Modeling of electric-field enhancement at nodular defects in dielectric mirror coatings

In dielectric multilayer optical coatings, laser induced damage is often associated with micrometers -scale surface defects such as the well known nodule defect. The interaction mechanism of the laser light with the coating defects is not understood, however. Historically, laser damage has been associated with peaks in the standing-wave electric-field distribution within the multilayer films. In the present work we use a finite-difference time-domain electromagnetic modeling code to study the influence of 3-D nodule defects on the E-field distribution. The coating studied is a dielectric multilayer HR consisting of alternating quarter- wave layers of HfO₂ and SiO₂ at 1.06 micrometers . The nodule is modeled as a parabolic defect initiated at a spherical seed. The modeling results show that E-field enhancements as large as a factor of 4 can be present at the defects. The enhancement shows a complex dependence on the size, depth, and dielectric constant of the seed material. In general, defects initiated by large, shallow seeds produce the largest E-fields. Voids at the nodule boundary influence the E-field distribution, but have a small effect on the peak field.