Simple birefringence measurement method for coated optical disks with a fixed incident angle ellipsometer

In a coated and laminated optical disk, only a reflectance method is available for oblique incidence retardation measurements to evaluate the birefringence in a polycarbonate substrate. I propose a simple measurement method that simultaneously measures both the lateral and vertical birefringence in a coated substrate. In this reflectance method, only two oblique incidence retardation values with a fixed incident angle are measured from the radial and the circumferential directions of the disk. Using the sum and the difference of these two retardation values, we can calculate both birefringences without any cumbersome curve-fitting procedure. This method can easily be introduced into the routine inspection for optical disk manufacturing.     

Method for determining the optical axis and (n(e), n(o)) of a birefringent crystal

There is a phase difference between s and p polarizations when a circularly polarized heterodyne light beam is reflected from a birefringent crystal. It can be measured accurately with a common-path heterodyne interferometric technique. We have derived an equation that describes the relationship between the phase differences and n(e), n(o), and alpha. Two groups of solutions for (n(e), n(o)) can be obtained from this equation by the phase measurements performed at three incident angles under moderate conditions. Each group consists of three pairs of solutions for (ne), n(o)). Finally, by justifying with physical conditions, we obtained the correct solution for (n(e), n(o)). Azimuth angle alpha of the birefringent crystal optical axis can also be determined. And the feasibility of this method is demonstrated.     

Effects of tissue surface curvature and incident light angle on diffuse correlation spectroscopy

Diffuse correlation spectroscopy is an emerging technique for the continuous, non-invasive monitoring of blood flow in biological tissues. However, the influence of oblique incidence and surface curvature has not been fully discussed. In this paper, we study the effects of the incident angle and surface curvature on diffuse correlation spectroscopy measurement and the blood flow index (BFI). For semi-infinite plane with lower absorption, oblique incidence angle has slightly stronger influence. Larger incident angles lead to high values and a reduced decay rate of the normalized electric field temporal autocorrelation. When the radius of curvature is more than 10?cm, the BFI estimation error reduced to less than 5% and very close to semi-infinite plane case. Besides, for the surface with small radius of curvature, larger incident angles sometimes may cause smaller estimated errors of the BFI. This work may help improve BFI estimation accuracy from diffuse correlation spectroscopy.     

基于两向设计地震动的二维自由场构建

针对在设计地震动基础上构建平面半空间自由场的问题,在综合考虑水平向与竖直向设计地震动基础上获得平面半空间自由场,实现了将设计地震动与以任意角度组合入射的P波、SV波构成的自由场相联系。首先在已有成果的基础上,研究了以任意角度入射情况下P波及其反射波、SV波及其反射波对水平向和竖直向设计地震动的贡献;然后在假设入射P波、SV波与两向设计地震动具有相同频率组成的基础上,获得了以特定角度组合入射条件下P波、SV波的频谱和相位信息;进而通过傅里叶逆变换获得入射P波、SV波的时间序列;最后依据P波、SV波及其反射波在平面半空间的传播情况获得自由场条件下平面半空间内任意点的水平向和竖直向地震动。该文所采用的波场构建方法可实现对包含任意频谱和相位信息的两向设计地震动所对应的平面半空间自由场的构建,所获得的斜入射P波和SV波也具有各自的频谱和相位信息。最终得到的平面半空间自由场任意点水平向和竖直向地震动时间序列具有非一致性;根据入射P波、SV波结合地基边界条件确定的空间点地震动时间序列可用于结构的非一致地震动输入。     

Integrated photoelasticity through imaging fourier polarimetry of an elliptic retarder

It is shown that three optical parameters that are necessary for stress computation in integrated photoelasticity can be measured with high accuracy by use of a Fourier polarimetry method. Inasmuch as a photoelastic sample, which is an object of investigation in integrated photoelasticity, is a kind of an elliptic retarder, the technique presented here measures relative retardation delta, azimuth angle theta, and ellipticity angle epsilon instead of the characteristic parameters that traditionally have been used in integrated photoelasticity. The ability of the new technique to provide better accuracy with a simpler setup has been proved experimentally. Furthermore, the technique is self-contained as for phase measurement; i.e., it automatically performs phase unwrapping at the points where phase data exceed the value of pi. The full value of a phase at a certain point is retrieved by processing of pi-modulo phase data that have been precisely measured at several wavelengths. The usefulness of the new method for integrated photoelasticity has been demonstrated through measurement of a diametrically compressed disk viewed at oblique light incidence.     

Measurement of two-dimensional small angle deviation with a prism interferometer

A new technique for the measurement of two-dimensional small angular deviation is presented. A compound prism, which effectively produces a combination of two right-angled prisms in orthogonal directions, and plane reference surfaces have been utilized for the measurement of the orthogonal components of the angular tilt of an incident plane wavefront. Each orthogonal component of the angular tilt is separately measured from the angular rotation of the resultant wedge fringes between two plane wavefronts generated due to splitting of the incident plane wavefront by the corresponding set of right-angled prism and plane reference surface. The technique is shown to have high sensitivity for the measurement of small angle deviation. A monolithic prism interferometer, which is practically insensitive to vibration, is also proposed. Results obtained for the measurement of a known tilt angle are presented.     

Transmission of a two-dimensional Gaussian beam into a uniaxial crystal.

We study the transmission of a two-dimensional (2-D) TM Gaussian beam through a plane interface between an isotropic medium (e.g., air) and a uniaxially anisotropic crystal. The optic axis of the crystal is taken to be in the plane of incidence but is arbitrarily oriented relative to the interface normal. We show that, in the paraxial approximation, a nontruncated transmitted 2-D TM Gaussian beam inside a uniaxial crystal can be expressed in a form similar to that of a scalar Gaussian beam that propagates in a homogeneous medium. We also show that the transmitted beam corresponding to an incident 2-D TM Gaussian beam with its main propagation direction along the interface normal is tilted inside the crystal by the same angle as is the transmitted axial ray that corresponds to a normally incident ray.     

Stokes-parameter photopolarimeter using an optically ormechanically rotatable two-detector assembly

A two-detector photopolarimeter for measuring the four Stokes parameters of a monochromatic or quasi-monochromatic light beam in an arbitrary state of partial elliptical polarization is described. Each detector is partially specularly reflecting at oblique incidence, and the plane of incidence is rotated (by other than 90°) between the two successive reflections. The two-detector assembly is itself rotated manually or with a stepping motor solidly as one unit around the axis of the incident beam. Mechanical rotation may be eliminated by using a Faraday rotator in front of a stationary arrangement of two detectors. Conditions under which singularities may occur (which lead to an incomplete measurement of polarization) are discussed. Optimum geometry and detector-surface characteristics are identified     

Dispersion of linearly polarized light propagating in a thin birefringent plate

We analyze theoretically the dispersion of linearly polarized light propagating in a uniaxial anisotropic medium where multibeam interference is present. Explicit expressions of the group-delay dispersion for transmitting waves are derived for the simplest situation, and the effect of dispersion on pulse broadening is analyzed for a few selected cases. Our results reveal that at normal incidence and in the situation where the optic axis is parallel to the surface of birefringent plate (in the x-y plane), the dispersion of the refracted wave decreases with the extent of birefringence. In particular, the dispersion for the electric field parallel to the polarization direction of the incident light changes with the rotation angle between the optic axis and the polarization direction of the incident field, whereas the dispersion for the refracted field whose direction is vertical to the polarization of incident light is independent of this angle. For oblique incidence, dispersion varies substantially for different incident angles. In the situation where the optic axis is in the x-z plane at either normal or oblique incidence, the dispersion increases in a periodically oscillating manner as a function of the relative thickness of the birefringent plate.     

Diffraction of horizontally polarized ultrasonic plane waves on a periodically corrugated solid-liquid interface for normal incidence and Brewster angle incidence

The theory, and the use at normal incidence, of shear-vertically polarized waves (with polarization vector in the plane containing the incident wave vector and the normal on the interface) using the mode conversion method has been tackled by others. Here we develop the theory for shear-horizontally polarized incident waves (with polarization vector perpendicular to both the normal on the interface and the incoming wave vector). We take into account normal incidence as well as oblique incidence. For normal incidence, we discover the generation of Love waves. If oblique incidence is considered, we discover the existence of a Brewster angle of incidence, comparable with the Brewster angle in optics, in which a diffraction grating can be used as a polarization filter.     

房间内早期反射声方向分布的声强法测量

早期反射声的方向分布,对空间感音质参量的评价具有重要意义。室内音质不仅与反射声到达的时间、能量有关,而且与反射声到达的方向特性具有密切的关系,反映反射声方向特性的客观音质参量在音质评价中得到了越来越多的应用。根据声强测量的互谱法原理,论文提出采用不在同一平面上的任意四只传声器进行瞬时声强的测量,经合成得到各频带早期反射声方向分布特性的方法。该测量方法弱化了常规传声器阵列测试方法中对传输器位置的严格要求,同时也可有效降低由于传输器之间的相位不匹配带来的测量误差,因而更适合于现场测量。运用该测量方法,在消声中对单入射声条件下的入射方向进行了实验测量验证,表明其具有较高的准确性,同时对一实际房间中早期反射声的方向分布进行了测量,给出了直角坐标系中三个相互垂直平面上的反射声能量与入射方向的分布图。测量结果表明该测试方法可应用于实际房间中早期反射声方向分布的测量。     

Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals

We present a numerical study of bidimensional photonic crystals with an emphasis on the behavior of the gaps versus the polarization and the conicity of the incident plane wave. We use a rigorous modal theory of diffraction at oblique incidence by a set of arbitrarily shaped parallel fibers. This theory allows the study of the refractive properties of bidimensional photonic crystals. We develop a heuristic method of homogenization that allows us to predict the position of the gaps and their behavior with respect to the polarization and the conicity angle. With this homogenization scheme, we also present some important elements for obtaining full gaps.     

双折射波片相位差的精确表达

为了更准确地描述双折射波片的特性,提出了取消普遍采用的传统相位差表达式中所包含的近似假设的思想。从晶体双折射的性质出发,结合双折射波片的结构特点,将e光波法线在波片中的折射角和折射率用入射角及晶体的参量表示出来,推导出e光波法线与o光波法线间相位差更准确的表达式。为了研究偏振光之间干涉的需要,推导出光线间相位差的精确表达式,以准确表述光线的路径,特别是晶片外的路径。更精确的相位差表述为更准确地分析双折射波片的特性提供了极大的方便。     

Anisotropic scatter patterns and anomalous birefringence of obliquely deposited cerium oxide films

Cerium oxide films formed by electron-beam evaporation onto oblique substrates are shown to scatter light strongly into spatially anisotropic distributions and to exhibit large normal-incidence birefringence Δ n = n(s) - n(p). The apparatus for direct recording of a useful projection of the scatter distributions is described. Characteristic differences in scatter patterns recorded for cerium oxide, relative to those from tilted columnar titania and zirconia films, are believed to be associated with unusual microstructures recorded for cerium oxide films by scanning electron microscopy. With increasing angle of deposition, the microstructure of cerium oxide was observed to change from densely packed columns to partially isolated needlelike columns at angles that do not obey the tangent rule. In particular, deposition at 55° yielded columns nearly perpendicular to the substrate, yet the normal-incidence birefringence was large. The retardation of the films was recorded as a function of angle of incidence for propagation in the deposition plane. A turning point near 0° incidence for the 55° film confirmed that one principal axis is perpendicular to the substrate. Significant bunching of columns into rows running perpendicular to the deposition plane was recorded by scanning electron microscopy and may account for both the scatter and the birefringence.     

Magnetic properties of rare-earth transition-metal alloy films prepared by oblique incidence method

Ferromagnetic thin films of Sm-Co and Sm-Fe system were prepared by the oblique incidence method. The saturation flux density of both systems decreases rapidly with the increase of Sm concentration. Coercive force of 2.0 kOe in Sm-Co and 1.0 kOe in Sm-Fe films were obtained at an incident angle of 45°. These films were magnetically anisotropic and the magnetic easy direction was always aligned for perpendicular direction of the incident plane. The structure of the film in the present work seemd to be amorphous in which microdomains were orientated by the oblique incidence, in contrast to the columnar grane structure found in Fe and Co films prepared by the oblique incidence.     

On a Measurement Method of the Tensor Permeability of Ferrite Using Faraday Rotation

A new measuring technique of the tensor permeability of ferrite in the microwave frequencies based on Faraday rotation is proposed. A circular cylindrical waveguide containing a longitudinally magnetized ferrite rod is used. A plane polarized TE11 wave is incident upon the section where the ferrite cylinder is placed. One end of the circular waveguide is short-circuited by a movable short-circuit plunger, which holds the ferrite cylinder through a hole drilled at the center. The angle of Faraday rotation and the position of the minimum voltage point of the elliptically polarized standing wave are measured far from the ferrite section. In addition to the measurement theory, several discussions are given: i) the relationship between a diameter of the specimen and the cutoff wavelengths of modes in the waveguide, ii) the extent of unwanted reflections due to the impedance mismatch at the end of the rod. As an experimental example, the tensor permeabilities of a polycrystalline rod of YIG are measured at the frequency 3.75 GHz with some dc magnetic field intensities.     

Use of a laser beam with an oblique angle of incidence to measure the reduced scattering coefficient of a turbid medium

A simple and quick approach is used to measure the reduced scattering coefficient (μ(s)') of a semi-infinite turbid medium having a much smaller absorption coefficient than μ(s)'. A laser beam with an oblique angle of incidence to the medium causes the center of the diffuse reflectance that is several transport mean-free paths away from the incident point to shift away from the point of incidence by an amount Δx. This amount is used to compute μ(s)' by μ(s)' = sin(α(i))/(nΔx) where n is the refractive index of the turbid medium divided by that of the incident medium and α(i) is the angle of incidence measured from the surface normal. For a turbid medium having an absorption coefficient comparable with μ(s)', a revision to the above formula is made. This method is tested theoretically by Monte Carlo simulations and experimentally by a video reflectometer.     

Measurement method of Stokes parameters using a quarter-wave plate with phase difference errors

The Stokes parameters (S0, S1, S2, and S3) of monochromatic light can be measured using the adjustable azimuth settings of a quarter-wave plate and a polarizer. When measuring the Stokes parameters of light of an arbitrary wavelength, the measurement of S3 is affected by the phase difference error Δq(λi), due to the mismatch with respect to wavelength with the quarter-wave plate. In this method, Δq(λi), due to such a mismatch of incident light of arbitrary wavelength, can be overcome by a judicious choice of azimuth settings of the quarter-wave plate and the use of a polarizer; however, the use of a precision quarter-wave plate is necessary. The present paper proposes a measurement method of Stokes parameters of incident light of arbitrary wavelength using a quarter-wave plate with phase difference errors.     

A free-space bistatic calibration technique for the measurement ofparallel and perpendicular reflection coefficients of planarsamples

A free-space bistatic measurement system suitable for operation in the frequency range of 5.85-40 GHz is calibrated to measure the parallel and perpendicular reflection coefficients of metal-backed planar samples for obliquely incident waves. The measurement system consists of transmit and receive antennas in the bistatic configuration, mode transitions, precision coaxial cables, and the network analyzer. Diffraction effects of the edges of the sample are minimized by using spot-focusing horn lens antennas, which focus most of the energy on a one-wavelength-diameter circular section of the sample. A new free-space bistatic calibration technique is developed to eliminate errors due to multiple reflections between transmit and receive antennas via the surface of the sample. The effect of defocusing due to the obliquely incident plane wave with focused antennas is minimized by introducing correction factors which modify measured reflection coefficients. Details of the calibration procedure and a discussion of the experimental results obtained for planar samples of Teflon and Eccogel 1365-90 in the frequency range 12.4-18 GHz are presented     

Finite-element time-domain modelling of plane wave scattering by a periodic structure using an exact boundary condition

A two-dimensional singly-periodic structure, at plane wave oblique incidence, is modelled using the finite-element time-domain method. Over the non-periodic boundaries of the computational domain, an exact Floquet modal absorbing boundary condition is developed, in detail, for the finite element method in the time domain. The proposed formulation is validated by comparing its results with that of the finite-element frequency-domain method and with independently obtained published results. Very accurate numerical results, over a wide frequency range and incident angle range, are obtained for both transverse electric and transverse magnetic polarised plane wave illuminations