Mueller-matrix ellipsometry using the division-of-amplitude photopolarimeter: a study of depolarization effects

A fully automated Mueller-matrix ellipsometer with a division-of-amplitude photopolarimeter as the polarization-state detector is described. This device achieves Mueller-matrix ellipsometry by measuring the Stokes parameters of reflected light as a function of the fast axis C of a quarter-wave retarder, which, in combination with a fixed linear polarizer, determines the polarization state of incident light. The reflected Stokes parameters were Fourier analyzed to give the 16 elements of the Mueller matrix. We investigated depolarization of polarized light on reflection from rough, heterogeneous, and anisotropic surfaces by obtaining measurements on rolled aluminum and plant leaves. The results demonstrate (1) a variation of degree of polarization of reflected light with the input polarization state, (2) the precision with which the measured matrices describe the depolarization results, (3) effects of surface anisotropy (rolling direction) on depolarization and cross polarization by reflection from aluminum surfaces, and (4) large values and differences in the depolarization effects from conifer and deciduous leaves. Depolarization of light reflected by the aluminum surfaces was most sensitive to the angle between the plane of incidence and the rolling direction when the incident Stokes parameters S(1), S(2), and S(3) were equal.     

Optical analysis of absorbing double layers by combined reflection and transmission ellipsometry

A method known as combined ellipsometry, which utilizes the simultaneous interpretation of the ellipsometric parameters determined for light reflected and transmitted by the air side and by the substrate side of thin films, was used to obtain an optical analysis of absorbing double layers deposited onto a non-absorbing substrate. It is shown that the use of this method enables the evaluation of all the optical parameters characterizing absorbing double layers consisting of a non- absorbing and an absorbing thin film. Combined ellipsometry can be used for analysing the double layers formed by two highly absorbing thin films in a reasonable way if this method is complemented by a precise auxiliary method, e.g. the Fizeau method. These conclusions are demonstrated by experimental results obtained for samples of the following double layers: MgF₂/Al, Al/MgF₂, TiO/Au and Au/Ni. The ellipsometric parameters were measured at a wavelength λ of 632.8 nm.     

Interference by multiple reflections in crystal plates of point group symmetries C 3 v,C 4 v,C 6 v

Crystals of symmetry point groups C _3v , C _4v , C _6v possess an antisymmetric tensor of linear spatial dispersion (LSD) and thus they do not rotate the plane of light polarization. The antisymmetric LSD (ALSD) influences the polarization of the electromagnetic eigenmodes of the crystal and it may be studied through reflection only. In this paper we study the interference by multiple reflection in anisotropic crystal plates of the aforementioned point groups (the optical axis is perpendicular to the plane of incidence). The amplitudes of the reflected and transmitted electromagnetic beams are calculated both in the case of single reflection and in the case of multiple reflection. Differential reflection methods have been proposed and analysed in the case of elliptically and linearly polarized incident beams. The dependences of the multiple reflection intensity and of the differential reflected and transmitted signals on the angle of incidence is calculated for the crystals Ag₃AsSe₃, ZnO and CdS. It is shown that in the case of total reflection in an anisotropic plate surrounded by an optically denser medium the effects of the ALSD on reflection are enhanced several times.     

New chiral liquid crystalline monomers, polymers, and elastomers derived from menthol derivatives: synthesis and mesomorphism

To investigate liquid crystalline properties and structure relationships of chiral compounds based on menthol, a series of new chiral monomers derived from menthol derivatives, a mesogenic crosslinking agent, the corresponding side chain homopolymers with siloxane backbone, and cholesteric elastomers were synthesized. The structures and purity of these chiral compounds obtained in this study were characterized using FTIR, ¹H NMR, and elemental analyses. The mesomorphism and thermal stabilities were investigated using differential scanning calorimetry, polarizing optical microscopy, thermogravimetric analysis, and X-ray diffraction. The selective reflection of light for the chiral monomers was studied with UV/visible/near IR. The effect of the crosslinking agent content on the phase transition temperatures of the elastomers was discussed. It was found that these chiral monomers seemed beneficial for the formation of the mesophases when a flexible spacer was inserted between the mesogenic core and the terminal menthyl groups. All obtained chiral monomers showed a cholesteric phase, chiral smectic C phase, and cubic blue phase. The crosslinking agent exhibited a smectic A (S_A) phase and nematic phase. However, their corresponding homopolymers with siloxane chains tended to form a lower order S_A phase. With an increase of the mesogenic rigidity, the melting temperatures, glass transition temperatures (T _g), and isotropic temperatures (T _i) of chiral monomers or homopolymers all increased. For the elastomers, general tendency was toward increased T _g and T _i with increasing the crosslinking agent content.     

Synchrotron Radiation. Techniques and Applications

The polarization properties of scattered monochromatic light fields are described by stochastic Stokes parameters S ₀, S ₁, S ₂ and S ₃ which fluctuate in space. We determine the theoretical first-order probability density functions of these Stokes parameters assuming a chi-square density for the intensity of orthogonal linear polarized field components, a uniform density for the relative phase between the corresponding fields and statistical independence of these stochastic quantities. If these assumptions hold, the density of S 0 equals the probability density of a sum of two speckle fields and S ₁, S ₂ and S ₃ are Laplace variates.     

Fiber-based single-channel polarization-sensitive spectral interferometry

We present a novel, to our knowledge, fiber-based single-channel polarization-sensitive spectral interferometry system that provides depth-resolved measurement of polarization transformations of light reflected from a sample. Algebraic expressions for the Stokes parameters at the output of the interferometer are derived for light reflected from a birefringent sample by using the cross-spectral density function. By insertion of a fiber-optic spectral polarimetry instrument into the detection path of a common-path spectral interferometer, the full set of Stokes parameters of light reflected from a sample can be obtained with a single optical frequency scan. The methodology requires neither polarization-control components nor prior knowledge of the polarization state of light incident on the sample. The fiber-based single-channel polarization-sensitive spectral interferometer and analysis are demonstrated by measurement of phase retardation and fast-axis angle of a birefringent mica plate.     

Ellipsometry as a means of mass-thickness determination in the earliest film growth stages

Gold was evaporated onto a fused silica substrate, and the normalized Stokes parameters S₁, S₂ and S₃, which represent the state of polarization of the light reflected from the sample, were determined in situ for films of average thickness less than a few monolayers with an automatic ellipsometer; the film mass m per unit substrate area was measured simultaneously with a torsion microbalance. It was found that $\text{ΔS = {(ΔS}{}_1\text{)}{}^2\text{+ (ΔS}{}_2\text{)}{}^2\text{+ (ΔS}{}_3\text{)}{}^2\text{}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ changes linearly with m for light of wavelength λ well outside the absorption band of the film. For λ = 440 nm the sensitivity is comparable with that of a good torsion microbalance. Thus an automatic ellipsometer can conveniently be employed in the microgravimetry of submonolayer films.     

Comprehensive analysis of retroreflection in Papilio crino Fabricius, 1792 wings

Multilayer thin‐film structures in the wings of a butterfly; Papilio crino produce a colourful iridescence from reflected light. In this investigation, scanning electron microscope images show both the concave cover scales and pigmented air‐chamber ground scales. The microstructures with the concavities retroreflect incident light, thus causing the double reflection. This gives rise to both the colour mixing and polarisation conversion clearly depicted in the optical images. The result of the numerical and theoretical analysis via the CIELAB, and optical reflection and transmission of light through the multilayer stacks with the use of transfer method show that the emerging colouration on the Papilio crino is structural and is due to the combination of colours caused by multiple bounces within the concavities. The butterfly wing structure can be used as the template for designing the photonic device.Inspec keywords: bio‐optics, scanning electron microscopy, photodiodes, optical sensors, optical images, light reflection, reflectivity, colour, optical links, multilayers, optical multilayers, light polarisationOther keywords: pigmented air‐chamber ground scales, concavities, incident light, double reflection, colour mixing, polarisation conversion, optical images, numerical analysis, theoretical analysis, optical reflection, multilayer stacks, emerging colouration, butterfly wing structure, papilio crino fabricius, thin‐film structures, colourful iridescence, reflected light, electron microscope images, concave cover scales     

Determination of Ratio of Complex Eigenvalues of Optical Systems with Known Eigenpolarizations by Ellipsometry

Surface ellipsometry involves measurement of the ratio of eigenvalues (reflection coefficients) associated with the orthogonal linear eigenpolarization parallel and perpendicular to the plane of incidence. This paper shows that the ratio of complex eigenvalues of any optical system with known arbitrary eigenpolarizations can be determined, with equal ease, using the same ellipsometer arrangements of surface ellipsometry. Expressions are derived that give the ratio of eigenvalues as a function of (1) the Cartesian complex polarization variables that describe the eigenpolarizations, (2) a set of nulling angles in the symmetrical PC₁SC₂A or asymmetrical PCSA and PSCA ellipsometer arrangements, (3) the slow-to-fast complex relative transmittance of the compensator(s). The results are applied to the ellipsometric measurement of optical rotatory dispersion and circular dichroism.     

Quantum phase measurements and non-classical polarization states of light

Abstract

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.     

光栅分振幅光偏振测量系统的研制

使用一个既能产生反射光衍射又能产生透射光衍射的特殊金属光栅作为分光器,研制一种新颖的高速光波偏振态测量系统。它没有使用转动光学部件或调制器,而是将金属光栅产生的四条1级衍射光的光强线性地转换为电信号,通过定标方法得到系统的非奇异的仪器矩阵,然后通过线性运算得到入射光的待测Stokes矢量。该系统结构紧凑、安装方便,可用作实时偏振测量术和椭偏测量术中的偏振态探测器。     

Cholesteric Liquid Crystals with a Broad Light Reflection Band

The cholesteric‐liquid‐crystalline structure, which concerns the organization of chromatin, collagen, chitin, or cellulose, is omnipresent in living matter. In technology, it is found in temperature and pressure sensors, supertwisted nematic liquid crystal displays, optical filters, reflective devices, or cosmetics. A cholesteric liquid crystal reflects light because of its helical structure. The reflection is selective – the bandwidth is limited to a few tens of nanometers and the reflectance is equal to at most 50% for unpolarized incident light, which is a consequence of the polarization‐selectivity rule. These limits must be exceeded for innovative applications like polarizer‐free reflective displays, broadband polarizers, optical data storage media, polarization‐independent devices, stealth technologies, or smart switchable reflective windows to control solar light and heat. Novel cholesteric‐liquid‐crystalline architectures with the related fabrication procedures must therefore be developed. This article reviews solutions found in living matter and laboratories to broaden the bandwidth around a central reflection wavelength, do without the polarization‐selectivity rule and go beyond the reflectance limit.     

Cylinder and metal grating polarization beam splitter

We propose a novel and compact metal grating polarization beam splitter (PBS) based on its different reflected and transmitted orders. The metal grating exhibits a broadband high reflectivity and polarization dependence. The rigorous coupled wave analysis is used to calculate the reflectivity and the transmitting spectra and optimize the structure parameters to realize the broadband PBS. The finite-element method is used to calculate the field distribution. The characteristics of the broadband high reflectivity, transmitting and the polarization dependence are investigated including wavelength, period, refractive index and the radius of circle grating. When grating period d = 400 nm, incident wavelength λ = 441 nm, incident angle θ = 60° and radius of circle d/5, then the zeroth reflection order R₀ = 0.35 and the transmission zeroth order T₀ = 0.08 for TE polarization, however, T₀ = 0.34 and R₀ = 0.01 for TM mode. The simple fabrication method involves only single etch step and good compatibility with complementary metal oxide semiconductor technology. PBS designed here is particularly suited for optical communication and optical information processing.     

Fabrication of a simultaneous red-green-blue reflector using single-pitched cholesteric liquid crystals

A cholesteric liquid crystal (CLC) is a self-assembled photonic crystal formed by rodlike molecules, including chiral molecules, that arrange themselves in a helical fashion. The CLC has a single photonic bandgap and an associated one-colour reflection band for circularly polarized light with the same handedness as the CLC helix (selective reflection). These optical characteristics, particularly the circular polarization of the reflected light, are attractive for applications in reflective colour displays without using a backlight, for use as polarizers or colour filters and for mirrorless lasing. Recently, we showed by numerical simulation that simultaneous multicolour reflection is possible by introducing fibonaccian phase defects. Here, we design and fabricate a CLC system consisting of thin isotropic films and of polymeric CLC films, and demonstrate experimentally simultaneous red, green and blue reflections (multiple photonic bandgaps) using the single-pitched polymeric CLC films. The experimental reflection spectra are well simulated by calculations. The presented system can extend applications of CLCs to a wide-band region and could give rise to new photonic devices, in which white or multicolour light is manipulated.     

Generalized ellipsometry for materials characterization

Ellipsometry experiments normally measure two to four parameters, which are converted to the ellipsometric parameters ψ and Δ. This is usually sufficient for many samples, but more complicated situations (such as anisotropic or depolarizing samples) require more sophisticated measurements. Over the last 7 years, we have developed the two-modulator generalized ellipsometer (2-MGE), which measures eight elements of the sample Mueller matrix simultaneously either in reflection or transmission. In reflection, the 2-MGE totally characterizes light reflection from anisotropic samples, measuring the normal ellipsometry parameters, as well as the cross-polarization and depolarization effects. Applications include the determination of the spectroscopic optical functions of uniaxial materials (such as TiO₂ and ZnO), and the measurement of cross-polarization from diffractive structures. In transmission, the 2-MGE completely characterizes a general linear diattenuator and retarder. Applications include the measurement of the retardation and diattenuation of film polarizers and internal electric fields in LiNbO₃ and CdZnTe under bias.     

Preflight calibration of the Imaging Magnetograph eXperiment polarization modulation package based on liquid-crystal variable retarders

We present the study, characterization, and calibration of the polarization modulation package (PMP) of the Imaging Magnetograph eXperiment (IMaX) instrument, a successful Stokes spectropolarimeter on board the SUNRISE balloon project within the NASA Long Duration Balloon program. IMaX was designed to measure the Stokes parameters of incoming light with a signal-to-noise ratio of at least 10³, using as polarization modulators two nematic liquid-crystal variable retarders (LCVRs). An ad hoc calibration system that reproduced the optical and environmental characteristics of IMaX was designed, assembled, and aligned. The system recreates the optical beam that IMaX receives from SUNRISE with known polarization across the image plane, as well as an optical system with the same characteristics of IMaX. The system was used to calibrate the IMaX PMP in vacuum and at different temperatures, with a thermal control resembling the in-flight one. The efficiencies obtained were very high, near theoretical maximum values: the total efficiency in vacuum calibration at nominal temperature was 0.972 (1 being the theoretical maximum). The condition number of the demodulation matrix of the same calibration was 0.522 (0.577 theoretical maximum). Some inhomogeneities of the LCVRs were clear during the pixel-by-pixel calibration of the PMP, but it can be concluded that the mere information of a pixel-per-pixel calibration is sufficient to maintain high efficiencies in spite of inhomogeneities of the LCVRs.     

Internal reflection ellipsometry for real-time monitoring of polyelectrolyte multilayer growth onto tantalum pentoxide

Internal reflection ellipsometry was used for detection of the consecutive coating of two polyelectrolytes, poly(allylamine hydrochloride) (PAH) and poly(acrylic acid) (PAA), onto a tantalum pentoxide (Ta₂O₅) substrate until the 10th bilayer. The UV patterned PAH-PAA-multilayer was characterized in air via ellipsometry and atomic force microscopy. Suited optical models enabled the determination of the layer thicknesses in wet and dry states. Linear multilayer formation could be proved by Attenuated Total Reflection — Fourier Transformed Infrared Spectroscopy measurements following the increase of the ν(C=O) band depending on the adsorption of the PAA. Streaming potential measurements after each layer deposition step indicated a change in surface charge after each layer deposition due to the consecutive coating of PAH and PAA. In this article the internal reflection ellipsometry is shown to be a convenient possibility to analyze the modification of a thin transparent Ta₂O₅ substrate.     

Simulation of the depolarization effect in porous silicon

We describe a radiative transfer (RT) equation for the simulation of optical scattering effects in a nanostructured semiconductor for spectroscopic ellipsometry (SE). As an example, we chose porous silicon (PS), whose pores are considered to act as light scatterers. We examined the effects of pore radius, slab thickness, and incident angle. The volume scattering effect in the internal morphology of the PS generates incoherent light, leading to depolarization. By simulating the four Stokes parameters through the RT equation, we could theoretically assess the degree of polarization that is essential for SE measurements of some nanostructured semiconductors.     

Dove prisms and polarized light

Abstract

A Dove prism inverts the transmitted image and, when rotated, rotates the image at twice the rotation frequency of the prism. However, although the image is rotated, for a wide range of design parameters the polarization state of the transmitted light is not rotated. This has important implications when using Dove prisms within laser cavities, interferometers and other optical experiments.     

Optical characterization of thin chalcogenide films by multiple-angle-of-incidence ellipsometry

Optical properties of thin chalcogenide films from the systems As-S(Se) and As-S-Se were investigated as a function of the film composition, film thickness and conditions of illumination by light using multiple-angle-of-incidence ellipsometry. Thin films were deposited by thermal evaporation and exposed to white light (halogen lamp) and to monochromatic light from Ar⁺ — (λ = 488, 514 nm) and He-Ne- (λ = 632.8 nm) lasers. The ellipsometric measurements were carried out at three different angles of light incidence in the interval 45-55°, at λ = 632.8 nm. An isotropic absorbing layer model was applied for calculation of the optical constants (refractive index, n and extinction coefficient, k) and film thickness, d. The homogeneity of the films was checked and verified by applying single-angle calculations at different angles. It was shown that the refractive index, n of As-S-Se films is independent of film thickness in the range of 50 to 1000 nm and its values varied from 2.45 to 3.05 for thin layers with composition As₂S₃ and As₂Se₃, respectively. The effect of increasing in the refractive index was observed after exposure to light which is related to the process of photodarkening in arsenic containing layers. The viability of the method for determining the optical constants of very thin chalcogenide films with a high accuracy was confirmed.