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Showing papers on "Total internal reflection published in 1973"


Journal ArticleDOI
TL;DR: In this paper, a model of the reflection process is developed that explains all of the observed phenomena, including a shift of the reflected beam from the position predicted by geometrical acoustics, a null or minimum of intensity within the reflected beacon, a 180° phase reversal of the field on either side of the null, a weak trailing field on only one side of a reflected beam and a frequency of least reflection when the solid is lossy.
Abstract: Various phenomena have been observed when a bounded acoustic beam is incident from a liquid onto the surface of a solid at or near the Rayleigh angle. These phenomena include: a shift of the reflected beam from the position predicted by geometrical acoustics, a null or minimum of intensity within the reflected beam, a 180° phase reversal of the field on either side of the null, a weak trailing field on only one side of the reflected beam and a frequency of least reflection when the solid is lossy. By carefully examining the reflection coefficient for angles in the vicinity of the Rayleight angle, and by taking into account the angular spectrum of plane waves that comprise a bounded beam, a model of the reflection process is developed that explains all of the observed phenomena. This model shows that the various critical-reflection effects result from the interference between a geometrically reflected field and the field of a leaky Rayleigh wave, which is excited by the incident beam. Moreover, this model resolves the conflict between various explanations made for these phenomena in the past; in particular, it is found that Schoch's classical description of a laterally displaced reflected beam is valid only for beams having a large width.

339 citations


Journal ArticleDOI
TL;DR: In this paper, the authors explore the properties of a semi-infinite non-local dielectric to assess the effect of spatial dispersion on the reflectivity of the material and on properties of surface polaritons.
Abstract: In this paper, we explore the properties of a model of a semi-infinite nonlocal dielectric to assess the effect of spatial dispersion on the reflectivity of the material and on the properties of surface polaritons. For the model, the nonlocal form of Maxwell's equations may be solved exactly. The additional boundary conditions follow from Maxwell's equations, and it is not necessary to introduce microscopic considerations to complete the theory. We exhibit closed expressions for the reflectivity of the material, for the case where the electric field is parallel to the plane of incidence, and for the case where it is perpendicular to the plane of incidence. At non-normal incidence, when the electric field vector is parallel to the plane of incidence, structure which owes its origin to spatial-dispersion effects appears in the reflectivity. We show that in the presence of spatial dispersion, the surface polaritons acquire a finite lifetime even in the case where the dielectric is lossless; i.e., in the presence of spatial dispersion the surface polaritons become virtual surface waves. In the quasistatic limit, we obtain an analytic expression for the dependence of the real and imaginary part of the surface-polariton frequency on wave vector in the long-wavelength limit. We then present the theory of frustrated internal reflection of radiation from a prism and crystal configuration similar to that employed in several recent experiments. In a final section, we present the results of some numerical calculations of the reflectivity of the crystal, and the width and position of the dip observed in the frustrated-internal-reflection method, for parameters characteristic of the fundamental exciton line in ZnSe.

168 citations


Journal ArticleDOI
Reisinger A1
TL;DR: A generalized procedure is presented that permits an accurate description of metal boundaries at optical frequencies and it is found that, with increasing buffer thickness, TM(N) modes undergo a continuous transformation to becomeTM(N+1).
Abstract: A number of analysis techniques aimed at determining the characteristics of optical guided waves propagating in lossy structures are examined. The exact theory is used as a guide to assess the validity of several approximate methods based on two basic approaches: (a) geometrical optics and (b) perturbation calculations. The limitations of the conventional perturbation techniques are specified. We present a generalized procedure that permits an accurate description of metal boundaries at optical frequencies. In this case, TM modes differ from their TE counterparts by a field buildup near conducting walls and by the existence of an additional surface plasma mode. The dependence of attenuation coefficients on film thickness and mode order are discussed. The use of low-index dielectric buffers to reduce ohmic losses is considered. It is found that, with increasing buffer thickness, TM(N) modes undergo a continuous transformation to become TM(N+1).

157 citations


Journal ArticleDOI
TL;DR: The morphology of surface damage of ED-2 laser glass is described, and a model based upon reflections from the laser induced plasma is proposed to explain the observations.
Abstract: A summary of recent investigations of surface damage of transparent dielectrics is presented. Damage threshold measurements made on Owens-Illinois ED-2 laser glass at normal incidence and at Brewster’s angle are reported. For 30-nsec pulses at normal incidence, exit surface damage thresholds are typically 100 J/cm2 for ED-2 glass. The observed ratio between entrance and exit damage thresholds for the two geometries can be explained by considering the electric field strengths at the surfaces and including interference between incident and reflected light waves. A similar analysis is applied to surface damage that occurs during total internal reflection. Finally the morphology of surface damage of ED-2 laser glass is described, and a model based upon reflections from the laser induced plasma is proposed to explain the observations.

149 citations



Journal ArticleDOI
TL;DR: The infrared spectral reflectance of a semi-infinite medium composed of irregular particles of different materials is calculated in terms of the sizes, shapes, and complex refractive indices of the particles.
Abstract: The infrared spectral reflectance of a semi-infinite medium composed of irregular particles of different materials is calculated in terms of the sizes, shapes, and complex refractive indices of the particles. For particles larger than the wavelength, the scattering and absorption are computed mainly by geometrical optics but with important wave-optical corrections for the additional absorption caused by edges and asperities, which are represented by dipoles distributed over the surface of the particle. For particles smaller than the wavelength, a Lorentz-Lorenz model is used to derive the average complex index of the medium, the particles being treated as ellipsoids with a wide range of shapes. The average scattering of an individual ellipsoidal particle is then found from the relative refractive index of the particle with respect to the Lorentz-Lorenz medium. For both large and small particles the single-particle scattering is represented by six discrete beams. Calculation of the reflectance is then facilitated by a radiative transfer method that also involves six beams. For particles of intermediate size a suitable formula bridging the results for large and small particles is found to be satisfactory.

86 citations


Patent
19 Jan 1973
TL;DR: A light coupler for transferring optical wave energy to or from light transmitting means including at least one optical waveguide is described in as mentioned in this paper, where the coupler comprises a tapered core of transparent material of refractive index n 1 and a layer of transparent cladding material of as mentioned in this paper.
Abstract: A light coupler for transferring optical wave energy to or from light transmitting means including at least one optical waveguide. The coupler comprises a tapered core of transparent material of refractive index n1 and a layer of transparent cladding material of refractive index n2 disposed upon the surface of the tapered core, n1 being greater than n2. The tapered core has a large diameter end which is aligned with an end of the light transmitting means and a small diameter end which is disposed adjacent to electro-optic energy conversion means such as a light emitting diode, a light detector or the like. A reflecting metallic layer is disposed upon at least that portion of the surface of the cladding layer which is adjacent to the small diameter end of the coupler to reflect light which is incident upon the core-cladding interface at angles less than the critical angle and which passes through the cladding layer.

76 citations


Journal ArticleDOI
Armin Segmüller1
TL;DR: In this paper, strong interferences have been obtained upon specular reflection of monochromatic X-rays at thin films of amorphous silicon on sapphire substrates under glancing angles slightly above the critical angle for total reflection.

67 citations


Journal ArticleDOI
TL;DR: A Raman spectra method corresponding to the ATR method, which observes Raman scattering due to evanescent wave in total reflection, which may be called Total Reflection Raman Spectra is developed.
Abstract: Several methods of infrared spectra have been devised for surface chemistry, including the attenuated total re­ flection (ATR) method, which was developed by Fahrenfort and by Harrick. The former calculated the relation between the reflectivities and values of the absorption coefficient at angles of incidence above the critical angle. The latter calculated the penetration depth of incident light into the optically rare medium and suggested that this method is sensitive to molecular absorption on the surface. Some workers applied the ATR methods to studies of electrode reactions in situ and adsorptions. In the infrared region water has strong absorption which is apt to disturb studies of adsorbed species. Therefore we developed a Raman spectra method corresponding to the ATR method. It observes Raman scattering due to evanescent wave in total reflection, which may be called Total Reflection Raman Spectra. We measured the de­ pendence of this intensity on the angle of incidence, which agrees with the inclination of the calculation.

51 citations


Journal ArticleDOI
TL;DR: This paper describes a simple electrooptic effect that can be achieved by placing a thin nematic liquid crystal layer between two glass prisms of appropriate refractive index, for a range of angles of incidence on the prism-liquid crystal interface.
Abstract: This paper describes a simple electrooptic effect that can be achieved by placing a thin nematic liquid crystal layer between two glass prisms of appropriate refractive index. For a range of angles of incidence on the prism–liquid crystal interface, light is partially transmitted or totally reflected, depending upon the electric-field-controlled orientation of the optic axis in the nematic layer.

41 citations


Journal ArticleDOI
TL;DR: In this paper, a compact formula for the Goos-Haenchen shifts occurring for total internal reflection of light from anisotropic media was given, which was used in a coupled-wave analysis of polarization conversion in thin-film waveguides.
Abstract: A compact formula is given for the Goos-Haenchen shifts occurring for total internal reflection of light from anisotropic media. This is used in a coupled-wave analysis of polarization conversion in thin-film waveguides deposited on optically birefringent substrates. A numerical example illustrates the considerable influence of the Goos-Haenchen shifts on the conversion length.

Journal ArticleDOI
TL;DR: In this paper, a theoretical analysis of acoustic waves refracted by a spherical boundary across which velocity and density increase abruptly and below which velocity or density may either increase or decrease continuously with depth is formulated in terms of waves generated at a harmonic point source and scattered by a radially heterogeneous spherical body.
Abstract: Summary A theoretical analysis of acoustic waves refracted by a spherical boundary across which velocity and density increase abruptly and below which velocity and density may either increase or decrease continuously with depth is formulated in terms of waves generated at a harmonic point source and scattered by a radially heterogeneous spherical body. Through the application of an Earth-flattening transformation on the radial solution and the Watson transform on the sum over eigenfunctions, the solution to the spherical problem for high frequencies is expressed as an integral for the corresponding half-space problem in which the effect of boundary curvature maps into an effective positive velocity gradient with depth. The results of both analytical and numerical evaluation of this integral can be summarized as follows for body waves in the crust and upper mantle: (1) In the special case of a critical velocity gradient (a gradient equal and opposite to the effective curvature gradient), waves interacting with the boundary at the critical angle of incidence have the same form as the classical head wave for flat, homogeneous layers. (2) For gradients more negative than critical, the amplitude of waves incident at the critical angle decay more rapidly with distance than the classical head wave. (3) For gradients that are positive, null, and less negative than critical, the amplitude of waves near the critical angle decays less rapidly with distance than the classical head wave, and at sufficiently large distances, the refracted wave field can be adequately described in terms of ray-theoretical diving waves. At intermediate distances from the critical point, the spectral amplitude of the refracted wave is scalloped due to multiple diving wave interference.

Journal ArticleDOI
TL;DR: In this article, it was shown that both the longitudinal Goos-H\"anchen shift and the new transverse shift are quantized, each having two eigenvalues and two Eigenfunctions, which are the principal linear polarization states in the first case and the circularly polarized state in the second case.
Abstract: In additional measurements following their experimental demonstration of the now well-known longitudinal shift of a light beam undergoing total reflection, Goos and H\"anchen have observed that an incident beam of natural light is separated into two beams with polarizations normal and parallel to the incidence plane. Although an explanation of this filtering effect of orthogonal modes is easy in terms of either the Artmann or the Renard formulas of the Goos-H\"anchen shift, which are deduced from a stationary phase and an energy-conservation argument, respectively, it seems that this explation has not yet been produced. We describe here associated theoretical and experimental work showing that both the longitudinal Goos-H\"anchen shift and the new transverse shift are quantized, each having two eigenvalues and two eigenfunctions, which are the principal linear polarization states in the first case and the circularly polarized states in the second case. Thus the longitudinal and the transverse shifts should not be simultaneously observable. This can be justified in terms of the so-called tangential and sagittal focal lines produced by total reflection from a point source. Our theoretical reasoning is based on formal properties of Poynting's energy-flux vector. Our experiments consist of (1) a confirmation, with photographic recording, of the Goos-H\"anchen "polarization effect," (2) a similar demonstration of the filtering of the two circular polarization modes by observation of the transverse shift. In the latter case our apparatus is similar to the one we have used for demonstrating the transverse shift, but with the circular polarization analyzer placed after rather than before the totally reflecting prism. Our new measurements also comprise an improved evaluation of the transverse shift.

Patent
10 Dec 1973
TL;DR: In this paper, an optical wave is coupled into and guided through a transparent thin film by means of the tunneling into the film of an evanescent wave from a beam of light incident on the surface of an adjacent coupling medium at an angle greater than the critical angle for total internal reflection in the medium.
Abstract: In order to measure the thickness and refractive index of a transparent thin film on a substrate of higher refractive index, such as a film of silicon oxide on a substrate of silicon, an optical wave is coupled into and guided through the film. The guided wave is coupled into the film by means of the phenomenon of the tunneling into the film of an evanescent wave from a beam of light incident on the surface of an adjacent coupling medium at an angle greater than the critical angle for total internal reflection in the medium. The intensity minima of the optical radiation which can be coupled out of the film back into the coupling medium (overall reflection), as a function of angle, yields data from which the desired thickness and refractive index can be determined.

Patent
26 Dec 1973
TL;DR: In this paper, a semiconductor light-emitting diode (LED), which is substantially transparent to its own generated radiation, is coated with a reflecting layer having an exit aperture for transmission of optical radiation, for example, to an optical fiber.
Abstract: A semiconductor light-emitting diode (LED), which is substantially transparent to its own generated radiation, is coated with a reflecting layer having an exit aperture for transmission of optical radiation, for example, to an optical fiber. The reflecting layer includes a layer of dielectric in contact with the semiconductor, the dielectric layer itself being coated with an optically reflecting metal layer. The dielectric layer is made sufficiently thick to prevent the evanescent waves (of the totally internally reflected light in the semiconductor) from contacting the metal, thereby affording very close to 100 percent optical reflection of the optical rays in the semiconductor which are incident on the dielectric at greater than the critical angle. In addition, a significant portion of the semiconductor-dielectric interface is rough, thereby scattering (randomizing) the totally internally reflected rays in the semiconductor, which rays otherwise would have no chance of being accepted into the optical fiber. Thus, the overall coupling efficiency of optical radiation from the diode to the optical fiber is enhanced.

Journal ArticleDOI
TL;DR: In this article, an electro-optic diffraction modulator/deflector using tota internal reflection and no external optics is described, where the zero-order extinction voltage decreases, and the interorder angle increases, with decreasing interdigitated electrode pitch.
Abstract: An electro-optic diffraction modulator/deflector using tota internal reflection and no external optics is described. The zero-order extinction voltage decreases, and the interorder angle increases, with decreasing interdigitated electrode pitch. With LiNbO3, all the zero-order energy is deflected by less than 60 V. The active-material volume is low, approximately 0.5 mm3. Further optimisation is possible.

Patent
27 Dec 1973
TL;DR: In this article, a plurality of optical glass cores of selected refractive index and dimension are clad with a first glass of lower viscosity providing substantially total internal reflection within the cores.
Abstract: A plurality of optical glass cores of selected refractive index and dimension are clad with a first glass of lower refractive index providing substantially total internal reflection within the cores. The clad cores are then clad with a glass displaying a lower viscosity than either the core or the first cladding and fused into a final assembly. The cross-sectional area of the second core cladding is selected to provide a minimum free space within the fused assembly.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the refractive index is a two-valued markovian random function of position, and the distribution of the phase of the reflection coefficient is calculated both analytically and numerically.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the basic wave mechanism responsible for both the lateral (Goos-Hanchen) shift of a gaussian light beam incident from a denser medium upon the interface to a rarer medium, and the weak radiance that accompanies the reflected beam.
Abstract: By utilizing a rigorous plane-wave representation, we investigate the basic wave mechanism that is responsible for both the lateral (Goos-Hanchen) shift of a gaussian light beam incident from a denser medium upon the interface to a rarer medium, and the weak radiance that accompanies the reflected beam. We thus find that the complete reflected field contains a geometric-optics component, whose domain is given by the mirror reflection of the incident beam, as well as a lateral-wave component which occupies a much larger domain. Our results show that the near field of the lateral-wave component interferes with the geometric-optics component and thereby produces the Goos-Hanchen shift of the reflected beam. The intermediate and far fields of the lateral-wave, on the other hand, are responsible for the weak radiance that trails the reflected beam. By demonstrating that both the beam shift and the trailing radiance represent two facets of the same wave process, the lateral-wave field is shown to provide a unified interpretation of two effects that have previously been regarded as separate phenomena. The dependence of these effects on beam width, angle of incidence, and polarization are also considered.

Journal ArticleDOI
TL;DR: The Van Cittert-Zernike theorem determines the degree of coherence γ of light from a source radiating in a uniform medium in terms of the angular size α of the source as discussed by the authors.

Journal ArticleDOI
01 Aug 1973
TL;DR: In this paper, the authors explored the feasibility of using internal reflection spectroscopy to study adsorption phenomena in situ at the liquid/solid interface, where stearic acid was adsorbed from CCl4 solution directly onto the surfaces of Ge and Al2O3 internal reflection prisms which acted as adsorbents.
Abstract: Experiments were carried out to explore the feasibility of using internal reflection spectroscopy to study adsorption phenomena in situ at the liquid/solid interface. To test the methods, stearic acid was adsorbed from CCl4 solution directly onto the surfaces of Ge and Al2O3 internal reflection prisms which acted as adsorbents. Infrared spectra of the adsorbed layer were measured with a Beckman IR-12 and also a Digilab FTS-14 Fourier transform spectrometer. It was possible to follow the build-up of the adsorbed layer as function of time and, with solutions of various concentrations, to note changes in the total adsorption as function of concentration. The maximum amount adsorbed was about 0.3 monolayer with solutions in the 10−4–10−2M range. The lowest coverage observed was about 0.03 monolayer. Some information about the orientation of the adsorbed species could be obtained through the use of polarized radiation. Although the method is restricted to adsorbates which can be fashioned into internal reflection elements, the techniques are suitable for obtaining information about kinetics of adsorption and desorption, adsorption isotherms, adsorbate-adsorbent perturbations, the orientation and structure of the absorded layer, and chemisorption.

Patent
07 Nov 1973
TL;DR: In this paper, the attenuation of a light signal transmitted by an isosceles prism with total internal reflection as the prism is progressively immersed in a liquid of differing refractive index from the atmosphere is considered.
Abstract: Tank filling monitor based on the attenuation of a light signal transmitted by an isosceles prism with total internal reflection as the prism is progressively immersed in a liquid of differing refractive index from the atmosphere. Optical fibres of appropriate length may be used to convey the incident light from the source to the prism and from the prism to a light detector.

Journal ArticleDOI
K. Tsuruda1
TL;DR: In this article, the effect of conductive ground reflection was taken into account in the calculation of the penetration and reflection coefficients of the VLF electromagnetic waves incident on to the plane-stratified ionosphere both from below and above.

Journal ArticleDOI
TL;DR: In this paper, the authors presented a concise analytic expression for the loss of all weakly attenuating rays on circular optical fibres, and provided a unifying theory of light transmission within fibres.
Abstract: Many of the rays on circular optical fibres that are predicted from geometric optics to be trapped by total internal reflection are, in fact, leaky Thus geometric optics fails for long fibres The letter presents a concise analytic expression for the loss of all weakly attenuating rays The method is simple, and applicable to a large class of problems The results provide a unifying theory of light transmission within fibres, representing a generalisation of Fresnel's and Snell's laws

Book ChapterDOI
Olof Bryngdahl1
TL;DR: The role of evanescent waves in optical imaging is discussed in this paper, where the authors focus on the physical reality and properties of these waves and the way their peculiar behavior can be advantageously used for optical imaging purposes.
Abstract: Publisher Summary This chapter focuses on the role of evanescent waves in optical imaging. It emphasizes the physical reality and properties of the evanescent waves and the way their peculiar behavior can be advantageously used for optical imaging purposes. Evanescent waves exist and are formed in optics in connection with some well-known phenomena: they are formed in the rarer medium when light is totally internally reflected, they occur in diffraction at objects with extremely fine structures, they are frequently encountered in connection with the angular spectrum representation of electromagnetic field, they are used for the treatment of radiation from moving charged particles, and they are used to describe fields without radiation. Evanescent waves are often also called “surface waves,” especially in the radio-wave field. Because of their evanescence, evanescent waves cannot be used for transferring optical information over any appreciable distance. Therefore, they always have to be used in combination with homogeneous propagating waves in such a way that propagating waves are converted into evanescent waves and/or vice versa. Before conversion, however, a change in the state of the evanescent wave—that is, in its amplitude, phase, frequency, and polarization—can be introduced.


Journal ArticleDOI
Dietrich Marcuse1
TL;DR: In this paper, the cutoff condition of slab waveguides and round fibers is discussed, and it is shown that the cutoff point is not related to the critical angle but has its origin in the radiation losses of curved dielectric waveguide.
Abstract: In slab waveguides, a mode reaches its cutoff point when the direction of the plane waves constituting the mode approach the critical angle for total internal reflection. Cutoff in round fibers is not related to the critical angle but has its origin in the radiation losses of curved dielectric waveguides. The cutoff condition of modes in slab waveguides and round fibers is discussed in this paper.

Journal ArticleDOI
E. A. J. Marcatili1
TL;DR: Snell's law has been extended to cover total internal reflection in dielectric guides of arbitrary cross section as discussed by the authors, and the main result is that rays totally reflected are those at angles with the generatrix of the cylinder smaller than cos−1(n2/n1), where n1, and n2 are the refractive indices of the core and cladding.
Abstract: Snell’s law has been extended to cover total internal reflection in dielectric guides of arbitrary cross section. The main result is that rays totally reflected are those at angles with the generatrix of the cylinder smaller than cos−1(n2/n1), where n1, and n2 are the refractive indices of the core and cladding.

Journal ArticleDOI
TL;DR: In this paper, the spatial shift of the intensity profile of the totally reflected beam was determined by determining the spatial displacement of a light beam on total internal reflection, and the results can be explained solely on classical grounds.

Journal ArticleDOI
TL;DR: In this paper, phase matching of nonlinear three-wave optical processes in optical waveguides is shown to be possible with the use of only zero-order TE and TM modes, such that the phase-match condition is made insensitive to waveguide thickness over a limited region.
Abstract: Phase matching of nonlinear three‐wave optical processes in optical waveguides is shown to be possible with the use of only zero‐order TE and TM modes, such that the phase‐match condition is made insensitive to waveguide thickness over a limited region. This is accomplished by adjusting the phase shifts on total internal reflection for lowest‐order modes, near cutoff, in a thin nearly symmetric waveguide. This ``noncritical'' situation eases the requirements on waveguide fabrication. Limitations due to bulk dispersion, waveguide asymmetry, and surface scattering losses are discussed.