Investigation of the error self-compensation effect associated with direct broad band monitoring of coating production

Computational manufacturing experiments are used to detect the types of optical coatings that are showing the presence of a strong error self-compensation effect in the coating production with direct broad band monitoring. It is shown that predictions made on the basis of these experiments coincide with the predictions of the previously developed rigorous mathematical approach to the investigation of the error self-compensation effect.

Error self-compensation mechanism in the optical coating production with direct broad band monitoring

The main theoretical results related to the investigation of the error self-compensation mechanism associated with direct broad band monitoring of optical coating production are presented. The presented results are illustrated using the production of Brewster angle polarizer where this effect is especially strong. Specific properties of the design merit function required for the presence of the error self-compensation effect are discussed and the mechanism of thickness errors correlation by the direct broad band monitoring is described. It is also discussed how one can check whether a strong error self-compensation effect may be expected for a given coating design and specific parameters of the monitoring procedure that will be used for coating production.

Modified sequential algorithm for the on-line characterization of optical coatings

We present a new algorithm for the on-line determination of thicknesses of deposited layers that can be used in the course of coating production with broadband optical monitoring. The proposed algorithm can be considered as a modification of the well-known sequential algorithm. The main idea of the new algorithm is to re-calculate thicknesses of some of the previously deposited layers along with the determination of the thickness of the last deposited layer. The algorithm implies analytical estimations that enable recalculating only those layer thicknesses that can be found with better accuracy than before. Simulation and computational manufacturing experiments confirm high accuracy of the proposed algorithm.

Advantages and challenges of optical coating production with indirect monochromatic monitoring

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.

Design and production of antireflection coating for the 8-10 µm spectral region

A special design procedure allowing to trap layer thicknesses inside specified limits is applied for designing of antireflection coating (AR) for the infrared spectral band of 8-10 µm. The obtained AR design has no too thick layers that may cause delaminating of the deposited AR coating. A special monitoring procedure taking into account wavelength positions of monitoring signal extrema is applied for coating deposition. The manufactured coating features excellent AR properties in the requested spectral region and possesses high mechanical stability.

Design, production and reverse engineering of ultra-steep hot mirrors

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.

Study of HfO2/SiO2 dichroic laser mirrors with refractive index inhomogeneity

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.

Quality control of oblique incidence optical coatings based on normal incidence measurement data

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.

Design and fabrication of ultra-steep notch filters

We present the design and production approach of an ultra-steep notch filter. The notch filter that does not have thin layers is optimized utilizing the constrained optimization technique, and this is well suitable for accurate monitoring with the electron beam deposition technique. Single layer SiO(2) and Ta(2)O(5) films were deposited and carefully characterized in order to determine tooling factors and refractive indices wavelength dependencies accurately. We produced the ultra-steep notch filter with indirect monochromatic monitoring strategy and demonstrated the excellent correspondence to the theoretical spectral performance.

Computational manufacturing as a tool for the selection of the most manufacturable design

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.

Computational manufacturing as a key element in the design-production chain for modern multilayer coatings

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.

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.

On the reliability of reverse engineering results

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.

Oscillations in spectral behavior of total losses (1 - R - T) in thin dielectric films

We explain reasons of oscillations frequently observed in total losses spectra (1 - R - T) calculated on the basis of measurement spectral photometric data of thin film samples. The first reason of oscillations is related to difference in angles of incidence at which spectral transmittance and reflectance are measured. The second reason is an absorption in a thin film. The third reason is a slight thickness non-uniformity of the film. We observe a good agreement between theoretical models and corresponding measurements, which proves above statements on the origins of oscillations in total losses.

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 characterization and reverse engineering based on multiangle spectroscopy

We perform characterization of thin films and reverse engineering of multilayer coatings on the basis of multiangle spectral photometric data provided by a new advanced spectrophotometer accessory. Experimental samples of single thin films and multilayer coatings are produced by magnetron sputtering and electron-beam evaporation. Reflectance and transmittance data at two polarization states are measured at incidence angles from 7 to 40 deg. We demonstrate that multiangle reflectance and transmittance data provide reliable characterization and reverse-engineering results.

Design, production, and reverse engineering of two-octave antireflection coatings

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.

Design and production of bicolour reflecting coatings with Au metal island films

Optical properties of metal island films (MIFs) can be combined with interference of dielectric coatings. A set of multilayer designs containing metal clusters reflecting different colours from front and back side of the coating was obtained by numerical optimization. The chosen designs presenting the range of feasible colours were deposited by electron beam evaporation. Spectrophotometric and ellipsometric measurements verified that the produced coatings present an excellent agreement with the optical performance calculated from the designs. Numerical optimization was verified as a useful method in designing of coatings containing MIFs. This approach can ease the implementation of metal clusters into multilayer designs and broaden the applications of MIFs.

Comparison of two techniques for reliable characterization of thin metal-dielectric films

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.

Comparison of algorithms used for optical characterization of multilayer optical coatings

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.

General approach to reliable characterization of thin metal films

Optical constants of thin metal films are strongly dependent on deposition conditions, growth mode, and thickness. We propose a universal characterization approach that allows reliable determination of thin metal film optical constants as functions of wavelength and thickness. We apply this approach to determination of refractive index dispersion of silver island films embedded between silica layers.

Estimations of production yields for selection of a practical optimal optical coating design

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.

Investigation of the error self-compensation effect associated with broadband optical monitoring

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.

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.

Robust synthesis of dispersive mirrors

A synthesis technique allowing to obtain a set of robust designs is reported. The robust synthesis is based on simultaneous optimization of spectral characteristics of multiple designs located in a small neighborhood of a so-called pivotal design. Efficiency of this technique is demonstrated by the synthesis and successful experimental realization of a high dispersive mirror. The fabricated dispersive mirror covers 690-890 nm wavelength range and provides the dispersion of -300 fs2 at 800 nm.

Phase optimization of dispersive mirrors based on floating constants

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.

Double-angle multilayer mirrors with smooth dispersion characteristics

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.

Indirect broadband optical monitoring with multiple witness substrates

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.

Comparison of dispersive mirrors based on the time-domain and conventional approaches, for sub-5-fs pulses

Dispersive mirrors based on time-domain approach are compared with mirrors resulting from conventional phase target designs. Phase targets have been applied to complementary-pair dispersive mirrors, used for sub-5-fs pulse compression. While the phase approach has hither to afforded the best performance for the shortest pulses, our new approach, based on time-domain targets and tailored for a specific input spectrum, appears to provide comparable performance for pulse compression for a pulse duration 4.6 fs. Experimental studies using dispersive mirrors made to both designs are described.

Measurement of group delay of dispersive mirrors with white-light interferometer

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.

Application of constrained optimization to the design of quasi-rugate optical coatings

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.

In situ optical characterization and reengineering of interference coatings

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.

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.

Computational experiments on optical coating production using monochromatic monitoring strategy aimed at eliminating a cumulative effect of thickness errors

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.

Elimination of cumulative effect of thickness errors in monochromatic monitoring of optical coating production: theory

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.

Band filters: two-material technology versus rugate

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.

Optical coating design approaches based on the needle optimization technique

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.

Statistical approach to choosing a strategy of monochromatic monitoring of optical coating production

We presents what we believe to be a new approach to choosing a sequence of monitoring wavelengths for monochromatic monitoring of optical coating production. The new approach is based on a preproduction estimation of expected levels of errors in thickness of layers of a deposited coating. It is demonstrated that the proposed monitoring strategy reduces the effect of accumulation of thickness errors. An advantage of the new monitoring strategy becomes especially noticeable when the number of monitored layers is equal to several dozens.

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.

Optical coating design algorithm based on the equivalent layers theory

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. (

New optimization algorithm for the synthesis of rugate optical coatings

A model of a rugate coating that takes into account production potentialities of the Leybold Syrus Pro 1100 deposition system is presented. An efficient algorithm for the synthesis of rugate coatings is proposed. Numerical results are also presented.

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.

Effects of interface roughness on the spectral properties of thin films and multilayers

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.

Automated design and sensitivity analysis of wavelengh-division multiplexing filters

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.

Topical meeting on optical interference coatings (OIC'2001): design contest results

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.

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.

Spectroscopic ellipsometry of slightly inhomogeneous nonabsorbing thin films with arbitrary refractive-index profiles: theoretical study

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.

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.