Asymmetric transverse-load characteristics and polarization dependence of long-period fiber gratings written by a focused CO(2) laser

Asymmetric transverse-load characteristics and the polarization dependence of long-period fiber gratings (LPFGs) written by high-frequency CO(2) laser pulses are investigated in detail. It is demonstrated that the resonant wavelength is dependent on the direction of the applied force and on the polarization state of the input light; however, the coupling strength is independent of these parameters. When a transverse load is applied along different orientations of the LPFG, the resonant wavelength may be shifted toward the longer wavelength, the shorter wavelength, or hardly shifted, whereas the absolute value of peak transmission attenuation is linearly decreased with an increase of the applied transverse load, with almost no sensitivity to the load direction. These unique transverse-load characteristics and the polarization dependence are due to the load-induced birefringence that leads to the rotation of optical principal axes in the LPFG.     

Ultrasonic Measurement of Stress Using a Rotating EMAT

Abstract

The acoustic birefringence method is primarily used to measure differences of principal stresses in regions where principal stresses coincide with material symmetry axes. To determine the differences of principal stresses also requires knowledge of the unstressed birefringence at the measurement locations. Consequently, variability in texture can introduce errors in stress determination. In contrast, the ultrasonic measurement of shear stress is independent of texture. The shear stress causes a rotation φ of the pure-mode polarization directions of the SH waves used in our experiments. We constructed a motorized electromagnetic-acoustic transducer (EMAT) and used it to measure phase as the EMAT is rotated. We developed an algorithm to determine φ and the birefringence B. We measured the shear stress along parallel scanlines in a residual-stress specimen with known stress state. We calculated the shear stress gradient and used it in the stress-equilibrium equation to determine the normal stress acting along the scanline direction. The other plane stress component was determined from an acoustoelastic relation between B and the difference of normal stresses. Good agreement was obtained with theoretical stress values.     

Ultrasonic Measurement of Stress Using a Rotating EMAT

The acoustic birefringence method is primarily used to measure differences of principal stresses in regions where principal stresses coincide with material symmetry axes. To determine the differences of principal stresses also requires knowledge of the unstressed birefringence at the measurement locations. Consequently, variability in texture can introduce errors in stress determination. In contrast, the ultrasonic measurement of shear stress is independent of texture. The shear stress causes a rotation φ of the pure-mode polarization directions of the SH waves used in our experiments. We constructed a motorized electromagnetic-acoustic transducer (EMAT) and used it to measure phase as the EMAT is rotated. We developed an algorithm to determine φ and the birefringence B. We measured the shear stress along parallel scanlines in a residual-stress specimen with known stress state. We calculated the shear stress gradient and used it in the stress-equilibrium equation to determine the normal stress acting along the scanline direction. The other plane stress component was determined from an acoustoelastic relation between B and the difference of normal stresses. Good agreement was obtained with theoretical stress values.     

Effects of substrate birefringence and tilt on the irradiance and phase patterns of the return beam in magneto-optical disk data storage

Substrate birefringence in a magneto-optical disk system is shown to have a predictable effect on the return beam. The irradiance and phase patterns of the return beam at the exit pupil of the objective lens are calculated and experimentally verified for the cases of no substrate birefringence, birefringence aligned with the incident polarization, and birefringence aligned at 45° to the incident polarization. The irradiance at the exit pupil is also calculated (and experimentally verified) for a grooved substrate for various amounts of substrate tilt.     

Measuring distribution of the ellipsoid of birefringence through the thickness of optical disk substrates

We have measured the birefringence of polycarbonate optical disk substrates, using ellipsometry. For a more comprehensive characterization, the probe beam was incident upon substrates in a wide range of polar angles and from different azimuths relative to track direction (?). Our measurements show that the ellipsoid of birefringence is tilted in the plane of radial (r) and normal (z) directions. The tilt angle varies through thickness, with a maximum value of approximately 10°. For beams passing through the substrate in the ?-z plane and at large incident angles, this tilt causes significant conversion (up to 100%) between p- and s-polarized components. Distributions of other parameters, such as the values of in-plane and vertical birefringence, are obtained simultaneously in the measurements.     

Reflection and refraction of an arbitrary electromagnetic wave at a plane interface separating an isotropic and a biaxial medium.

Exact solutions are obtained for the reflected and transmitted fields resulting when an arbitrary electromagnetic field is incident on a plane interface separating an isotropic medium and a biaxially anisotropic medium in which one of the principal axes is along the interface normal. From our exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component. This gives a change in polarization that can be utilized to determine the properties of the biaxial medium. The time-harmonic solution for the reflected field is in the form of two quadruple integrals, one of which is a superposition of plane waves polarized perpendicular to the plane of incidence and the other a superposition of plane waves polarized parallel to the plane of incidence. The time-harmonic solution for the transmitted field is also in the form of two quadruple integrals. Each of these is a superposition of extraordinary plane waves with displacement vectors that are perpendicular to the direction of phase propagation.     

Formulation of rigorous coupled-wave theory for gratings in bianisotropic media

A formulation of rigorous coupled-wave theory for diffraction gratings in bianisotropic media that exhibit linear birefringence and/or optical activity is presented. The symmetric constitutive relations for bianisotropic materials are adopted. All of the incident, exiting, and grating materials can be isotropic, uniaxial, or biaxial, with or without optical activity. The principal values of the electric permittivity tensor, the magnetic permeability tensor, and the gyrotropic tensor of the media can take arbitrary values, and the principal axes may be arbitrarily and independently oriented. Procedures for Fourier expansion of Maxwell's equations are described. Distinctive polarization coupling effects due to optical activity are observed in sample calculations.     

Ultrasonic birefringence as a measure of mechanically induced fatigue damage in laminated composites

A non-destructive testing method based on polarization effects of ultrasonic transverse waves is suggested to monitor fatigue damage in polymer matrix composites. Using a transverse wave probe in reflection mode, phase and amplitude of its output signal are measured as a function of the polarization angle. From the material properties of a single ply and the proposed calculation approach, the birefringence response of carbon fibre reinforced polymers composed of many plies with different fibre orientations is predicted. The effect of ply sequence is investigated using two types of quasi-isotropic specimens with different layups. Cyclic tensile loading of composites results in fatigue damage that is characterised by matrix cracking along the fibre direction through the thickness of each ply. These myriads of transverse cracks affect the ultrasonic attenuation and degrade the homogenised stiffness of single plies. In the experiments, stepwise increase of fatigue damage is alternated with ultrasonic measurements, which show the effect of ply-dependent crack densities on the birefringence behaviour. Simulated and measured transverse wave response are matched by variation of the input parameters shear moduli and attenuations, which are therefore the final results. The obtained data from the investigated composite specimens is proposed to characterise the distinct fatigue state for each ply orientation.     

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.     

Rank Prize Funds Minisymposium on Non-classical Light for Communication

Abstract

We studied both experimentally and theoretically the transmission and polarization characteristics of a Cr⁴⁺ : YAG saturable absorber crystal as a function of the intensity and polarization state of an incident laser beam. We found that a birefringent absorption behaviour is induced and we show that the experimental results are well described by a full numerical model which includes excited-state absorption as well as a ground-state cross-absorption term. By using pump-probe measurements we show that a finite cross-saturation of the absorption is achieved along the crystal axes orthogonal to the polarization of the optical radiation. No induced refractive index birefringence is observed.     

Retroreflecting ellipsometer for measuring the birefringence of optical disk substrates

A retroreflecting ellipsometer has been constructed for measuring the birefringence of optical disk substrates. In contrast to conventional ellipsometers with two mechanical arms, this system has only one arm along which both the incident and reflected beams travel. This construction eliminates the mechanical limitations of conventional ellipsometers, thereby permitting normal incidence on the sample. In addition, the single arm is adjustable in two dimensions, with the polar incident angle, θ(inc), varying from 0° to 70°, and the azimuthal incident angle, Φ(inc), varying from 0° to 360°. The condition of normal incidence permits accurate measurement of in-plane birefringence. The adjustability of both θ(inc) and Φ(inc) is necessary for the measurement of possible tilts of the index ellipsoid, and also for the variation of birefringence through the substrate thickness. Measurement results showing the useful features of the equipment are presented. The optics of the hemispherical assembly used for retroreflection as well as for the elimination of undesirable refractions are also studied by use of the ZEMAX lens design program.     

Effect of terbium gallium garnet crystal orientation on the isolation ratio of a Faraday isolator at high average power

We present a comprehensive and systematic investigation of the fundamental physical limitations of Faraday isolation performance at high average powers that are due to thermally induced birefringence. First, the operation of various Faraday isolator designs by use of arbitrary orientation of cubic magneto-optic crystals is studied theoretically. It is shown that, for different Faraday isolator designs, different crystal orientations can optimize the isolation ratio. Second, thermo-optic and photoelastic constants for terbium gallium garnet crystals grown by different manufacturers were measured. Measurements of self-induced depolarization are made for various orientations of crystallographic axes. The measurements are in good agreement with our theoretical predictions. Based on our results, it is possible to select a crystal orientation that optimizes isolation performance at high average powers, resulting in a 5-dB enhancement over nonoptimized orientations.     

Transverse-electric/transverse-magnetic polarization converter using 1D finite biaxial photonic crystal

We show that by using a one-dimensional anisotropic photonic structure, it is possible to realize optical wave polarization conversion by reflection and transmission processes. Thus a single incident S(P) polarized plane wave can produce a single reflected P(S) polarized wave and a single transmitted P(S) polarized wave. This polarization conversion property can be fulfilled with a simple finite superlattice (SL) constituted of anisotropic dielectric materials. We discuss the appropriate choices of the material and geometrical properties to realize such structures. The transmission and reflection coefficients are calculated in the framework of the Green's function method. The amplitude and the polarization characteristics of reflected and transmitted waves are determined as functions of frequency, wave vector k(parallel) (parallel to the interface), and the orientations of the principal axes of the layers constituting the SL. Specific applications of these results are given for a SL consisting of alternating biaxial anisotropic layers NaNO(2)/SbSI sandwiched between two identical semi-infinite isotropic media.     

A Jones matrix formalism for simulating three-dimensional polarized light imaging of brain tissue

The neuroimaging technique three-dimensional polarized light imaging (3D-PLI) provides a high-resolution reconstruction of nerve fibres in human post-mortem brains. The orientations of the fibres are derived from birefringence measurements of histological brain sections assuming that the nerve fibres—consisting of an axon and a surrounding myelin sheath—are uniaxial birefringent and that the measured optic axis is oriented in the direction of the nerve fibres (macroscopic model). Although experimental studies support this assumption, the molecular structure of the myelin sheath suggests that the birefringence of a nerve fibre can be described more precisely by multiple optic axes oriented radially around the fibre axis (microscopic model). In this paper, we compare the use of the macroscopic and the microscopic model for simulating 3D-PLI by means of the Jones matrix formalism. The simulations show that the macroscopic model ensures a reliable estimation of the fibre orientations as long as the polarimeter does not resolve structures smaller than the diameter of single fibres. In the case of fibre bundles, polarimeters with even higher resolutions can be used without losing reliability. When taking the myelin density into account, the derived fibre orientations are considerably improved.     

Serial bideposition of anisotropic thin films with enhanced linear birefringence

We describe a serial bideposition technique in which a tilted substrate is rotated stepwise by half a turn about a normal axis during the evaporation of a metal oxide from a single electron-beam source. Coatings formed by the new method develop a columnar nanostructure that is perpendicular to the substrate and has greatest width or bunching perpendicular to the common deposition plane. With appropriate choice of deposition parameters, the method produces biaxial films with large birefringence, principal axes aligned parallel and perpendicular to the substrate, and improved uniformity. Measured phase retardances for light incident normally on the films are double the corresponding values for tilted-columnar films.     

Studies of optical anisotropy in opals by normal incidence ellipsometry

Anisotropy of thin opal films was studied by ellipsometric technique in a visible spectral range. At normal light incidence, the ellipsometric data were directly related to anisotropy parameters measured by polarization modulation technique. In the (111)-oriented thin films, the optical anisotropy was mainly caused by internal strain-induced birefringence with anisotropy axes oriented along [110] and [-112] directions. The deviation from 180°-symmetry, which has been observed for ellipsometric parameters in the in-plane sample rotation experiments at normal incidence, was enhanced at oblique incidence and assigned to particular properties of opal. Experimental data were discussed in the model of stacked anisotropic layers.     

Phase unwrapping method for three-dimensional stress analysis by scattered-light photoelasticity with unpolarized light

In scattered-light photoelasticity with unpolarized light, the secondary principal stress direction psi and the relative phase retardation rho in a three-dimensional stressed model with rotation of the principal stress axes can be obtained by use of Stokes parameters. For completely automated stress analysis, measurements of the total relative phase retardation and the secondary principal stress direction over the entire field are required, and it is necessary to unwrap psi and rho. A phase unwrapping method is thus proposed for the determination of these values based on scattered-light photoelasticity. The values are easily obtained via an arctangent function, overcoming the error associated with the quarter-wave plate by employing an incident light of different wavelengths. The proposed technique provides automated and nondestructive determination of the total relative phase retardation and the secondary principal stress direction in a model exhibiting rotation of the principal stress axes.     

Fusion splicing of polarization preserving fibers

A novel technique is developed to detect any principal axis misalignment of polarization preserving fiber. The technique is based on measurement of reflect-returned power for the fiber oputput endface that is depolarized by the birefringence of the fiber. It is confirmed theoretically and experimentally that principal axis alignments of 0 and 45 degrees can be successfully made only by minimizing and maximizing the monitoring level, respectively. On the basis of the alignment method, a fusion splicing technique is proposed for polarization preserving fibers. It is confirmed theoretically and experimentally that all principal axes alignment, core axis alignment, and splices loss estimations can be simply and sequentially attained with the present technique. Using the technique, +/-0.5 degree angular alignment resolution and +/-0.05-dB splice loss estimation accuracy are satisfactorily achieved.     

Theoretical analysis of optical characteristics of the alpha spodumene in ultraviolet region

It is presented an analysis of some important optical characteristics of the natural spodumene crystal, based on the first-principles calculations of its electronic structure and complex dielectric tensor. The optical absorption spectrum is interpreted in terms of electronic band structure for incident radiation energy up to 35 eV. The orientation of the three orthogonal principal optical axes is determined relative to the crystallographic axes, and expressed as function of the incident radiation wavelength. Reflectivity and electron energy loss are calculated along the three principal axes. All calculated optical properties are found to be highly anisotropic.     

Scattering by a dense layer of infinite cylinders at normal incidence

The solution for scattering by a layer of densely distributed infinite cylinders is presented. The layer is irradiated by an arbitrarily polarized plane wave that propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilized the effective field and quasi-crystalline approximation to treat the multiple scattering interactions in the dense finite medium. Governing equations for the propagation constants and amplitudes of the effective fields are derived for TM and TE mode incident waves, from which the scattered intensity distribution and scattering cross section for arbitrary polarization are obtained. The dense medium gives rise to coherent and incoherent scattered radiation that propagates in the plane normal to the axes of the cylinders. The coherent scattered radiation includes the forward component in the direction of the incident wave and the backward component in the direction of specular reflection. The incoherent scattered intensity distribution shows a pronounced forward peak that coincides with the angle of refraction of the effective waves inside the medium. Numerical results are presented to illustrate the scattering characteristics of a dense layer of cylinders as a function of layer thickness for a given solid volume fraction.