Abstract

A new wave-vector space method of finding electromagnetic wave propagation in bounded media without using boundary conditions is applied to finding surface waves. The method is demonstrated by finding the complete solution of the surface polariton wave for a cubic dielectric crystal. The three eigenvectors of the wave equation are found as a step in the method. This gives a convenient way of showing that only the TM mode is freely propagating, while the TE and longitudinal modes are not. The unique capability of the method in treating wave-vector-dispersive interactions for which the boundary conditions are typically not known is pointed out.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Chen and D. F. Nelson, “Wave-vector-space method for wave propagation in bounded media,” Phys. Rev. B 48, 15365–15371 (1993).
    [CrossRef]
  2. B. Chen and D. F. Nelson, “Wave propagation of exciton polaritons by a wave-vector-space method,” Phys. Rev. B 48, 15372–15389 (1993).
    [CrossRef]
  3. D. F. Nelson, “Deriving the transmission and reflection coefficients of an optically active medium without using boundary conditions,” Phys. Rev. E 51, 6142–6153 (1995).
    [CrossRef]
  4. D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817–926 (1974).
    [CrossRef]
  5. V. V. Bryksin, D. N. Mirlin, and Yu. A. Firsov, “Surface optical phonons in ionic crystals,” Usp. Fiz. Nauk 113, 29–67 (1974) [Sov. Phys. Usp. 17, 305–325 (1974)].
    [CrossRef]
  6. V. M. Agranovich, “Crystal optics of surface polaritons and the properties of surfaces,” Usp. Fiz. Nauk 115, 199–237 (1975) [Sov. Phys. Usp. 18, 99–117 (1975)].
    [CrossRef]
  7. P. Halevi, “Polariton modes at the interface between two conducting or dielectric media,” Surf. Sci. 76, 64–90 (1978).
    [CrossRef]
  8. D. N. Mirlin, “Surface phonon polaritons in dielectrics and semiconductors,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 3–67.
  9. V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons (Springer-Verlag, Berlin, 1984), Chap. 5.
    [CrossRef]
  10. Yu. A. Il’inskii and L. V. Keldysh, Electromagnetic Response of Material Media (Plenum, New York, 1994), Sec. 5.7.
    [CrossRef]

1995 (1)

D. F. Nelson, “Deriving the transmission and reflection coefficients of an optically active medium without using boundary conditions,” Phys. Rev. E 51, 6142–6153 (1995).
[CrossRef]

1993 (2)

B. Chen and D. F. Nelson, “Wave-vector-space method for wave propagation in bounded media,” Phys. Rev. B 48, 15365–15371 (1993).
[CrossRef]

B. Chen and D. F. Nelson, “Wave propagation of exciton polaritons by a wave-vector-space method,” Phys. Rev. B 48, 15372–15389 (1993).
[CrossRef]

1978 (1)

P. Halevi, “Polariton modes at the interface between two conducting or dielectric media,” Surf. Sci. 76, 64–90 (1978).
[CrossRef]

1975 (1)

V. M. Agranovich, “Crystal optics of surface polaritons and the properties of surfaces,” Usp. Fiz. Nauk 115, 199–237 (1975) [Sov. Phys. Usp. 18, 99–117 (1975)].
[CrossRef]

1974 (2)

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817–926 (1974).
[CrossRef]

V. V. Bryksin, D. N. Mirlin, and Yu. A. Firsov, “Surface optical phonons in ionic crystals,” Usp. Fiz. Nauk 113, 29–67 (1974) [Sov. Phys. Usp. 17, 305–325 (1974)].
[CrossRef]

Agranovich, V. M.

V. M. Agranovich, “Crystal optics of surface polaritons and the properties of surfaces,” Usp. Fiz. Nauk 115, 199–237 (1975) [Sov. Phys. Usp. 18, 99–117 (1975)].
[CrossRef]

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons (Springer-Verlag, Berlin, 1984), Chap. 5.
[CrossRef]

Bryksin, V. V.

V. V. Bryksin, D. N. Mirlin, and Yu. A. Firsov, “Surface optical phonons in ionic crystals,” Usp. Fiz. Nauk 113, 29–67 (1974) [Sov. Phys. Usp. 17, 305–325 (1974)].
[CrossRef]

Burstein, E.

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817–926 (1974).
[CrossRef]

Chen, B.

B. Chen and D. F. Nelson, “Wave-vector-space method for wave propagation in bounded media,” Phys. Rev. B 48, 15365–15371 (1993).
[CrossRef]

B. Chen and D. F. Nelson, “Wave propagation of exciton polaritons by a wave-vector-space method,” Phys. Rev. B 48, 15372–15389 (1993).
[CrossRef]

Firsov, Yu. A.

V. V. Bryksin, D. N. Mirlin, and Yu. A. Firsov, “Surface optical phonons in ionic crystals,” Usp. Fiz. Nauk 113, 29–67 (1974) [Sov. Phys. Usp. 17, 305–325 (1974)].
[CrossRef]

Ginzburg, V. L.

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons (Springer-Verlag, Berlin, 1984), Chap. 5.
[CrossRef]

Halevi, P.

P. Halevi, “Polariton modes at the interface between two conducting or dielectric media,” Surf. Sci. 76, 64–90 (1978).
[CrossRef]

Il’inskii, Yu. A.

Yu. A. Il’inskii and L. V. Keldysh, Electromagnetic Response of Material Media (Plenum, New York, 1994), Sec. 5.7.
[CrossRef]

Keldysh, L. V.

Yu. A. Il’inskii and L. V. Keldysh, Electromagnetic Response of Material Media (Plenum, New York, 1994), Sec. 5.7.
[CrossRef]

Mills, D. L.

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817–926 (1974).
[CrossRef]

Mirlin, D. N.

V. V. Bryksin, D. N. Mirlin, and Yu. A. Firsov, “Surface optical phonons in ionic crystals,” Usp. Fiz. Nauk 113, 29–67 (1974) [Sov. Phys. Usp. 17, 305–325 (1974)].
[CrossRef]

D. N. Mirlin, “Surface phonon polaritons in dielectrics and semiconductors,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 3–67.

Nelson, D. F.

D. F. Nelson, “Deriving the transmission and reflection coefficients of an optically active medium without using boundary conditions,” Phys. Rev. E 51, 6142–6153 (1995).
[CrossRef]

B. Chen and D. F. Nelson, “Wave propagation of exciton polaritons by a wave-vector-space method,” Phys. Rev. B 48, 15372–15389 (1993).
[CrossRef]

B. Chen and D. F. Nelson, “Wave-vector-space method for wave propagation in bounded media,” Phys. Rev. B 48, 15365–15371 (1993).
[CrossRef]

Phys. Rev. B (2)

B. Chen and D. F. Nelson, “Wave-vector-space method for wave propagation in bounded media,” Phys. Rev. B 48, 15365–15371 (1993).
[CrossRef]

B. Chen and D. F. Nelson, “Wave propagation of exciton polaritons by a wave-vector-space method,” Phys. Rev. B 48, 15372–15389 (1993).
[CrossRef]

Phys. Rev. E (1)

D. F. Nelson, “Deriving the transmission and reflection coefficients of an optically active medium without using boundary conditions,” Phys. Rev. E 51, 6142–6153 (1995).
[CrossRef]

Rep. Prog. Phys. (1)

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817–926 (1974).
[CrossRef]

Surf. Sci. (1)

P. Halevi, “Polariton modes at the interface between two conducting or dielectric media,” Surf. Sci. 76, 64–90 (1978).
[CrossRef]

Usp. Fiz. Nauk (2)

V. V. Bryksin, D. N. Mirlin, and Yu. A. Firsov, “Surface optical phonons in ionic crystals,” Usp. Fiz. Nauk 113, 29–67 (1974) [Sov. Phys. Usp. 17, 305–325 (1974)].
[CrossRef]

V. M. Agranovich, “Crystal optics of surface polaritons and the properties of surfaces,” Usp. Fiz. Nauk 115, 199–237 (1975) [Sov. Phys. Usp. 18, 99–117 (1975)].
[CrossRef]

Other (3)

D. N. Mirlin, “Surface phonon polaritons in dielectrics and semiconductors,” in Surface Polaritons, V. M. Agranovich and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), pp. 3–67.

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion and Excitons (Springer-Verlag, Berlin, 1984), Chap. 5.
[CrossRef]

Yu. A. Il’inskii and L. V. Keldysh, Electromagnetic Response of Material Media (Plenum, New York, 1994), Sec. 5.7.
[CrossRef]

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.


Equations (47)

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

××Ex,t+1c22t2Ex,t+10Px,t=0
P(x,t)=rcrηr(x,t)
2ηrt2=cr·E-Ωr2ηr,
F(k,ω)=1(2π)4 F(x,t)exp(-ik·x+iωt)dxdt,
F(x,t)= F(k,ω)exp(ik·x-iωt)dkdω.
m(x)=mθ(z),
θ(z)=1 z>0=0 z<0.
m(k)=mθ(k)=mδ(kx)δ(ky)2πi(kz-i),
-kjijkklmklEmk,ω-ω2c2Eik,ω-ω22πic20r cirηrkx,ky,kz,ωdkzkz-kz-iexpik·x-iωtdkdω=0.
kikjEj(k,ω)-k2Ei(k,ω)+k02Ei(k,ω)+k022πi0rcir  ηr(kx,ky,kz,ω)kz-kz-idkz=0.
F(kz)=F(+)(kz)+F(-)(kz),
12πi F(kz)dkzkz-kz-i=F+(kz).
[(k02-k2)δij+kikj][Ej(+)(k,ω)+Ej(-)(k,ω)]+k020r cirηr(+)(k,ω)=0.
ω2ηr(+)-Ωr2ηr(+)+cr·E(+)=0,
ηs(+)=cs·E(+)Ωs2-ω2.
[k02κij(ω)-k2δij+kikj]Ej(+)(k,ω)+[(k02-k2)δij+kikj]Ej(-)(k,ω)=0,
κij(ω)δij+10r circjrΩr2-ω2.
κij(ω)=κ(ω)δij.
[(k02κ-k2)δij+kikj]Ej(+)(k,ω)+[(k02-k2)δij+kikj]Ej(-)(k,ω)=0,
K(+) E(+)=Λ(+) E(+),
Kij(+)(k02κ-k2)δij+kikj
kkxiˆ+iqzkˆ,
Λ+=κk02-k200 0κk02-k20 00κk02,
k2k·k=kx2-qz2
Eˆ(k)=1k(-iqziˆ+kxkˆ),
Eˆ(k)=jˆ,
EˆL(k)=1k(kxiˆ+iqzkˆ).
Eˆα·Eˆβ=δαβ,α,β=,,L.
V=[Eˆ(k),Eˆ(k),EˆL(k)],
V-1K(-)V=Λ(-),
Λ-=k02-k200 0k02-k20 00k02,
κk02-k2=0.
k02-k2=0,
qz=[k12-κ(ω)k02]1/2qm
qz=-(k12-k02)1/2-qv,
E(+)(k,ω)=E1δ(ω-ω0)δ(ky)δ(kx-k1)×Eˆ(k1,0,iqm)2πi(kz-iqm),
E(-)(k,ω)=E2δ(ω-ω0)δ(ky)δ(kx-k1)×Eˆ(k1,0,-iqv)2πi(kz+iqv),
(-E1qm+E2κ1/2qv)kz+i[(k12-qm2)E1+(k12-qv2)κ1/2E2]=0.
E2=qmE1qvκ1/2,
k1=k0κωκω+11/2.
qm=k0|κω|-κω-11/2,
qv=k0[-κ(ω)-1]1/2.
κ(ω)<-1.
EL-k1E1k0,
Ek,ω=EL2πiδω-ω0δkyδkx-k1×iˆ+ikˆ-κ-1/2kz-iqm-iˆ-ikˆ-κ1/2kz+iqv.
E(x,z,t)=EL exp(ik1x-iω0t){[iˆ+ikˆ(-κ)-1/2]×exp(-qmz)θ(z)+[iˆ-ikˆ(-κ)1/2]×exp(+qvz)θ(-z)},
B(x,z,t)=ic(-κ-1)1/2ELjˆ exp(ik1x-iω0t)×[exp(-qmz)θ(z)+exp(+qvz)θ(-z)].

Metrics