In the present paper we determine the optical constants and thicknesses of multilayer thin film stacks, in the visible and near infrared ranges. These parameters are derived from the transmittance and reflectance spectra measured by a spectrophotometer, for several angles of incidence. Several examples are studied, from a simple single layer structure up to a 22-layer dielectric filter. We show that the use of a large number of incidence angles is an effective means of reducing the number of mathematical solutions and converging on the correct physical solution when the number of layers increases. More specifically, we provide an in-depth discussion of the approach used to extract the index and thickness of each layer, which is achieved by analysing the various mathematical solutions given by a global optimization procedure, based on as little as 6 and as many as 32 variable parameters. The results show that multiple incidences, lead to the true solution for a filter with a large number of layers. In the present study, a Clustering Global Optimization algorithm is used, and is shown to be efficient even for a high number of variable parameters. Our analysis allows the accuracy of the reverse engineering process to be estimated at approximately 1 nm for the thickness, and 2 10−3 for the index of each layer in a 22-layer filter.

Exploitation of multiple incidences spectrometric measurements for thin film reverse engineering

In this paper we use spectrophotometric measurements and a Clustering Global Optimization procedure to determine the complex refractive index of SiO2 layer from 250 nm to 1250 nm. A special commercial optical module allows the reflection and transmission measurements to be made under exactly the same illumination and measurement conditions. We compare the index determination results obtained from two different single layer SiO2 samples, with high and low index glass substrates, respectively. We then determine the refractive index of SiO2 for a bi-layer design in which the first deposited layer is Ta2O5. The corresponding solutions are discussed and we show that the real part of the complex refractive index obtained for a bi-layer is slightly different to that found for a single layer investigation. When SiO2 is included inside a thin film stack, we propose the use of an index determination method in which a bi-layer is used for the real part of the complex refractive index, and single layer determination is used for the imaginary part of the refractive index in the UV range.

https://www.jeos.org/index.php/jeos_rp/article/download/13010/931

Refractive index determination of SiO2 layer in the UV/Vis/NIR range: spectrophotometric reverse engineering on single and bi-layer designs

A well-motivated class of dark matter candidates, including axions and dark photons, takes the form of coherent oscillations of a light bosonic field. If the dark matter couples to standard model states, it may be possible to detect it via absorptions in a laboratory target. Current experiments of this kind include cavity-based resonators that convert bosonic dark matter to electromagnetic fields, operating at microwave frequencies. We propose a new class of detectors at higher frequencies, from the infrared through the ultraviolet, based on the dielectric haloscope concept. In periodic photonic materials, bosonic dark matter can efficiently convert to detectable single photons. With feasible experimental techniques, these detectors can probe significant new parameter space for axion and dark photon dark matter in the $0.1--10\text{ }\text{ }\mathrm{eV}$ mass range.

Axion and hidden photon dark matter detection with multilayer optical haloscopes

Self-consistent optical constants of SiO2 and Ta2O5 films have been obtained for their relevance in optical coatings from the near ultraviolet to the near infrared spectral ranges, where they are transparent and have a high refractive index contrast Particular attention has been paid to wavelengths close to and shorter than each material cutoff The far and the extreme ultraviolet ranges are also covered here, where few (SiO2) or almost no optical constant data (Ta2O5) were available for films of these materials This work is aimed at filling the lack of self-consistent sets of optical constants with data in a very broad spectral range, which can be widely applied in multilayer design for the everyday use of these materials in multilayer coatings Oxide films were deposited by reactive electron-beam evaporation onto various sorts of substrates at 573 K Transmittance, reflectance, and ellipsometry measurements were performed for each oxide in spectral intervals jointly covering from the extreme ultraviolet to the near infrared; starting with these measurements along with extrapolations, an iterative and double Kramers-Kronig analysis procedure has been followed to obtain a self-consistent set of optical constants per material With the final data sets, we have satisfactorily reproduced the experimental measurements Global data self-consistency was successfully evaluated through sum rules, and local consistency at each photon energy range was also evaluated through a novel sum-rule method which involves window functions

Self-consistent optical constants of SiO_2 and Ta_2O_5 films

A porous medium is a special type of material where voids are created in a solid medium. The introduction of pores into a bulk solid can profoundly affect its physical properties and enable interesting mechanisms. In this paper, we report the use of mesoporous GaN to address a long-standing challenge in GaN devices: tuning the optical index in epitaxial structures without compromising the structural and electrical properties. By controlling the doping and electrochemical etching bias, we are able to control the pore morphology from macro- to meso- and microporous. The meso- and microporous GaN can be considered a new form of GaN with unprecedented optical index tunability. We examine the scattering loss in a porous medium quantitatively using numerical, semiempirical, and experimental methods. It is established that the optical loss due to scattering is well within the acceptable range. While being perfectly lattice-matched to GaN, the porous GaN layers are found to be electrically highly conductive. As a...

Mesoporous GaN for Photonic Engineering-Highly Reflective GaN Mirrors as an Example

Comparison of different dispersion models for single layer optical thin film index determination

A laser damage test facility delivering pulses from 100 fs to 3 ps and designed to operate at 1030 nm is presented. The different details of its implementation and performances are given. The originality of this system relies the online damage detection system based on Nomarski microscopy and the use of a non-conventional energy detection method based on the utilization of a cooled CCD that offers the possibility to obtain the laser induced damage threshold (LIDT) with high accuracy. Applications of this instrument to study thin films under laser irradiation are presented. Particularly the deterministic behavior of the sub-picosecond damage is investigated in the case of fused silica and oxide films. It is demonstrated that the transition of 0–1 damage probability is very sharp and the LIDT is perfectly deterministic at few hundreds of femtoseconds. The damage process in dielectric materials being the results of electronic processes, specific information such as the material bandgap is needed for the interpretation of results and applications of scaling laws. A review of the different approaches for the estimation of the absorption gap of optical dielectric coatings is conducted and the results given by the different methods are compared and discussed. The LIDT and gap of several oxide materials are then measured with the presented instrument: Al2O3, Nb2O5, HfO2, SiO2, Ta2O5, and ZrO2. The obtained relation between the LIDT and gap at 1030 nm confirms the linear evolution of the threshold with the bandgap that exists at 800 nm, and our work expands the number of tested materials.

A high accuracy femto-/picosecond laser damage test facility dedicated to the study of optical thin films

A large number of parameters is often required to describe optical dispersion laws, and it is only through the use of an appropriate global optimization procedure that an accurate thin-film index determination can be achieved. In this paper, we propose to investigate the respective performances of three different optimization algorithms, namely Simulated Annealing, Genetic Algorithm and Clustering Global Optimization and compare results with a commercial software dedicated to thin-film index determination. This study is restricted to the single-layer thin-film index determination of transparent and absorbing materials. It includes the theoretical study of simulated reflection and transmission spectra, and the experimental characterization of Ta2O5 and Si layers.

Lihong Gao

Papers

Exploitation of multiple incidences spectrometric measurements for thin film reverse engineering

Refractive index determination of SiO2 layer in the UV/Vis/NIR range: spectrophotometric reverse engineering on single and bi-layer designs

Comparison of different dispersion models for single layer optical thin film index determination

A high accuracy femto-/picosecond laser damage test facility dedicated to the study of optical thin films

Reverse engineering from spectrophotometric measurements: performances and efficiency of different optimization algorithms