Ar. Mcgurn et al., ANDERSON LOCALIZATION IN ONE-DIMENSIONAL RANDOMLY DISORDERED OPTICAL-SYSTEMS THAT ARE PERIODIC ON AVERAGE, Physical review. B, Condensed matter, 47(20), 1993, pp. 13120-13125
We compute the frequency dependence of the localization length in a on
e-dimensional randomly disordered optical system, which on average is
periodic, by studying the dependence of the transmissivity on the leng
th of a finite random sample. Specifically, we consider a layered syst
em of dielectric slabs with electromagnetic waves propagating perpendi
cular to the interfaces and compute the localization length for freque
ncies of these waves in and around the neighborhood of the band gaps i
n the photonic band structure of the average periodic system. The loca
lization length is found to be very small in the gaps and much larger
in the bands. We also compute the dependence of the localization lengt
h in the presence of dissipation (complex dielectric constant) and obt
ain a simple relationship, for frequencies of the electromagnetic wave
s in the allowed bands, between the localization length in the nondiss
ipative system, the decay length in the nonrandom periodic system with
dissipative terms, and the localization length in the presence of dis
sipation. For frequencies in the gaps the localization length appears
to be insensitive to the presence of dissipation.