Showing papers on "Total internal reflection published in 1978"

Elastic waves in rods and clad rods

Abstract: Clad rods have been investigated for use as long delay lines because they offer isolation of the signal from the surface and low dispersion. In addition, single‐mode propagation is achieved with a larger (and hence more conveniently transduced) cross section than is possible with a homogeneous rod at the same frequency. This paper describes the modes that have a steady‐state sin(ωt−βz) dependence on (t,z), with emphasis on the modes and ranges of parameters that are of interest for delay lines. Only rods of circular cross section, and isotropic, linear elastic materials are considered. Attention is drawn to correspondences with homogeneous rods and with the hypothetical case of infinite thickness cladding, which is most useful as a model for understanding the behavior of corresponding modes in an actual clad rod. Written for the nonspecialist, the paper includes a tutorial review of the concepts and results needed to understand wave propagation in rods and clad rods. In addition, the following new results are reported: (1) for homogeneous rods, a representation of the lowest flexural mode dispersion curve that is for practical purposes independent of Poisson’s ratio; (2) for homogeneous rods, displacement distributions of the first three high‐frequency shear modes, i.e., the ’’flexural’’ modes that are asymptotic to the shear velocity (it was found that the distribution previously attributed to the lowest such mode actually belongs to the next); (3) for clad rods, the first demonstration of interface modes of the Stoneley type for nonaxially symmetric waves; (4) classification of clad rods according to the nature and ordering of their asymptotic velocities showing that there are eight types of clad rod, rather than four as stated in the previous literature; (5) for infinitely clad rods having the same shear modulus, proof that the dispersion of torsional waves and their penetration into cladding are universal functions of f/fc∞. The ratio of the shear velocities of the two materials affects the cutoff frequency fc∞, but not the universal penetration and dispersion functions. Subjects on which significant tutorial or descriptive material is given include typical waveguide dispersion, characteristic velocities of an isotropic elastic material, the effect of coupling of dilatational and shear waves at a boundary, waves in homogeneous rods, the connection of isolation to total internal reflection (with Love waves and SH waves in a clad plate as an example), Stoneley waves at a plane interface, and previous results on the clad rod.

Optical channel waveguide switch and coupler using total internal reflection

Abstract: Light beam switching and coupling in a four-port channel waveguide-horn structure has been accomplished using electrooptic modulation of the critical angle of a refractive index interface in a Y -cut LiNbO 3 substrate. The resulting double-pole double-throw switch/coupler is potentially capable of simultaneously providing a combination of desirable characteristics.

Electromagnetic wave propagation in inhomogeneous plasmas

Abstract: The absorption and transformation of electromagnetic waves in the vicinity of electron cyclotron harmonics is considered. The results of a simple WKB theory and a full wave theory are compared. It is found that for waves perpendicularly incident on a resonant surface (where the wave frequency equals an integer multiple of the electron cyclotron frequency), the full wave treatment is necessary to determine reflection and mode conversion coefficients, whereas, the WKB theory and full wave theory predict the same transmission coefficient. As the angle of incidence is decreased from 90°, the reflection and mode conversion coefficients become unimportant so that the full wave theory and WKB theory agree. The relevance of these processes to the heating of toroidal plasmas with high frequency waves is discussed.

Characteristics of a Gaussian beam at a dielectric interface

Abstract: The characteristics of a Gaussian beam that is reflected or transmitted by an interface separating a denser medium from a rarer medium are mainly described by means of numerical integration. An approximate result is shown to compare with the exact value obtained by numerical integration. The cases where the incident angle θ is arbitrary, that is, θ = θc (critical angle), θ → θc, θ ≷ θc are treated. Transmitted power in the rarer medium is obtained, from which properties of a lateral wave are found.

Analysis of gain-induced waveguiding in stripe geometry diode lasers

Abstract: This paper analyzes two-dimensional waveguiding in stripe geometry diode lasers. Refractive index discontinuities guide the light by total internal reflection in the direction perpendicular to the p-n junction plane, but the guidance mechanism along the p-n junction and transverse to the propagation direction is that of gain variation. In the active region, the gain is a maximum under the pump stripe center and decreases to loss (optical absorption) in the unpumped region. This variation is modeled by three different functions for which analytic solutions are obtained. The first is the usual quadratic. The second, by choice of parameters, represents transition cases from quadratic to square gain profiles, which occur with increasing stripe width. The third is quadratic near stripe center and continuously decreases to a constant loss value in the unpumped region. We present mode patterns, laser threshold gains, and propagation constants for a variety of cases to illustrate the effects of laser length, stripe width, and active region thickness in these devices.

Shadowing an inhomogeneous plane wave by an edge

Abstract: When an inhomogeneous plane wave or other type of evanescent field in a lossless medium strikes a large opaque object, the boundary of the shadow zone is displaced from the familiar geometric optical location for nonevanescent fields. This change is attributable to the complex propagation direction of evanescent waves. To study the mechanism of shadow formation, and indeed the significance of a shadow zone when the incident evanescent field may be weaker than diffracted fields generated by the obstacle, the problem of inhomogeneous plane diffraction by a perfectly conducting semi-infinite screen is investigated. By a careful asymptotic treatment and error analysis of the known exact solution, the location of the shadow boundary is determined, as is the transition region surrounding it wherein the field cannot be separated into incident and diffracted constituents. It is found that for strongly evanescent fields, the shadow boundary and transition zones differ markedly from those for a homogeneous plane wave. Effects of losses in the medium are also considered.

Surface chemical analysis of Avcothane and Biomer by Fourier transform IR internal reflection spectroscopy.

Abstract: During the solvent casting process, one side of the polymer film is exposed to air while the other side is in contact with a substrate, used as a mold. We have studied the effect of this difference in exposure during casting on the chemical composition of two types of segmented polyurethane,5 Biomer1 and Avcothane,2 by using Fourier transform IR internal reflection spectroscopy. Also, a depth-composition profile was obtained by placing a thin barrier film between the reflection plate and the polymer film. In Avcothane, the air side, which is the blood-contact side, contains a greater amount of the soft segment than the substrate side, and this is more pronounced in the layer closer to the surface. The anisotropy in composition is more drastic when the silicone content is compared. In a layer about 1.5 μ thick, one can detect a greater amount of silicone in the substrate side than in the air side. However, when one averages the concentration in a layer of about 0.8 μ, the trend is reversed; i.e., the greater amount of silicone is now present in the air side than in the substrate side. In Biomer films, the anisotropy in chemical composition is less pronounced. Only a modest increase in the relative content of the soft segment/hard segment is observed in the air side when a depth-composition profile is obtained.

Theory of atomic scattering at the free surface of liquid He 4

Abstract: The scattering of free helium atoms at the surface of liquid $^{4}\mathrm{He}$ at zero temperature is discussed in terms of the Feynman variational method. If the scattered atom is distinguishable from those in the liquid target, as is true for the scattering of $^{3}\mathrm{He}$, the problem reduces to the motion of a single particle in an effective potential. Above the surface the effective potential is the same as the real van der Waals potential and, in the surface and below, it is related to the density and kinetic-energy distribution in the liquid ground state. If the theory is applied to the scattering of $^{4}\mathrm{He}$, neglecting the indistinguishability of the scattered atom, an excellent fit to the experimental reflection coefficient is obtained. When the trial wave function is fully symmetrized to calculate the reflection coefficient for $^{4}\mathrm{He}$ more realistically, the theory describes the production of a single excitation (phonon) from each absorbed atom. The resulting reflection coefficient disagrees with experiment, predicting total reflection at certain critical angles. Even when multiple production of low-energy phonons is considered, total reflection will still occur. It follows that the multiple production of some other type of excitation, in particular low-energy ripplons, must be a dominant process in agreement with the calculations of Echenique and Pendry. It seems that the simple unsymmetrized theory fits the data because the reflection coefficient is mainly determined by the static van der Waals potential outside the liquid where the effects of symmetry, inelastic scattering, etc., are negligible. An atom which penetrates below this region is then effectively lost as far as the original beam is concerned because it begins to produce low-energy ripplons and is incoherently scattered. The problem of determining the density profile at the liquid surface from the experimental scattering data is briefly considered.

Thin silicon film p-i-n photodiodes with internal reflection

Abstract: A new kind of silicon p-i-n photodiode is presented which combines broad wavelength response at high quantum efficiencies (450 to 900 nm ~85 percent) and extremely fast response time (typically below 100 ps). The diodes use internal light reflection. Theoretical expressions for different types of gratings are presented. The fabrication steps for both the different kinds of gratings and the diode itself are given. Experimental data of the time and wavelength response prove this expected excellent behavior.

Amplitude modulation of light beam

Abstract: An optical modulator suitable for use with a collimated light beam having a moderate cross section and a fast response time and operational at relatively low voltage includes, for example, a glass prism and a smooth metal surface that are separated by an adjustable gap. The gap is filled with a medium, for example, air, having an index of refraction lower than the prism. A beam of monochromatic light is passed into the prism at a specific angle of incidence to undergo total internal reflection at the glass prism-gap interface. A change of approximately 1 micron in the thickness of the gap is sufficient to change the reflectivity from greater than 95% to essentially zero. The size of the gap is mechanically adjusted and this mechanical device determines the frequency response of the light modulation.

Total internal reflection integrated-optics switch: a theoretical evaluation.

Abstract: Previously demonstrated planar thin-film optical switch employing the total internal reflection phenomenon is given a full theoretical evaluation for its possible adaptability to an optical channel waveguide system and also to polarization insensitive immultiport fiber-channel switch.

Total internal reflection: a deeper look

Abstract: In the present paper, we have presented a Maxwellian boundary-type solution for total internal reflection with unbounded incident waves at an interface between two nonabsorbing media, in which the instantaneous, time varying, and time averaged radiant fluxes have been determined at all points in the two media. Solutions for the s and p polarizations were found for which the instantaneous tangential E and H components and normal components of the radiant flux were continuous in crossing the interface. From these radiant fluxes, it was possible to derive equations for the flow lines, to determine the instantaneous radiant fluxes along these flow lines, and to see how the methods of propagation differed in the two media and for the two polarizations. At the interface, the flow lines and their radiant fluxes experience unusual reflection and refraction processes, follow curved flow lines in the second medium, and return into the first medium with boundary conditions, which are mirror images of those at the points of incidence. These unfamiliar processes in the second medium are due to inhomogeneous waves, whose properties have not been understood. When these instantaneous solutions are extended to time varying and time averaged radiant fluxes, it is interesting to see how incident planes of constant radiant flux and phase experience such complex processes in the second medium and are still able to generate other reflected planes of constant radiant flux and phase in the first medium. These ideas prescribe specific detailed functions for the E and H fields and radiant fluxes in the second medium, which help to answer many long standing questions about the physical processes involved in total internal reflection.

Surface polariton in the ATR angular spectra of a thin iron film bounded by dielectric layers

Abstract: The complex dielectric constant of Fe has a large imaginary part and small real part throughout most of the visible region (∊i ≫ |∊r|). Under this condition a thin film of Fe(≤ 20 nm), bounded by a dielectric, can support a surface polariton. For p-polarized fields the antisymmetric solution to the dispersion relation has a nearly real propagation vector parallel to the surface. Hence this antisymmetric polariton can be excited optically. We use the attenuated total reflection (ATR) configuration with three successive layers, cryolite-Fe-cryolite, evaporated onto the base of a glass prism. The surface polariton is detected as a narrow minimum in the ATR angular spectrum. We choose the frequency at which ∊r = 0 and then an incident p-polarized plane wave yields zero energy propagation in the Fe film in the direction parallel to the plane on the film. There are also other broader minima in the p-polarized spectrum corresponding to large field oscillations localized in the second dielectric. Minima in the s-polarized spectrum correspond to oscillations localized in the first dielectric. In addition the angular reflectance spectrum of both polarizations contains sharp maxima caused by resonance standing wave patterns which persist through the incident medium as well as the film system.

Reflection and refraction of SH waves in presence of slip and friction

Abstract: The reflection of elastic waves is customarily treated by assuming that the interface neither separates nor slips. This paper considers the reflection of SH waves that are strong enough to break friction between two solids which are pressed together, so that localized slip takes place. It is also assumed that the solids are sheared, which enhances slip in one direction and leads to a global sliding motion. The problem might at first appear as forbidding because of the mixed boundary conditions and the inequalities involved. It is discovered, however, that it can be solved in closed form for angles of incidence that avoid total reflection. The global sliding velocity, the sizes of the slip zones, and the rate at which mechanical energy is dissipated are displayed in terms of the independent variables involving the amplitude of the incident waves, and the applied pressure and shearing tractions.

Interaction of Surface Waves and Bulk Waves in Gratings: Phase Shifts and Sharp Surface-Wave/Reflected Bulk Wave Resonances

Abstract: Surface acoustic wave propagation in shallow, normal incidence and oblique incidence gratings has been studied on YZ LiNbOj. The phase shift or slowing of the surface acoustic wave upon transmission through gratings was measured by comparing the phase response of two adjacent identical delay lines in one of which the surface wave passes through the grating. were made at frequencies between 120 and 220 MHz for 100- and 200-groove normal- and oblique-incidence gratings. If the data is fitted to an expression of the form 4 = (360°/n) C'(h/X)Z, the values of C' which are determined differ significantly from the value of C' determined by earlier measurements of the imaginary part of the reflection coefficient of such gratings. This implies a limitation of the model which relates the two types measurements. A series of very sharp stop bands is observed in the transmissi-on response of a 200 groove normal incidence grating when the wave-length is within 520% of the grating period. These stop bands are produced by resonant conversion of surface waves to bulk waves in the grating, reflection of these waves back and forth from bottom to top of the crystal, and reconversion into surface waves in the grating. Measurements

Internal-Reflection-Spectroscopy Studies Of Thin Films And Surfaces

Abstract: Internal-reflection spectroscopy has found considerable use in the infrared for studying vibration-band properties, optical constants, surface electromagnetic waves, and guided modes in thin-film channels. This paper discusses the principal ideas, including the forms of the evanescent waves and the effects of refractive indices and absorption coefficients of various magnitudes, for various prism-sample combinations--for example, prism pressed against bulk sample, prism separated slightly from sample and prism with thin film. Also discussed are examples of applications of the techniques to the studies of (a) vibration bands in opaque materials and thin films, (b) molecules adsorbed to surfaces, (c) Raman scattering in thin films, (d) fluorescence in thin films and (e) surface plasmons on bulk metal surfaces and on thin films.

Theoretical evidence for negative Goos-Haenchen shifts

Abstract: The Goos-Haenchen shift which occurs at total reflection from a glass-air interface is normally assumed to be positive, implying that the reflected beam of light is displaced with respect to the incident beam along the interface and in the sense and direction of the projection of the incident wavevector onto the interface The authors show that the longitudinal displacement of electromagnetic radiation on reflection can be both positive and negative depending on the nature of the two media at whose interface reflection occurs The shift is computed within the framework of classical electrodynamics by application of the principle of stationary phase Two examples are worked out The first is a case of a bundle of microwaves incident onto a corrugated metallic surface, whereas the second involved electromagnetic radiation falling on a magnetised plasma In both examples the longitudinal displacement is found to be positive, negative or zero depending on the angle of incidence and other parameters It is also shown that negative Goos-Haenchen shifts do not contradict the law of conservation of photon momentum

Nonreactive scattering of K by Br2 in the energy range of 0–10 eV

Abstract: In a crossed molecular beam experiment the nonreactive differential scattering of K by Br2 has been measured at several laboratory kinetic energies below 10 eV The experimental angular distributions have been analyzed with the aid of trajectory surface hopping calculations, which are partly in (qualitative) accord with the measurements The nonreactive neutral differential scattering can be divided into two angular regions, separated by a critical angle, with a “reduced” value νc, that increases with the collision energy The critical angle is related to a critical impact parameter bc, which is determined by the crossing radius Rc of the potential surfaces involved The major part of the small angle scattering ( bc, yielding elastic scattering, and drops rapidly with the cm scattering angle x according to o(x) sin x α x−1−α, with α = 15 (experiments) respectively 19 (calculations), independent of the collision energy The large angle scattering (> τc) comes from impact parameters b ⩽ τc and corresponds to inelastic neutral scattering At low collision energies most inelastic neutral scattering is from orbiting trajectories with b ≈ bc, and decreases exponentially with angle, following o(x) sin x ∝ exp (−x/ao) Here the cm parameter a0 has been measured to decrease little with energy from a0 = 028 rad (at 053 eV) to a0 = 021 rad (at 305 eV) At laboratory energies above 4 eV orbiting behaviour has not been observed The total inelastic neutral cross section is calculated to be around 20 A2, rather independent of energy The appearance of the inelastic neutral scattering is attributed to non-adiabatic effects as well as to recrossing from the ionic state back to the covalent state

Displacement of an electromagnetic beam upon reflection from a dielectic slab

Abstract: The longitudinal displacement of an elelctromagnetic beam upon reflection from a dielectric slab has been investigated. The experimental results, using 3 cm microwaves, are compared to those predicted by a theory based on a plane-wave approach. The experiment has been completed for both perpendicular and parallel polarization using a slab several wavelengths thick for angles of incidence around 45°. The agreement between experimental values and theoretical predictions is good.

Mechanisms for the reflection of light atoms from crystal surfaces at kilovolt energies

Abstract: The computer program MARLOWE was used to investigate the backscattering of protons from the (110) surface of a nickel crystal. Grazing incidence was considered so that anisotropic effects originated mainly from the surface region. The contribution of aligned scattering was studied by comparing the results with similar calculations for an amorphous target. Energy distributions of backscattered particles were investigated for incident energies ranging from 0.1 to 5keV. The structure of these distributions was explained by making calculations for several target thickness. Specular reflection was found to depend on the structure of the first few atomic planes only. The (110) rows in the surface plane were responsible for focusing into surface semichannels. Focusing in these semichannels was found to be the strongest under total reflection conditions (below about 1.3 KeV) while the scattering intensity from surface rows increased with increasing incident energy. The orientation of the plane of incidence was found to have large influence on the relative contributions of the reflection mechanisms involved.

Consequences of light reflection at the interface between two transparent media such that the angle of refraction is 45

Abstract: The reflection of light at the interface between two transparent, homogeneous and optically isotropic media such that the angle of refraction is 45° has the following interesting consequences: (i) the interface relfectivity for the parallel (p) polarization is the square of that for the perpendicular (s) polarization; (ii) the angular deviation of the propagation direction upon refraction is equal to the polarization (or ellipsometric) angle ψ and (iii) the complex reflection coefficient for the p polarization is stationary, in both magnitude and phase, with respect to small charges of the (refractive and/or absorptive) optical properties of either one or both media. Furthermore, it follows from (iii) that: (iv) reflectivity of the p polarization, considered as a function of the ratio of refractive indices of the two media, is at a maximum; and (v) changes of the absolute magnitude and absolute phase of the reflection coefficient for the s polarization, caused by small perturbations of the optical properties, can be measured directly by ellipsometry.

Astigmatic illuminating system in an internal reflection spectometer

Abstract: In a spectrometer, an internal reflectance crystal having opposed internally reflecting surfaces extending between light-entrance and light-exit end surfaces is illuminated by a light source through a slit. The beam of light from the slit is reflected from a spherical mirror illuminated off-axis to form first and second astigmatic images of the slit. The tangential image, having a distorted (elongated or extended) height, is formed at the entrance surface of the internal reflectance crystal. The width of the tangential image matches the width of the entrance surface. The sagittal image is formed at the exit surface of the internal reflectance crystal. The width of the sagittal image, which would be distorted (extended) absent the internal reflectance crystal, is limited by the internally reflecting surfaces of the crystal. Thus, there is substantially no loss of radiant energy through the length of the crystal. In one embodiment, the exit surface is curved along its height to make the diverging beam leaving the internal reflectance crystal less divergent and thus more compact at the light detector lens.

Measurement of the Refractive Index of a Prism by a Critical Angle Method

Abstract: A new method of measuring the refractive index of a prism using the critical angle is described. The accuracy of the technique and tolerances on angle measurements are discussed. Two standard prisms were measured using this method and the values agreed with those measured by the minimum deviation method to five units in the fifth decimal place, consistent with the error analysis given.

Light beam switching and modulation using a built-in dielectric channel in LiNbO(3) planar waveguide.

Abstract: The results of light beam switching and modulation experiments utilizing electrooptic control of the refractive index of a built-in dielectric channel in a Y-cut LiNbO3 planar waveguide are reported. The resulting device is capable of simultaneously providing a combination of desirable characteristics.

Light scattering on internal reflection from surface acoustic waves

Abstract: The intensity of light scattered by surface acoustic waves (SAW) on internal reflection has been calculated for the geometry where the incident and scattered light are in a plane perpendicular to the SAW wave vector. The calculation was carried out for an arbitrary piezoelectric crystal having a free or metallized surface. Measurements on a y‐cut LiNbO3 crystal and a z‐propagating SAW give good agreement with the theory.