary wall approach,” Ann. Phys. 323, 1644–1676 (2008).
[CrossRef]

H. Waalkens, J. Wiersig, and H. R. Dullin, “Triaxial ellipsoidal quantum billiards,” Ann. Phys. 276, 64–110 (1999).
[CrossRef]

Eur. J. Phys. (1)

M. V. Berry, “Regularity and chaos in classical mechanics, illustrated by three deformations of a circular ‘billiard’,” Eur. J. Phys. 2, 91–102 (1981).
[CrossRef]

Int. J. Math. Comput. Sci. (1)

İ. M. Erhan, “Eigenvalue computation of prolate spheroidal quantum billiard,” Int. J. Math. Comput. Sci. 6, 108–113 (2010).

J. Comput. Appl. Math. (1)

İ. M. Erhan and H. Taşeli, “A model for the computation of quantum billiards with arbitrary shapes,” J. Comput. Appl. Math. 194, 227–244 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B At. Mol. Opt. Phys. (1)

F. M. Zanetti, M. L. Lyra, F. A. B. F. de Moura, and M. G. E. da Luz, “Resonant scattering states in 2D nanostructured waveguides: a boundary wall approach,” J. Phys. B At. Mol. Opt. Phys. 42, 025402 (2009).
[CrossRef]

J. Stat. Phys. (3)

R. L. Liboff and J. Greenberg, “The hexagon quantum billiard,” J. Stat. Phys. 105, 389–402 (2001).
[CrossRef]

K. Na and L. E. Reichl, “Electron conductance and lifetimes in a ballistic electron waveguide,” J. Stat. Phys. 92, 519–542 (1998).
[CrossRef]

H. Ishio, “Quantum transport and classical dynamics in open billiards,” J. Stat. Phys. 83, 203–214 (1996).
[CrossRef]

Lett. Math. Phys. (1)

R. L. Liboff, “Conical quantum billiard,” Lett. Math. Phys. 42, 389–391 (1997).
[CrossRef]

Phys. Lett. A (2)

T. Prosen, “Quantization of a generic chaotic 3D billiard with smooth boundary. I. Energy level statistics,” Phys. Lett. A 233, 323–331 (1997).
[CrossRef]

T. Prosen, “Quantization of generic chaotic 3D billiard with smooth boundary. II. Structure of high-lying eigenstates,” Phys. Lett. A 233, 332–342 (1997).
[CrossRef]

Phys. Rev. B (3)

C. D. Schwieters, J. A. Alford, and J. B. Delos, “Semiclassical scattering in a circular semiconductor microstructure,” Phys. Rev. B 54, 10652–10668 (1996).
[CrossRef]

S. Ree and L. E. Reichl, “Aharonov–Bohm effect and resonances in the circular quantum billiard with two leads,” Phys. Rev. B 59, 8163–8169 (1999).
[CrossRef]

I. Březinová, L. Wirtz, S. Rotter, C. Stampfer, and J. Burgdörfer, “Transport through open quantum dots: making semiclassics quantitative,” Phys. Rev. B 81, 125308 (2010).
[CrossRef]

Phys. Rev. E (6)

K. Fuchss, S. Ree, and L. E. Reichl, “Scattering properties of a cut-circle billiard waveguide with two conical leads,” Phys. Rev. E 63, 016214 (2000).
[CrossRef]

M. G. A. Crawford and P. W. Brouwer, “Density of proper delay times in chaotic and integrable quantum billiards,” Phys. Rev. E 65, 026221 (2002).
[CrossRef]

C. P. Dettmann and O. Georgiou, “Transmission and reflection in the stadium billiard: time-dependent asymmetric transport,” Phys. Rev. E 83, 036212 (2011).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Transverse cut of the open spherical quantum billiard on the y=0 plane.

Fig. 2.
Fig. 2.

Input and output profiles as a function of the wave number k for spherical cavity radii r0={0.75,1.00,1.25}.

Fig. 3.
Fig. 3.

Output profile Iout as a function of the wave number k for different values of the angular half-width of the input channel Δθin. The black vertical dotted lines indicate the wave numbers kn,l for the first four eigenenergies En,l of the traditional spherical quantum billiard of radius r0=1.

Fig. 4.
Fig. 4.

Output profile Iout as a function of the wave number k for different values of the angular half-width of the output channel Δθout. The black vertical dotted lines indicate the wave numbers kn,l for the first four eigenenergies En,l of the traditional spherical quantum billiard of radius r0=1.

Fig. 5.
Fig. 5.

Input and output profile as a function of the wave number k for different values of the angular position of the output channel θout. The black vertical dotted lines indicate the wave numbers kn,l for the first four eigenenergies En,l of the traditional spherical quantum billiard of radius r0=1.

Fig. 6.
Fig. 6.

Transverse cut at y=0 of the amplitude |ψ(r)| and phase Φ(r) of the wave scattered by the open spherical resonator with θ2=π/2+2π/8 and an incident wave with wave number k=6.00 corresponding to the minimum indicated in Fig. 5(b).

Fig. 7.
Fig. 7.

Transverse cut at (a) y=0 and (b) z=0 of the amplitude |ψ(r)| and phase Φ(r) of the wave function generated by the open spherical quantum billiard with θ2=π and an incident beam with wave number k=17.00 carrying OAM L=1, formed by 20 plane waves incident along a cone of θ=π/5.

Fig. 8.
Fig. 8.

Transverse cut at (a) y=0 and (b) z=0 of the amplitude |ψ(r)| and phase Φ(r) of the wave function generated by the open spherical quantum billiard with θ2=π/2+π/3 and an incident beam with wave number k=17.00 carrying OAM L=1, formed by 20 plane waves incident along a cone of θ=π/5.

Equations (23)

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H0(r)ϕ(r)=Eϕ(r),
ϕ(r)=exp[ik(xcosφsinθ+ysinφsinθ+zcosθ)].
ϕ(r)=exp(ikz),
k0.75=5.858,k1.00=4.395,k1.25=3.513,
(k0.75k1.00)2=1.7766and(1.000.75)2=1.7778,(k1.00k1.25)2=1.5650and(1.251.00)2=1.5625.
k0.75=5.866,k1.00=4.399,k1.25=3.518.
(k0.75k1.00)2=1.7782and(1.000.75)2=1.7778,(k1.00k1.25)2=1.5636and(1.251.00)2=1.5625.
Δk1.002=10.9999andΔk1.252=7.0505
ϕ(r)=j=0N1exp(iLφj)×exp[ik(xcosφjsinθ+ysinφjsinθ+zcosθ)],
ψ(r)=ϕ(r)+drG0(r,r)V(r)ψ(r),
V(r)=γCdsδ(rr(s)),
ψ(r)=ϕ(r)+γCdsG0(r,r(s))ψ(r(s)),
ψ(r)=ϕ(r)+CdsG0(r,r(s))Tϕ(r(s)).
ψ(r(s))=ϕ(r(s))+γCdsG0(r(s),r(s))ψ(r(s)).
ψ˜=[I˜γG˜0]1ϕ˜,
T=γ[I˜γG˜0]1,
Tϕ(r(s))=dsT(r(s),r(s))ϕ(r(s)).
ψ˜=[I˜+G˜0T]ϕ˜.
ψ(r)=ϕ(r)+j=1NCjdsγG0(r,r(s))ψ(r(s)),ϕ(r)+j=1Nψ(r(sj))CjdsγG0(r,r(s)),
ψ(ri)=ϕ(ri)+j=1NγMijψ(ri),
Mij=CjdsG0(ri,r(s)).
γΨi=(TΦ)i=γj=1N[(IγM)1]ijΦj,
ψ(r)=ϕ(r)+j=1NG0(r,rj)Δj(TΦ)j,

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