Physical insight toward electric field enhancement at nodular defects in optical coatings

Although the finite-difference time-domain (FDTD) technique has been prevailingly used to calculate the electric field intensity (EFI) enhancement at nodular defects in high-reflection (HR) coatings, the physical insight as to how the nodular features contribute to the intensified EFI is not explicitly revealed yet, which in turn limits the solutions that improve the laser-induced damage threshold (LIDT) of nodules by decreasing the EFI enhancement. Here, a simplified model is proposed to describe the intensified EFI in nodules: 1) the nodule works as a microlens and its focal length can be predicted using a simple formula, 2) the portion of incident light that penetrates through the HR coating can be estimated by knowing the angular dependent transmittance (ADT) of the nodule, 3) strong EFI enhancement is created when the focal point is within the nodule and simultaneously a certain portion of light penetrates to the focal position. In the light of the proposed model, a broadband HR coating was used to reduce the EFI enhancement at the seed by a factor about 10, which leads to a 20 times increment of the LIDT. This work therefore not only deepens the physical understanding of EFI enhancement at nodules but also provides a new way to increase the LIDT of multilayer reflective optics.