Universal antireflection coatings for substrates for the visible spectral region

It is possible to design normal-incidence antireflection coatings that reduce the reflectance of any substrate with a refractive index that lies in the range of 1.48 to 1.75. The performance of such coatings depends on the width of the spectral region over which the reflectance is to be suppressed, on the coating materials used for their construction, and on the overall optical thickness of the layer system. For example, the calculated average spectral reflectance of a set of six different substrates with refractive indices 1.48, 1.55, 1.60, 1.65, 1.70, and 1.75, when coated with a 0.56-μm-thick, eight-layer antireflection coating designed for the 0.40-0.80-μm spectral region, was 0.34%. This is higher than the average reflectance that is attainable with a conventional antireflection coating of similar optical thicknesses designed for a particular refractive index. However, it is an acceptable value for most applications. With the universal type of antireflection coating described, it is thus possible to coat a number of different refractive-index substrates in one deposition run, and this can result in considerable cost and time savings.     

Symmetrical periods in antireflective coatings for plastic optics

Plastic optical parts require antireflective as well as hard coatings. A novel design concept for coating plastics combines both functions. Symmetrical three-layer periods with a phase thickness of 3/2pi are arranged in a multilayer to achieve a step-down refractive-index profile. It is shown mathematically that the equivalent index of symmetrical periods can be lower than the lowest refractive index of a material used in the design, if the phase thickness of the symmetrical period is set equal to 3/2pi instead of the usual pi/2. The straightforward application of the concept to the design of antireflection coatings in general is demonstrated by example.     

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.     

Optical properties of an optically rough coating from inversion of diffuse reflectance measurements

A method is developed for determining the optical properties of an optically rough coating on an opaque substrate from reflectance measurements. A modified Kubelka-Munk two- flux model is used to calculate the reflectance of the coating as a function of the refractive index, absorption coefficient, scattering coefficient, and thickness. The calculated reflectance is then fitted to measurements using a spectral projected gradient algorithm, allowing the optical properties to be obtained. The technique is applied to titanium dioxide coatings on a titanium substrate. Realistic values of refractive index and absorption coefficients are generally obtained. Quantities that are useful for solar water-splitting applications are calculated, including the depth profile of absorption and the proportion of the incident photon flux absorbed in the coating under solar illumination.     

Elasto-optics in double-coated optical fibers induced by axial strain and hydrostatic pressure

Stresses, microbending loss, and refractive-index changes induced simultaneously by axial strain and hydrostatic pressure in double-coated optical fibers are analyzed. The lateral pressure and normal stresses in the optical fiber, primary coating, and secondary coating are derived. Also presented are the microbending loss and refractive-index changes in the glass fiber. The normal stresses are affected by axial strain, hydrostatic pressure, material properties, and thickness of the primary and secondary coatings. It is found that microbending loss decreases with increasing thickness, the Young's modulus, and the Poisson's ratio of the secondary coating but increases with the increasing Young's modulus and Poisson's ratio of the primary coating. Similarly, changes in refractive index in the glass fiber decrease with the increasing Young's modulus and Poisson's ratio of the secondary coating but increase with the increasing Young's modulus and Poisson's ratio of the primary coating. Therefore, to minimize microbending loss induced simultaneously by axial strain and hydrostatic pressure in the glass fiber, the polymeric coatings should be suitably selected. An optimal design procedure is also indicated.     

Toward perfect antireflection coatings. 3. Experimental results obtained with the use of Reststrahlen materials

The equipment and methods used to produce wide-angle antireflection coatings based on Reststrahlen materials are described. The optical constants of the coating materials used in the construction of the multilayers were determined by spectrophotometric ellipsometry and are compared with the literature values. The measured performance of an experimentally produced antireflection coating is compared with the expected calculated performance. The reflectance is low over a wide range of angles, but only in the narrow-wavelength region at which the refractive index of the Reststrahlen material is close to unity.     

Refractive index profile modelling of dielectric inhomogeneous coatings using effective medium theories

The coatings having refractive index changing with the thickness present interesting optical performance, improved mechanical properties and smaller light scattering in comparison with classical multilayer stacks. Lot of theoretical work and experimental advances have been done for designing and production of mixture layers with such particular performances. The effective refractive index of the mixture coatings can be calculated by the use of effective medium theories. The refractive index profile characterization of inhomogeneous films that are mixtures of SiO₂ and Nb₂O₅ is presented. The composition is linearly changed through the thickness of the layers. Ex-situ spectrophotometric measurements, i.e. reflectance and transmittance at different incidence angles, are used for the precise characterization of the refractive index profiles. Linear, Maxwell-Garnet, Bruggeman and Lorentz-Lorenz effective medium theories are applied and quality and differences of the results are studied and analyzed. It is shown that the Lorentz-Lorenz model is the most appropriate for the given mixture, suggesting components are well mixed and there are no separated phases.     

Extracting infrared absolute reflectance from relative reflectance measurements

Absolute reflectance measurements are valuable to the optics industry for development of new materials and optical coatings. Yet, absolute reflectance measurements are notoriously difficult to make. In this paper, we investigate the feasibility of extracting the absolute reflectance from a relative reflectance measurement using a reference material with known refractive index.     

Narrow line-width filters based on rugate structure and antireflection coating

Filters that have high transmittance over the passband region of the reflectance spectrum are designed by combining rugate structures and antireflection (AR) coatings. It is found that, under certain conditions, the refractive index of the substrate could be “converted” to the air-side refractive index of the graded-refractive-index coating. A method for the fabrication of graded-index coatings by rapidly alternating deposition of low (SiO₂) and high (Nb₂O₅) refractive index materials is introduced, and this technology was used to fabricate a rugate structure. An AR coating with a refractive index of 1.23 was grown onto the rugate structure by glancing angle deposition technology. Optical measurements of the combined structure show excellent transmittances over the wavelength regions around the reflection band and high reflectances in the stopband.     

Antireflecting coating from Ta<Subscript>2</Subscript>O<Subscript>5</Subscript> and SiO<Subscript>2</Subscript> multilayer films

Sol-gel method is important for depositing antireflective coating that allows control over thickness as well as the index of refraction. Antireflective coatings which are produced from Ta₂O₅ and SiO₂ multi-layer thin films using sol-gel spin coating method are presented. The refractive index and the thickness are controlled by the composition and the concentration of the solution respectively. The thickness, refractive index and extinction coefficient of the films were calculated through transmission and reflection measurement by an NKD analyser. Mechanical properties of the films were checked by the cross tape test and dry sun test at 760 W/m². The result shows that the sample heat treated at 450^∘C for 15 min approaches a reflectance with less than 0.5% at around 840 nm.     

The theory of double-layer antireflection coatings

The theory of double-layer antireflection coatings using non-quarter-wave films is reviewed and extended. Normal incidence only is considered.The spectral reflectance of a double-layer coating depends on the refractive indices of the layers and the adjacent media, and on Ø₁ and Ø₂, the phase thickness of the layers. It is known that the reflectance is theoretically zero if the refractive indices satisfy certain inequalities and if the phase thicknesses are those calculated from certain equations.To obtain a fuller appreciation of double-layer coatings, the reflectance throughout the whole (Ø₁, Ø₂) plane is studied analytically. The pattern formed by the lines of constant reflectance exhibits translational symmetry, and the unit pattern which generates the whole pattern has a twofold axis of symmetry. The shape of the unit pattern depends on the refractive indices of the four media. Numerical examples are given to illustrate the similarities and differences between the unit patterns of some double-layer systems.     

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.     

Improved scratch resistance for antireflective coatings on sapphire

Antireflective coatings on sapphire were optimized by variation of the coating design, the total thickness, and the highly refractive material used. The coatings were characterized with a focus on their scratch resistance. An increased resistance against scratching wear is shown for hafnia-containing coatings with a total thickness of about 500?nm.     

Use of Michelson and Fabry-Perot interferometry for independent determination of the refractive index and physical thickness of wafers

We present a method to independently measure the refractive index and the thickness of materials having flat and parallel sides by using a combination of Michelson and Fabry-Perot interferometry techniques. The method has been used to determine refractive-index values in the infrared with uncertainties in the third decimal place and thicknesses accurate to within +/- 5 microm for materials at room and cryogenic temperatures.     

Optical characterization of hybrid antireflective coatings using spectrophotometric and ellipsometric measurements

A hybrid antireflective coating combining homogeneous layers and linear gradient refractive index layers has been deposited using different techniques. The samples were analyzed optically based on spectrophotometric and spectroscopic ellipsometry measurements under different angles of incidence in order to precisely characterize the coatings. The Lorentz-Lorenz model has been used to calculate the refractive index of material mixtures in gradient and constant index layers of the coating. The obtained refractive index profiles have been compared with the targeted ones to detect errors in processes of deposition.     

Reflectance enhancement with sub-quarterwave multilayers of highly absorbing materials

A new theory of multilayers with enhanced normal reflectance has been developed based on the superposition of a few layers of various different radiation-absorbing materials. Every layer in the multilayer had a subquarterwave optical thickness. The theory was developed for materials with small refractive-index differences, although it is also valid in some cases for materials with large refractive-index differences. Reflectance enhancements were obtained in a very broad band and over a wide range of incidence angles. The theory is particularly suited to designing multilayers with enhanced reflectance in the extreme ultraviolet for wavelengths above 50 nm. In this spectral region the reflectance of single layers of all materials is relatively low, and standard multilayers are not possible because of the high absorption of materials.     

Measurement of the induced refractive index in a photothermorefractive glass by a liquid-cell shearing interferometer

A liquid-cell shearing interferometer was developed to measure refractive-index variations (delta n) in transparent materials. The cell was filled with a liquid having a matched refractive index. The achieved resolution was better than 1/1000 of a fringe shift and resulted in a delta n measurement sensitivity down to 10(-7) for 1-mm-thick samples. A refractive-index increment in photothermorefractive glass of up to 5 x 10(-6) was observed after UV exposure at 325 nm. A refractive-index decrement of up to 1 x 10(-3) was observed after thermal development of the exposed sample. It was proved that photothermorefractive glass obeys the reciprocity law; i.e., delta n depends on the UV dosage but does not depend on the irradiance.     

Physically based reflectance model utilizing polarization measurement

A surface bidirectional reflectance distribution function (BRDF) depends on both the optical properties of the material and the microstructure of the surface and appears as combination of these factors. We propose a method for modeling the BRDF based on a separate optical-property (refractive-index) estimation by polarization measurement. Because the BRDF and the refractive index for precisely the same place can be determined, errors cased by individual difference or spatial dependence can be eliminated. Our BRDF model treats the surface as an aggregation of microfacets, and the diffractive effect is negligible because of randomness. An example model of a painted aluminum plate is presented.     

Refractive-index profiling of embedded microstructures in optical materials

We describe use of a phase-sensitive low-coherence reflectometer to measure spatial variation of refractive index in optical materials. The described interferometric technique is demonstrated to be a valuable tool to profile the refractive index of optical elements such as integrated waveguides and photowritten optical microstructures. As an example, a refractive-index profile is mapped of a microstructure written in a microscope glass slide with an ultrashort-pulse laser.     

Realistische Modellierung der NIR/VIS/UV‐optischen Konstanten dünner optischer Schichten im Rahmen des Oszillatormodells

Modelling the NIR/VIS/UV optical constants of thin solid films: An oscillator model approach Based on a multioscillator approach, we demonstrate the determination of optical constants of different optical coating materials. The advanced LCalc‐software allows calculating the dielectric function as well as refractive index and extinction coefficient through a fit of transmittance and reflectance spectra measured at one or several angles of incidence. Sufficiently accurate spectrophotometric measurements are carried out by means of self‐developed VN‐ The thus obtained optical constants are automatically Kramers‐Kronig‐consistent and in reasonable correspondence to various kind of side information available about the coatings. This is demonstrated for dielectric oxide coatings as well as for one transparent conductive oxide (ITO) and a metal layer (aluminium). In application to reproducibility experiments, the method allows estimating process‐inherent stochastic variations in optical constants, which represent themselves an essential input for advanced computational manufacturing runs for design optimization prior to deposition.