Estimation of the average residual reflectance of broadband antireflection coatings

Abstract

Estimation of the average residual reflectance of broadband antireflection coatingsWe deal with optimal two-material antireflection (AR) coatings for the visible and adjacent spectral regions. It has been shown before that, for a given set of input parameters (refractive indices of the substrate, ambient medium and high-and low-index coating materials, and for a given spectral width of the AR coating), such designs consist of one or more clusters of layers of approximately constant optical thickness and number of layers. We show that, through the analysis of many different optimal coatings, it is possible to derive two parameters for a simple empirical expression that relates the residual average reflectance in the AR region to the number of clusters. These parameters are given for all possible combinations of relative spectral bandwidth equal to 2, 3, and 4; low-index to ambient-medium index ratio equal to 1.38 and 1.45; and high-to-low index ratio equal to 1.4, 1.5, and 1.7. The agreement between the numerically and the empirically calculated values of residual average reflectance is excellent. From the information presented the optical thin-film designer can quickly calculate the required number of layers and the overall optical thickness of an AR coating having the desired achievable residual average reflectance.

Monitoring error compensation in general optical coatings

“…This same type of natural pattern for a broadband AR coating is also seen in Fig. 1 of the work of Tikhonravov et al [14], reproduced here with permission as Fig. 4.…”

Further guidance for broadband antireflection coating design

“…2 show some of the design results. This extends the previous work and that of others [10][11][12]14] statistically fitted to a sixth-order polynomial using DOEKISS [15] regression analysis software to the following equation, and it is plotted as the upper solid curve in The previous best estimate equation from p. 151 of Ref. [5] for bandwidths up to 4.0 is plotted as the dashed line in Fig.…”

“…Tikhonravov et al [14] and Amotchkina [12] have done similar investigations to this using somewhat different approaches, and their estimation equations give almost identical results over the ranges which they have investigated (B only up to 4.0).…”

“…Dobrowolski et al [11] and Tikhonravov et al [14] have also mentioned the number of layers in their design studies. A layer is defined here as the space between two index of refraction interfaces that is occupied by a single homogeneous index, independent of any relationship to its physical or optical thickness.…”

Towards a Compact Thin-Disk-Based Femtosecond XUV Source

“…In this thesis an AR coating specifically designed for a large angle of incidence is considered. In [190,191,192] the authors empirically predict a residual reflectance from the AR coating …”