Matrixing Coupled Wave Theory of Photorefractive Hologram Recorded by Two-beam Coupling

Abstract

In a volume phase hologram recorded by two-beam coupling in photorefractive crystal, the refractive index modulation and the phase shift are both path dependent. In this paper, the concept of dividing the crystal slab into layers together with the mathematics of the diagonalization matrix are developed to calculate the diffraction of the hologram. As a result, a general analytic solution is achieved. For the use of novelty filtering in image processing and interferometric measurement, the conditions for keeping the same fields of the reconstructed signal beam and the transmitted signal beam are discussed.     

Diffractive light attenuators with variable transmission

Abstract

A new application of diffractive optical elements (DOEs) for continuous or multistage adjustment of optical radiation intensity is described. The diffractive attenuators are linear or circular gratings (amplitude or phase) with constant period and diffraction efficiency that varies across the grating. The zero order of diffraction is used as the output and transmitted through the grating without angular deviation. The diffractive attenuators, in distinction to conventional analogues, allow one to change the intensity of the light beam according to predetermined function and have no limitations for power of the regulated light beam. These elements can be used in optical systems as a beam splitter with adjusted splitting coefficient. The experimental results on a circular diffractive attenuator fabricated by direct laser writing on a chromium film are presented. The range of transmission variation was 20 times within a 340° angle of attenuator turn. The possibility to use a phase diffractive attenuator as a light radiation modulator for a powerful technological laser is discussed.     

Dependence of Bessel Beam Characteristics on Angular Spectrum Phase Variations

Abstract

The Bessel beam propagation characteristics are investigated in the presence of azimuthally dependent phase variations of its angular components. The phase variations influence the beam symmetry and strongly reduce an axial intensity. An experimental interpretation of presented results is also discussed.     

Application of Moments for Restoration of an Image Transmitted Through Long Multimode GRIN Fibres

Abstract

In this paper a new method of restoration of an image transmitted through a gradient-index (GRIN) fibre waveguide is considered. Instead of the difficulty in optical system mode decomposition of an output signal we suggest an easily realized moment decomposition. Compensation for the phase differences between moments instead of those between modes leads to better reconstruction of the transmitted signal at certain output planes. The numerical results of the image restoration using this method are discussed.     

Decorrelation with wavelength of laser intensity fluctuations after passage through a thermal plume

Abstract

Experiments are described in which two laser beams of different wavelength (mean λ=1550 nm, with variable detuning Δλ up to ±4%) are simultaneously transmitted through a thermal phase screen created by a convection heater. The work is motivated by applications such as differential absorption lidar (DIAL) in which beams of multiple wavelength are transmitted through the atmosphere. The experiment is optical fibre based with common transmit and receive optics being used for the two wavelengths, thus ensuring near-identical spatial modes. The far-field case is examined by placing the receiver at a focus of the beam, and reflective optics are used to avoid problems of chromatic aberration. A heterodyne detection scheme measures the intensity fluctuations at a point in the centre of the beam for each wavelength, and the degree of correlation between the two resulting intensity time series is determined as a function of detuning. The decorrelation increases as the square of the detuning, and the results are consistent with the predictions of theory in which it is assumed that the phase screen undergoes Gaussian phase fluctuations, and off-axis terms are ignored.     

Multi-Gaussian Ultrasonic Beam Modeling for Multiple Curved Interfaces—an ABCD Matrix Approach

ABSTRACT

A multi-Gaussian beam model uses a superposition of Gaussian beams to simulate the waves radiated from an ultrasonic transducer. We show that propagation and reflection/transmission laws for Gaussian beams in fluids and elastic solids can be written in the form of A , B , C , D matrices that are analogous to the A, B, C, D scalars used in Gaussian optics. This representation leads to simple expressions for a Gaussian beam even after that beam has been transmitted or reflected at multiple curved interfaces and produces a highly modular multi-Gaussian beam model that is also computationally very efficient. Some examples of the use of this model for both planar and curved interfaces are given.     

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.     

Displacement of the refracted wave in presence of inhibited reflection

Abstract

A displacement of the transmitted wave for a uniaxial crystalisotropic medium interface is found, when the angle of incidence is larger than the limiting inhibited reflection angle. The phenomenon treated is a generalization of the well-known Goos—Hünchen effect [1] which is the longitudinal displacement of the reflected wave associated with total reflection in isotropic interfaces. Nevertheless, because of the crystal anisotropy, the displacement vector here has both a longitudinal and a transverse component even when the incident beam is linearly polarized. Expressions for these components are given and their meaning is analysed     

Propagation characteristics of the ten-parameter family of partially coherent general anisotropic gaussian schellmodel (AGSM) beams passing through first-order optical system

Abstract

Based on the closed property of AGSM beams under the action of first-order optical systems, the explicit transformation and twist expressions for the principal axes of intensity distribution, transverse coherence distribution and the principal curvatures of phase front in the cross-spectral density function of AGSM beams are derived. For typical applications, for AGSM beams passing through free space, the twist and variation regularities of the principal axes and the principal curvatures are analysed in detail. The twist-free conditions are discussed and the twist influenced by the physical parameters of the incident beam analysed. It is shown from the analysis that the principal curvatures of phase front are not zero at the reference planes where any of the corresponding principal axes of the beam spot obtains its minimum, and the conditions where the principal curvatures are zero is discussed.     

Quantum Noise Reduction by Photodetection with Feedback

Abstract

A simple model is proposed to account for the generation of sub-shot noise light by feedback of the photocurrent. The model is based on a variable beam splitter controlled by the photocurrent from a detector placed after the beam splitter. The zero-feedback transmittivity is not necessarily unity. The field transmitted by the beam splitter shows reduced photon noise when the feedback causes a decreasing transmittivity.     

Relative phase shift in laguerre-gaussian beams propagating through an apertured paraxial ABCD system

Abstract

Based on the generalized Huygens-Fresnel diffraction integral, closed-form expressions for the relative phase shift of Laguerre-Gaussian beams propagating through an apertured paraxial optical ABCD system are derived. The dependence of the relative phase shift on the beam and system parameters, and the condition for eliminating phase shift are analysed and illustrated with numerical examples.     

Absorbing beam splitter in a Michelson interferometer

The equality of the reflected and the transmitted irradiances by a beam splitter that consists of a thin absorbing coating (typically a metallic film) on a transparent plate is considered. The absorption and the phase difference between the reflected and transmitted fields are also studied. The lack of reversibility of this beam splitter introduces an asymmetry that is discussed for a Michelson interferometer.     

Orientation of biological cells using plane-polarized gaussian beam optical tweezers

Abstract

Optical tweezers are widely used for the manipulation of cells and their internal structures. However, the degree of manipulation possible is limited by poor control over the orientation of the trapped cells. We show that it is possible to controllably align or rotate disc-shaped cells—chloroplasts of Spinacia oleracea—in a plane-polarized Gaussian beam trap, using optical torques resulting predominantly from circular polarization induced in the transmitted beam by the non-spherical shape of the cells.     

Analysis of dark spot formation in absorbing liquid media

Abstract

A theoretical analysis based on coupled field-matter equations is given to describe the recently observed phenomenon of a central dark spot formation of a Gaussian beam transmitted through an absorbing defocusing liquid medium. We find that such a pattern formation, which is accompanied by normal defocusing rings in the far field, originates from interplay between the wave-front curvature of the Gaussian beam and strong spatial self-phase medulation arising from thermally induced refractive index change in the medium. Results of numerical analysis for a thin medium are shown to be in a good quantitative agreement with our experimental findings. Further, the dark spot formation is also predicted by using a focused Gaussian beam and self-focusing medium.     

Augmented ABCD Matrix for Non-specular Diffraction of Gaussian Beams

Abstract

Optical beams reflected or transmitted by a dielectric interface undergo several non-specular deformations: changes in the beam amplitude, lateral, focal and angular shifts of the beam axis and a magnification of the beam width. In this communication the non-specular interaction of the beam with, in general, multilayered, planar dielectric structure is described in terms of the ray transfer matrix formalism. A relationship between the beam deformations and a 3 × 3 ray transfer matrix of the structure is built. Transfer matrix elements are shown in a simple form dependent on the real deformations.     

Fiber Optics: Research and Development

Abstract

With twisted stacks of N polarizers P or retarders R, the polarization of a light beam can be cycled around the Poincaré sphere on N similar arcs of great P or small R circles. We calculate the phase changes around these cycles (geometric for P; geometric + dynamical for R). In the continuum limit N → ∞ of a smoothly twisting medium, a P stack forces the light to follow its changing polarization, and the phase is the solid angle of the associated loop on the sphere; for an R stack, on the other hand, it is only in the adiabatic limit of slow twist (where the dynamical phase is large) that the geometric phase corresponds to that of the loop specified by the changing eigenpolarization of the medium. The predicted phase shifts are observed as fringe shifts in an interferometer for N=2, 3 and 4.     

Fracture of steel beam to box column connections

Abstract

This study is aimed at examining the behavior of the beam to interior box column connection. Cruciform type test setups are selected with the column under constant gravity load while both beams under gradually increased cyclic loading in opposite directions to simulate earthquake load. The tearing strength of the column plate by the transmitted out‐of‐plane load from the beam web is analyzed by yield line theory. A simplified method is proposed to establish the relationship between the thickness of beam web and column plate. A series of experimental studies are also conducted to examine the effect of a diaphragm plate on the transmission of applied force from beam flanges. Based on the results of this study, suggestions are made for the design and construction of beam to box column connections to achieve better strength and ductility.     

Amplitude matching strategy for wave-optical design of monofunctional systems

Abstract

The design of optical systems capable of transforming one given input field into an output field which maximizes one prescribed merit function is discussed in the functional embodiment of the system, that is by dealing with transmission functions instead of structured matter. Customary beam shaping techniques are identified as a special case of a more general strategy which is called amplitude matching. This strategy makes use of the field quantities amplitude and phase and therefore it is a wave-optical design approach. The flexibility of the technique is demonstrated by various examples. Parameters like conversion efficiency, signal-to-noise ratio, distances between transmission functions, and the number of transmission functions necessary for the implementation of wave transformations are discussed.     

Lamellar Gratings as Polarization Components for Specularly Reflected Beams

Abstract

High spatial frequency lamellar gratings are shown to function as phase compensators, quarter-wave and half-wave retarders, and polarization rotators that operate on specularly reflected (zeroth-order) beams. These gratings are designed using rigorous coupled-wave and modal grating diffraction theories. Controlling the geometrical parameters of these gratings allows for engineering the phase retardation and polarization conversion introduced to a reflected beam. Fabrication and operational tolerances for these elements are discussed. Wavelength and polar angle of incidence variation affect the performance of these elements more strongly than variations in other geometrical and operational parameters.     

Optically Active Fabry-Perot Etalon

Abstract

The paper studies multibeam interference in the case of multiple reflection of an electromagnetic wave (EMW) from a plane-parallel, isotropic, optically active and non-absorbing plate (Fabry-Perot etalon). Due to the optical activity the two refracted EMW in the plate are left- and right-circularly polarized and have unequal refractive indices. During their propagation through the plate the two waves accumulate a phase difference which modulates the multibeam interferogram. Both in the reflected and in the transmitted beams a polarization perpendicular to the polarization of the incident EMW appears (whose intensity is up to several tens of per cent of the incident beam intensity). Due to the gyrotropy of the plate at large angles of incidence the interference bands split. Thus the optical activity of the etalon may affect its precision as an optical element. The multibeam interference may be used as a source of spectroscopic information about the optical activity of the plate.