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Metal–dielectric phase-shifting multilayer optical elements have been developed, providing broadband, virtually dispersion-free polarization manipulation down to the few-cycle level. These optical elements are A g / A l 2 O 3 mirrors that operate in the spectral range from 500 to 100 nm, exhibiting reflectance higher than 95%, and a differential phase shift between the s- and p-polarization of about 90° distributed over four bounces. The mirrors have been designed, produced, and reliably characterized based on spectral photometric and ellipsometric data using a non-parametric approach as well as a multi-oscillator model. The optical elements were implemented into a few-cycle laser system, where they transformed linearly polarized few-cycle light pulses to circular polarization.

Many existing well-known multilayer design methods are based on so-called greedy algorithms. New deep search algorithms developed for needle optimization, gradual evolution, and design cleaner methods are presented. The algorithms possess machine learning features. The advantages of the deep search methods are demonstrated on a set of examples including the OIC Design Contest 2019.

A dispersive mirror and a coating uniformity challenge were the topics of the design contest held in conjunction with the 2016 Optical Interference Coatings topical meeting of The Optical Society (OSA). A total of 18 designers from China, France, Germany, Japan, and the United States submitted 38 total designs for problems A and B. Michael Trubetskov submitted the winning designs for all four design challenges. The design problems and the submitted solutions are described and evaluated.

A non-polarizing beam splitter and a light color-mixing challenge were the topics of the design contest held in conjunction with the 2019 Optical Interference Coatings topical meeting of the Optical Society of America. A total of 10 designers from China, France, Germany, Japan, and the United States submitted over 70 designs for problems A and B. The design problems and the submitted solutions are described and evaluated.

Thin films of Ge, ZnS, Y b F 3 , and L a F 3 produced using e-beam evaporation on ZnSe and Ge substrates were characterized in the range of 0.4–12 µm. It was found that the Sellmeier model provides the best fit for refractive indices of ZnSe substrate, ZnS, and L a F 3 films; the Cauchy model provides the best fit for Y b F 3 film. Optical constants of Ge substrate and Ge film as well as extinction coefficients of ZnS, Y b F 3 , L a F 3 , and ZnSe substrate are presented in the frame of a non-parametric model. For the extinction coefficient of ZnS, the exponential model is applicable. Stresses in Ge, ZnS, Y b F 3 , and L a F 3 were estimated equal to ( − 50 ) M P a , ( − 400 ) M P a , 140 MPa, and 380 MPa, respectively. The surface roughness does not exceed 5 nm for all films and substrates.

We focus our efforts on development of an advanced monochromatic monitoring strategy to assist the optical coating engineer in finding a single wavelength or a sequence of monitoring wavelengths that meet simultaneously several practical demands, namely, specified input and output swing values, specified amplitude of a monitoring signal variation, and the distance between trigger point and the last signal extremum. Additionally, the most important demand is that the number of different monitoring wavelengths must be as small as possible. Manual construction of such a monitoring strategy is almost impossible because of a large number of conditions to be satisfied. We propose an algorithm that automatically generates a monitoring spreadsheet so that all demands can be satisfied as closely as possible. We consider six typical design problems and obtain a series of solutions for each of them. Then, we provide computational simulations of deposition processes assuming that they are controlled by monochromatic monitoring with the monitoring strategy generated by our algorithm, and we demonstrate how an optical coating engineer can select design solutions that exhibit the highest production yields.

HfO2/SiO2 dichroic mirrors, having high reflectance at 1064 nm and high transmittance at 532 nm, play an important role in high-power laser systems. However, the half-wave hole effect, caused mainly by the refractive index inhomogeneity of hafnia, affects the spectra and application of these mirrors. Two approaches to eliminate the half-wave hole effect have been proposed. Both approaches attempt to shift the location of the half-wave hole in comparison with the original wavelength. One approach broadens the reflectance band of the first harmonic wavelength and simultaneously adjusts the central reflectance band to a longer wavelength, whereas the other approach combines the two stacks to adjust the location of the half-wave hole far away from the wavelength of interest. Two kinds of dichroic mirrors have been successfully fabricated; moreover, it was found that the method of a two-stack combination, 0.9(HL)8 and 1.1(HL)8, provides designs that can be fabricated more easily and with better quality spectral characteristics.

We propose a reliable reverse engineering approach for a postproduction characterization of complicated optical coatings for ultrafast laser applications. We perform the postproduction characterization on the basis of in situ broadband monitoring data and validate the results using ex situ transmittance data and group delay measurements.

The production of polarizers for high-intensity applications based on a ZrO2/SiO2 pair of thin film materials is discussed. A special approach to accurate determination of a ZrO2 refractive index and the application of direct broadband optical monitoring enable obtaining good manufacturing results.

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.

We deal with design and production of optimal two-component antireflection (AR) coatings for an ultra broadband spectral range from 450 nm to 1800 nm. We demonstrate the whole design-production chain including design selection, choosing monitoring technique, coating production, and reverse engineering of the deposited coatings. At each step of this chain we provide thorough analysis on the basis of theoretical results and adequate computational manufacturing experiments. In order to produce the designed AR coatings we use magnetron sputtering deposition technique and accurate time monitoring.

Two algorithms used for the on-line and off-line characterization of multilayer optical coatings are experimentally compared using test samples produced by two different deposition processes and different monitoring approaches. One of these algorithms, called the triangular algorithm, demonstrates its superiority in all considered situations. We performed experiments with multilayer samples formed by high-density thin films, which allowed us to neglect possible errors in the film refractive indices and concentrate only on errors in the thicknesses of the layers of the produced coatings.

Modern design approaches enable one to construct a series of theoretical designs with excellent spectral properties for almost all optical coating design problems. Selection of a practical optimal design among a variety of possible theoretical designs becomes a key issue. We demonstrate how preproduction estimations of expected production yields can be used for selection of a practical optimal design. The question of reliability of such estimations is also addressed.

A rigorous definition of the error self-compensation effect is provided. An existence of this effect in the case of coating production with broadband optical monitoring of layer thicknesses is investigated for several widely used types of optical 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.

A new model for the determination of group delay (GD) and GD dispersion of dispersive mirrors is presented. The algorithm based on this model enables one to process interferometric data provided by a white-light interferometer and to obtain GD wavelength dependence over a broad spectral range.

The constrained optimization approach is applied to the design of quasi-rugate optical coatings. These coatings are defined as multilayers with no thin layers where refractive index profiles resemble rugate-type refractive index profiles and where spectral properties are typical for rugate filters. It is shown that all design problems that are usually solved using rugate filters can be solved successfully in the frame of quasi-rugate optical coatings. Comparison between quasi-rugate and two-component multilayer designs is provided.

A new optical monitoring system has been developed that allows recording of transmission spectra in the wavelength range between 400 and 920 nm of a growing optical coating during deposition. Several kinds of thin film sample have been prepared by use of a hybrid monitoring strategy that is essentially based on a combination of quartz monitoring and in situ transmission spectra measurements. We demonstrate and discuss the applicability of our system for reengineering procedures of high-low stacks and measurements of small vacuum or thermal shifts of optical coatings.

We develop a new approximation for the amplitude reflection coefficients of a slightly inhomogeneous thin film. This approximation incorporates exactly the interference effects at the substrate and the ambient interfaces. Interference effects inside the inhomogeneous film are incorporated in the Born approximation. We also develop a new approach to the reconstruction of the refractive-index profile from ellipsometric spectra. It is based on a physically sound parameterization of the refractive-index profile. The new approach is tested on the model reconstruction problem.

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.

We demonstrate theoretically and experimentally a band filter with two reflection and broadband transmission ranges, which was obtained with standard two-material technology. The fabricated filter has transmission and reflectivity characteristics better than those achievable with rugate technology.

In this paper, we present our recent studies on raising the quality of optical coating production with an indirect monochromatic monitoring system. Preproduction error analysis and computational manufacturing are used to estimate potential advantages of application of indirect optical monitoring. It is then demonstrated that a key issue for realization of this advantage is accurate specification of tooling factors for layer thicknesses on test glasses. The tooling factors are precalibrated using single layer depositions and then are corrected using results of reverse engineering for the first production run. It is found that a gradual variation of tooling factors of low index layers is the main error factor in the first deposition run. Finally, we redeposit our coating with a modified monitoring strategy, taking into account this factor. The new experimental results show excellent correspondence with the theoretical spectral performance.

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.

New optical coating design algorithm with the equivalent layers theory is presented. The algorithm is based on the merit-function-constrained optimization in the accessible domain of equivalent phase thicknesses and equivalent refractive indices. It allows for creation of design coatings with sophisticated narrowband spectral characteristics. (

An automated approach to the design of wavelength-division multiplexing (WDM) filters is based on the combination of ideas from classical design approaches with an integer optimization technique. This approach turns out to be extremely efficient from a computational point of view and makes it possible to construct a set of significantly different filter designs with nearly equivalent spectral properties. The sensitivity of WDM filters is analyzed by a computer simulation of the deposition process with turning-point optical monitoring. This analysis enables the designer to compare feasibility properties of various filter designs.

A gain-flattening filter (GFF) for minimum manufacturing errors (12 designs submitted) and dense wavelength-division multiplex (DWDM) filters for low group-delay (GD) variation (9 designs submitted) was the subject of a design contest held in conjunction with the Optical Interference Coatings 2001 topical meeting of the Optical Society of America. Results of the contest are given and evaluated. It turned out that the parameter space for GFFs with optimum performance when manufacturing errors are not considered is much different from that when manufacturing errors are considered. DWDM filter solutions with low GD variation are possible.

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.

An efficient first-order algorithm with an exact calculation of the gradients is described and applied to the refinement of inhomogeneous dielectric thin films. Numerical results calculated at normal and oblique angles of incidence are correlated with an important mathematical theorem. It is shown that, when appropriate conditions are satisfied, the synthesis process generates binary type solutions based on two materials, including classical multilayers.

We studied e-beam evaporated TiO2 films deposited at two different substrate temperatures between 120°C and 300°C. We reliably characterized the film samples on the basis of in situ and ex situ measurements. We carried out annealing on the samples and studied the induced changes in the properties of the films. The results can be useful for further laser-induced damage threshold investigations.

Applications of computational manufacturing experiments (CMEs) for selection of the most manufacturable designs among a variety of different design solutions are demonstrated. We compare design solutions with respect to estimations of their production yields. Computational experiments are performed using two simulation software tools. In the course of CMEs, we take into account all major factors causing errors in our deposition process. Real deposition experiments are in agreement with CMEs; the most manufacturable design exhibits better target performances compared to other designs.

We propose a general approach that allows one to reveal factors causing production errors in the course of the deposition process controlled by broadband optical monitoring. We consider computational experiments simulating the real deposition process as a crucial point of this approach. We demonstrate application of the approach using multiple experimental deposition runs of the selected multilayer coatings.

Determination of actual parameters of manufactured optical coatings (reverse engineering of optical coatings) provides feedback to the design-production chain and thus plays an important role in raising the quality of optical coatings production. In this paper, the reliability of reverse engineering results obtained using different types of experimental data is investigated. Considered experimental data include offline normal incidence transmittance data, offline ellipsometric data, and online transmittance monitoring data recorded during depositions of all coating layers. Experimental data are obtained for special test quarter-wave mirrors with intentional errors in some layers. These mirrors were produced by a well-calibrated magnetron-sputtering process. The intentional errors are several times higher than estimated errors of layer thickness monitoring, and the reliability of their detection is used as a measure of reliability of reverse engineering results. It is demonstrated that the most reliable results are provided by online transmittance data.

In the present study we determine the optical parameters of thin metal–dielectric films using two different characterization techniques based on nonparametric and multiple oscillator models. We consider four series of thin metal–dielectric films produced under various deposition conditions with different optical properties. We compare characterization results obtained by nonparametric and multiple oscillator techniques and demonstrate that the results are consistent. The consistency of the results proves their reliability.

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.

We present an indirect broadband optical monitoring approach based on using several witness substrates that are brought to a measurement position in a special sequence. Different witness substrates are used to monitor not groups of successive design layers but specially chosen design layers. An attractive feature of the presented monitoring approach is the ability to reliably control thin dielectric and metal layers. Considered examples demonstrate a good accuracy of the proposed approach.

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.

We present an algorithm for the automatic generation of a monitoring spreadsheet that enables the most effective application of the termination level correction algorithm proposed in our previous publication. On a whole the presented monochromatic monitoring strategy entirely eliminates a cumulative effect of thickness errors in optical coating production using direct optical monitoring. The effectiveness of the new monitoring strategy is demonstrated by computational manufacturing experiments in which such error factors as instability of deposition rates, errors in measured transmittance data, shutter delays, and variations of layer refractive indices from their theoretical values are simulated.

We propose an algorithm for correcting deposition termination levels that allows elimination of the cumulative effect of errors in previously deposited layers. For the application of this algorithm at least one monitoring signal extremum should be registered during a layer deposition. We also derive a theoretical relation for the estimation of errors in layer refractive indices based on the results of on-line monitoring measurements. At least two monitoring signal extrema are required for its application.

Design approaches for optical thin films that recognize the key role of a design's 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.

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.

We introduce two parameters, large-scale and small-scale rms roughness, to take into account the interface properties of thin films and multilayers in the calculation of their specular reflectance and transmittance. A theoretical motivation for the introduction of these two parameters instead of a standard single rms roughness is provided. Experimental power spectral density functions of several samples are used to illustrate ways in which the parameters introduced can be evaluated.

The authors' experience with the application of the needle optimization technique to the design of optical coating is summarized. A physical interpretation of the technique is provided, and its main features are identified. Guidelines on the application of the needle optimization technique to various types of design problems are given.