Showing papers on "Step-index profile published in 1978"
TL;DR: In this article, a simple method is presented for finding the modes on those optical waveguides with a cladding refractive index that differs only slightly from the core, and the resulting modal fields and their progagation constants display the polarization properties of the waveguide contained within the ∇ ∊ term of the vector wave equation.
Abstract: A simple method is presented for finding the modes on those optical waveguides with a cladding refractive index that differs only slightly from the refractive index of the core. The method applies to waveguides of arbitrary refractive index profile, arbitrary number of propagating modes, and arbitrary cross section. The resulting modal fields and their progagation constants display the polarization properties of the waveguide contained within the ∇ ∊ term of the vector wave equation. Examples include modes on waveguides with circular symmetry and waveguides with two preferred axes of symmetry, e.g., an elliptical core. Only a minute amount of eccentricity is necessary for the well-known LP modes to be stable on an elliptical core, while the circle modes couple power among themselves.
285 citations
TL;DR: The permissible bending radius R* defined for a given value of bending loss is derived and it is deduced that R* is nearly proportional to wavelength lambda when the normalized frequency nu and the refractive-index difference Delta are fixed.
Abstract: A bending loss formula for optical fibers with an axially symmetric arbitrary-index profile is derived by approximating the refractive-index profile with a staircase function. The permissible bending radius R* defined for a given value of bending loss is derived. It is deduced that R* is nearly proportional to wavelength lambda when the normalized frequency nu and the refractive-index difference Delta are fixed. The ratio of R* at two different values of nu depends only on the ratio of nu. The influence of an index dip and profile smoothing on R* is numerically evaluated.
170 citations
TL;DR: In this paper, the density and the refractive index for various compositions of binary SiO2GeO2 glass prepared by a flame deposition technique, similar to that used to make low-loss optical waveguides, have been measured by standard Archimedes method and the Becke line method, respectively.
Abstract: The density and the refractive index for various compositions of binary SiO2GeO2 glass prepared by a flame deposition technique, similar to that used to make low-loss optical waveguides, have been measured by standard Archimedes method and the Becke line method, respectively The density as a function of composition is calculated considering the effective volume of the ions contained in the glass to be invariant The refractive index as a function of composition is also calculated, based on the Lorenz-Lorenz equation, by computing the electronic polarizability of fused silica and germania All calculated results are in good agreement with the observed data
134 citations
TL;DR: Using this launching technique, it is possible to determine the index profile and index difference of graded core fibers and other important fiber parameters, such as the differential attenuation and the differential propagation delay time as a function of the mode parameter, giving insight into the fundamental propagation characteristics of the fiber.
Abstract: A method is described permitting excitation of a small number of modes in graded index fibers, the order of the launched mode being easily varied and determined. Using this launching technique, it is possible to determine the index profile and index difference of graded core fibers; results are compared with those obtained by other techniques. Other important fiber parameters, such as the differential attenuation and the differential propagation delay time as a function of the mode parameter, are also obtained, giving an insight into the fundamental propagation characteristics of the fiber.
75 citations
TL;DR: In this article, a theoretical study has been carried out on propagation in single-mode fibres having a dip in the refractive index at the core of the core, where the energy of the mode gradually spreads from the centre of a core with increase of the degree of the dip.
Abstract: A theoretical study has been carried out on propagation in single-mode fibres having a dip in the refractive index at the centre of the core. The energy of the mode gradually spreads from the centre of the core with increase of the degree of the dip. Nevertheless the near- and far-field distributions of such single-mode fibres are very nearly Gaussian in shape. A simple method of estimating the limit of the single-mode region for any kind of index profile is presented. For a particular class of profiles, dip widths up to 30% have a negligible effect on the propagation characteristics.
38 citations
TL;DR: In this paper, photoinduced changes in refractive index and thickness in evaporated As2S3 films have been measured by means of a prism-coupling technique, and the irreversible and reversible structural transformations are associated with increases in the refractive indices of 0.133 and 0.029 at a wavelength of 633 nm.
Abstract: Photoinduced changes in refractive index and thickness in evaporated As2S3 films have been measured by means of a prism‐coupling technique. The irreversible and reversible structural transformations are associated with increases in the refractive index of 0.133 and 0.029, respectively, at a wavelength of 633 nm. Additionally, a dynamical change in refractive index by 0.003 appears under the band‐gap illumination of about 10 mW/cm2. The origin of this change is attributable to a result from photoelectronic excitation. In the irreversible process, the films expand first and subsequently contract as the refractive index increases monotonically, whereas any change in thickness was not detected within an experimental error of ±10 A for the reversible process.
38 citations
TL;DR: For a number of absorber-reflector combinations the reflectance spectrum as well as the figure of merit a/e has been computed numerically in order to find an optimum set of parameters.
Abstract: For a number of absorber-reflector combinations the reflectance spectrum as well as the figure of merit a/e has been computed numerically in order to find an optimum set of parameters. Values of a/e in excess of 20 result for an absorber consisting of 0.5 μm Ge on a silver reflector, overlaid by 2.0 μm Si carrying a four-layer antirereflection sequence in which the refractive index varies from 2.79 to 1.43. To maximize the optical acceptance angle the antireflection coatings must vary the refractive index in a graded profile from the value of index of silicon to the one of air.
33 citations
TL;DR: In this paper, the effect of noncircularity on a method proposed by Chu for the measurement of the refractive index profile of an optical fiber preform was analyzed and the results showed that Chu's method can be applied to elliptical preforms.
27 citations
Patent•
11 Dec 1978
TL;DR: In this article, an effective graded index profile optical fiber waveguide comprises alternating regions of high and low indexes of refraction of controlled thickness, where the regions of the high index have either a constant or decreasing thickness and the low index regions increase outwardly from the center.
Abstract: An effective graded index profile optical fiber waveguide comprises alternating regions of high and low indexes of refraction of controlled thickness. The effective refractive index of the fiber has a graded profile of decreasing refractive index when the regions of high index have either a constant or decreasing thickness and the low index regions increase outwardly from the center. The effective refractive index has a particular graded profile of refractive index when the thicknesses of the regions of low refractive index and the high refractive index are appropriately chosen.
24 citations
TL;DR: A set of successive approximation formulas for calculating the refractive index profile of optical fibers from their transverse interference patterns has been derived, and the accuracy of index determination is improved.
Abstract: A set of successive approximation formulas for calculating the refractive index profile of optical fibers from their transverse interference patterns has been derived. The probing ray refraction due to the index gradient in the core is corrected for by these formulas, and the accuracy of index determination is improved. The error is confirmed to be less than 3 x 10(-3)% of the index difference by means of computer simulations. The index profiles of some optical fibers are practically determined with the help of these formulas.
24 citations
TL;DR: A new technique for measuring the refractive index profile of single-mode fibers based on the reflection method is described, and experimental results are demonstrated.
Abstract: A new technique for measuring the refractive index profile of single-mode fibers based on the reflection method is described, and experimental results are demonstrated. When the core radius of a test fiber is only a few times larger than the laser beam spot size, the reflected power distribution does not indicate the refractive index correctly. However, the true index profile can be calculated from the beam spot size and the reflected power distribution with high accuracy: 0.3-microm spatial resolution and 5% relative refractive-index resolution are obtained for practical single-mode fibers.
Patent•
14 Apr 1978
TL;DR: In this article, the density distribution of the light focused by the fiber/preform core is measured along a direction normal to the fiber and preform axis at a distance L from the axis that is less than the focal length of the fiber.
Abstract: This application describes a nondestructive method for determining the refractive index profile of optical fibers and fiber preforms by measuring the density distribution of the light that is focused by the fiber/preform core acting as the lens. The fiber/preform is immersed in an index matching medium and illuminated by means of a collimated light beam directed at right angles to the fiber/preform axis. The density distribution of the light focused by the fiber/preform core is then measured along a direction normal to the fiber/preform axis at a distance L from the axis that is less than the focal length of the fiber/preform. The index profile is determined from these measurements by two numerical integrations.
TL;DR: In this article, the authors used spectrally filtered white light from a xenon arc lamp that is sinusoidally modulated by an electrooptic crystal to measure the functional dependence of bandwidth on wavelength.
Abstract: Transmission bandwidths of optical fibers would be maximized if their refractive index profiles were optimally graded. However, dispersive differences between fiber material constituents make the optimal power law profile exponent α depend on wavelength. This profile dispersion effect is significant for germanium borosilicate fibers and makes their observed transmission bandwidths change by more than 300 percent within a 650-1050 nm wavelength range. Measurements are made in spectrally filtered white light from a xenon arc lamp that is sinusoidally modulated by an electrooptic crystal. Reduction of sine wave envelope intensity due to transmission in a fiber gives its baseband frequency response. The functional dependence of bandwidth on wavelength is used to diagnose whether α is larger or smaller than the optimal value which minimizes intermodal dispersion at particular wavelengths.
TL;DR: In this article, a simple formula is given for determining the deviation of a given refractive-index profile from optimum after the differential mode delay has been measured, which is a very simple formula.
Abstract: A very simple formula is given for determining the deviation of a given refractive-index profile from optimum after the differential mode delay has been measured.
TL;DR: In this article, the variation of effective refractive index due to the manufacturing process is studied for silver-sodium-ion-exchanged slab waveguides, and the results are related to a theoretical model which is derived from the linear REINFORCE profile.
Abstract: The variation of effective refractive index due to the manufacturing process is studied for silver-sodium-ion-exchanged slab waveguides, and the results are related to a theoretical model which is derived from the linear refractive index profile. The consequences of the observed variability are considered for the fibre-film directional coupler and the three-dimensional silver-sodium ion-exchanged waveguide.
TL;DR: In this article, the influence of reduced resolution due to the limited local numerical aperture of a fibre, on the intensity profile determined by the near-field method was investigated and it was found that this effect could lead to small but significant errors in the determination of the actual profile, especially at large relative radii.
Abstract: Calculations were performed to assess the influence of reduced resolution, due to the limited local numerical aperture of a fibre, on the intensity profile determined by the near-field method. It was found that this effect could lead to small but significant errors in the determination of the actual profile, especially at large relative radii.
TL;DR: In this paper, a wide class of multimode optical fibres with near-optimum index profiles is investigated and the index profile is described by three parameters: the power law exponent, the magnitude and the width of a dip at the centre of the core.
Abstract: Impulse responses of a wide class of multimode optical fibres with near-optimum index profiles are investigated. The index profile is described by three parameters: the power law exponentα, the magnitude and the width of a dip at the centre of the core. It is found that for overcompensated profiles (α<α
opt) a moderate dip decreases the r.m.s. dispersion. Leaky modes are found to improve the dispersion characteristics for fibres with a dip in the index profile. Impulse response measurements are interpretated to give information about the index profile.
Patent•
12 Dec 1978TL;DR: An optical system in which at least one of the elements is made from so-called gradient glass having a radial difference in refractive index has been studied in this paper, where the element having this radial difference may be either a lens with at least a curved surface, or a plane-parallel plate.
Abstract: An optical system in which at least one of the elements is made from so-called gradient glass having a radial difference in refractive index. The element having this radial difference may be either a lens with at least one curved surface, or a plane-parallel plate. The radial variation in refractive index varies in accordance with a formula which is given.
Patent•
20 Feb 1978
TL;DR: In this article, a fiber I and a fiber II are bonded at an angle of inclination (a), where the luminous flux having an angle theta 1 with respect to the fiber axis entered the fiber I from the outside, then the mode distribution in the fibers becomes constant.
Abstract: PURPOSE:To provide directivity to light propagation direction by bonding optical fibers having different refractive indices. CONSTITUTION:A fiber I and a fiber II are bonded at an angle of inclination (a). The core refractive index of the fiber I is let n1, the clad refractive index n3, the core diameter (a) and the core refractive index of the core II is let n2, the clad refractive index n4 and the core diameter (b). If it is assumed that the luminous flux having an angle theta1 with respect to the fiber axis entered the fiber I from the outside, then the mode distribution in the fibers becomes constant. Here, when n2<= n3, the light from the first fiber may be led to the second fiber without any loss of light.
TL;DR: An efficient method is presented which helps to explain the interaction of both effects, shows a new way of minimizing the total dispersion by matching the two effects, and simplifies the calculation of pulse broadening in imperfect real fibers.
Abstract: Group delay differences among modes, which limit the bandwidth of optical fibers, arise not only from distortions of the refractive profile but also from profile dispersion caused by the dependence of the profile contour on wavelength. An efficient method is presented which helps to explain the interaction of both effects, shows a new way of minimizing the total dispersion by matching the two effects, and simplifies the calculation of pulse broadening in imperfect real fibers.
TL;DR: The coupling angles in the experiments were consistent with the calculated values using the equivalent refractive index method, and from the near field patterns, the light confinement was confirmed.
Abstract: Light propagation in a waveguide without a high refractive index layer as a guiding region is described. The waveguide consists of a ridge fabricated from a fused quartz substrate, a low refractive index clad layer of Au, and a high refractive index clad layer of a solution of glycerin in water or of air. From the near field patterns, the light confinement was confirmed. The coupling angles in the experiments were consistent with the calculated values using the equivalent refractive index method.
TL;DR: In this article, a theoretical analysis of the characteristics of multimode dielectric fiber waveguides, prepared by deposition from the gaseous phase and characterized by M-shaped radial variation of the refractive index, is made.
Abstract: A theoretical investigation is made of the characteristics of multimode dielectric fiber waveguides, prepared by deposition from the gaseous phase and characterized by M-shaped radial variation of the refractive index. The WKB method is used to analyze the influence of deviations of the refractive index profile from a parabola on the dispersive properties of the waveguides. These calculations are made for various values of the depth, width, and steepness of a dip of the refractive index which appears at the center of the waveguide because of the evaporation of the dopant. It is shown that the dip increases the spreading of a pulse and accelerates lower-order modes. The optimal shape of the outer edge of the permittivity profile, corresponding to a reduction in the width of the pulse characteristic, is found for a fixed dip of the refractive index.
TL;DR: In this article, the breakdown of the usual WKB expressions for tunneling ray power transmission coefficients on multimode optical wavequides with power law refractive index dependence, when the profile approaches the step index limit was demonstrated.
Abstract: We demonstrate the breakdown of the usual WKB expressions for tunneling ray power transmission coefficients on multimode optical wavequides with power law refractive index dependence, when the profile approaches the step index limit. A qualitative analysis provides a solution valid in this transition region, which also quantifies the domain of applicability of the WKB analysis. The latter is much more restricted than the usual condition on the slope of the profile predicts, and is due to the abrupt change in slope at the core-cladding interface.
TL;DR: In this article, a non-destructive technique for determining the refractive index profile of an optical fiber from its forward-scattered pattern arising from a normally incident laser beam is presented.
Abstract: A nondestructive technique is presented for determining the refractive-index profile of an optical fibre from its forward-scattered pattern arising from a normally incident laser beam. This method does not require any index-matching liquid and is not limited to single-mode fibres. It uses as essential information only the angular positions of the extrema in the measured pattern.
TL;DR: In this paper, a vector wave analysis is presented of a multimode optical fiber with an α-power law index profile that includes an additional fourth-order term, and the ultimate limit of the width of the impulse response is derived.
Abstract: A vector wave analysis is presented of a multimode optical fiber with an α-power law index profile that includes an additional fourth-order term. By optimizing a and the coefficient of the fourth-order term, the ultimate limit of the width of the impulse response is derived. The effect of the second-order material dispersion of the refractive index is completely compensated by the fourth-order term in the index distribution. As a result, the rms width of the impulse response is reduced to 20 ps/km, one-fifth of the value achievable with the ordinary a-power distribution, even if all modes carry equal power and there is no mode coupling. For a fiber whose normalized frequency is less than 40, the ultimate width of the impulse response is determined by the term with the gradient of the square of the index or ∇n2 in the wave equation.
TL;DR: In this article, a method for the determination of the refractive index of the surface layer of a matenal, about 5.0-10.0 nm thick, was developed and tested experimentally.
Abstract: A method for the determination of the refractive index of the surface layer of a matenal, about 5.0–10.0 nm thick, was developed and tested experimentally. The method was used to find the refractive index profile of thin-film waveguides prepared by diffusion in glass.
TL;DR: In this article, a theoretical model is developed that demonstrates the presence of a ring in the far field pattern when a graded-index fibre is excited by a collimated beam, incident at a given radius from the core centre.
Abstract: A theoretical model is developed that demonstrates the presence of a ring in the far-field pattern when a graded-index fibre is excited by a collimated beam, incident at a given radius from the core centre. The angular position of this ring can be used to obtain an estimate of the fibre refractive-index profile. provided a correction for the finite beam spot size is applied.
TL;DR: In this work the influence of the refractive index gradient was calculated in convergent and divergent lenses, disks, and deflecting prisms on the diffraction measurement of optical imaging-Strehl definition.
Abstract: In this work the influence of the refractive index gradient was calculated in convergent and divergent lenses, disks, and deflecting prisms on the diffraction measurement of optical imaging–Strehl definition.
TL;DR: In this paper, a statistical method of analyzing nonuniform refractive index profiles in optical waveguides is presented, which is illustrated by experimental results which indicate that any profile function can be readily differentiated from any other form.
Abstract: We present a statistical method of analysing nonuniform refractive index profiles in optical waveguides. The method is illustrated by experimental results which indicate that any profile function can be readily differentiated from any other form.