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Adequate modeling of high quality non-absorbing dielectric thin films requires the inclusion of the degree of bulk inhomogeneity as one of the parameters in the model describing the film. We show that in the case of a satisfactory choice of a thin film model, the main source of errors in the computed optical parameters of high quality films are systematic errors in spectrophotometric data. Based on practical examples and theoretical predictions we estimate that an accuracy of 0.5% in the determination of optical parameters of dielectric thin films should be considered as a good result when viewed in the context of the current state of the art in optical characterization based on spectrophotometric data. A level of accuracy significantly better than this would require an extraordinary effort.

The combination of the integer optimization technique with ideas from classical design approaches results in an efficient automated approach to the design of WDM filters. An analysis of the pre-production manufacturing feasibility of different designs is addressed through numerical simulation of the deposition process.

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.

We present the whole design-production chain of an ultra-steep hot mirror produced using the indirect monochromatic monitoring technique. The hot mirror without thin layers is designed utilizing the stochastic optimization procedure that takes in account upper and lower constraints for layer optical thickness. We produced the hot mirror with the ion-assisted electron beam deposition technique using indirect monochromatic monitoring strategy, performed reverse engineering of the deposited coatings, and illustrated that the random variation of the tooling factors in low-index layers is the main factor causing production errors. We modified the monitoring strategy with low-index layers monitored by quartz crystal monitor, and demonstrated the excellent correspondence to the theoretical spectral performance.

The proposed automated monitoring approach is based on the ideas of the theory of inverse problems. Computer simulation proves the robustness of the approach and provides insight on the influence of measurement errors.

A simple relationship between the radiant energy transmittance and group delay in the passband region is established. This relationship is based on the consideration of complex poles of the amplitude transmittance.

A system for on-line characterization and reoptimization of evaporated hafnia/silica coatings has been developed, incorporating inhomogeneity of evaporated films and changes in properties between vacuum and air. Tests verify the capability of improving manufactured coatings.

Spectroscopic ellipsometry is a sensitive and reliable diagnostic tool for the optical properties of thin films and multi-layer coatings. In this paper we have derived new formulas permitting qualitative and quantitative analysis of the surface micro-roughness in the case where the refractive index of the film is close to that of the substrate. Theoretical results are applied to the developing of experimental data for lanthanum fluoride and magnesium fluoride thin films.

Results of the optical characterization of dielectric thin films depend on the quality of experimental data. This work investigates the iinfluence of systematic errors in measurement data on the determination of thin film parameters.

The designing of WDM filters is a specific integer optimization problem. An automated approach to the design of such filters combines the ideas of classical design approaches with the advanced concepts of integer optimzation.

It is shown that large scale and small scale surface roughness harmonics impact the amplitude reflection and transmission coefficients of optical thin films in different ways. An effective calculation algorithm taking into account surface roughness effect is proposed.

The shape of the angular and spectral reflection curves of depth-graded x-ray multilayer mirrors may be controlled by the proper variation of the layer thicknesses. The determination of the thickness distribution of the layers that gives the best possible approximation to the desired reflection curve profile is a complicated mathematical problem. The present work reports on the application of the needle variations method to the design of graded x-ray multilayer mirrors in both angular and spectral domain.

The needle optimization technique is applied to the designing of broadband coatings with simultaneously specified intensity and phase derivatives targets. Specifically the designing of output couplers with the transmittance equal to 6 percent in the spectral region form 650 nm to 1100 nm is considered. Other targets include group delay dispersion upon transmission (GDDT) and group delay dispersion upon reflection (GDDR). Theoretical considerations exposing the nature of GDDT and GDDR oscillations are provided.

The progress in the design of optical coatings is essentially connected with the invention of the needle optimization technique and with the accumulated experience of its practical implementation. These factors enable raising a question about the developing of an entirely automated optical coating design technique. The presented paper discusses difficulties of the formalization of the design problem and the ways to overcome the intrinsic uncertainty of its formulation. It formulates the basic principles of implementation of the entirely automated design technique and considers the main pro et contra of the push-button design technology.

New technology applications require new types of x-ray mirrors, in particular, mirrors working at different grazing angles. The angular range of standard x-ray mirrors is rather narrow and they cannot provide effective collimating and focusing of x-ray beams. It is shown that the needle optimization technique can be effectively applied to the design of x-ray mirrors with an extended angular range. Experimental results confirm a practical reproducibility of the designs obtained using this procedure.

Recently a new approximation for the ellipsometer angles of a slightly inhomogeneous thin film was developed. This approximation enables performing a more detailed qualitative analysis of ellipsometric angles than the widely used approximation assuming the linear bulk inhomogeneity. In particular, the new approximation describes not only the impact of inhomogeneity on the ellipsometric angle (Psi) but also its impact on the ellipsometer angle (Delta) . This paper reports specific properties of ellipsometric spectra connected with the surface micro-roughness. In the particular case of fluoride films the ellipsometric angle (Delta) turns to be quite sensitive to this type of inhomogeneity if ellipsometric measurements are performed at high angles of incidence.

A thin film synthesis technique based on the refinement of inhomogeneous systems is improved by the implementation of simultaneous refractive index and thickness optimization. Severe artifacts generated at oblique incidence by an earlier version of the method are eliminated. Complex designs comparable to published solutions synthesized with the Needle Method are demonstrated., Optical Thin Films V: New Developments, July 30, 1997, San Diego, CA, United States

We demonstrate that the needle optimization technique enables the effective design of optical coatings for applications which require a specific spectral response over a wide angular range. A preliminary choice of the most useful layer materials is discussed in connection with the question of the design optimality. It is shown that in many cases two-material designs with the lowest and highest accessible refractive index values are optimal from a practical point of view. It is also shown that in some cases intermediate refractive index values are quite necessary to achieve a good approximation of design targets.

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.

1. Inhomogeneous films have been the subject of detailed study for many years.1,2 Multilayers consisting of slightly inhomogeneous layers may be considered as a particular case of inhomogeneous films. This class is of special practical interest because layers of many optical coatings are slightly inhomogeneous.

1. Publications1,2 showed that dielectric mirrors with special phase properties, the so-called chirped mirrors, can be successfully used to design femtosecond lasers with very short pulse duration. These publications caused a considerable interest to the design and theory of chirped mirrors. The original approach1 to the design of chirped mirrors was based on the refinement of a properly chosen starting design. A starting design was a multilayer mirror with monotonically varying layer thicknesses. An alternative approach3,4 based on the transmission line theory resulted in the analytic technique for the design of chirped mirrors.

Spectroscopic ellipsometry is a sensitive tool for the determination of thin film parameters and, in particular, for the investigation of thin film inhomogeneity. It was shown theoretically1,2 that the ellipsometric angle Ψ is most sensitive to the film inhomogeneity at the so-called half-wave (HW) wavelength points. The values of Ψ at the HW points can be used to determine the degree of inhomogeneity.1,2 These conclusions were obtained on the basis of the approximation that can be traced back to the early work by Schröder.3 Schroder’s approximation predicts essential properties of the ellipsometric angle Ψ but it is rather inaccurate with respect to the ellipsometric angle Δ. In particular, in this approximation the ellipsometric angle Δ is independent from the film inhomogeneity. At the same time ellipsometric experiments show that this is not true. Recently a new approximation was derived4 that allows for a more accurate study of the effects connected with the film inhomogeneity. In this paper we use this approximation to study the influence of the inhomogeneity on the ellipsometric angle Δ. The results of our theoretical study are applied to the investigation of structural properties of lanthanum fluoride films.

Wideband in-situ optical monitoring enables the on-line characterization of optical coatings. Such characterization is an important part of the deposition error compensation process.1,2 In the case of bulk-like thin films and highly stable deposition processes it is possible to determine only one parameter, the current layer thickness, after the deposition of each layer.2 In the case of porous thin films and less stable deposition processes a reliable determination of optical coating parameters is more difficult, and a search for several parameters may be required after each layer deposition. A direct determination of multiple parameters from a single spectral monitoring scan may result in the instability of the determination of optical coating parameters. For this reason, a special mathematical treatment is required to provide stability of the on-line characterization procedure.

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.

We demonstrate selection of reliable approaches for post-production characterization of oblique incidence multilayer optical coatings. The approaches include choice of input information, selection of adequate coating model, corresponding numerical characterization algorithm, and verification of the results. Applications of the approaches are illustrated with post-production characterization of oblique incidence edge filter, oblique incidence beam splitter and oblique incidence 43-layer quarter-wave mirror.

With the help of the most advanced algorithms we obtained many dozens of multilayer dispersive mirror designs to empirically find limits for the maximum achievable negative value of the group delay dispersion (GDD). This value depends on the total thickness of coatings and layer material combination. Nb(2)O(5)/SiO(2) and Ta(2)O(50/SiO(2) combinations are studied in detail, for combinations HfO(2)/SiO(2) and TiO(2)/SiO(2) we obtained estimations for two bandwidths. We also show that reasonable values of third-order dispersion have no significant impact on the obtained results. Current state-of-the-art technology allows to produce designs with total physical thicknesses slightly higher than 10 µm and to achieve maximum negative GDD values corresponding to this total design thickness. Designs with total physical thickness of 15 µm and 20 µm are not realized yet due to high sensitivity to deposition errors.

According to the maximum principle in thin film optics multilayer designs are optimal at least at the normal light incidence. Nevertheless multilayer designs featuring spectral properties typical for inhomogeneous coatings are not widespread. This is connected with the computational problems related to the design of multilayers with large number of layers. This paper shows that using needle optimization technique it is possible to design multilayer counterparts to rugate filters. These multilayers possess even better spectral properties than their inhomogeneous prototypes.

The problem of optical coating design was first formulated as an optimization problem by Philip Baumeister in 1958 [1]. This approach is now the most widely used design technique for optical thin films. When formulated as an optimization problem it is possible to apply all the powerful tools of modern computational mathematics to the design of optical coatings. However, in many cases numerical solution of the resulting optimization problems are extremely difficult due to the large number of local minima in the merit function. Virtually all optimization methods are subject to convergence at local minima and for this reason a search for the global minimum or even "a locally optimal minimum" is a formidable problem.

The most common optical thin film design technique is certainly refinement. It is used successfully to generate conventional homogeneous multilayers as well as inhomogeneous, or graded index, systems [1]–[3]. The latter have been found to be useful not only for their unique optical properties, but also as an intermediate stage in the design of conventional multilayers [4]. Another successful approach in inhomogeneous thin film design is based on the use of Fourier transforms [4]. It is sometimes classified as a synthesis technique because, contrary to refinement, it requires little knowledge of a suitable starting point. Typically, it converges quickly and provides useful insight into the problem. However, its accuracy tends to be limited in regions of high reflectance, due to approximations made in the theory. The lack of the speed of standard refinement techniques and/or their reliance on a good starting design are limitations in design problems involving a large number of parameters. Inhomogeneous systems often fall in this category. Special implementations are needed to design such systems [5]. In this work, we describe an efficient algorithm for the design of inhomogeneous films. This algorithm is based on the exact theoretical formulas.

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.

The needle optimization technique is being further developed to provide a synthesis of optical coatings with layers of more than two materials. In the new version of OptiLayer, optimal layer materials are found automatically. Designing of coatings intended for wide angle of incidence ranges is possible. Several examples demonstrate an application of the needle optimization technique to complicated design problems

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.

In this work we describe ellipsometric software that has been developed at Moscow State University. This software is based on the assurance that hierarchy of models should be used for the thin film. The hierarchy of layer models and the concept of the model being in the agreement with the accuracy of experimental data are discussed.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Second order optimization methods such as the Newton-type methods are known to be extremely effective in solving various inverse and synthesis problems. Despite this they were not used for thin film optical coating design. The reason is a great difficulty in Hesse matrix calculation. We have found a mathematically strict approach increasing the performance of Hesse matrix calculation many times. It allows us to use various second order optimization methods in our new design program called OptiLayer. On the other hand, specific optimization methods based on the optimal control theory results were used to enhance the program efficiency. As a result a very powerful tool for optimal coatings design was received. The developed software allows the user to design complicated optical coatings consisting of many layers (up to several tens) and possessing non-standard spectral properties. The software easily allows the user to take into account various feasibility demands.

Color properties of a multielement optical lens are usually described by a color formula which depends on lens design, optical properties of materials, and transmission coefficients of applied AR coatings. If color properties are of importance in lens design we receive a multicriterion optimization problem. To solve the problem one can use a special choice of coatings from the available coatings set and change continuously some AR coatings parameters also. The user-friendly software was expanded, which allows simultaneous optimization of color and transmission properties of modern multielement optical lenses.

A novel floating constants phase-optimization technique is developed and applied to the design of dispersive mirrors. This technique reduces the dispersive mirror's sensitivity to layer thickness errors. To demonstrate the significant improvement in design stability, we theoretically and experimentally compare our new phase-optimization approach to the conventional one. The fabricated dispersive mirror has a reflectivity of >99.99% and provides an accurate dispersion control over a bandwidth of around 60 nm.

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 report the feasibility of precision broadband dispersion control with multilayer mirrors produced in a single coating run. Inherent fluctuations of the group-delay dispersion (GDD) are suppressed by using the mirrors at two different angles of incidence. With a specialized version of the needle optimization algorithm, we have designed the multilayer structure to yield a complementary pair with a resultant GDD substantially free from spectral oscillations characteristic of broadband chirped multilayers. Since the mirrors employed at two different incidence angles are produced in a single deposition run, their overall dispersion is more robust to errors in layer thicknesses than that of previous complementary mirror pairs manufactured in two different steps. This offers the potential for improving production yield and quality of femtosecond dispersion control. We have successfully used the first "double-angle" mirrors for compressing pulses to a duration of 4.3 fs.

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.

This paper discusses modern approaches to the design of multilayer optical coatings, based on the use of various modifications of the method of needle synthesis. The great possibilities of this method and the power of modern computer facilities make it possible to obtain practicable designs of the elements of multilayer optics with any complexity.

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.