Phase formation, morphology, and optical properties of Ti(O,N) thin films with varied oxygen-to- nitrogen ration content were investigated. The films were deposited by magnetron sputtering at 500 & DEG;C on Si(100) and c-plane sapphire substrate. A competition between a NaCl B1 structure TiN1-xOx, a rhombohedral structure Ti-2(O1-yNy)(3), and an anatase structure Ti(O1-zNz)(2) phase was observed. While the N-rich films were composed of a NaCl B1 TiN1-xOx phase, an increase of oxygen in the films yields the growth of rhombohedral Ti-2(O1-yNy)(3) phase and the oxygen-rich films are comprised of a mixture of the rhombohedral Ti-2(O1-yNy)(3) phase and anatase Ti(O1-zNz)(2) phase. The optical properties of the films were correlated to the phase composition and the observation of abrupt changes in terms of refractive index and absorption coefficient. The oxide film became relatively transparent in the visible range while the addition of nitrogen into films increases the absorption. The oxygen rich-samples have bandgap values below 3.75 eV, which is higher than the value for pure TiO2, and lower than the optical bandgap of pure TiN. The optical properties characterizations revealed the possibility of adjusting the band gap and the absorption coefficient depending on the N-content, because of the phases constituting the films combined with anionic substitution.

Zinc aluminogallate, Zn(AlxGa1−x)2O4 (ZAGO), a single-phase spinel structure, offers considerable potential for high-performance electronic devices due to its expansive compositional miscibility range between aluminum (Al) and gallium (Ga). Direct growth of high-quality ZAGO epilayers however remains problematic due to the high volatility of zinc (Zn). This work highlights a novel synthesis process for high-quality epitaxial quaternary ZAGO thin films on sapphire substrates, achieved through thermal annealing of a ZnGa2O4 (ZGO) epilayer on sapphire in an ambient air setting. In-situ annealing x-ray diffraction measurements show that the incorporation of Al in the ZGO epilayer commenced at 850 °C. The Al content (x) in ZAGO epilayer gradually increased up to around 0.45 as the annealing temperature was raised to 1100 °C, which was confirmed by transmission electron microscopy (TEM) and energy dispersive x-ray spectroscopy. X-ray rocking curve measurement revealed a small full width at half maximum value of 0.72 °, indicating the crystal quality preservation of the ZAGO epilayer with a high Al content. However, an epitaxial intermediate �–(AlxGa1−x)2O3 layer (� - AGO) was formed between the ZAGO and sapphire substrate. This is believed to be a consequence of the interdiffusion of Al and Ga between the ZGO thin film and sapphire substrate. Using density functional theory, the substitution cost of Ga in sapphire was determined to be about 0.5 eV lower than substitution cost of Al in ZGO. Motivated by this energetically favorable substitution, a formation mechanism of the ZAGO and AGO layers was proposed. Spectroscopic ellipsometry studies revealed an increase in total thickness of the film from 105.07 nm (ZGO) to 147.97 nm (ZAGO/AGO) after annealing to 1100 °C, which were corroborated using TEM. Furthermore, an observed increase in the direct (indirect) optical bandgap from 5.06 eV (4.7 eV) to 5.72 eV (5.45 eV) with an increasing Al content in the ZAGO layer further underpins the formation of a quaternary ZAGO alloy with a tunable composition.

Thin films in the aluminosilicate (AlSiO) system containing up to 31 at. % Al and 23 at. % Si were prepared by reactive RF magnetron co-sputtering in order to investigate the dependence of film formation and optical properties on substrate temperature and Si and Al contents. The obtained films were amorphous with smooth microstructure. The growth rate at different substrate temperatures ranged from 1.2 to 3.3 nm/min and increase with increasing the Si target power. The roughness decreases and thickness increases with increasing Si content. The thickness of the films grown at a deposition temperature of 100 °C is found to be higher than the films deposited at 300 and 500 °C. The AlSiO-coated glasses have a higher transmission in the visible region than the uncoated glass. The spectroscopic ellipsometry analysis reveals that the refractive index value decreased with decreasing the Al content, having extinction coefficient values of zero in the measured spectral region and band gap values ≥ 3.4 eV. The obtained thin films have over 90% transmittance in the visible range and no systematic variation of transmittance was observed with substrate temperature. The results suggest that glass substrate coated with AlSiO thin films have improved optical properties.

Transmission Mueller-matrix spectroscopic ellipsometry is applied to the cuticle of the beetle Cetonia aurata in the spectral range 300-1000 nm. The cuticle is optically reciprocal and exhibits circular Bragg filter features for green light. By using differential decomposition of the Mueller matrix, the circular and linear birefringence as well as dichroism of the beetle cuticle are quantified. A maximum value of structural optical activity of 560 degrees/mm is found. (C) 2016 Optical Society of America

In this report we present studies on beetles of the Scarabaeidae family. The selected beetles show brilliant colors and in addition interesting polarization features. Mueller matrices of such beetles are of large interest to explore for biomimetics and for the understanding of the biological relevance of the observed polarization phenomena. Several species of the Scarabaeidae family have been studied by Hodgkinson, Goldstein  and our group to mention some. Ellipticity, degree of polarization and other derived parameters have been reported and Arwin et al. also did optical modeling to determine structural parameters of the scutellum part of the exoskeleton of Cetonia aurata. Mueller matrices are very rich in information about the sample properties and can also be analyzed by addressing depolarization. Cloude showed that a depolarizing Mueller matrix can be represented by a sum of up to four non-depolarizing Mueller matrices weighted by the eigenvalues of the covariance matrix of the Mueller matrix. These eigenvalues are all positive for a physically realizable Mueller matrix and this, so called sum decomposition can be used to filter matrices and obtain a measure of experimental fidelity. The result of the decomposition can also be used to describe a Mueller matrix as a set of basic optical elements having direct physical meaning, such as polarizers and retarders. Pioneering work on decomposition of Mueller-matrix images, including studies of beetles, was performed by Ossikovski et al. We have also previously demonstrated this with Cloude as well as regression decomposition of Mueller matrix spectra and images measured at near-normal incidence on C. aurata. Using Cloude decomposition we found that the experimentally determined Mueller matrix of C. aurata decomposes into a set of a mirror and a circular polarizer. Those results were then the basis for a more stable regression decomposition where the result was confirmed.

Chirality, tailored by external morphology and internal composition, has been realized by controlled curved-lattice epitaxial growth (CLEG) of uniform coatings of single-crystalline In_xAl_1-xN nanospirals. The nanospirals are formed by sequentially stacking segments of curved nanorods on top of each other, where each segment is incrementally rotated around the spiral axis. By controlling the growth rate, segment length, rotation direction, and incremental rotation angle, spirals are tailored to predetermined handedness, pitch, and height.  The curved morphology of the segments is a result of a lateral compositional gradient across the segments while maintaining a preferred crystallographic growth direction, implying a lateral gradient in optical properties as well. Left- and right-handed nanospirals, tailored with 5 periods of 200 nm pitch, as confirmed by scanning electron microscopy, exhibit uniform spiral diameters of ~80 nm (local segment diameters of ~60 nm) with tapered hexagonal tips.  High resolution electron microscopy, in combination with nanoprobe energy dispersive X-ray spectroscopy and valence electron energy loss spectroscopy, show that individual nanospirals consist of an In-rich core with ~15 nm-diameter hexagonal cross-section, comprised of curved basal planes. The core is surrounded by an Al-rich shell with a thickness asymmetry spiraling along the core. The ensemble nanospirals, across the 1 cm² wafers, show high in-plane ordering with respect to shape, crystalline orientation, and direction of compositional gradient. Mueller matrix spectroscopic ellipsometry shows that the tailored chirality is manifested in the polarization state of light reflected off the CLEG nanospiral-coated wafers. In that, the polarization state is shown to be dependent on the handedness of the nanospirals and the wavelength of the incident light in the ultraviolet-visible region.

We use angle-dependent Mueller-matrix spectroscopic ellipsometry (MMSE) to determine Mueller matrices of Scarabaeidae beetles which show fascinating reflection properties due to structural phenomena in the exocuticle which are often depolarizing. It has been shown by Cloude [1] that a depolarizing matrix can be decomposed into a sum of up to four non-depolarizing matrices according to M= aM­­₁+bM₂+cM₃+dM₄, where a, b, c and d are eigenvalues of the covariance matrix of M. Using the same eigenvalues the matrices M_i can be calculated. This method provides the full solution to the decomposition with both the non-depolarizing matrices and the weight of each of them in the sum.

An alternative to Cloude decomposition is regression decomposition. Here any Mueller matrix can be decomposed into a set of matrices M_i which are specified beforehand. Whereas in Cloude decomposition the only constraint on the matrices is that they are physically realizable non-depolarizing Mueller matrices, we can now limit the constraint and only use Mueller matrices representing pure optical devices having direct physical meaning, such as polarizers, retarders, etc. This leaves a, b, c, d as fit parameters to minimize the Frobenius norm M^exp -M^reg where M^exp is the experimentally determined Mueller matrix to be decomposed and M^reg is the sum of all M_i. Depending on M^exp an appropriate choice of M^reg matrices has to be made and different values of a, b, c and d are obtained through regression analysis.

We have previously shown that regression decomposition can be used to show that the Mueller matrix of Cetonia aurata can be decomposed into a sum of a circular polarizer and a mirror [2]. Here we expand the analysis to include angle-resolved spectral Mueller matrices, and also include more species of Scarabaeidae beetles.

One effect of the decomposition is that when depolarization is caused by an inhomogeneous sample with regions of different optical properties the Mueller matrices of the different regions can be retrieved under certain conditions. Regression decomposition also has potential to be a classification tool for biological samples where a set of standard matrices are used in the decomposition and the parameters a, b, c, d are used to quantify the polarizing properties of the sample.

[1] Cloude S.R. 1989. Conditions for the physical realisability of matrix operators in polarimetry. Proc. SPIE 1166, Polarization Considerations for Optical Systems II, pp. 177-185

[2] Arwin H, Magnusson R, Garcia-Caurel E, Fallet C, Järrendahl K, De Martino A, Ossikovski R, 2015. Sum decomposition of Mueller-matrix images and spectra of beetle cuticles. Opt. Express, vol. 23, no. 3, pp. 1951–1966

A Mueller matrix of a sample can be used to determine the polarization of  reflected light  for  incident light with arbitrary polarization. The polarization can be quantified  in terms of ellipticity, polarization azimuth and degree of polarization. We apply spectroscopic Mueller-matrix ellipsometry at multiple angles of incidence  to study the cuticle of beetles and derive  polarization features for incident unpolarized light.  In particular we address chiral phenomena in scarab beetles,  the origin of their structural colors and the observed high degree of circular polarization is discussed. Results from beetles in the Scarabaeidae subfamilies Cetoniinae and Rutelinae are presented including specimens with broad-band silver- or gold-like colors with metallic shine as well as specimens with narrow-band green or red reflectors. The variation of polarization with angle of incidence and occurrence of both left-handed and right-handed polarization from a single species are presented. We also use Mueller-matrix spectra in electromagnetic modeling and show how to determine structural parameters including cuticle layer thicknesses and optical properties. Interference oscillations in the observed spectra are due to allowed optical modes and we show how to develop a structural model of a cuticle based on this effect. Sum decomposition of  Mueller matrices measured on a depolarizing cuticle of a beetle is briefly discussed.

The scarab beetle Cetonia aurata is known to reflect light with brilliant colors and a high degree of circular polarization. Both color and polarization effects originate from the beetles exoskeleton and have been attributed to a Bragg reflection of the incident light due to a twisted laminar structure. Our strategy for mimicking the optical properties of the Cetonia aurata was therefore to design and fabricate transparent, chiral films. A series of films with tailored transparent structures of helicoidal In_xAl_1-xN nanorods were grown on sapphire substrates using UHV magnetron sputtering. The value of x is tailored to gradually decrease from one side to the other in each nanorod normal to its growth direction. This introduces an in-plane anisotropy with different refractive indices in the direction of the gradient and perpendicular to it. By rotating the sample during film growth the in-plane optical axis will be rotated from bottom to top and thereby creating a chiral film. Based on Muellermatrix ellipsometry, optical modeling has been done suggesting that both the exoskeleton of Cetonia aurata and our artificial material can be modeled by an anisotropic film made up of a stack of thin layers, each one with its in-plane optical axis slightly rotated with respect to the previous layer. Simulations based on the optical modeling were used to investigate how pitch and thickness of the film together with the optical properties of the constitutive materials affects the width and spectral position of the Bragg reflection band.

Spectral Mueller matrices are very rich in information about physical properties of a sample. We have recently shown that polarizing properties like ellipticity and degree of polarization can be extracted from a Mueller matrix measured on a beetle cuticle (exoskeleton). Mueller matrices can also be used in regression analysis to model nanostructures in cuticles. Here we present the use of sum decomposition of Mueller matrices from these depolarizing biological reflectors to explore the fundamental character of these reflectors. The objective is to decompose a Mueller matrix into well- defined ideal non-depolarizing matrices corresponding to mirrors, circular polarizers, halfwave retarders etc.Generally it is possible to decompose a measured depolarizing Mueller matrix M into four (or fewer) non-depolarizing matrices according to M=λ1M1+λ2M2+λ3M3+λ4M4, where λ1, λ2, λ3 and λ4 are eigenvalues of the covariance matrix of M. Two strategies for decomposition will be discussed. A Cloude decomposition will provide the eigenvalues and also the Mi’s although the latter will contain severe noise in some spectral regions. However, a major advantage with the Cloude decomposition is that the number of nonzero eigenvalues is directly obtained, i.e. the number of contributing Mi matrices. In an alternative decomposition, the Mi’s are assumed and the eigenvalues are found by regression analysis based on M. In the case with two non-zero eigenvalues we define a model Mueller matrix MD=αRM1+βRM2 with αR+βR=1. With αR as adjustable parameter, the Frobenius norm ||M-MD|| is minimized for each wavelength in the spectral range of M. For more complex structures, the regression can be extended by adding more matrices up to a total of four. Advantages with a regression approach are its simplicity and stability compared to a Cloude decomposition.Mueller-matrix spectra of beetle cuticles are recorded with a dual rotating compensator ellipsometer in the spectral range 400 – 900 nm at angles of incidence in the range 20 - 75°. The application of decomposition on biological reflectors is demonstrated on M measured on the beetle Cetonia aurata, which represents a narrow-band chiral Bragg reflector with two non-zero eigenvalues. A decomposition in an ideal mirror and a circular polarizer is feasible. In another example, the broad-band and gold-colored beetle Chrysina argenteola, we show that more than two eigenvalues can be nonzero, especially at oblique incidence, and additional matrices are involved.