Geometrical renormalization approach to calculating optical properties of fractal carbonaceous soot

We develop a theoretical approach to calculating optical properties of carbonaceous soot in the long-wavelength limit. Our method is based on geometrical renormalization of clusters; it avoids both the inaccuracy of the dipole approximation in its pure form and the numerical complexity of rigorous direct methods of solving the EM boundary problem. The results are verified by comparison with the experimental measurements for specific extinction of diesel soot in the spectral region from 0.488 microm to 0.857 cm that were performed by Bruce et al. [Appl. Opt. 30, 1537 (1991)]. The theory leads to analytical expressions that are applicable to different soots, with various geometrical properties and optical constants. We show that the functional form of the long-wavelength asymptote of the specific extinction can depend critically on a parameter characterizing the sample geometry, and we identify the critical value of this parameter.