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Light in strongly scattering semiconductors - diffuse transport and Anderson
localization
Gomez Rivas, J.
Publication date
2002
Link to publication
Citation for published version (APA):
Gomez Rivas, J. (2002). Light in strongly scattering semiconductors - diffuse transport and
Anderson localization.
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A A
Energyy density coherent
poten-tiall approximation
Inn chapter 3 the energy density coherent potential approximation (EDCPA) is usedd to calculate the scattering mean tree path 4 and the localization parameter k£s inn system formed by silicon scatterers. This theory has been developed by CM. Soukouliss and coworkers and its principles are summarized in this appendix. A detailedd description of the EDCPA can be found in Refs. [84,163,164],
Considerr a random system of spheres with radius r and dielectric constant £j inn matrix formed by a material of dielectric constant £2. The scatterers volume fractionn is <|>. The EDCPA uses a coated sphere with a radius rcs as the basic
scatteringg unit. The dielectric constant of the sphere core is £1, while the dielectric constantt of the coating is £2- The distribution of the spacing between adjacent spheress is approximated by a delta function at rcs, which assumes that the spheres
cann not overlap.
Thee dielectric constant of the effective medium £e is self-consistently deter-minedd by considering that the averaged energy density is uniform over length scaless larger than the coated sphere. This consideration requires that the energy off a plane wave stored in a coated sphere should be the same as the energy stored byy a plane wave in a volume of the effective medium equal to that of the coated sphere.. The self-consistent equation for E<, can be thus written as
rS[ / i ( r , £ , , £2) d r == f" Uzfaejdr, (5.5)
JoJo Jo
wheree U\ (r,£i,£2) and £/2(r>£e) are the energy density in the coated sphere and in thee effective medium.
Withh £e the scattering properties, such as £s, k£s, DB and ve, can be calculated
usingg multiple-scattering theory [164,165].
105 5
106 6 APPENDIXX A
Onee of the most remarkable conclusions of the EDCPA is that localization of lightt can be easier achieved in an inverse structure fe > £1), rather than in a direct structuree (ei > £2). This result is depicted in Fig. Al, where contour plots of the localizationn parameter k£s versus the dielectric contrast and the scatterers volume fractionn are represented. Figure (a) corresponds to a direct structure and (b) to an inversee structure. As can be appreciated, for each value of the dielectric contrast
k£k£ss is lower in the inverse structure.
0.11 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9
(j)) (j)
Figuree A.l: Contour plots of the localization parameter k£s as a function of the dielectric contrastt and of the scatterers volume fraction. Figure (a) corresponds to a direct structure (eii > £2) and (b) corresponds to an inverse structure (£2 > £1). Figure reproduced from Ref.. [85].
