Showing papers on "Total internal reflection published in 1971"

Lateral Displacement of a Light Beam at a Dielectric Interface

Abstract: The lateral (Goos–Hanchen) shift of a gaussian light beam incident from a denser medium upon the interface to a rarer medium is investigated by means of a rigorous integral representation comprising a continuous plane-wave spectrum. By applying a Fresnel approximation to that integral, we derive the lateral displacement for angles of incidence that are arbitrarily close to the critical angle of total reflection. Our results show that, in general, the lateral displacement is a function of the beam width, as well as the incidence angle; the classical expression appears as a limit case which holds only for large beam widths and for incidence angles that are not too close to the critical angle. An analysis of our expression for the beam shift reveals that, as the incidence angle approaches the critical angle of total reflection, the beam shift approaches a constant value that is strongly dependent on the beam width, in contrast to the classical expression, which predicts an infinitely large displacement; we also find that the maximum lateral displacement occurs at an angle that is slightly larger than the critical angle. Numerical results are presented in terms of normalized curves that are applicable to a wide range of realistic beams.

Quantization of Evanescent Electromagnetic Waves

Abstract: The problem of the quantization of evanescent waves, which appear in the angular spectrum representation of the electromagnetic field in a half-space, is discussed. Although evanescent waves are associated with material sources, scatterers, etc., we are able to treat the electromagnetic field, including the evanescent waves, effectively as a free field, by making use of the idea of the refractive index of a passive, macroscopically continuous medium. We consider a space which is filled with a homogeneous dielectric to the left of the plane $z=0$, and is empty to the right of the plane. Triplets of incident, reflected, and transmitted waves at the interface form the fundamental orthogonal modes of the space. By expanding the field in terms of these triplet modes, we show that the field Hamiltonian reduces to the sum of independent harmonic-oscillator Hamiltonians. The quantization is therefore straightforward. We introduce the creation and annihilation operators for the triplet wave modes, and encounter Fock states, coherent states, etc., for a field having evanescent wave components. The field commutator at two space-time points in the right half-space is shown to have an explicit contribution from evanescent waves, characterized by an exponential decay to the right and a propagation parallel to the interface. We also examine the problem of atomic excitation by quantized evanescent waves, and show that the results are of the form given by semiclassical treatments.

Selective Reflection by Cholesteric Liquid Crystals

Abstract: Selective light reflection at the plane structure of a cholesteric liquid crystal is treated by the theory of de Vries(1) for normal incidence only. A more general approach is outlined for arbitrary angles of incidence. Conditions for the borders of the reflection bands are given. Also the cases of ordinary total reflection are included. Using the derived formula, the two principal dielectric constants are determined from the angles of total reflection measured with a refrectometer. Their values are used to calculate ther eflection spectrum of a layer of finite thickness at normal incidence which is compared with an experimental spectrum. In agreement with the experimental curve the calculated spectrum shows a central band with a nearly rectangular shape flanked by a series of maxima and minima due to interferences, the positions of which depend strongly on the dielectric constants.

Uniform illumination with edge lighting

Abstract: Uniform illumination is provided from an edge lighted optical medium of a given thickness by diffusing a surface portion normally providing internal reflection of the light radiated into the edge such that at least some of the light rays striking the diffused area are reflected through the opposite surface of the medium and some are refracted through the one surface. A cleared area about the source of light free of the diffusion is provided and treated by application of coatings on opposite surface portions of the medium defining the cleared area. These coatings have an index of refraction less than that of the medium such that light is channeled by internal reflection between the surfaces of the medium and inhibited from escaping from the medium in the vicinity of the cleared area. This cleared area has a radius of preferably three to four times the thickness of the optical medium. The resulting light emmination from the surface of the medium is substantially uniform beyond the cleared area.

Phase-Shift Measurement of Evanescent Electromagnetic Waves*

Abstract: Phase shifts suffered by evanescent electromagnetic waves traversing an air gap between two glass prisms have been measured. Because the evanescent waves propagate parallel to the glass-to-air interface, they should be able to penetrate in a direction normal to the interface, without change of phase, although the amplitude is expected to decrease with depth of penetration. This has been confirmed by the experiment, which showed that the phase shifts are substantially independent of the width of the air gap.

Reflection and Refraction Coefficients at a Fluid‐Solid Interface

Abstract: For an infinite plane elastic wave which strikes the plane interface separating two semiinfinite isotropic media, the calculation of the complex reflection coefficient, R*, for varying angles of incidence, θ, is not difficult. In the past, calculations have been made for a number of lossless media and, consequently, an important facet of the R*−θ curve for real materials has been overlooked. The total reflection, |R*|=1, which occurs at the longitudinal‐ and shear‐wave critical angles is well known, but the appearance of a minimum (sometimes a zero) in R* is not and its existence defines a third critical angle, sometimes inappropriately called the Rayleigh‐wave angle, at which a wave with large surface components is generated. During experiments with beams of acoustic waves, there is an apparent lateral displacement of the reflected beam at the third critical angle which manifests itself markedly only when there is a near‐zero in |R*|. Notwithstanding the calculations of Schoch [Ergeb. Exakt. Naturw. 23, 127–234 (1950)] and the experimental measurements of others apparently to the contrary, it is strongly suggested that no actual lateral displacement occurs and that re‐radiation from the region outside that ensonified by the incident beam gives rise to the apparent lateral displacement. Some outcomes of the investigation are discussed and of these the more important are: (1) Rayleigh and other interface and surface waves in real media are degenerate; (2) no interface wave can exist independently at the junction of two nonideal media; (3) Huyghens's principle in its elementary secondary‐wavelet form does not apply to lossy media; (4) the usefulness of the sensitivity of R* to minute changes in elastic parameters at the Rayleigh angle as a measuring tool has a wide application; (5) elliptical polarization of both shear and longitudinal waves can occur, owing to boundary influences in lossy refracting media. The real part of the propagation vector lies in the plane of the ellipse.

The elastic constants of oriented glassy polymers

Abstract: The paper is concerned with the measurement of the anisotropic elastic properties of drawn glassy polymers, namely perspex and polystyrene. The method used involved the measurement of the critical angle for total reflection of an ultrasonic beam incident on the surface of the polymer when immersed in a suitable liquid. Measurements were made for both compressional and shear waves propagated at various angles to the direction of drawing; from the data so obtained the values of the five stiffness constants required to define the properties of an axially symmetric material were calculated. The design of the instrument for the critical-angle measurements is described, and the basic theory required for the calculations presented. Results are given showing the dependence of stiffness constants on degree of orientation (birefringence). Only the axial stiffness constant is found to be markedly dependent on orientation and for this the increase is only about 30%. These conclusions are supported by data on the angular dependence of Young's modulus for the same polymers obtained by a static loading method.

Ultrasonic apparatus and method for nondestructively measuring the physical properties of a sample

Abstract: The physical properties of a sample are measured by generating a collimated beam of pulsed ultrasound and transmitting the ultrasound at an incident angle relative the sample greater than the longitudinal-ultrasonic-wave critical angle and less than the longitudinally induced-shear-ultrasonic-wave critical angle for the sample to generate simultaneously within the sample longitudinal and mode-converted-shear ultrasonic waves. The propagation of the generated longitudinal and shear ultrasonic waves through the sample is measured to provide a measure of the physical properties of the sample.

On the use of optical waveguide techniques for internal reflection spectroscopy

Abstract: A detailed analysis is presented of the absorption of energy from a thin-film dielectric waveguide by an absorbing medium that is brought into contact with one wall of the dielectric guide. It is shown that the exponential decay constant for the mode of the guide so obtained can closely approach that obtained for the free wave in the absorbing medium alone. The dependence of the attenuation on the guide parameters is examined and means for overcoming some of the problems imposed by the guidance process are discussed. It is concluded that the techniques can offer greatly enhanced sensitivity over the conventional internal-reflection spectroscopy and yet retain the attractive features of small sample volume and easy sample preparation. The technique also offers the possibility of constructing microscopic probes for the examination of spectra in otherwise inaccessible places.

Optical shaft encoder

Abstract: Light is transmitted through the edge of a transparent cylinder, a portion of the light inside the cylinder being incident to at least one face thereof at greater than the critical angle between the cylinder and air. Light escapes from the faces at a plurality of selected locations thereon in a plurality of unique output patterns, associated with angular positions of the cylinder. Stationary optical detectors, opposite the faces, detect the escaping light when the cylinder is rotated to a position that places a selected location opposite an optical detector. The optical detectors provide signals representative of a unique pattern and hence the angular position of the cylinder. In one embodiment a material having an index of refraction intermediate to that of the cylinder and air is disposed at the selected locations, providing a critical angle greater than the critical angle between the cylinder and the environment, thereby causing light to escape through the faces only at the selected locations. In another embodiment, notches in the faces of the cylinder are disposed at the selected locations, the notches being at an angle so that light is incident thereto at an angle less than the critical angle, thereby causing light to escape through the faces only at the selected locations.

Internal reflection spectroscopy: validity of effective thickness equations.

Abstract: The validity of effective thickness expressions for sample films used in internal reflection spectroscopy is obtained by comparing them to exact computer calculations for various refractive indices, angles of incidence, extinction coefficients, and film thicknesses.

Energy--momentum quanta in fresnel's evanescent wave.

Abstract: Fresnel's theory of the evanescent wave in total reflection entails that the propagation vectork and the momentum quantaħ k have an imaginary component and, thus, a projection on the reflecting plane that is larger (in units such thatc=1) than the angular frequencyω and the energy quantaħω. We discuss the ‘tachyon properties’ of these energy-momentum quanta and propose an experimental test using absorption or stimulated emission by an atomic or ionic beam. We then show that the Maxwell-Minkowski tensor (although certainly appropriate to discuss the macroscopic energy-momentum exchange between wave and diopter) does not describe adequately the energy-momentum density of the quanta in the evanescent wave, this stemming from its too remote connection with the generator ∂i of space-time displacements. On the other hand de Broglie's energy-momentum tensorA k[∂i]B jk is the density canonically associated with the generator of space-time displacements; we show that it describes quite satisfactorily both the energy fluxes (as measured through the longitudinal Goos-Hanchen and our new transverse shifts of the reflected beam in total reflection) and the momentum densities of the quanta inside the evanescent wave. Finally, we show that it is the gauge which is transverse in the diopter's rest frame that directly yields the physically measured energy fluxes. We take this fact as a new argument, strongly supported by experimental evidence, in favour of the physical reality of electromagnetic potentials.

Far-Field Diffraction Pattern for Corner Reflectors with Complex Reflection Coefficients*

Abstract: The far field diffraction pattern of a geometrically perfect corner reflector is examined analytically for normally incident monochromatic light. The states of polarization and the complex amplitudes of the emerging light are expressed through transformation matrices in terms of those of the original incident light for each sextant of the face in a single coordinate system. The analytic expression of the total diffraction pattern is obtained for a circular face. This expression consists of three component functions in addition to the basic Airy function. The coefficient of each function is expressed in terms of complex coefficients of reflectance of the reflecting surface. Some numerical results for different reflecting surfaces, including total internal reflection, are presented. The iso-intensity contours of the diffraction pattern evaluated from the analytical expressions for an uncoated solid corner reflector are also presented along with the photographs of the pattern.

Excitation of waveguides for integrated optics with laser beams

Abstract: We discuss in this paper the excitation of dielectric waveguides used for integrated optical circuitry. Thin optical films are usually excited by means of coupling prisms using frustrated total internal reflection. We propose instead excitation of thin-film waveguides directly by gaussian laser beams. Harmful effects of imperfect substrate edges can be avoided by letting the dielectric waveguide end inside of the substrate. The exciting laser beam is directed towards the end of the guide from the inside of the substrate material. The analysis is based on neglecting reflection at the end of the thin-film waveguide and on assuming that the thin film is infinitely extended in one dimension. The maximum excitation efficiency predicted with this model is 97 percent. It is expected that the excitation efficiency of more realistic guides for integrated optics can be as high as 90 percent.

Total Reflection of Matter Waves: The Goos–Haenchen Effect for Grazing Incidence*

Abstract: At total reflection, beams are not reflected ideally from their point of incidence at the reflecting boundary but shifted by a length D (Goos–Haenchen effect). Based on the model of wave bundles consisting of a composite of totally reflected partial waves with varying angles of incidence, we treat the case of matter waves for a vanishing potential step at the boundary (the critical angle of total reflection tending to π/2). It is well known from Renard’s formula that the partial wave for grazing incidence has a vanishing shift D, with an angle α0 of incidence midway between the critical angle and π/2. However, the Goos–Haenchen shift of a wave bundle goes to infinity at α0 → π/2. The width W of the bundle also goes to infinity because the angular interval of the partial waves goes to zero. But the quantity D/W remains constant. D/W has a value of 18% if Artmann’s formula for D is used and is 4.5% with Renard’s more refined formula for D.

Optical Properties of Cs for Photons of Energy 3.6–9.6 eV*

Abstract: The optical and dielectric constants of Cs have been obtained above the plasma frequency. The measurements were made on Cs films evaporated on a plane surface of quartz and CaF2 semicylindrical substrates, at 10−6 torr. The refractive index n is determined from the critical angle for total internal reflection at the Cs–substrate interface. The absorption coefficient k is determined from the slope of the curve at the critical angle. The real part of the complex dielectric constant ∊1 differs from the value predicted by the nearly free-electron model. The effect is attributed to the existence of transitions from inner shells at higher photon energies and to interband transitions and plasmon-assisted transitions at lower energies. The derived parameters in this energy region are 4πnoα = 0.37±0.01, meff = 1.05±0.05 m, and ℏωp = 2.87±0.07 eV.

Frustrated total internal reflection laser q-switch

Abstract: A demand synchronized laser Q-switch of high optical efficiency and fast operation includes two prisms of fused quartz separated by a fraction of a wavelength of the laser light to be Q-switched and piezoelectric transducers mounted on the back sides of each prism. With no electrical signal applied to the piezoelectric transducers the prism separation produces frustrated total internal reflection that prevents laser oscillations between the two end mirrors of a laser cavity. Application of a voltage pulse to the piezoelectric transducers produces a shock wave in each prism that drives them into physical contact. The prisms then separate rapidly in response to reflection of the shock wave. When the prisms are sufficiently separated, laser oscillation between the cavity end mirrors occurs, and a high power output pulse is produced. The output pulse is terminated upon relaxation of the prisms or upon depletion of the population inversion, whichever occurs first. Alternatively, the prisms are separated sufficiently to allow total internal reflection, and application of a voltage pulse to the piezoelectric transducers brings the opposing faces of the prisms sufficiently close to produce high transmission of laser light through the two opposing faces.

Phase Measurements of Reflected Ultrasonic Waves near the Rayleigh Critical Angle

Abstract: The phase shift with incident angle of reflected ultrasonic waves incident near the Rayleigh critical angle is reported. These measurements substantiate the predictions of our model. These predictions differ substantially from previous theories which neglect attenuation. For frequencies above 15 MHz the slope of the phase shift of an ultrasonic wave reflected from a water‐stainless steel boundary reverses at the Rayleigh critical angle. For frequencies below 15 MHz the phase shifts from 0° to +360°; above 15 MHz it shifts from 0° to +60° then to −60° and back to zero again on passing through the Rayleigh critical angle. The sensitivity of this phenomenon suggests that it could be useful in determining or evaluating changes in material properties such as cold work, residual stress, or grain sizes.

Reflection and Refraction of Plane Waves from Plane Ferrite Surfaces

Abstract: Wave vector surfaces, phase velocity surfaces, and ray velocity surfaces have been evaluated for electromagnetic waves traveling through magnetized ferrite. These surfaces are shown to have unique shapes depending upon the precessional, magnetization, and excitation frequencies. Double refraction of the waves occur at the interface between different ferrites. A transcendental equation for determining the angle of transmission is presented and a discussion is made on the possibility of total reflection. Since the direction of propagation, boundary surface normal, and direction of magnetization each present a degree of freedom to the incident plane wave problem a general set of coordinates is introduced that takes into account their relative orientation. The two cases for which the static magnetization is parallel and perpendicular to the plane of incidence is solved in detail and expressions are given for the reflection and transmission coefficients. It is shown that for the parallel magnetic polarization case the reflected component of the electric vector can be eliminated if the incident wave strikes the boundary plane at a magnetically dependent Brewster angle.

Compression of a Bundle of Light Rays

Abstract: The performance of ray compression devices is discussed on the basis of a phase space treatment using Liouville’s theorem. It is concluded that the area in phase space of the input bundle of rays is determined solely by the required compression ratio and possible limitations on the maximum ray angle at the output of the device. The efficiency of tapers and lenses as ray compressors is approximately equal. For linear tapers and lenses the input angle of the useful rays must not exceed the compression ratio. The performance of linear tapers and lenses is compared to a particular ray compressor using a graded refractive index distribution.

Phase-Matched Critical Total Reflection and the Goos-Haenchen Shift in Second-Harmonic Generation

Abstract: : It is well established that a totally reflected light beam of finite diameter undergoes a lateral displacement, known as the Goos-Haenchen shift. The theory for the corresponding effect in nonlinear optics is presented. The special phase-matched case, in which both the fundamental and second harmonic are at critical total reflection, is shown to have a characteristic radiation pattern. Since the finite beam diameter is taken into account, divergencies of earlier theories are eliminated. (Author)

Electrically modulated radiation filters

Abstract: The intensity of a monochromatic light beam is modulated by passing it through a multilayer arrangement near the critical angle of incidence thereby causing multiple reflections in one of these layers acting as an optical resonator and by varying the refractive index of at least one of said multilayers by an electrical or electromagnetic field.

Brewster Angle and the Einstein Velocity Addition Theorem

Abstract: Linearly polarized light incident on a stationary medium at an angle whose tangent equals the relative refractive index is not reflected, provided the polarization is in the plane of incidence. Analysis of this situation for a moving medium leads to the prediction of a novel effect which is an unusual application of the phenomenon of aberration. The effect suggests a generalized experiment of the Fizeau type to determine the velocity of propagation in a moving refractive medium where the direction of propagation is not parallel to that of the motion of the medium. Such an experiment would examine the Einstein velocity addition theorem. The significance of the Fresnel drag law in relation to the Fizeau experiment is discussed, as well as Potier's principle which sets forth a universal consequence of the Fresnel law.

Fiber optic plate with dense opal glass cladding

Abstract: An image storage device is disclosed which consists of a multiplicity of light conducting fibers secured together in sideby-side relation to form a fiber optic plate. Each of the fibers comprises a photochromic glass core and a layer of dense opal glass disposed on the surface of the core, the index of refraction of the opal glass being lower than that of the core. In image storage devices of this type light which is incident on the core-cladding interface at an angle less than the critical angle passes into the cladding and may darken adjacent photochromic fibers. The opal glass functions to scatter light passing through the core-cladding interface and thereby reduce the amount of light leaking to adjacent fibers, some of the scattered light being returned to the photochromic core from which it originated and contributing to the darkening thereof.