Diana Tonova

Application of the Tauc-Lorentz formulation to the interband absorption of optical coating materials

Recent progress in ellipsometry instrumentation permits precise measurement and characterization of optical coating materials in the deep-UV wavelength range. Dielectric coating materials exhibit their first electronic interband transition in this spectral range. The Tauc-Lorentz model is a powerful tool with which to parameterize interband absorption above the band edge. The application of this model for the parameterization of the optical absorption of TiO2, Ta2O5, HfO2, Al2O3, and LaF3 thin-film materials is described.

Numerical methods for the design of gradient-index optical coatings

We formulate the problem of designing gradient-index optical coatings as the task of solving a system of operator equations. We use iterative numerical procedures known from the theory of inverse problems to solve it with respect to the coating refractive index profile and thickness. The mathematical derivations necessary for the application of the procedures are presented, and different numerical methods (Landweber, Newton, and Gauss-Newton methods, Tikhonov minimization with surrogate functionals) are implemented. Procedures for the transformation of the gradient coating designs into quasi-gradient ones (i.e., multilayer stacks of homogeneous layers with different refractive indices) are also developed. The design algorithms work with physically available coating materials that could be produced with the modern coating technologies.

Design and realization of advanced multi-index systems.

Practically all thin film systems for normal incidence can be realized using only two-layer materials. But for oblique incidence, polarization effects occur, designs may become complex, and polarization control is difficult or impossible to achieve. Here multi-index or gradient designs offer additional degrees of freedom, and can simplify or even enable challenging designs. Such gradient thin film stacks can be designed ab initio without any start or index profile approximations using a new design software developed by Carl Zeiss. With this software, a rugate omnidirectional AR coating was calculated and transferred to three different multi-index systems. All three examples were realized using ion beam sputter technology, and characterized at Laser Zentrum Hannover. Here we present comparative measurements of the optical performance together with femtosecond laser-induced damage threshold measurements.

Broadband and wide-angle hybrid antireflection coatings prepared by combining interference multilayers with subwavelength structures

Abstract. To reduce the intensity of the Fresnel reflections of optical components, subwavelength structures prepared by reactive ion etching of SiO2 thin films were combined as the outermost layer with a multilayer system made of conventional thin-film materials. A hybrid coating was thus realized, with the nanoscaled structured outermost layer expected to further improve the antireflection properties of common interference stacks. The microscopic and optical spectroscopic analysis of the subwavelength structures revealed that pillar-shaped nanostructures formed during etching exhibit low-refractive-index properties and have a depth-dependent refractive index. To take into account the refractive-index gradient in the coating design, the optical properties of the nanostructures were modeled using the effective-medium approximation. The calculated average effective refractive index turned out to be 1.11 at 500-nm wavelength. A hybrid coating was designed to minimize the residual reflectance in the 400-nm to 900-nm spectral range for BK7 glass substrate. Experimental results demonstrated that the hybrid-coating approach yields a low residual reflectance with very good omnidirectional properties, owing to the properties of the nanostructured surface.

Correlation between the optical performance of TiO2-Ag-TiO2 multilayers and the interface roughness between the layers

Ag-dielectric multilayers are widely used in the production of heat reflecting filters, induced transmission filters, beam splitters, etc. The performance of such coatings in the visible part of the spectrum is sometimes strongly influenced by a plasmon absorption in the Ag-layer or a surface plasmon absorption in the Ag-dielectric interfaces. The strength of the plasmon absorption is very sensitive to the layer structure, the light polarization and the angle of incidence. As a result, the target specifications for reflection and transmission are not reached easily. We investigate PVD-deposited TiO2-Ag-TiO2 multilayers by means of optical reflection and transmission and Grazing Incidence X-ray Reflectometry (GIXR). The GIXR-method yields the individual layers thicknesses and the interface roughness. Some of the coatings have a broad absorption peak between 500 and 400nm that cannot be modeled using the bulk dielectric function of Ag. The magnitude of the absorption peak is correlated with the measured roughness of the TiO2-Ag interfaces. The analysis of the results shows the critical parameters for the deposition process.

Characterization of multilayer dielectric coatings by ellipsometry and x-ray grazing incidence reflectometry

Thin film multilayer dielectric coatings are widely used for the fabrication of various optical components. The precise knowledg of the optical constants and the thickness of the individual layers is one of the most important factors for the successful design and production of optical interference coatings with optimal performance. As thin film materials within a multilayer stack often have different optical constants compared to single layers deposited at the same conditions a disagreement between measured and predicted optical response of a multilayer system is observed. A better agreement can be achieved if the optical constants of the layer materials are determined from measurements of multilayer stacks. In the present work such an approach is applied for the optical characterization of popular optical coating materials. The optical constants of TiO2, Ta2O5, Al2O3 and HfO2 are determined in the spectral region 200 nm up to 800 nm using the following measurement techniques: spectroscopic ellipsometry, intensity transmission and X-ray grazing incidence reflectometry. The measured samples are periodic stacks consisting of 12 layers made of one of these materials in combination with SiO2. The ellipsometric and intensity transmission data are fitted simultaneously using the Tauc-Lorentz parameterization for the optical constants of the layers. The results are compared with the thickness of the layers obtained from X-ray grazing incidence reflectometry. The comparison of the predicted and measured optical response of a 3 material multilayer stack demonstrates the accuracy of the extracted optical constants.

Wideband antireflection coatings combining interference multilayers and subwavelength structures prepared by reactive ion etching

To further reduce the intensity of the Fresnel reflections of optical components, subwavelength structures prepared by reactive ion etching of SiO2 thin films are combined as outermost layer with a multilayer system made of conventional thin film materials and prepared by magnetron sputtering. In this approach, a hybrid coating is realized in which the nanoscaled structured outermost layer is expected to further improve the antireflection properties of common interference stacks. The subwavelength structures are examined by spectroscopic ellipsometry, spectral photometry and scanning electron microscopy. The microscopic and optical spectroscopic analysis revealed that pillar-shaped nanostructures are formed during etching which exhibit low-index properties and have a depth-dependent refractive index. To take into account the index gradient in the coating design, the optical properties of the nanostructures are modeled using the effective medium approximation. The calculated average effective refractive index is 1.11 at 500 nm wavelength. A hybrid coating was designed to minimize the residual reflectance in the 400 – 900 nm spectral range for BK7 glass substrate. Experimental results showed that the hybrid coating achieves a low residual reflectance with very good omni-directional properties, owing to the properties of its nanostructured surface. The residual reflection of the hybrid coating is found to be two times smaller than the reflection obtained by applying a common interference multilayer system which demonstrates the benefit of the use of hybrid systems for the realization of broadband antireflective coatings with wide-angle properties.

Advanced femtosecond laser coatings raise damage thresholds

Advanced optical thin film design is the key to increase laser durability significantly: either by optimizing the electric field distribution within the coating, or by multi-index or rugate designs. Both ways may be even combined. The electric field distribution within a thin film stack was optimized to avoid peak intensities in critical layers using refractive index engineering and/or layer thickness grading. Femtosecond laser mirrors and dichroics for 780 nm and 390 nm were designed, realized and characterized. Here we present LIDT measurements of electric field optimized mirrors and dichroics, which are almost a factor of three higher compared to standard coating designs. At 780 nm a LIDT of 1.49 J/cm2 has been achieved and at 390 nm 0.58 J/cm2. With the exception of Al2O3, all investigated coating materials show a proportional dependence of the LIDT with electric field maximum, as expected by theory. For Al2O3 based systems the electrical field penetrates deep into the layer stack, a high number of interfaces are involved and interface effects probably limit the achievable LIDT. A similar effect was observed for rugate designs. To exclude such interface effects from the LIDT measurement, a special AR design was developed, which is practically equal for all high index materials. Here a LIDT above substrate damage threshold of 1.7 J/cm2 was achieved.

Optimization of the spectral performance of multilayer coatings on complex optics in plasma assisted deposition processes

The performance of optical components is usually improved by optical coatings. Some of these optical components exhibit complex geometrical shapes and are therefore very difficult to coat in a homogeneous way. The spectral performance of the optical coatings on such substrates will vary as a function of its geometry making it very difficult to keep the spectral performance within customer specifications all over the substrate. Examples for optics with complex geometries are half sphere lenses, freeform surfaces, diffraction gratings, microlense arrays, large substrates etc. We developed a simulation tool that can calculate and optimize the spectral performance of a given multilayer stack on arbitrarily shaped optics as a function of the processing parameters of the coating plant. This tool will obviously reduce the risk and the development costs. The spectral performance of a multilayer stack is given in general by the coating design, that means by the individual layer thicknesses and the refractive indices of the different layer materials. On curved optics different coating materials exhibit different thickness and refractive index distributions. Consequently the optical layer stack will exhibit varying spectral performance at different positions on the substrate. Empirical models for thickness and refractive index distributions have been developed as a function of the most important processing parameters (e.g., deposition rate, deposition angle, ion impingement rate and temperature).

Design and realization of advanced multi-index-systems

Gradient thin film stacks can be designed ab initio without any start- or index-profile approximations using Carl Zeiss in-house developed new design software. Discrete versus gradient-designs are discussed and first realized advanced multi-index-systems are presented.