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Using the classical molecular dynamics method, the influence of absorption of laser radiation on heat transfer and temperature distribution in silicon dioxide thin films is studied. It is revealed that heating the film to a temperature close to the melting point leads to the appearance of compressive stresses with an amplitude of about 800–1000 MPa. Such high stresses can cause a thermoelastic breakdown of films.

Littrow diffraction, the ability to reflect light back along incident direction, is a key functionality of retroreflectors, exhibiting wide applications in nanophotonics. However, retroreflectors have hitherto low working efficiencies and narrow bandwidths, and work only for a specific polarization, being unfavorable for integration-optics applications. Here, we propose a type of metagrating consisting of an all-dielectric Bragg reflector and a periodic metasurface with freeform-shaped dielectric resonators, which enables broadband depolarized perfect Littrow diffraction at optical frequencies. The physics is governed by exact cancellations of specular reflections contributed by two Bragg modes in metagratings, enabled by careful structural optimization to yield the desired reflection-phase difference of Bragg modes within a wide frequency band and for two polarizations. As a proof of concept, we experimentally demonstrate retroreflections with unpolarized absolute efficiency higher than 98% (99% in design) at 1030–1090 nm using multilayer freeform metagratings. Our results pave the way for numerous applications based on high-efficiency Littrow diffraction (e.g., spectral laser beam combining), which is not bonded to a specific polarization or frequency.

The correlation of errors for various broadband optical monitoring strategies for controlling deposition of multilayer coatings, including strategies with replaceable monitoring chips, is investigated. It is shown that it is necessary to take into account the effect of error self-compensation when choosing a monitoring strategy. The results of this study can be used to select the most promising monitoring strategy for a given type of multilayer coatings.

For optical monitoring of layer thickness in the deposition of multilayer optical coatings, a stable method is proposed that completely eliminates the cumulative effect of errors in the thicknesses of deposited layers. The considered monitoring method relies on a nonlocal algorithm for analyzing data measured in the course of coating deposition monitoring. Computer simulation of coating deposition is used to demonstrate the effectiveness of the proposed type of monitoring as compared with other optical monitoring methods.

The paper presents a theoretical study of the correlation of errors in the thickness of layers of multilayer optical coatings produced using monochromatic monitoring of the deposition process. Estimates of the degree of error correlation in layer thicknesses are obtained for various algorithms for determining termination instants for layer depositions. It is shown that the parameter introduced to assess the degree of correlation gives an adequate idea of the error correlation in the case of monochromatic monitoring.

On-line optical monitoring of multilayer coating production requires solving inverse identification problems of determining the thicknesses of coating layers. Regardless of the algorithm used to solve inverse problems, the errors in the thicknesses of the deposited layers are correlated by the monitoring procedure. Studying the correlation of thickness errors is important for the production of the most complex optical coatings. We develop a general geometric approach to study this correlation. It is based on a statistical analysis of large numbers of error vectors obtained during computational experiments on optical coating production. The application of the proposed approach is demonstrated using computational manufacturing experiments on the production of a 50-layer filter with four different monitoring strategies. A special coefficient is introduced to evaluate the strength of the error correlation effect. The results obtained confirm that the introduced parameter can be used as a measure of the strength of the correlation effect in practical applications.

Ab initio quantum molecular dynamics simulation is used to transform a silicon dioxide crystal into silica amorphous states. Two type of amorphous states are obtained from the melts stabilized at temperatures well above the crystal melting point. The first type of amorphous states are obtained from the melts stabilized at comparably low temperatures of $$3000$$ and $$4000$$ K. These states are characterized by a perfect structure similar to those of the initial crystal and vitreous silica glass without point defects. Completely different amorphous states are obtained from the high temperature melts of $$5000$$ and $$6000$$ K. Structures of these amorphous states are less regular and contain point defects of silicon dioxide such as over-coordinated fivefold silicon, threefold oxygen atoms and a new silica defect 2-Bridging Oxygen Center. The latter is detected in the model of amorphous silica for the first time and it is formed by two neighbouring $$SiO_{4}$$ -tetrahedra with two common oxygen vertexes. The amorphous silica models can be useful for description of amorphous silicon dioxide films obtained by high energy ion-beam deposition process where a fast local melting-quenching process should exist.

A new computational approach is developed to evaluate the strength of the error self-compensation effect in the case of broadband optical monitoring of the multilayer coating deposition process. A new form of estimating the strength of the error self-compensation effect is suggested. Computational experiments simulating the deposition process are used to study the presence of the self-compensation effect and it is shown that the assessment of two parameters characterizing the degree of error correlation and the strength of the self-compensation effect is sufficient from a practical point of view.

Under consideration is the inverse problem of controlling the deposition of a multilayer coating using optical monitoring. Some new nonlocal algorithm is introduced for data analysis. Using the simulation of deposition process, the errors are compared of the proposed nonlocal algorithm and the traditional local algorithm. Some scheme of correction of the levels of the deposition process termination is considered that allows us to improve the accuracy of deposition monitoring. We show that the nonlocal algorithm is more efficient both for the deposition without correction of the signal level for the deposition interruption and with correction of this level.

It is shown that the previously proposed geometric approach adequately describes the effect of error correlation based on the results of computational manufacturing experiments with the selected type of optical monitoring. The question of a sufficient number of simulation runs is investigated, and it is shown that a reliable estimate of the correlation coefficient describing the strength of the error correlation effect is obtained with a realistic number of computational manufacturing experiments. To investigate the presence of the error self-compensation effect, the error self-compensation coefficient is introduced. Using sets of correlated error vectors obtained in computational manufacturing experiments, the probability density function of the distributions of this coefficient is calculated. To assess the strength of the error self-compensation effect, the estimate is proposed based on a comparison of the influence of correlated and uncorrelated thickness errors.

The classical molecular dynamics simulation of the glancing angle deposition of silicon dioxide films with practically meaningful dimensions is performed. The formation of separated slanted columnar structures is investigated for different deposition angles and different energies of sputtered silicon atoms. It is shown that a decrease in the angle between the flux of deposited atoms and the normal to the substrate leads to the decrease of column thicknesses and distances between the columns. The high-energy deposition with small deposition angles results in the formation of dense films without separate columnar structures. The increase of substrate temperature leads to partial merging of nearby columns. The glancing angle deposition with low energies of sputtered silicon atoms results in the growth of disordered columns with different dimensions, shapes, and tilt angles. Annealing of high-energy glancing angle deposited films results in partial merging of slanted columns. The obtained simulation results are in a good agreement with existing experimental data.

We consider the applicability of broad band optical monitoring to the production of gain flattening filters for telecommunication applications. Based on the simulation of filter deposition and on the rigorous mathematical analysis, we show that it is possible to achieve filter target characteristics due to the correlation of thickness errors and to the error self-compensation effect connected with this correlation. We also discuss the choice of a practically optimal spectral range of the monitoring procedure.

The basic algorithms for determining the thicknesses of layers of deposited multilayer optical coatings are discussed and compared. Using a series of model numerical experiments, the advantage of one of these algorithms—the modified T-algorithm—is demonstrated; this algorithm reduces the influence of the effect of error accumulation in the determined thicknesses of layers.

Dependence of the thin films porosity on substrate temperature and deposition energy is studied using the classical atomistic simulation. It is revealed that pore dimensions increase with the decrease of the energy of deposited atoms. In the case of low-energy deposition up to several percents of cluster volume are available for atoms and small molecules having van der Waals radii less than 0.2 nm. Dimensions of pores can achieve several nanometers. The growth of substrate temperature from 300 to 500 K results in the decrease of porosity. Structural properties of deposited films vary insignificantly with the variation of energy distribution of deposited atoms if the average energy is fixed.

The laser-induced thermal stresses in silicon dioxide films are calculated using molecular dynamics simulations. The absorption of the laser energy is simulated by the linear temperature growth from room temperature to 1300 K in a time equal to the laser pulse duration. The maximum values of stresses for picosecond pulses are approximately twice as high as for nanosecond pulses. The stresses in highly porous glancing angle deposited films are approximately two times lower than in dense films. Stress waves caused by picosecond pulses are observed in dense films. An increase in the heating temperature to 1700 K leads to an increase in the absolute stress values for picosecond pulses, and a decrease for nanosecond pulses.

In this article, a combined approach for studying the optical anisotropy of porous thin films obtained by the glancing angle deposition is presented. This approach combines modeling on the atomistic and continuum levels. First, thin films clusters are obtained using the full-atomistic molecular dynamics simulation of the deposition process. Then, these clusters are represented as a medium with anisotropic pores, the shapes parameters of which are determined using the Monte Carlo based method. The difference in the main components of the refractive index is calculated in the framework of the anisotropic Bruggeman effective medium theory. The presented approach is tested and validated by comparing the analytical and simulation results for the model problems, and then is applied to silicon dioxide thin films. It is found that the maximum difference between the main components of the refractive index is 0.035 in a film deposited at an angle of 80&deg, The simulation results agree with the experimental data reported in the literature.

This paper introduces an estimate for the strength of the correlation of layer thickness errors in the process of coating deposition with broadband optical monitoring. It is shown that a strong effect of self-compensation of deposition errors is observed in the case of a strong correlation of layer thickness errors. An estimate for the strength of this effect is introduced. Theoretical conclusions are confirmed by comparison with practical deposition results that demonstrate the presence of a strong self-compensation effect.

A method for improving the accuracy of the broad-band monitoring of the process of depositing optical coatings is proposed. The method is based on determining the actual set of thicknesses of deposited layers in the deposition process. The effectiveness of the proposed approach is demonstrated in a series of model numerical experiments using a simulator of deposition process.

The full-atomistic classical molecular dynamics simulation of the laser heating of silicon dioxide thin films is performed. Both dense isotropic films and porous anisotropic films are investigated. It is assumed that heating occurs due to nodal structural defects, which are currently considered one of the possible causes of laser induced damage. It is revealed that heating to a temperature of 1000 K insignificantly affects the structure of the films and the concentration of point defects responsible for the radiation absorption. An increase in the heating temperature to 2000 K leads to the growth of the concentration of these defects. For “as deposited” films, this growth is greater in the case of a porous film deposited at a high deposition angle. Annealing of film reduces the difference in the concentration of laser induced defects in dense and porous films. The possible influence of optical active defects arising due to heating on the laser induced damage threshold is discussed.

The classical molecular dynamics simulation of the low-energy glancing angle deposition of titanium dioxide films is performed. The deposition angle varies from 60° to 80°. It is found that the film structure consists of parallel slanted columns which lead to the anisotropy of films properties. The difference between the main components of the refractive index tensor is about 0.14, which is close to the values obtained for high-energy titanium dioxide films and larger than 0.03 obtained earlier for silicon dioxide films.

This work is devoted to checking of the validity of the results of high-performance modeling of SiO2 film growth. Modeling of the high-energy deposition process shows that the refractive indices of deposited SiO2 films exceed the refractive index of a fused silica substrate. This is entirely supported by the analysis of spectrophotometric data obtained for practical thin films deposited using the respective deposition technique.

The inverse problem of optical coatings control during their deposition is an important practical and industrial problem. The paper presents the mathematical investigation of the layer thickness errors self-compensation effect that is quite important for the quality production of modern types of thin film optical coatings. It studies the mechanism of thickness errors correlation in the case of direct monitoring of optical coating production by broadband online spectral photometric devices. The mathematical description of this mechanism is provided. The obtained results make it possible to predict the existence of a strong error self-compensation effect when theoretical optical coating design and parameters of the monitoring procedure are known. Mathematical results of the conducted research are confirmed by computational experiments with the data obtained for the optical coating design problem where a very strong error self-compensation effect has been practically observed.

A new algorithm for determining the optical parameters of deposited multilayer optical coatings based on comparing the positions of the extrema of the optical characteristics of multilayer optical coatings is proposed. Two versions of this algorithm are compared. Using a series of numerical simulation experiments, the advantage of one of these versions is demonstrated. It is shown that this version decreases the influence of systematic errors in the spectral data.

An error self-compensation mechanism is investigated for use during the deposition of optical coatings with broadband optical monitoring. The correlation of thickness errors caused by monitoring procedure is mathematically described. It is shown that this correlation of errors may result in the effect of selfcompensation of errors.

The previously developed high-performance parallel method of the atomistic simulation of the ion beam sputtering deposition process is applied to the SiO 2 thin films. Structural properties of deposited films such as density, concentration of point defects, ring statistics, as well as effects arising from the interaction of high energy sputtered Si atoms with the growing film are discussed.

Anisotropy of SiO2 films fabricated by glancing angle deposition is investigated using the classical atomistic simulation and anisotropic Bruggeman effective medium theory. The voids between the slanted columns, occurring as a result of glancing angle deposition, are considered as ellipsoids. Averaged shape parameters of these ellipsoids are defined using the density gradient tensor. Calculated values of difference of refractive index components of glancing angle deposited SiO2 films are in accordance with experiment.

The stress distribution over the thickness of silicon dioxide thin films is studied using simulated thin film cluster. The atomistic cluster representing the film is deposited on a glassy substrate using the full-atomistic molecular dynamic simulation. The deposition angle is equal to 80°, which leads to the growth of a highly porous anisotropic film with low refractive index. The method for calculating the stress distribution is based on the integral relationship between the thickness-averaged stress and the stress distribution. In the present work, we focus on the application of this relationship to the atomistic modeling of stresses at the initial stage of thin film growth. It is found that in the transition layer between the substrate and the film the stress distribution function corresponds to the compressive stress. With the increase in film thickness, the stress distribution function changes sign and becomes tensile. It is shown that these results correspond to experimental data.

The paper investigates production of the multiband filter by broadband monitoring. A special 4-line filter was designed and the simulation demonstrated the layer thickness errors self-compensation effect that was quite significant.

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.

Algorithms for the online determination of thicknesses of already-deposited layers are important for the reliable control of optical coating production. Possible ways of constructing such algorithms in the case of coating production with direct broadband monitoring are discussed. A modified triangular algorithm is proposed. In contrast to the well-known triangular algorithm, the new algorithm does not determine all thicknesses of previously deposited layers but only those for which an increase in the accuracy of their determination is to be expected. The most promising algorithms are compared in terms of their accuracy and operational speed. It is shown that the modified triangular algorithm is much faster than the triangular algorithm, and both algorithms have close accuracy. The operational speed of the modified triangular algorithm can be a decisive factor for its use in modern broadband monitoring systems.

The earlier developed molecular dynamics approach is applied to the investigation of porosity and surface structure of thin films obtained under different deposition conditions. The empirical Monte-Carlo simulation procedure is developed and applied for the search of pores in silicon dioxide thin films. The pores distribution depending on the thickness of growing films and porosity dependence on substrate temperature and deposition energy are studied. It is revealed that the dimensions of pores increase with the decrease of deposition energy. The growth of substrate temperature from 300 K to 500 K results in the increase of porosity in the case of high-energy deposition and in the decrease of porosity in the case of low-energy deposition. It is found that in the case of high-energy deposition film structural properties vary insignificantly with the variation of energy distribution of deposited atoms providing that the average energy of deposited atoms is constant.

The production of large area coatings in the vacuum chamber with the dimensions of 100×100×100 inches is considered. The chamber has the planetary rotation system with three planets. The original monitoring system with two broad band optical monitors combines the advantages of direct and indirect optical monitoring. The results of production of large area coatings are presented to illustrate the capabilities of the combined direct-indirect monitoring system.

Optical monitoring strategies are especially important for reliable control of deposition processes because they allow one to monitor optical thicknesses of coating layers, which are the most important production parameters. The chapter discusses broadband and monochromatic monitoring strategies, direct and indirect monitoring approaches, and passive and active monitoring strategies. In the case of monochromatic monitoring, special attention is given to turning point, level monitoring, and monitoring by swing. The most essential effects connected with optical monitoring, such as error self-compensation effect and cumulative effect of thickness errors, are considered.

The previously developed full-atomistic approach to the thin film growth simulation is applied for the investigation of the dependence of silicon dioxide films properties on deposition conditions. It is shown that the surface roughness and porosity are essentially reduced with the growth of energy of deposited silicon atoms. The growth of energy from 0.1 eV to 10 eV results in the increase of the film density for 0.2 - 0.4 g/cm3 and of the refractive index for 0.04-0.08. The compressive stress in films structures is observed for all deposition conditions. Absolute values of the stress tensor components increase with the growth of e energy of deposited atoms. The increase of the substrate temperature results in smoothing of the density profiles of the deposited films.

The history of High Performance Computing at the Moscow State University (MSU) began with the creation of the Research Computing Center (RCC) in 1955. Since its inception, the MSU Computing Center was equipped with up-to-the-minute equipment. "Lomonosov" supercomputer was installed at the M. V. Lomonosov Moscow State University in 2009. This supercomputer was created by the Russian company "T-Platforms." At the beginning of 2012, MSU's supercomputing center based on "Lomonosov" had over 550 users from MSU, the Russian Academy of Sciences (RAS), and other organizations. The system network provides communication between parallel application processes in the compute nodes using MPI protocol, and an access to a parallel filesystem for the service servers and all compute nodes. The power of the MSU supercomputer system is widely used for the Russian Federation Presidential Commission Project on the modernization and technological development of the Russian economy: "Supercomputing Education."

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.

The molecular dynamic algorithm for simulation of thin-film growth is reported. The achieved performance of this algorithm is sufficient for detailed investigations of structural effects in thin films with practically meaningful dimensions.

This article presents a computational approach for comparing various broadband monitoring strategies, taking into account the positive and negative effects associated with the correlation of thickness errors caused by the monitoring procedure. The approach is based on statistical estimates of the strength of the error self-compensation effect and the expected level of thickness errors. Its application is demonstrated by using a 50-layer, nonpolarizing edge filter. The presented approach is general and can be applied to verify the prospects of broadband monitoring for the production of various types of optical coatings.

The previously developed atomistic method of the thin film deposition simulation is used to study the differences of the structural and mechanical properties of silicon dioxide thin films and fused silica. It’s found that the bulk modulus, Young modulus and Poisson’s ratio are higher for high-energy deposited film than for low-energy deposited film and fused silica. All calculated values are in accordance with experimental data. The excess of the high-energy deposited film density above density of low-energy deposited film and fused silica in discussed in terms of the radial distribution function and cumulative number function.

The high-energy glancing angle deposition of silicon dioxide films with alternation of deposition angle is studied using classical atomistic simulation. Both slow and fast alternations are investigated. The growth of vertical tree-like columns and chevron-like regular structures is demonstrated under fast and slow alternations, respectively. Due to high porosity, the density of the deposited silicon dioxide films is reduced to 1.3 &divide, 1.4 g/cm3. This results in reduction of the refractive index to 1.3, which agrees with known experimental data. For slow continuous substrate rotation, formation of a helical structure is demonstrated.

The interaction of deposited atoms with a silicon dioxide film is simulated for the case of using high-energy processes for the deposition of optical nanocoatings. The method of molecular dynamics with a classical force field is used for describing the interaction between the atoms. The characteristic time of fast relaxation of the kinetic energy of the deposited atom and the characteristic depth of its penetration into the film are estimated. It is shown that the angular distribution of the velocities of the deposited atoms is significant for the formation of a coating.