Abstract

A set of analogous electron-light parameters for linearly polarized electromagnetic fields has been found for Schrödinger electrons. It is shown that the use of light polarization as an easily controllable parameter offers the possibility of a feasible practical implementation of optical structures with the same reflection coefficient as the corresponding ballistic structures for either Schrödinger or Dirac electrons.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Dragoman and M. Dragoman, Quantum-Classical Analogies (Springer, 2002).
  2. S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
    [CrossRef]
  3. G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
    [CrossRef]
  4. T. K. Gaylord, G. N. Henderson, and E. N. Glytsis, “Application of electromagnetics formalism to quantum mechanical electron wave propagation in semiconductors,” J. Opt. Soc. Am. B 10, 333–339 (1993).
    [CrossRef]
  5. G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Electromagnetic analogies to general Hamiltonian effective-mass electron wave propagation in semiconductors with spatially varying effective mass and potential energy,” Phys. Rev. B 45, 8404–8407 (1992).
    [CrossRef]
  6. S. Longhi, D. Janner, M. Marano, and P. Laporta, “Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: dynamic-mode stabilization and radiation-loss suppression,” Phys. Rev. E 67, 036601 (2003).
    [CrossRef]
  7. F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
    [CrossRef]
  8. D. Dragoman and M. Dragoman, “Optical analogue structures to mesoscopic devices,” Prog. Quantum Electron. 23, 131–188 (1999).
    [CrossRef]
  9. S. Longhi, “Optical realization of relativistic non-Hermitian quantum mechanics,” Phys. Rev. Lett. 105, 013903 (2010).
    [CrossRef]
  10. S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B 81, 075102 (2010).
    [CrossRef]
  11. S. Ghosh and M. Sharma, “Electron optics with magnetic vector potential barriers in graphene,” J. Phys. Condens. Matter 21, 292204 (2009).
    [CrossRef]
  12. T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80, 155103 (2009).
    [CrossRef]
  13. S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104, 043903 (2010).
    [CrossRef]
  14. P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constriction: subwavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803(2009).
    [CrossRef]
  15. O. Klemperer and M. E. Barnett, Electron Optics3rd ed.(Cambridge University, 2011).
  16. K. Sakoda, Optical Properties of Photonic Crystals2nd ed. (Springer, 2004).
  17. H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
    [CrossRef]
  18. D. Dragoman and M. Dragoman, “The modeling of the quantum tunneling time through heterostructures using optical layered media,” Opt. Commun. 133, 129–134 (1997).
    [CrossRef]
  19. D. Dragoman and M. Dragoman, “Optical modelling of quantum wire arrays,” IEEE J. Quantum Electron. 33, 375–381 (1997).
    [CrossRef]
  20. D. Dragoman and M. Dragoman, “Optical modelling of quantum dots,” Opt. Commun. 150, 331–338 (1998).
    [CrossRef]
  21. A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
    [CrossRef]
  22. C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
    [CrossRef]
  23. P. Balcou and L. Dutriaux, “Dual optical tunnelling times in frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
    [CrossRef]
  24. S. Longhi, P. Laponta, M. Belmonte, and E. Recami, “Measurement of superluminal optical tunneling times in double-barrier photonic band gaps,” Phys. Rev. E 65, 046610 (2002).
    [CrossRef]
  25. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics2nd ed. (Wiley, 2007).
  26. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
    [CrossRef]
  27. Y. H. Wu, T. Yu, and Z. X. Shen, “Two-dimensional carbon nanostructures: fundamental properties, synthesis, characterization, and potential applications,” J. Appl. Phys. 108, 071301 (2010).
    [CrossRef]
  28. A. V. Shytov, M. S. Rudner, and L. S. Levitov, “Klein backscattering and Fabry–Pérot interference in graphene heterojunctions,” Phys. Rev. Lett. 101, 156804 (2008).
    [CrossRef]
  29. V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252–1255 (2007).
    [CrossRef]
  30. J. Cserti, A. Pályi, and C. Péterfalvi, “Caustics due to a negative refractive index in circular graphene p-n junctions,” Phys. Rev. Lett. 99, 246801 (2007).
    [CrossRef]
  31. C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydŀo, “Quantum Goos–Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
    [CrossRef]
  32. M. Sharma and S. Ghosh, “Electron transport and Goos–Hänchen shift in graphene with electric and magnetic barriers: optical analogy and band structure,” J. Phys. Condens. Matter 23, 055501 (2011).
    [CrossRef]
  33. D. Dragoman, “Polarization optics analogy of quantum wavefunctions in graphene,” J. Opt. Soc. Am. B 27, 1325–1331(2010).
    [CrossRef]
  34. I. Mihalache and D. Dragoman, “Graphene analogy to electromagnetic field propagation,” J. Opt. Soc. Am. B 28, 1746–1751(2011).
    [CrossRef]

2011 (2)

M. Sharma and S. Ghosh, “Electron transport and Goos–Hänchen shift in graphene with electric and magnetic barriers: optical analogy and band structure,” J. Phys. Condens. Matter 23, 055501 (2011).
[CrossRef]

I. Mihalache and D. Dragoman, “Graphene analogy to electromagnetic field propagation,” J. Opt. Soc. Am. B 28, 1746–1751(2011).
[CrossRef]

2010 (5)

D. Dragoman, “Polarization optics analogy of quantum wavefunctions in graphene,” J. Opt. Soc. Am. B 27, 1325–1331(2010).
[CrossRef]

Y. H. Wu, T. Yu, and Z. X. Shen, “Two-dimensional carbon nanostructures: fundamental properties, synthesis, characterization, and potential applications,” J. Appl. Phys. 108, 071301 (2010).
[CrossRef]

S. Longhi, “Optical realization of relativistic non-Hermitian quantum mechanics,” Phys. Rev. Lett. 105, 013903 (2010).
[CrossRef]

S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B 81, 075102 (2010).
[CrossRef]

S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104, 043903 (2010).
[CrossRef]

2009 (7)

P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constriction: subwavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803(2009).
[CrossRef]

S. Ghosh and M. Sharma, “Electron optics with magnetic vector potential barriers in graphene,” J. Phys. Condens. Matter 21, 292204 (2009).
[CrossRef]

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80, 155103 (2009).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[CrossRef]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydŀo, “Quantum Goos–Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

2008 (1)

A. V. Shytov, M. S. Rudner, and L. S. Levitov, “Klein backscattering and Fabry–Pérot interference in graphene heterojunctions,” Phys. Rev. Lett. 101, 156804 (2008).
[CrossRef]

2007 (2)

V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252–1255 (2007).
[CrossRef]

J. Cserti, A. Pályi, and C. Péterfalvi, “Caustics due to a negative refractive index in circular graphene p-n junctions,” Phys. Rev. Lett. 99, 246801 (2007).
[CrossRef]

2005 (1)

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[CrossRef]

2003 (1)

S. Longhi, D. Janner, M. Marano, and P. Laporta, “Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: dynamic-mode stabilization and radiation-loss suppression,” Phys. Rev. E 67, 036601 (2003).
[CrossRef]

2002 (1)

S. Longhi, P. Laponta, M. Belmonte, and E. Recami, “Measurement of superluminal optical tunneling times in double-barrier photonic band gaps,” Phys. Rev. E 65, 046610 (2002).
[CrossRef]

1999 (1)

D. Dragoman and M. Dragoman, “Optical analogue structures to mesoscopic devices,” Prog. Quantum Electron. 23, 131–188 (1999).
[CrossRef]

1998 (1)

D. Dragoman and M. Dragoman, “Optical modelling of quantum dots,” Opt. Commun. 150, 331–338 (1998).
[CrossRef]

1997 (3)

P. Balcou and L. Dutriaux, “Dual optical tunnelling times in frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
[CrossRef]

D. Dragoman and M. Dragoman, “The modeling of the quantum tunneling time through heterostructures using optical layered media,” Opt. Commun. 133, 129–134 (1997).
[CrossRef]

D. Dragoman and M. Dragoman, “Optical modelling of quantum wire arrays,” IEEE J. Quantum Electron. 33, 375–381 (1997).
[CrossRef]

1994 (1)

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef]

1993 (2)

1992 (1)

G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Electromagnetic analogies to general Hamiltonian effective-mass electron wave propagation in semiconductors with spatially varying effective mass and potential energy,” Phys. Rev. B 45, 8404–8407 (1992).
[CrossRef]

1991 (1)

G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
[CrossRef]

Akhmerov, A. R.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydŀo, “Quantum Goos–Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

Altshuler, B. L.

V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252–1255 (2007).
[CrossRef]

Balcou, P.

P. Balcou and L. Dutriaux, “Dual optical tunnelling times in frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
[CrossRef]

Barnett, M. E.

O. Klemperer and M. E. Barnett, Electron Optics3rd ed.(Cambridge University, 2011).

Beenakker, C. W. J.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydŀo, “Quantum Goos–Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

Belmonte, M.

S. Longhi, P. Laponta, M. Belmonte, and E. Recami, “Measurement of superluminal optical tunneling times in double-barrier photonic band gaps,” Phys. Rev. E 65, 046610 (2002).
[CrossRef]

Cao, H.

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[CrossRef]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Cheianov, V. V.

V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252–1255 (2007).
[CrossRef]

Chiao, R. Y.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef]

Cserti, J.

J. Cserti, A. Pályi, and C. Péterfalvi, “Caustics due to a negative refractive index in circular graphene p-n junctions,” Phys. Rev. Lett. 99, 246801 (2007).
[CrossRef]

Darancet, P.

P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constriction: subwavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803(2009).
[CrossRef]

de Dood, M. J. A.

S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104, 043903 (2010).
[CrossRef]

Dragoman, D.

I. Mihalache and D. Dragoman, “Graphene analogy to electromagnetic field propagation,” J. Opt. Soc. Am. B 28, 1746–1751(2011).
[CrossRef]

D. Dragoman, “Polarization optics analogy of quantum wavefunctions in graphene,” J. Opt. Soc. Am. B 27, 1325–1331(2010).
[CrossRef]

D. Dragoman and M. Dragoman, “Optical analogue structures to mesoscopic devices,” Prog. Quantum Electron. 23, 131–188 (1999).
[CrossRef]

D. Dragoman and M. Dragoman, “Optical modelling of quantum dots,” Opt. Commun. 150, 331–338 (1998).
[CrossRef]

D. Dragoman and M. Dragoman, “The modeling of the quantum tunneling time through heterostructures using optical layered media,” Opt. Commun. 133, 129–134 (1997).
[CrossRef]

D. Dragoman and M. Dragoman, “Optical modelling of quantum wire arrays,” IEEE J. Quantum Electron. 33, 375–381 (1997).
[CrossRef]

D. Dragoman and M. Dragoman, Quantum-Classical Analogies (Springer, 2002).

Dragoman, M.

D. Dragoman and M. Dragoman, “Optical analogue structures to mesoscopic devices,” Prog. Quantum Electron. 23, 131–188 (1999).
[CrossRef]

D. Dragoman and M. Dragoman, “Optical modelling of quantum dots,” Opt. Commun. 150, 331–338 (1998).
[CrossRef]

D. Dragoman and M. Dragoman, “The modeling of the quantum tunneling time through heterostructures using optical layered media,” Opt. Commun. 133, 129–134 (1997).
[CrossRef]

D. Dragoman and M. Dragoman, “Optical modelling of quantum wire arrays,” IEEE J. Quantum Electron. 33, 375–381 (1997).
[CrossRef]

D. Dragoman and M. Dragoman, Quantum-Classical Analogies (Springer, 2002).

Dreisow, F.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef]

Dutriaux, L.

P. Balcou and L. Dutriaux, “Dual optical tunnelling times in frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
[CrossRef]

Fal’ko, V.

V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252–1255 (2007).
[CrossRef]

Gaylord, T. K.

T. K. Gaylord, G. N. Henderson, and E. N. Glytsis, “Application of electromagnetics formalism to quantum mechanical electron wave propagation in semiconductors,” J. Opt. Soc. Am. B 10, 333–339 (1993).
[CrossRef]

G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Electromagnetic analogies to general Hamiltonian effective-mass electron wave propagation in semiconductors with spatially varying effective mass and potential energy,” Phys. Rev. B 45, 8404–8407 (1992).
[CrossRef]

G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
[CrossRef]

Geim, A. K.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Ghosh, S.

M. Sharma and S. Ghosh, “Electron transport and Goos–Hänchen shift in graphene with electric and magnetic barriers: optical analogy and band structure,” J. Phys. Condens. Matter 23, 055501 (2011).
[CrossRef]

S. Ghosh and M. Sharma, “Electron optics with magnetic vector potential barriers in graphene,” J. Phys. Condens. Matter 21, 292204 (2009).
[CrossRef]

Glytsis, E. N.

T. K. Gaylord, G. N. Henderson, and E. N. Glytsis, “Application of electromagnetics formalism to quantum mechanical electron wave propagation in semiconductors,” J. Opt. Soc. Am. B 10, 333–339 (1993).
[CrossRef]

G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Electromagnetic analogies to general Hamiltonian effective-mass electron wave propagation in semiconductors with spatially varying effective mass and potential energy,” Phys. Rev. B 45, 8404–8407 (1992).
[CrossRef]

G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
[CrossRef]

Guinea, F.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Heinrich, M.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef]

Henderson, G. N.

T. K. Gaylord, G. N. Henderson, and E. N. Glytsis, “Application of electromagnetics formalism to quantum mechanical electron wave propagation in semiconductors,” J. Opt. Soc. Am. B 10, 333–339 (1993).
[CrossRef]

G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Electromagnetic analogies to general Hamiltonian effective-mass electron wave propagation in semiconductors with spatially varying effective mass and potential energy,” Phys. Rev. B 45, 8404–8407 (1992).
[CrossRef]

G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
[CrossRef]

Janner, D.

S. Longhi, D. Janner, M. Marano, and P. Laporta, “Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: dynamic-mode stabilization and radiation-loss suppression,” Phys. Rev. E 67, 036601 (2003).
[CrossRef]

Klemperer, O.

O. Klemperer and M. E. Barnett, Electron Optics3rd ed.(Cambridge University, 2011).

Krausz, F.

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef]

Kwiat, P. G.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef]

Laponta, P.

S. Longhi, P. Laponta, M. Belmonte, and E. Recami, “Measurement of superluminal optical tunneling times in double-barrier photonic band gaps,” Phys. Rev. E 65, 046610 (2002).
[CrossRef]

Laporta, P.

S. Longhi, D. Janner, M. Marano, and P. Laporta, “Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: dynamic-mode stabilization and radiation-loss suppression,” Phys. Rev. E 67, 036601 (2003).
[CrossRef]

Levitov, L. S.

A. V. Shytov, M. S. Rudner, and L. S. Levitov, “Klein backscattering and Fabry–Pérot interference in graphene heterojunctions,” Phys. Rev. Lett. 101, 156804 (2008).
[CrossRef]

Longhi, S.

S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B 81, 075102 (2010).
[CrossRef]

S. Longhi, “Optical realization of relativistic non-Hermitian quantum mechanics,” Phys. Rev. Lett. 105, 013903 (2010).
[CrossRef]

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef]

S. Longhi, D. Janner, M. Marano, and P. Laporta, “Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: dynamic-mode stabilization and radiation-loss suppression,” Phys. Rev. E 67, 036601 (2003).
[CrossRef]

S. Longhi, P. Laponta, M. Belmonte, and E. Recami, “Measurement of superluminal optical tunneling times in double-barrier photonic band gaps,” Phys. Rev. E 65, 046610 (2002).
[CrossRef]

Marano, M.

S. Longhi, D. Janner, M. Marano, and P. Laporta, “Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: dynamic-mode stabilization and radiation-loss suppression,” Phys. Rev. E 67, 036601 (2003).
[CrossRef]

Mayou, D.

P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constriction: subwavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803(2009).
[CrossRef]

Mihalache, I.

Nolte, S.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef]

Novoselov, K. S.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Ochiai, T.

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80, 155103 (2009).
[CrossRef]

Olevano, V.

P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constriction: subwavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803(2009).
[CrossRef]

Onoda, M.

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80, 155103 (2009).
[CrossRef]

Pályi, A.

J. Cserti, A. Pályi, and C. Péterfalvi, “Caustics due to a negative refractive index in circular graphene p-n junctions,” Phys. Rev. Lett. 99, 246801 (2007).
[CrossRef]

Peres, N. M. R.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Pertsch, T.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef]

Péterfalvi, C.

J. Cserti, A. Pályi, and C. Péterfalvi, “Caustics due to a negative refractive index in circular graphene p-n junctions,” Phys. Rev. Lett. 99, 246801 (2007).
[CrossRef]

Recami, E.

S. Longhi, P. Laponta, M. Belmonte, and E. Recami, “Measurement of superluminal optical tunneling times in double-barrier photonic band gaps,” Phys. Rev. E 65, 046610 (2002).
[CrossRef]

Rudner, M. S.

A. V. Shytov, M. S. Rudner, and L. S. Levitov, “Klein backscattering and Fabry–Pérot interference in graphene heterojunctions,” Phys. Rev. Lett. 101, 156804 (2008).
[CrossRef]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals2nd ed. (Springer, 2004).

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics2nd ed. (Wiley, 2007).

Sepkhanov, R. A.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydŀo, “Quantum Goos–Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

Sharma, M.

M. Sharma and S. Ghosh, “Electron transport and Goos–Hänchen shift in graphene with electric and magnetic barriers: optical analogy and band structure,” J. Phys. Condens. Matter 23, 055501 (2011).
[CrossRef]

S. Ghosh and M. Sharma, “Electron optics with magnetic vector potential barriers in graphene,” J. Phys. Condens. Matter 21, 292204 (2009).
[CrossRef]

Shen, Z. X.

Y. H. Wu, T. Yu, and Z. X. Shen, “Two-dimensional carbon nanostructures: fundamental properties, synthesis, characterization, and potential applications,” J. Appl. Phys. 108, 071301 (2010).
[CrossRef]

Shytov, A. V.

A. V. Shytov, M. S. Rudner, and L. S. Levitov, “Klein backscattering and Fabry–Pérot interference in graphene heterojunctions,” Phys. Rev. Lett. 101, 156804 (2008).
[CrossRef]

Spielmann, C.

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef]

Steinberg, A. M.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef]

Stingl, A.

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef]

Szameit, A.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef]

Szipöcs, R.

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics2nd ed. (Wiley, 2007).

Tünnermann, A.

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef]

Tworzyd?o, J.

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydŀo, “Quantum Goos–Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

Wu, Y. H.

Y. H. Wu, T. Yu, and Z. X. Shen, “Two-dimensional carbon nanostructures: fundamental properties, synthesis, characterization, and potential applications,” J. Appl. Phys. 108, 071301 (2010).
[CrossRef]

Yu, T.

Y. H. Wu, T. Yu, and Z. X. Shen, “Two-dimensional carbon nanostructures: fundamental properties, synthesis, characterization, and potential applications,” J. Appl. Phys. 108, 071301 (2010).
[CrossRef]

Zandbergen, S. R.

S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104, 043903 (2010).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. Dragoman and M. Dragoman, “Optical modelling of quantum wire arrays,” IEEE J. Quantum Electron. 33, 375–381 (1997).
[CrossRef]

J. Appl. Phys. (1)

Y. H. Wu, T. Yu, and Z. X. Shen, “Two-dimensional carbon nanostructures: fundamental properties, synthesis, characterization, and potential applications,” J. Appl. Phys. 108, 071301 (2010).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. A (1)

H. Cao, “Review on latest developments in random lasers with coherent feedback,” J. Phys. A 38, 10497–10535 (2005).
[CrossRef]

J. Phys. Condens. Matter (2)

S. Ghosh and M. Sharma, “Electron optics with magnetic vector potential barriers in graphene,” J. Phys. Condens. Matter 21, 292204 (2009).
[CrossRef]

M. Sharma and S. Ghosh, “Electron transport and Goos–Hänchen shift in graphene with electric and magnetic barriers: optical analogy and band structure,” J. Phys. Condens. Matter 23, 055501 (2011).
[CrossRef]

Laser Photon. Rev. (1)

S. Longhi, “Quantum-optical analogies using photonic structures,” Laser Photon. Rev. 3, 243–261 (2009).
[CrossRef]

Opt. Commun. (2)

D. Dragoman and M. Dragoman, “The modeling of the quantum tunneling time through heterostructures using optical layered media,” Opt. Commun. 133, 129–134 (1997).
[CrossRef]

D. Dragoman and M. Dragoman, “Optical modelling of quantum dots,” Opt. Commun. 150, 331–338 (1998).
[CrossRef]

Phys. Rev. B (3)

S. Longhi, “Klein tunneling in binary photonic superlattices,” Phys. Rev. B 81, 075102 (2010).
[CrossRef]

T. Ochiai and M. Onoda, “Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states,” Phys. Rev. B 80, 155103 (2009).
[CrossRef]

G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Electromagnetic analogies to general Hamiltonian effective-mass electron wave propagation in semiconductors with spatially varying effective mass and potential energy,” Phys. Rev. B 45, 8404–8407 (1992).
[CrossRef]

Phys. Rev. E (2)

S. Longhi, D. Janner, M. Marano, and P. Laporta, “Quantum-mechanical analogy of beam propagation in waveguides with a bent axis: dynamic-mode stabilization and radiation-loss suppression,” Phys. Rev. E 67, 036601 (2003).
[CrossRef]

S. Longhi, P. Laponta, M. Belmonte, and E. Recami, “Measurement of superluminal optical tunneling times in double-barrier photonic band gaps,” Phys. Rev. E 65, 046610 (2002).
[CrossRef]

Phys. Rev. Lett. (10)

A. V. Shytov, M. S. Rudner, and L. S. Levitov, “Klein backscattering and Fabry–Pérot interference in graphene heterojunctions,” Phys. Rev. Lett. 101, 156804 (2008).
[CrossRef]

J. Cserti, A. Pályi, and C. Péterfalvi, “Caustics due to a negative refractive index in circular graphene p-n junctions,” Phys. Rev. Lett. 99, 246801 (2007).
[CrossRef]

C. W. J. Beenakker, R. A. Sepkhanov, A. R. Akhmerov, and J. Tworzydŀo, “Quantum Goos–Hänchen effect in graphene,” Phys. Rev. Lett. 102, 146804 (2009).
[CrossRef]

F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, and S. Longhi, “Bloch–Zener oscillations in binary superlattices,” Phys. Rev. Lett. 102, 076802 (2009).
[CrossRef]

S. R. Zandbergen and M. J. A. de Dood, “Experimental observation of strong edge effects on the pseudodiffusive transport of light in photonic graphene,” Phys. Rev. Lett. 104, 043903 (2010).
[CrossRef]

P. Darancet, V. Olevano, and D. Mayou, “Coherent electronic transport through graphene constriction: subwavelength regime and optical analogy,” Phys. Rev. Lett. 102, 136803(2009).
[CrossRef]

S. Longhi, “Optical realization of relativistic non-Hermitian quantum mechanics,” Phys. Rev. Lett. 105, 013903 (2010).
[CrossRef]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Measurement of the single-photon tunneling time,” Phys. Rev. Lett. 71, 708–711 (1993).
[CrossRef]

C. Spielmann, R. Szipöcs, A. Stingl, and F. Krausz, “Tunneling of optical pulses through photonic band gaps,” Phys. Rev. Lett. 73, 2308–2311 (1994).
[CrossRef]

P. Balcou and L. Dutriaux, “Dual optical tunnelling times in frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
[CrossRef]

Proc. IEEE (1)

G. N. Henderson, T. K. Gaylord, and E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
[CrossRef]

Prog. Quantum Electron. (1)

D. Dragoman and M. Dragoman, “Optical analogue structures to mesoscopic devices,” Prog. Quantum Electron. 23, 131–188 (1999).
[CrossRef]

Rev. Mod. Phys. (1)

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Science (1)

V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, “The focusing of electron flow and a Veselago lens in graphene p-n junctions,” Science 315, 1252–1255 (2007).
[CrossRef]

Other (4)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics2nd ed. (Wiley, 2007).

D. Dragoman and M. Dragoman, Quantum-Classical Analogies (Springer, 2002).

O. Klemperer and M. E. Barnett, Electron Optics3rd ed.(Cambridge University, 2011).

K. Sakoda, Optical Properties of Photonic Crystals2nd ed. (Springer, 2004).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

(a) Schematic representation of refraction at a planar interface between two media. (b) Directions of the E and H fields for the TE and TM polarizations.

Fig. 2.
Fig. 2.

(a) Energy and incidence angle dependence of R for Schrödinger electrons at an interface between media with V1=0, V2=0.2eV, m1=0.08m0, and m2=0.15m0. (b) Dependence of R for light on α and θin at an interface between two nonmagnetic media with n1=1, n2=2.5. In both cases, higher R values correspond to darker regions.

Fig. 3.
Fig. 3.

Energy dependence of α for electron-optical structures with the same reflection coefficient R as in Fig. 2, for electrons/light beams incident at angles of 40°/50° (solid line), 15°/50° (dotted line), and 60°/77° (dashed line).

Fig. 4.
Fig. 4.

Dependence of R on energy and incidence angle for Dirac electrons at an interface between media when V1=0 and V2=0.2eV.

Fig. 5.
Fig. 5.

Correlation between E and α which leads to the same R for the electron-optical structures in Figs. 4 and 2(b), respectively, for electrons/light incident at angles 15°/75° (solid line), 15°/70° (dotted line), and 25°/75° (dashed line).

Fig. 6.
Fig. 6.

Schematic representation of refraction of electrons or light waves in a structure consisting of N regions with different but constant parameters.

Tables (1)

Tables Icon

Table 1. Set of Analogous Parameters between Ballistic Electrons and Electromagnetic Fields with Different Polarizations

Equations (16)

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

22m2Ψ+(VE)Ψ=0,
2F+k2F=0.
k1sinθin=k1sinθr=k2sinθt,γ1sinθin=γ1sinθr=γ2sinθt.
{Ψin+Ψr=Ψtγ1m1cosθin(ΨinΨr)=γ2m2cosθtΨt,
{Ain+Ar=Atk1μ1cosθin(AinAr)=k2μ2cosθtAt.
{k1μ1(Ain+Ar)=k2μ2Atcosθin(AinAr)=cosθtAt.
{(A,in+A,r)z^(A,inA,r)y^cosθin=A,tz^A,ty^cosθtεr,1/μr,1[(A,in+A,r)z^+(A,inA,r)y^cosθin]=εr,2/μr,2[A,tz^+A,ty^cosθt].
(A+βεr/μrA)z^+(A+βεr/μrA)y^cosθΨ+δ(γ/m)Ψcosθ.
R=(cosα)2RTE+(sinα)2RTM=(cosα)2|A,r/A,in|2+(sinα)2|A,r/A,in|2,
RTE=|(k1/μ1)cosθin(k2/μ2)cosθt(k1/μ1)cosθin+(k2/μ2)cosθt|2,RTM=|(k2/μ2)cosθin(k1/μ1)cosθt(k2/μ2)cosθin+(k1/μ1)cosθt|2,
R=|(γ1/m1)cosθin(γ2/m2)cosθt(γ1/m1)cosθin+(γ2/m2)cosθt|2.
vF(0γxiγyγx+iγy0)(ψ1ψ2)=(EV)(ψ1ψ2),
(ψ1ψ2)=exp(iγysinθ)(Aexp(iγxcosθ)+Bexp(iγxcosθ)s[Aexp(iγxcosθ+iθ)Bexp(iγxcosθiθ)]),
(EV1)sinθ1=(EV2)sinθ2,
R=|s1exp(iθ1)s2exp(iθ2)s1exp(iθ1)+s2exp(iθ2)|2.
kjcosθjLopt,j=γjcosθjLel,j.

Metrics