Abstract

An electromagnetic field is localized in one half of a simple cavity by periodic modulation of the dielectric susceptibility. A simple two-scale averaging method is employed to compute the interference effects. An analogy with the localization of electrons in the double well is drawn.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. A. Lin and L. E. Ballentine, Phys. Rev. Lett. 65, 2927–2930 (1990); F. Grossman, T. Dittrich, P. Jung, and P. Hanngi, Phys. Rev. Lett. 67, 516–519 (1991); F. Grossman, P. Jung, T. Dittrich, and P. Hanngi, Z. Phys. B ZPCMDN 84, 315 (1991).
    [CrossRef] [PubMed]
  2. G. Witham, Linear and Non-Linear Waves (Wiley, New York, 1974).
  3. N. N. Bogolyubov and Yu. A. Mitropool’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations (Gordon & Breach, New York, 1964).
  4. B. P. Kirsanov and M. V. Krongauz, J. Opt. Soc. Am. A 13, 2423–2433 (1996).
    [CrossRef]
  5. A. Jeffrey and T. Kawahara, Asymptotic Methods in Nonlinear Wave Theory (Pitman, Boston, Mass., 1982).
  6. L. M. Breshkovskikh, Waves in Layered Media (Academic, New York, 1960).
  7. H. Kogelnik, Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]

1996 (1)

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

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

Other (5)

W. A. Lin and L. E. Ballentine, Phys. Rev. Lett. 65, 2927–2930 (1990); F. Grossman, T. Dittrich, P. Jung, and P. Hanngi, Phys. Rev. Lett. 67, 516–519 (1991); F. Grossman, P. Jung, T. Dittrich, and P. Hanngi, Z. Phys. B ZPCMDN 84, 315 (1991).
[CrossRef] [PubMed]

G. Witham, Linear and Non-Linear Waves (Wiley, New York, 1974).

N. N. Bogolyubov and Yu. A. Mitropool’skii, Asymptotic Methods in the Theory of Nonlinear Oscillations (Gordon & Breach, New York, 1964).

A. Jeffrey and T. Kawahara, Asymptotic Methods in Nonlinear Wave Theory (Pitman, Boston, Mass., 1982).

L. M. Breshkovskikh, Waves in Layered Media (Academic, New York, 1960).

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 (4)

Fig. 1
Fig. 1

Parallel-plate resonator. The ideally reflecting mirrors are located at z=0,l and orthogonal to the z axis.

Fig. 2
Fig. 2

Dielectric susceptibility space dependence.

Fig. 3
Fig. 3

Frequency shift α21 of the modes as function of modulation frequency ω measured relative to the level distance ω21.

Fig. 4
Fig. 4

Localization curve:the set of points in the (Ω =ω/ω1,|bp|2/2) plane at which these parameters yield the localization condition ω21-α21=0.

Equations (37)

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

t2(E)-c2ΔE=0.
(x, t)=0(x)+δ(x, t)
x2u+kx2(ω, x)u=0,u(x=±)=0,
kx2(ω, x)=ω2c2 (x)-kz2.
0(x)c2 t2E+1c2 t2[δ(x, t)E]-ΔE=0.
limx±u(x)0.
E(x, z, t)=A1(t)u1(x)sin(kzz)+A2(t)u2(x)sin(kzz)+l>2Al(t)ul(x)sin(klz).
A¨j+w12Aj=-2t2 dx δ(x, t)0(x) [Aj(t)uj(x)+Ak(t)uk(x)]uj,
jk.
δ(x, t)=ρ(t)μ(x),
A¨j+w12Aj=-aj 2t2 (ρAj)-b 2t2 (ρAk),kj,
aj=- μ(x)0(x) uj2(x)dx,j=1,2,
b=- μ(x)0(x) u1(x)u2(x)dx.
a1=a2=0,
A¨j+w12Aj=-2t2 (ρj Aj)-2t2 (ρAk),kj.
A(x)¯=1T x-T/2x+T/2A(s)ds.
max1ω, 1ωj, 1ω21T.
max1ω, 1ωj, 1ω21A¯tA¯,|t2A¯||ωjtA¯|.
fj¯+=fj exp(-iωjt)¯;fj¯-=fj exp(+iωjt)¯.
A˜=A-Σj[A+¯ exp(iωjt)+A-¯ exp(-iωjt)].
t2A¯j++2iωjtA¯j+=-b{exp(-iωjt)t2[ρ(t)Ak]}¯,
kj.
t2A˜j±+ωj2A˜j±=-bt2(ρAk)±,kj.
tA¯j±=ib/2{exp(-iωjt)t2[ρ(t)Ak]}¯,kj.
t2A˜j±+ωj2A˜j±=-bt2{[p exp(iωt)+p* exp(-iωt)][A˜k±+A¯k±exp(iωt)]},kj.
Aj˜=bp (ωk+ω)2 exp[i(ωk+ω)t]ωj2-(ωk+ω)2+p* (ωk-ω)2 exp[i(ωk-ω)t]ωj2-(ωk-ω)2Ak¯,kj.
tAj¯±=iαjAj¯±.
αj=-b2|p|2ωj2 (ωk+ω)2 exp[i(ωk+ω)t]ωj2-(ωk+ω)2+(ωk-ω)2 exp[i(ωk-ω)t]ωj2-(ωk-ω)2.
ω21=ω21+α2-α1=ω21+α21.
α21(ω)=b2|p|2ω21>0,ω.
ω21=0.
u1=(2)-1[ϕl(x)+ϕr(x)],
u2=(2)-1[ϕl(x)-ϕr(x)],
-0|ϕl|2dx=0|ϕr|2dx=-|u1,2|2dx=1.
Wl=0ldz-0dx|E(t, x)|2=-0dx|A1(0)exp(iω1t)u1(x)+A2(0)exp(iω2t)u2(x)|2=½ [A12(0)+A22(0)]+2A1(0)A2(0)cos(ω21t),
W=A12(0)+A22(0)=1.
E=eyE(x)exp(iωt)sin(qx)=ρ(t)μ(x).

Metrics