Analysis of a Fibre-optic Ring Resonator with Polarization Effects: Application to Polarization Sensing with Improved Sensitivity

Abstract

A theoretical analysis for a fibre-optic ring resonator is given by assuming a polarization modulation in the loop fibre. If the change in polarization angle θ in the loop is large, the output intensity has two resonance dips separated in phase by an angle equal to 2θ, when the loop phase is scanned from 0 to 2π. When θ is small, the resonator output produces only one resonance dip and the amplitude of this resonance dip is a measure of θ. By placing a polarizer at the resonator output, a resonance peak in the intensity is produced with an amplitude that increases with increasing θ. Such a system has potential applications, for example, in Faraday current sensing, with an increased sensitivity. The effects of birefringence in the loop and the angle of polarization of the input light are also analysed.     

Influence of orientation of rough grooves on spectral reflectivity of a surface in the thermal radiation wavelength range

Roughness is one of the principal factors influencing reflectance of a surface that takes place in radiation heat transfer. In the present work, we investigate the influence of the orientation of single-oriented roughness grooves on the directed–directed spectral reflectance of surfaces within the wavelength range of 0.2–20.0 μm. The surfaces have a mean square deviation of the roughness (σ) of 0.2 μm and 2.0 μm and the areas exceed the size of the incident light beam. The angles of reflection are equal to the angles of incidence and are equal to 50° and 70°. The degree of influence of the groove orientation on the reflectance is defined as the ratio of the reflectances of one and the same surface with the grooves oriented parallel and perpendicular to the plane of incidence. In the theoretical investigation, we engage the unidimensionally rough surface model. An experimental study by means of physical modeling was performed: the degree of influence of the groove orientation on the spectral reflection of the surface was estimated, within the investigated wavelength range, according to the degree of influence of the groove orientation on the monochromatic reflectance of the reference ground surfaces within the σ-range of 0.01–4.33 μm on the wavelength 0.405 μm. The studies performed show that the spectral range of the groove orientation influence on the surface reflectance increases with an increase in σ and a decrease in the angle of incidence; the degree of that influence has a maximum the value of which increases with the increase in the angle of incidence. We determine the conditions of agreement of the theory and the experiment.     

Simple parameter determination for twisted nematic liquid-crystal display

A simple and accurate measurement method for determining the cell parameters of a twisted nematic liquid-crystal display (TN-LCD) is proposed. Based on the measurement of the maximum reflectance and the maximum transmittance of a TN-LCD by rotating the polarizer at a particular angle, between the front director of the liquid crystals and the transmission axis of the polarizer, the cell gap and the twist angle can be determined according to the Jones matrix theory, and the twist sense can also be determined easily by applying an external small voltage to slightly change the effective refractive index of the liquid crystal.     

The study of bridge phase conjugation in photorefractive Tb:Cu:KNSBN crystal

Abstract

Photorefractive bridge phase conjugation is studied theoretically by two-region coupled-wave theory. The dependence of phase conjugate reflectivity and transmissivity on the input intensity ratio is measured. When two incoherent beams symmetrically enter opposite Tb:Cu:KNSBN crystal faces, the maximum reflectivities are higher than 351%, 236% and 147% for incident angles of 17.5°, 27.5 and 39° respectively; we also obtain a transmissivity higher than 58% for an incident angle of 33.5°. A comparison between the experimental data and theoretical results is also given.     

Visual performance after correcting the monochromatic and chromatic aberrations of the eye

The development of technology to measure and correct the eye's higher-order aberrations, i.e., those beyond defocus and astigmatism, raises the issue of how much visual benefit can be obtained by providing such correction. We demonstrate improvements in contrast sensitivity and visual acuity in white light and in monochromatic light when adaptive optics corrects the eye's higher-order monochromatic aberrations. In white light, the contrast sensitivity and visual acuity when most monochromatic aberrations are corrected with a deformable mirror are somewhat higher than when defocus and astigmatism alone are corrected. Moreover, viewing conditions in which monochromatic aberrations are corrected and chromatic aberrations are avoided provides an even larger improvement in contrast sensitivity and visual acuity. These results are in reasonable agreement with the theoretical improvement calculated from the eye's optical modulation transfer function.     

Determination of optical parameters of a twisted-nematic liquid crystal by phase-sensitive optical heterodyne interferometric ellipsometry

What is believed to be a novel phase-sensitive optical heterodyne interferometric ellipsometer is set up to characterize a twisted-nematic liquid crystal (TN-LC) by the elliptical parameters of the output polarization state. This ellipsometer presents the advantages of both polarized optical heterodyne interferometry and optical photometry, which introduce a polarization modulation that is capable of performing with high-sensitivity on phase detection in real time. The twist angle phi and the untwisted phase retardation gamma of TN-LC are measured precisely. The experimental results verify that a TN-LC can be treated as identical to an elliptical retarder.     

A New Method for Spectral Performance Evaluation of a Chromatic and Achromatic Quarter-Wave Retarder

When a polarized polychromatic beam passes through a quarter-wave retarder, the constituent spectral components suffer different changes in the state of polarization. As a result, when the beam passes through an analyzer, the intensity of the resultant beam changes, depending on the orientation of the analyzer, state of polarization of the input beam, spectral and spatial intensity distribution of the source and the wavelength-dependent retardance of the quarter-wave retarder. The intensity variation of the resulting beam is theoretically and experimentally observed, with the variation of the azimuthal angle of the analyzer for film-type chromatic and prism-type achromatic quarter-wave retarders. The spectral performances of achromatic retarders are generally evaluated by measuring retardances at discrete wavelengths by using a monochromatic beam of light over the wavelength range of interest. In this study, a simple method is used for computing the fractional nonlinear polarization (FNLP) from theoretically and experimentally obtained intensity variations for evaluating the spectral performance of both achromatic and chromatic quarter-wave retarders operating over a broad spectral range in the visible region using a polychromatic beam of light. FNLP variation is also shown for a film-type chromatic quarter-wave retarder using a monochromatic source of light. The experimentally obtained values are compared with theoretical values and a good agreement is observed. The applications of the method for the performance evaluation of quarter-wave retarders are discussed.     

Polarization effects in a KGd(WO4)2:Nd crystal

Data are presented that demonstrate that, when a laser beam polarized at 45° to the vertical (horizontal) is passed through plane-parallel plates cut from a Nd-doped (4%) potassium gadolinium tungstate crystal and placed between crossed polarizers, the intensity and polarization of the transmitted light are periodic functions of the angle of incidence of the light. When scanned in two mutually perpendicular directions, the plates exhibit highly anisotropic transmission. The polarization at the intensity minima and maxima at the analyzer output is not orthogonal, in contrast to uniaxial crystals.     

Dynamic characteristics of dual-frequency nematic liquid crystal with quasi-homeotropic twist structure

Dynamic characteristics of a liquid crystal (LC) cell with a quasi-homeotropic twist structure formed in a dual-frequency nematic liquid crystal (DFNLC) layer with the director pretilt angle increased to 60° have been experimentally studied. The cell was switched from the off to on state using a 30-kHz electric field, while the reverse (off/on) switching was effected by a 1-kHz field. An increase in the director pretilt angle allowed the switch-on time of a 6.4-μm-thick DFNLC cell to be reduced to 1 ms and the relaxation (switch-off) time, to 0.5 ms.     

Faraday compensator of reciprocal optical anisotropy utilizing a polarization ring interferometer

It is shown that a polarization ring interferometer containing a Faraday cell can be used to compensate the reciprocal anisotropy in round-trip optical circuits. It is established theoretically and experimentally that, unlike the case of conventional Faraday mirrors, the quality of the restoration of the polarization in a compensator based on a polarization ring interferometer is practically independent of the Faraday rotation angle. A deviation of the Faraday rotation angle from 45° leads only to an additional power loss. The novel compensators can be used in fiber-optic circuits with a wideband light source or with several sources having different wavelengths. Pis’ma Zh. Tekh. Fiz. 25, 57–63 (May 26, 1999)     

Real-time polarization state measurement based on a birefringent crystal wedge

Abstract

We present a method of single-shot polarization state measurement based on a birefringent crystal wedge. The phase delay and amplitude angle of detected light are encoded into two groups of fringes through the interference in a crystal wedge and further decoded by fringe position locations. This method has the merit of real-time measurement, a compact set-up and simple calibration. The principle, set-up, calibration and error analysis are presented in details. In the end, a single-shot measurement set-up with 80 kHz temporal resolution is demonstrated to investigate the molecule dynamic behaviour in a TN liquid crystal under a rectangular voltage.     

Reduction of skylight reflection effects in the above-water measurement of diffuse marine reflectance: comment

Use of a vertical polarizer has been suggested to reduce the effects of surface reflection in the above-water measurements of marine reflectance. We suggest using a similar technique for airborne or spaceborne sensors when atmospheric scattering adds its own polarization signature to the upwelling radiance. Our own theoretical sensitivity study supports the recommendation of Fougnie et al. [Appl. Opt. 38, 3844 (1999)] (40-50 degrees vertical angle and azimuth angle near 135 degrees , polarizer parallel to the viewing plane) for above-water measurements. However, the optimal viewing directions (and the optimal orientation of the polarizer) change with altitude above the sea surface, solar angle, and atmospheric vertical optical structure. A polarization efficiency function is introduced, which shows the maximal possible polarization discrimination of the background radiation for an arbitrary altitude above the sea surface, viewing direction, and solar angle. Our comment is meant to encourage broader application of airborne and spaceborne polarization sensors in remote sensing of water and sea surface properties.     

Extended phase modulation depth in twisted nematic liquid crystal displays

We show how the phase modulation depth in twisted nematic liquid crystal displays (TNLCDs) can be increased dramatically by selecting a polarization configuration with a reduced mean intensity transmission. This phenomenon, which we have validated with various devices, is shown here for a device that presents a phase-only modulation only slightly over π radians in our classical rotated eigenvector configuration, but it is capable of producing close to a 2π phase depth for a configuration with 5% mean intensity transmission. A quantitative explanation is presented by means of a phasor analysis of the TNLCD eigenvector projections over input and output polarization states. The proposed technique can be a very useful solution in modern TNLCDs that have a very thin liquid crystal layer and a reduced maximum achievable phase modulation.     

Novel Polarimetric Technique Exploring Spatiotemporal Birefringent Response of an Anti-ferroelectric Liquid Crystal Cell

Abstract

This paper describes a novel polarimetric technique for mapping the spatiotemporal birefringent parameters characterizing an anti-ferroelectric liquid crystal cell. A linearly polarized beam of light transmitted by the liquid crystal cell turns into an elliptically polarized beam. Some birefringent irregularities existing over the cell make state of polarization of the elliptically polarized beam of light be spatiotemporal. This beam works as a signal beam to interfere with a reference beam consisting of two orthogonal linearly polarized components. The resultant interference pattern is taken by a charge-coupled device video camera and recorded in a computer. The computer gives the information required for determining the spatiotemporal birefringent parameters that characterize the liquid crystal cell. The major advantage is that the two-dimensional distribution of the birefringent axes as well as the two principal refractive indices can be determined simultaneously, and no use of any optical components for polarization alignment makes it possible to follow a rapid change in birefringent parameters within the maximum frame rate of the video camera. A change in time-dependent birefringent parameter is measured at every 0·1 ms for the demonstration experiment.     

A Method for the Optical Characterization of Thin Uniaxial Samples

An optical characterization procedure for small fragments of uniaxial materials is described involving the simple use of crossed polarizers with one polished face of the material. The reflectance at a fluid-uniaxial slab boundary beyond, but near, the critical angle of incident light is examined for linear incidence polarization using an orthogonal output polarizer. It is found that, as the crossed incident and output polarizers are rotated together, there are, for a given angle of incidence, particular polarization angles for which the reflectivity is a minimum. These angles give information on the optical tensor of the crystal under study. Further the intensity of the reflected light, for incidence angles beyond critical with the input and output polarizers crossed, has as a function of the incident polarization angle an oscillatory form which, when fitted to theory, can also yield the full uniaxial tensor of the material under study. This is confirmed experimentally for a thin single crystal of calcite with one polished face.     

Fringing fields in a liquid crystal spatial light modulator for beam steering

Abstract

Phase modulating spatial light modulators (SLMs) can be used to alter the shape of a laser wavefront to achieve a deflection or change in the shape of a laser beam. This paper reports the results of characterization, simulation and optimization of a one-dimensional liquid crystal (LC) SLM. The device has a large ratio between LC layer thickness and pixel pitch that results in a fringing field between pixels. In effect, the applied phase patterns will be lowpass filtered and the loss of high frequency components limits, for instance, the usable steering range. A method is presented where intensity measurements in the far field are used to determine how the phase modulation at the SLM is distorted. The inhomogeneous optical anisotropy of the device was determined by modelling the liquid crystal director distribution within the electrode-pixel structure. Finite-difference time-domain (FDTD) simulations were used to calculate the light propagation through the LC. The simulated phase distortion was compared with the experimental results. A voltage compensation scheme to improve the diffraction efficiency was developed utilizing the measured and simulated results. It is demonstrated that a modification of the voltage patterns can give a better realization of high frequency components in the phase distribution and an increase in maximum steering angle by a factor two.     

Reflective liquid crystal wavefront corrector used with tilt incidence

To allow angular separation of the beam reflected off a liquid crystal wavefront corrector from the incident beam, it is convenient to introduce a small incident angle. This avoids using a beam splitter and the associated energy losses. The effect of the tilt incidence on the liquid crystal wavefront corrector was investigated in this paper. For a parallel aligned liquid crystal wavefront corrector, a simplified model was established and used to analyze the change of the phase modulation under the tilt incidence. The simulated results showed that the effect of the tilt incidence on the phase modulation can be ignored when the angle of tilt incidence is less than 6 degrees. The phase modulation related to the incident angle was measured and the changing trend was similar to the calculated results. The effect of the tilt incidence on the diffraction efficiency of the liquid crystal wavefront corrector was also discussed. The simulated results indicated that the reduction of the diffraction efficiency is less than 1% for incidence angles under 3 degrees. Last, a closed loop correction experiment was done with an incident angle of 1 degrees. After correction, the averaged peak to valley (PV) and root mean square (RMS) of the wavefront were down to 0.15 lambda and 0.03 lambda, respectively, and a resolvable image was acquired.     

Reduction of skylight reflection effects in the above-water measurement of diffuse marine reflectance

Reflected skylight in above-water measurements of diffuse marine reflectance can be reduced substantially by viewing the surface through an analyzer transmitting the vertically polarized component of incident radiance. For maximum reduction of effects, radiometric measurements should be made at a viewing zenith angle of ~45 degrees (near the Brewster angle) and a relative azimuth angle between solar and viewing directions greater than 90 degrees (backscattering), preferably 135 degrees . In this case the residual reflected skylight in the polarized signal exhibits minimum sensitivity to the sea state and can be corrected to within a few 10(-4) in reflectance units. For most oceanic waters the resulting relative error on the diffuse marine reflectance in the blue and green is less than 1%. Since the water body polarizes incident skylight, the measured polarized reflectance differs from the total reflectance. The difference, however, is small for the considered geometry. Measurements made at the Scripps Institution of Oceanography pier in La Jolla, Calif., with a specifically designed scanning polarization radiometer, confirm the theoretical findings and demonstrate the usefulness of polarization radiometry for measuring diffuse marine reflectance.     

Reflection properties of oriented thin CdS films formed by laser ablation

Oriented thin (≈2 μm) films, CdS, prepared by laser ablation were characterized by the dependence of external and internal reflection on both the angle of incidence and the polarization of laser light. The samples exhibit perpendicular and parallel orientation of the crystallographic axis with respect to the surface of the glass substrate. The experiments were performed at 300 K using low intensity (<1 W/cm²) cw emissions at 476.5, 514.5 and 632.8 nm of argon and He–Ne lasers respectively. For blue and green light, the results are very well described by the theoretical models based on Fresnel reflection. In contrast to the external features, the internal reflectance exhibits dichroism and birefringence of the samples at 514.5 nm, revealing the sensitivity of the internal reflection technique to the optical anisotropy of the films. Considering multiple-beam interference, the model of Fresnel also describes satisfactorily the results for red light. However, a rather sensitive dependence on the incoming He–Ne laser intensity was observed. In fact, by increasing the intensity of 64 mW/cm² by about one order of magnitude, only the external reflectance shows good agreement with the theory, whereas the internal reflection properties are obviously influenced by additional effects, such as non-linear change of the optical constants, which are not included in Fresnel reflection considerations.     

Polarization-dependent diffraction efficiency of a photorefractive volume grating and suppression of this efficiency

In terms of refractive-index ellipsoid of a uniaxial crystal, the relationship between the diffraction efficiency of a volume grating and the polarization state of a readout beam is theoretically analyzed. The direction of a refractive light beam and the corresponding refractive-index modulation will both be changed by a variation of the polarization state. In the polarization state of the readout beam, which may lead to a strong variation in the diffraction efficiency of the volume grating. This kind of polarization-dependent diffraction efficiency of a volume grating in an anisotropic crystal is extremely disadvantageous for some applications. A method to suppress the polarization-dependent diffraction efficiency by use of double volume gratings is presented, and experiments with LiNbO3:Fe crystal are also demonstrated. The experimental results indicate that this method can well suppress the polarization-dependent diffraction efficiency of a volume grating. Furthermore, the diffraction properties of the double volume gratings are almost independent of the polarization state of the readout beam. The relative values of the diffraction peaks are calculated on the basis of the relationship between index modulation and the state of polarization. The experimental values are in good agreement with the theoretical analyses.