Michael K. Trubetskov

Optimal single-band normal-incidence antireflection coatings.

Mathematical and computational evidence that strongly suggests that optimal solutions exist to single-band, normal-incidence antireflection coating problems is presented. It is shown that efficient synthesis and refinement techniques can quickly and accurately find such solutions. Several visible and infrared antireflection coating examples are presented to support this claim. Graphs that show the expected optimal performance for different representative substrates, refractive-index ratios, wavelength ranges, and overall optical thickness combinations are given. Typical designs exhibit a pronounced semiperiodic clustering of layers, which has also been observed in the past. Explanations of this phenomenon are proposed.

Optical coating design approaches based on the needle optimization technique

Design approaches for optical thin films that recognize the key role of a designs total optical thickness are presented. These approaches are based primarily on the needle optimization technique but also utilize other optimization procedures. Using the described design approaches, an optical coating engineer can obtain a set of theoretical designs with different combinations of principal design metrics (merit function value, number of layers, and total design optical thickness); this extends opportunities for choosing the most practical and manufacturable design. We also show that some design problems have multiple solutions with nearly the same combinations of principal design metrics.

Influence of small inhomogeneities on the spectral characteristics of single thin films

It is well known that the spectral transmittance and reflectance of a thin film can be influenced by even small inhomogeneities or variations in its complex refractive-index profile. Formulas are derived that describe the theoretical variation of the spectral characteristics for small changes in the refractive index and the extinction coefficient of a homogeneous thin film. These formulas, accurate to the first order in the change in the complex refractive index, are compared with exact calculations for a number of different types of inhomogeneities. It is shown that specific qualitative features in the refractive-index profile of a nearly homogeneous thin film frequently can be determined from an examination of the change in the spectral transmittance and reflectance at normal incidence.

Computational manufacturing as a bridge between design and production

Computational manufacturing of optical coatings is a research area that can be placed between theoretical designing and practical manufacturing in the same way that computational physics can be placed between theoretical and experimental physics. Investigations in this area have been performed for more than 30 years under the name of computer simulation of manufacturing and monitoring processes. Our goal is to attract attention to the increasing importance of computational manufacturing at the current state of the art in the design and manufacture of optical coatings and to demonstrate possible applications of this research tool.

Estimation of the average residual reflectance of broadband antireflection coatings

We 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.

Investigation of the effect of accumulation of thickness errors in optical coating production by broadband optical monitoring

We present a theoretical approach enabling one to perform a preproduction investigation of the effect of accumulation of thickness errors in the course of optical coating production using broadband optical monitoring. On the basis of this approach we investigate and compare thickness errors that may be associated with such factors as random and systematic errors in measurement data, instabilities of deposition rates, and inaccuracies of on-line algorithms predicting termination instants for layer depositions.

Modern design tools and a new paradigm in optical coating design

Several modern optical coating designs tools are discussed in the frame of a new design paradigm proposing the search not for a formally optimal solution with the lowest possible merit function value but for the most practical solution that takes into account additional feasibility demands. Considered design tools include a stochastic optimization procedure that takes into account upper and lower constraints for layer optical thicknesses. This procedure allows one to obtain multiple solutions to a design problem, which presents additional opportunities for choosing a practically optimal design. Two special design techniques involving integer optimization also take into account additional demands. The first one is aimed at designing multicavity narrow bandpass filters with quarter wave or multiple quarter wave layer optical thicknesses. It enables obtaining bandpass filters with extremely steep transmittance slopes, bandwidths of several tens of nanometers, and very small ripples in transmission zones. The second technique is aimed at covering design problems that have been traditionally solved using the theory of equivalent layers. One more technique considered in this paper is aimed at reducing the influence of noncorrelated thickness errors on design spectral characteristics.

Effect of systematic errors in spectral photometric data on the accuracy of determination of optical parameters of dielectric thin films

The determination of optical parameters of thin films from experimental data is a typical task in the field of optical-coating technology. The optical characterization of a single layer deposited on a substrate with known optical parameters is widely used for this purpose. Results of optical characterization are dependent on not only the choice of the thin-film model but also on the quality of experimental data. The theoretical results presented highlight the effect of systematic errors in measurement data on the determination of thin-film parameters. Application of these theoretical results is illustrated by the analysis of experimental data for magnesium fluoride thin films.

High-dispersive mirrors for high power applications

We report on the development and manufacturing of two different types of high-dispersive mirrors (HDM). One of them provides a record value for the group delay dispersion (GDD) of -4000 fs2 and covers the wavelength range of 1027-1033 nm, whereas the other one provides -3000 fs2 over the wavelength range of 1020-1040 nm. Both of the fabricated mirrors exhibit a reflectance of >99.9% and are well suited for intracavity applications. Mirrors of the second type have been successfully employed in a Kerr-lens mode-locked Yb:YAG thin-disk oscillator for the generation of 200-fs pulses with multi-10-W average power.

Optical parameters of oxide films typically used in optical coating production

Wavelength dependencies of refractive indices of thin film materials differ for various deposition conditions, and it is practically impossible to attribute a single refractive index wavelength dependence to any typical thin film material. Besides objective reasons, differences in the optical parameters of thin films may also be connected with nonadequate choices of models and algorithms used for the processing of measurement data. The main goal of this paper is to present reliable wavelength dependencies of refractive indices of the most widely used slightly absorbing oxide thin film materials. These dependencies can be used by other researchers for comparison and verification of their own characterization results.