Abstract

We investigate the dispersion mechanism of surface magnetoplasmons for periodic layered structures in the Voigt configuration. An analytical dispersion relation that retains a similar form with ordinary surface plasmons is obtained. The splitting of surface plasma frequency is accompanied with unequal field strengths of surface modes at the two interfaces and is characterized by a simple dynamic model that recasts the role of magnetic force on to the effective mass. The underlying mechanism is illustrated with the transverse currents induced by the cyclotron motion of electrons, which appears as the typical feature of the dynamic Hall effect. In particular, the acoustical and optical branches exhibit an anticrossing scheme for small filling fractions, due to the like symmetry of modes in the two branches. As the parallel wave number changes, the two interaction branches experience a transition of mode pattern from symmetry to antisymmetry, or vice versa.

© 2009 Optical Society of America

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  2. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
    [CrossRef]
  3. J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455-1458 (1972).
    [CrossRef]
  4. K. W. Chiu and J. J. Quinn, “Magnetoplasma surface waves in metals,” Phys. Rev. B 5, 4707-4709 (1972).
    [CrossRef]
  5. R. E. De Wames and W. F. Hall, “Magnetic field effect on plasma-wave dispersion in a dielectric layer,” Phys. Rev. Lett. 29, 172-175 (1972).
    [CrossRef]
  6. J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
    [CrossRef]
  7. B. Sepúlveda, L. Lechuga, and G. Armelles, “Magnetooptic effects in surface-plasmon-polaritons slab waveguides,” J. Lightwave Technol. 24, 945-955 (2006).
    [CrossRef]
  8. Y. C. Lan, Y. C. Chang, and P. H. Lee, “Manipulation of tunneling frequencies using magnetic fields for resonant tunneling effects of surface plasmons,” Appl. Phys. Lett. 90, 171114 (2007).
    [CrossRef]
  9. D. C. Glattli, E. Y. Andrei, G. Deville, J. Poitrenaud, and F. I. B. Williams, “Dynamical Hall effect in a two-dimensional classical plasma,” Phys. Rev. Lett. 54, 1710-1713(1985).
    [CrossRef] [PubMed]
  10. M. Kushwaha, “Plasmons and magnetoplasmons in semiconductor heterostructures,” Surf. Sci. Rep. 41, 1-416(2001).
    [CrossRef]
  11. R. F. Wallis, R. Szenics, J. J. Quinn, and G. F. Giuliani, “Theory of surface magnetoplasmon polaritons in truncated superlattices,” Phys. Rev. B 36, 1218-1224 (1987).
    [CrossRef]
  12. P. Halevi and C. Guerra-Vela, “Magnetoplasma polaritons at the interface between a semiconductor and a metallic screen,” Phys. Rev. B 18, 5248-5253 (1978).
    [CrossRef]
  13. P. Halevi, “Magnetoplasma polaritons at the interface between a semiconductor and a metallic screen. II. The Faraday geometry,” Phys. Rev. B 23, 2635-2639 (1981).
    [CrossRef]
  14. M. S. Kushwaha, “Effect of an applied magnetic field on interface excitations in finite layered structures,” Phys. Rev. B 35, 3871-3878 (1987).
    [CrossRef]
  15. M. S. Kushwaha and P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration,” Phys. Rev. B 36, 5960-5967(1987).
    [CrossRef]
  16. M. S. Kushwaha, “Collective excitations of magnetoplasma in semi-infinite n-i-p-i superlattices,” Phys. Rev. B 48, 15445-15448 (1993).
    [CrossRef]
  17. C. C. Chang, R. L. Chern, C. C. Chang, and R. R. Hwang, “Interfacial operator approach to computing modes of surface plasmon polaritons for periodic structures,” Phys. Rev. B 72, 205112 (2005).
    [CrossRef]
  18. F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (Plenum, 1984).
  19. J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2000).
  20. L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Pergamon, 1977).

2007 (2)

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Y. C. Lan, Y. C. Chang, and P. H. Lee, “Manipulation of tunneling frequencies using magnetic fields for resonant tunneling effects of surface plasmons,” Appl. Phys. Lett. 90, 171114 (2007).
[CrossRef]

2006 (1)

2005 (1)

C. C. Chang, R. L. Chern, C. C. Chang, and R. R. Hwang, “Interfacial operator approach to computing modes of surface plasmon polaritons for periodic structures,” Phys. Rev. B 72, 205112 (2005).
[CrossRef]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2001 (1)

M. Kushwaha, “Plasmons and magnetoplasmons in semiconductor heterostructures,” Surf. Sci. Rep. 41, 1-416(2001).
[CrossRef]

1993 (1)

M. S. Kushwaha, “Collective excitations of magnetoplasma in semi-infinite n-i-p-i superlattices,” Phys. Rev. B 48, 15445-15448 (1993).
[CrossRef]

1987 (3)

R. F. Wallis, R. Szenics, J. J. Quinn, and G. F. Giuliani, “Theory of surface magnetoplasmon polaritons in truncated superlattices,” Phys. Rev. B 36, 1218-1224 (1987).
[CrossRef]

M. S. Kushwaha, “Effect of an applied magnetic field on interface excitations in finite layered structures,” Phys. Rev. B 35, 3871-3878 (1987).
[CrossRef]

M. S. Kushwaha and P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration,” Phys. Rev. B 36, 5960-5967(1987).
[CrossRef]

1985 (1)

D. C. Glattli, E. Y. Andrei, G. Deville, J. Poitrenaud, and F. I. B. Williams, “Dynamical Hall effect in a two-dimensional classical plasma,” Phys. Rev. Lett. 54, 1710-1713(1985).
[CrossRef] [PubMed]

1981 (1)

P. Halevi, “Magnetoplasma polaritons at the interface between a semiconductor and a metallic screen. II. The Faraday geometry,” Phys. Rev. B 23, 2635-2639 (1981).
[CrossRef]

1978 (1)

P. Halevi and C. Guerra-Vela, “Magnetoplasma polaritons at the interface between a semiconductor and a metallic screen,” Phys. Rev. B 18, 5248-5253 (1978).
[CrossRef]

1972 (3)

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455-1458 (1972).
[CrossRef]

K. W. Chiu and J. J. Quinn, “Magnetoplasma surface waves in metals,” Phys. Rev. B 5, 4707-4709 (1972).
[CrossRef]

R. E. De Wames and W. F. Hall, “Magnetic field effect on plasma-wave dispersion in a dielectric layer,” Phys. Rev. Lett. 29, 172-175 (1972).
[CrossRef]

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Andrei, E. Y.

D. C. Glattli, E. Y. Andrei, G. Deville, J. Poitrenaud, and F. I. B. Williams, “Dynamical Hall effect in a two-dimensional classical plasma,” Phys. Rev. Lett. 54, 1710-1713(1985).
[CrossRef] [PubMed]

Armelles, G.

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

B. Sepúlveda, L. Lechuga, and G. Armelles, “Magnetooptic effects in surface-plasmon-polaritons slab waveguides,” J. Lightwave Technol. 24, 945-955 (2006).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Brion, J. J.

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455-1458 (1972).
[CrossRef]

Burstein, E.

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455-1458 (1972).
[CrossRef]

Cebollada, A.

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Chang, C. C.

C. C. Chang, R. L. Chern, C. C. Chang, and R. R. Hwang, “Interfacial operator approach to computing modes of surface plasmon polaritons for periodic structures,” Phys. Rev. B 72, 205112 (2005).
[CrossRef]

C. C. Chang, R. L. Chern, C. C. Chang, and R. R. Hwang, “Interfacial operator approach to computing modes of surface plasmon polaritons for periodic structures,” Phys. Rev. B 72, 205112 (2005).
[CrossRef]

Chang, Y. C.

Y. C. Lan, Y. C. Chang, and P. H. Lee, “Manipulation of tunneling frequencies using magnetic fields for resonant tunneling effects of surface plasmons,” Appl. Phys. Lett. 90, 171114 (2007).
[CrossRef]

Chen, F. F.

F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (Plenum, 1984).

Chern, R. L.

C. C. Chang, R. L. Chern, C. C. Chang, and R. R. Hwang, “Interfacial operator approach to computing modes of surface plasmon polaritons for periodic structures,” Phys. Rev. B 72, 205112 (2005).
[CrossRef]

Chiu, K. W.

K. W. Chiu and J. J. Quinn, “Magnetoplasma surface waves in metals,” Phys. Rev. B 5, 4707-4709 (1972).
[CrossRef]

Clarke, R.

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Clavero, C.

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

De Wames, R. E.

R. E. De Wames and W. F. Hall, “Magnetic field effect on plasma-wave dispersion in a dielectric layer,” Phys. Rev. Lett. 29, 172-175 (1972).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Deville, G.

D. C. Glattli, E. Y. Andrei, G. Deville, J. Poitrenaud, and F. I. B. Williams, “Dynamical Hall effect in a two-dimensional classical plasma,” Phys. Rev. Lett. 54, 1710-1713(1985).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Garcia-Martin, A.

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Garcia-Martin, J. M.

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Giuliani, G. F.

R. F. Wallis, R. Szenics, J. J. Quinn, and G. F. Giuliani, “Theory of surface magnetoplasmon polaritons in truncated superlattices,” Phys. Rev. B 36, 1218-1224 (1987).
[CrossRef]

Glattli, D. C.

D. C. Glattli, E. Y. Andrei, G. Deville, J. Poitrenaud, and F. I. B. Williams, “Dynamical Hall effect in a two-dimensional classical plasma,” Phys. Rev. Lett. 54, 1710-1713(1985).
[CrossRef] [PubMed]

Gonzalez-Diaz, J. B.

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Guerra-Vela, C.

P. Halevi and C. Guerra-Vela, “Magnetoplasma polaritons at the interface between a semiconductor and a metallic screen,” Phys. Rev. B 18, 5248-5253 (1978).
[CrossRef]

Halevi, P.

M. S. Kushwaha and P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration,” Phys. Rev. B 36, 5960-5967(1987).
[CrossRef]

P. Halevi, “Magnetoplasma polaritons at the interface between a semiconductor and a metallic screen. II. The Faraday geometry,” Phys. Rev. B 23, 2635-2639 (1981).
[CrossRef]

P. Halevi and C. Guerra-Vela, “Magnetoplasma polaritons at the interface between a semiconductor and a metallic screen,” Phys. Rev. B 18, 5248-5253 (1978).
[CrossRef]

Hall, W. F.

R. E. De Wames and W. F. Hall, “Magnetic field effect on plasma-wave dispersion in a dielectric layer,” Phys. Rev. Lett. 29, 172-175 (1972).
[CrossRef]

Hartstein, A.

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455-1458 (1972).
[CrossRef]

Hwang, R. R.

C. C. Chang, R. L. Chern, C. C. Chang, and R. R. Hwang, “Interfacial operator approach to computing modes of surface plasmon polaritons for periodic structures,” Phys. Rev. B 72, 205112 (2005).
[CrossRef]

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2000).

Kumah, D. P.

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Kushwaha, M.

M. Kushwaha, “Plasmons and magnetoplasmons in semiconductor heterostructures,” Surf. Sci. Rep. 41, 1-416(2001).
[CrossRef]

Kushwaha, M. S.

M. S. Kushwaha, “Collective excitations of magnetoplasma in semi-infinite n-i-p-i superlattices,” Phys. Rev. B 48, 15445-15448 (1993).
[CrossRef]

M. S. Kushwaha, “Effect of an applied magnetic field on interface excitations in finite layered structures,” Phys. Rev. B 35, 3871-3878 (1987).
[CrossRef]

M. S. Kushwaha and P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration,” Phys. Rev. B 36, 5960-5967(1987).
[CrossRef]

Lan, Y. C.

Y. C. Lan, Y. C. Chang, and P. H. Lee, “Manipulation of tunneling frequencies using magnetic fields for resonant tunneling effects of surface plasmons,” Appl. Phys. Lett. 90, 171114 (2007).
[CrossRef]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Pergamon, 1977).

Lechuga, L.

Lee, P. H.

Y. C. Lan, Y. C. Chang, and P. H. Lee, “Manipulation of tunneling frequencies using magnetic fields for resonant tunneling effects of surface plasmons,” Appl. Phys. Lett. 90, 171114 (2007).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Pergamon, 1977).

Lukaszew, R. A.

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Poitrenaud, J.

D. C. Glattli, E. Y. Andrei, G. Deville, J. Poitrenaud, and F. I. B. Williams, “Dynamical Hall effect in a two-dimensional classical plasma,” Phys. Rev. Lett. 54, 1710-1713(1985).
[CrossRef] [PubMed]

Quinn, J. J.

R. F. Wallis, R. Szenics, J. J. Quinn, and G. F. Giuliani, “Theory of surface magnetoplasmon polaritons in truncated superlattices,” Phys. Rev. B 36, 1218-1224 (1987).
[CrossRef]

K. W. Chiu and J. J. Quinn, “Magnetoplasma surface waves in metals,” Phys. Rev. B 5, 4707-4709 (1972).
[CrossRef]

Sepúlveda, B.

Skuza, J. R.

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

Szenics, R.

R. F. Wallis, R. Szenics, J. J. Quinn, and G. F. Giuliani, “Theory of surface magnetoplasmon polaritons in truncated superlattices,” Phys. Rev. B 36, 1218-1224 (1987).
[CrossRef]

Wallis, R. F.

R. F. Wallis, R. Szenics, J. J. Quinn, and G. F. Giuliani, “Theory of surface magnetoplasmon polaritons in truncated superlattices,” Phys. Rev. B 36, 1218-1224 (1987).
[CrossRef]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455-1458 (1972).
[CrossRef]

Williams, F. I. B.

D. C. Glattli, E. Y. Andrei, G. Deville, J. Poitrenaud, and F. I. B. Williams, “Dynamical Hall effect in a two-dimensional classical plasma,” Phys. Rev. Lett. 54, 1710-1713(1985).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

Y. C. Lan, Y. C. Chang, and P. H. Lee, “Manipulation of tunneling frequencies using magnetic fields for resonant tunneling effects of surface plasmons,” Appl. Phys. Lett. 90, 171114 (2007).
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Phys. Rev. (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Phys. Rev. B (9)

K. W. Chiu and J. J. Quinn, “Magnetoplasma surface waves in metals,” Phys. Rev. B 5, 4707-4709 (1972).
[CrossRef]

J. B. Gonzalez-Diaz, A. Garcia-Martin, G. Armelles, J. M. Garcia-Martin, C. Clavero, A. Cebollada, R. A. Lukaszew, J. R. Skuza, D. P. Kumah, and R. Clarke, “Surface-magnetoplasmon nonreciprocity effects in noble-metal/ferromagnetic heterostructures,” Phys. Rev. B 76, 153402 (2007).
[CrossRef]

R. F. Wallis, R. Szenics, J. J. Quinn, and G. F. Giuliani, “Theory of surface magnetoplasmon polaritons in truncated superlattices,” Phys. Rev. B 36, 1218-1224 (1987).
[CrossRef]

P. Halevi and C. Guerra-Vela, “Magnetoplasma polaritons at the interface between a semiconductor and a metallic screen,” Phys. Rev. B 18, 5248-5253 (1978).
[CrossRef]

P. Halevi, “Magnetoplasma polaritons at the interface between a semiconductor and a metallic screen. II. The Faraday geometry,” Phys. Rev. B 23, 2635-2639 (1981).
[CrossRef]

M. S. Kushwaha, “Effect of an applied magnetic field on interface excitations in finite layered structures,” Phys. Rev. B 35, 3871-3878 (1987).
[CrossRef]

M. S. Kushwaha and P. Halevi, “Magnetoplasmons in thin films in the Voigt configuration,” Phys. Rev. B 36, 5960-5967(1987).
[CrossRef]

M. S. Kushwaha, “Collective excitations of magnetoplasma in semi-infinite n-i-p-i superlattices,” Phys. Rev. B 48, 15445-15448 (1993).
[CrossRef]

C. C. Chang, R. L. Chern, C. C. Chang, and R. R. Hwang, “Interfacial operator approach to computing modes of surface plasmon polaritons for periodic structures,” Phys. Rev. B 72, 205112 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

D. C. Glattli, E. Y. Andrei, G. Deville, J. Poitrenaud, and F. I. B. Williams, “Dynamical Hall effect in a two-dimensional classical plasma,” Phys. Rev. Lett. 54, 1710-1713(1985).
[CrossRef] [PubMed]

R. E. De Wames and W. F. Hall, “Magnetic field effect on plasma-wave dispersion in a dielectric layer,” Phys. Rev. Lett. 29, 172-175 (1972).
[CrossRef]

J. J. Brion, R. F. Wallis, A. Hartstein, and E. Burstein, “Theory of surface magnetoplasmons in semiconductors,” Phys. Rev. Lett. 28, 1455-1458 (1972).
[CrossRef]

Surf. Sci. Rep. (1)

M. Kushwaha, “Plasmons and magnetoplasmons in semiconductor heterostructures,” Surf. Sci. Rep. 41, 1-416(2001).
[CrossRef]

Other (3)

F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (Plenum, 1984).

J. A. Kong, Electromagnetic Wave Theory (EMW Publishing, 2000).

L. D. Landau and E. M. Lifshitz, Quantum Mechanics, 3rd ed. (Pergamon, 1977).

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Figures (4)

Fig. 1
Fig. 1

Schematic of a periodic layered structure in the Voigt configuration.

Fig. 2
Fig. 2

Dispersion relations for the periodic layered structure with f = 0.8 for Ω c = 0 (solid lines) and Ω c = 0.2 (dashed lines). The insets show the mode patterns at K = 1.5 , where the shaded areas correspond to the semiconductor region.

Fig. 3
Fig. 3

Transverse current vectors J t and surface charges for the periodic layered structure with f = 0.5 at K = 1 and Ω c = 0.2 for (a) the acoustical mode and (b) the optical mode. The gray scale of current vectors denotes the current strength, and the red (dark gray) and green (light gray) colors correspond to positive and negative charges, respectively. Schematics of the currents, charges, and magnetic forces are shown in the right plots, where the blue (thin) and red (thick) arrows indicate the directions of vertical components of J t and of the magnetic force, respectively. Circles enclosing the symbols + or − represent the signs of charges.

Fig. 4
Fig. 4

Anticrossing scheme and mode transition for the periodic layered structure with f = 0.2 for Ω c = 0 (solid lines) and Ω c = 0.2 (dashed lines): (a) optical modes for Ω c = 0 , (b) acoustical modes for Ω c = 0 , (c) optical modes for Ω c = 0.2 , and (d) acoustical modes for Ω c = 0.2 . The red (solid), green (dashed), and blue (dash-dotted) lines correspond to K = 0.25 , 0.51, and 1.5, respectively.

Equations (14)

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

[ ε ] = [ ε x x ε x y 0 ε y x ε y y 0 0 0 ε z z ] ,
d 2 H z i d x 2 + γ i 2 H z i = 0 ,
H z 1 ( x ) = A e i γ 1 x + B e i γ 1 x ,
H z 2 ( x ) = C e i γ 2 x + D e i γ 2 x ,
E y 1 ( x ) = γ 1 Ω ε 1 ( A e i γ 1 x B e i γ 1 x ) ,
E y 2 ( x ) = 1 i Ω ( ε x y 2 + ε x x 2 ) [ C ( ε x y k y ε x x γ 2 ) e i γ 2 x + D ( ε x y k y + ε x x γ 2 ) e i γ 2 x ] .
| e i γ 1 d 1 e i γ 1 d 1 e i γ 2 d 1 e i γ 2 d 1 1 1 e i ( γ 2 k x ) a e i ( γ 2 + k x ) a i γ 1 e i γ 1 d 1 ε 1 i γ 1 e i γ 1 d 1 ε 1 i ( ε x y k y γ 2 ε x x ) e i γ 2 d 1 ε x y 2 + ε x x 2 i ( ε x y k y + γ 2 ε x x ) e i γ 2 d 1 ε x y 2 + ε x x 2 i γ 1 ε 1 i γ 1 ε 1 i ( ε x y k y γ 2 ε x x ) e i ( γ 2 k x ) a ε x y 2 + ε x x 2 - i ( ε x y k y + γ 2 ε x x ) e i ( γ 2 + k x ) a ε x y 2 + ε x x 2 | = 0.
cos ( k x a ) = cos ( d 1 γ 1 ) cos ( d 2 γ 2 ) 1 2 ( k y 2 ε 1 γ 1 γ 2 ε 2 ε x y ε x x + γ 2 ε 1 γ 1 ε 2 + γ 1 ε 2 γ 2 ε 1 ) sin ( d 1 γ 1 ) sin ( d 2 γ 2 ) .
Ω ± = ( Ω p 2 ε L + ε d + Ω c 2 4 ) 1 / 2 ± 1 2 Ω c ,
[ m ] = [ m i m Ω c / Ω i m ω c / Ω m ] .
Ω p ± 2 n e 2 ε 0 m = Ω p 2 1 Ω c / Ω .
Ω sp ± = ω p ± ε L + ε d .
Ω ± 2 ( 1 Ω c Ω ± ) = Ω p 2 ε L + ε d ,
J d = D t = i Ω [ ε ] E = J l + J t ,

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