Showing papers on "Single-mode optical fiber published in 1976"

Curvature loss formula for optical fibers

Abstract: The loss formula for optical fibers with constant radius of curvature of their axes is derived by expressing the field outside of the fiber in terms of a superposition of cylindrical outgoing waves. The expansion coefficients are determined by matching the superposition field to the field of the fiber along a cylindrical surface that is tangential to the outer perimeter of the curved fiber. This method is a direct extension of my derivation of the curvature-loss formula for slab guides.

Analysis of Wave Propagation in Optical Fibers Having Core with alpha-Power Refractive-Index Distribution and Uniform Cladding

Abstract: This paper describes first that a simple closed-form characteristic equation can be derived from the variational formulation of the wave propagation in an optical fiber, provided that 1) the permittivity in the core is proportional to r/sup alpha/, where r is the radial coordinate and 1 < alpha < /spl infin/, and 2) the cladding is uniform. The obtained equation is then solved for various permittivity (or refractive-index) profiles. The results obtained are useful both for the understanding of the dispersion characteristics and for the design of inhomogeneous optical fibers. The optimum profile for a multimode fiber is derived and discussed

Modes in weakly guiding elliptical optical fibres

Abstract: Approximate and much simplified dispersion relations are obtained for the problem of optical wave propagation within weakly guiding elliptical fibres. The refractive index difference between the core and its cladding of weakly guiding optical fibres that are contenders for use as practical optical communication lines is very small; i.e., (n 1/n0−1) ≪1 wheren 1 is the core index andn 0 is the cladding index. These greatly simplified dispersion relations are then used to calculate the propagation constants for several higher order modes on an elliptical optical fibre.

Microbending losses of single-mode, step-index and multimode, parabolic-index fibers

Abstract: We present formulas for the microbending losses of fibers that are caused by random deflections of the fiber axis. We consider single-mode (or almost single-mode), step-index fibers and multimode, parabolic-index fibers and compare their losses. Loss formulas for the single-mode fiber are derived from coupled-mode theory using radiation modes. Simple empirical approximations of the general formulas are also presented. The losses of the parabolic-index, multimode fiber have been derived earlier. The losses of both fiber types are compared by assuming either that each fiber samples the spatial Fourier spectrum of the distortion function at the same spatial frequency, or by comparing typical fibers of each type with each other regardless of any similarity between them. It is found that the multimode, parabolic-index fiber has lower losses if it supports a sufficient number of guided modes.

New method for measuring V-value of a single-mode optical fibre

Abstract: A simple method is proposed for the direct measurement of the V-value for a single-mode optical fibre. This method consists of measurement of loss peaks, corresponding to cutoff wavelengths of the higher modes, which are easily observed for a fibre with a bend.

Propagation model for long step-index optical fibers.

Abstract: This paper reports some theoretical and experimental investigations on the propagation of a pulse in long step-index optical fibers where mode conversion is present. We derive simple analytical expressions for the frequency response and the radiation pattern as a function of the fiber’s length provided the launching conditions are known. A comparison with experimental observations made on a 3-km long Corning fiber shows reasonable agreement. We conclude that the approximations used to obtain the simple analytical solutions are satisfactory for predicting the transmission characteristics of the fiber.

Method and apparatus for introducing geometrical perturbations in optical fiber waveguides

Abstract: The present invention relates to method and apparatus for fabricating multimode optical fiber waveguides having reduced modal dispersion as a result of deliberate enhancement of mode coupling in the waveguide. The axial alignment and/or the diameter of an optical fiber waveguide is varied by means of one or more modulated heat sources, such as, for example, a microflame jet or CO 2 laser, directed against the fiber waveguide. By controlling the modulation of the heat source, the spatial distribution of the geometrical perturbation pattern can be controlled, thereby producing controlled mode coupling in the fiber waveguide.

Noncircular symmetric optical fiber waveguide having minimum modal dispersion

Abstract: An optical fiber waveguide is disclosed wherein the cladding surrounds a fiber core having a noncircularly symmetric cross section. Equations are presented which dictate the value of the index of refraction that must be provided at each spatial point within the fiber core in order to construct a fiber waveguide having minimum modal dispersion. An especially useful optical fiber waveguide is disclosed with an elliptical fiber core thereby providing a fiber which can be more efficiently coupled to a light emitting source having an elongated source area such as in a heterojunction laser or an edge-emitting light emitting diode.

Secure optical multiplex communication system

Abstract: The communication system includes a holographic system to provide a plurality of spatially multiplexed optical beams each modulated by a different one of a plurality of binary intelligence signals. The plurality of modulated spatially multiplexed optical beams are coherently transmitted on an optical waveguide to a hologram and an array of photosensors to recover each of the intelligence signals. The waveguide may be an optical fiber of the parabolic index type to coherently transmit all of the plurality of modulated spatially multiplexed optical beams, or a plurality of single mode step index optical fibers each coherently transmitting a different one of the plurality of modulated spatially multiplexed optical beams.

Rotational motion transducer

Abstract: A fiber optical waveguide of the glass or single crystal types is formed into a loop or spiral with its ends joined to maximize optical or infrared single mode transmission. The waveguide is modified by doping or some other technique to lase when the loop or spiral is radiated with sufficient electromagnetic or optical energy. A single or multiturn ring laser is thus formed. The ring or spiral may be essentially in one plane. The frequency of lasing or oscillating is a factor of waveguide length. Two lasing frequency pickoffs spaced a maximum distance apart on the waveguide each extract a small portion of the energy from the waveguide propagating in both the clockwise (CW) and counterclockwise (CCW) directions. The lasing frequency in the CW and CCW directions is a factor of the rotation rate of the transducer, decreasing in the direction of rotation and increasing in the direction opposite to rotation. The CW and CWW radiation frequencies are heterodyned to give low frequencies proportional to rotation rate, and phase relationships which are proportional to rotational rate and number of turns of the waveguide.

Modes of crossed rectangular waveguide

Abstract: The cutoff frequencies and modal fields of dually polarized crossed rectangular waveguide are calculated numerically and the cutoff frequencies verified experimentally Symmetry arguments and group theory are used to explain mode degeneracies and mode splitting The single mode bandwidth is 38 percent of center frequency for both polarizations when the guide dimensions are chosen appropriately For applications where symmetric excitation is assured, bandwidths in excess of 2:1 can be obtained

Method of making optical fiber optical power divider

Abstract: An optical power divider is disclosed for single mode optical fibers. The fibers to be coupled are inserted in converging bores in a lower refractive index glass block which is collapsed about the fibers and drawn down. In the drawn down region the fibers are reduced in cross-section so that an appreciable proportion of the optical energy will be guided by the fibers while propagating in the surrounding lower refractive index glass block.

Reduction of modal and chromatic material dispersion in a multimode optical fiber

Abstract: Modal dispersion and chromatic material dispersion in a multimode optical fiber is reduced by feeding the rays of the light beam into the end of the optical fiber the angle of each ray relative to the axis of the fiber varied in accordance with the wavelength of the ray. The shortest ray is fed at a zero angle and the longest wavelength at angle of φ max. φ max. is defined by the equation ##EQU1## This invention relates to the reduction of both modal and chromatic material dispersion in a multimode optical fibre. Multimode guides are currently used in fibre-bundle optical communications and will also appear in the next generation of individual-fibre systems. Their 50 to 100μm diameter cores are compatible with multimode LED sources and simple connecting and tapping techniques. Unfortunately, their information carrying capacity is limited by the variation of signal group velocity both with mode number and with light wavelength; this presents a serious limitation with large numerical aperture fibres and broadband sources. Prior art in this field has concentrated on gradient-index optical fibres to approximately equalize all ray paths and hence reduce mode dispersion. However, these require fabrication procedures more complex than for step-index guides, are capable of accepting only about half as much light from an LED and neccessitate twice the curvature radius in bends. Source collimation to excite only low order modes can reduce mode dispersion. Differential mode attentuation reducing the role of higher order modes and intermodal coupling tending to average the resultant modal velocity are both effective, but these processes are inherently lossy. All the above methods reduce modal but not chromatic material dispersion. A technique for reducing chromatic material dispersion is disclosed in copending application, Ser. No. 591,498 filed June 30, 1975 in the name of the present assignee, now U.S. Pat. No. 3,988,614. The present invention provides for the suitable alteration of the angular light distribution entering the fibre so as to oppose the modal and chromatic effects, thereby achieving a substantial reduction in the net dispersive pulse broadening.

Coupled‐mode theory of Raman amplification in lossless optical fibers

Abstract: Raman amplification in weakly guiding optical fibers is investigated for the two cases of weak and strong mode coupling. Use is made of the statistical ensemble of similar fibers introduced by Marcuse for studying mode coupling in optical waveguides. In the weak‐coupling case, the Stokes powers of different modes increase independently, and the gain of each mode depends on the initial poewrs of all laser modes. In the strong‐coupling case, power equipartition between Stokes modes takes place throughout the fibers, and the common gain is the average of the individual mode gains.

Single mode optical transmission line

Abstract: A single mode optical transmission line consisting of a core and a clad, both formed from essentially the same type of multicomponent glass, e.g. borosilicate, for use with electromagnetic energy having a wavelength between 0.5μm and 2.0μm. The core has a higher refractive index than the clad because the relative concentrations of the constituents of the glass composition are varied between core and clad, e.g., the ratio of SiO2 /B2 O3 concentrations is higher in the core than in the clad.

Single-mode stripe optical waveguides formed by silver ion exchange

Abstract: We report on the fabrication and mode structure of narrow stripe optical waveguides formed by silver ion exchange. Single-mode propagation at 0.633 µm wavelength has been obtained in guides whose width exceeds 7 µm.

Optical fiber eigenvalue equation: plane wave derivation.

Abstract: The asymptotic form of the eigenvalue equation for optical waveguides of circular cross section is derived using only plane wave concepts, i.e., phase changes, Fresnel’s and Snell’s laws. Both step and parabolic refractive index profiles are treated using this method.

Wavelength dependence of frequency-response measurements in multimode optical fibers

Abstract: A newly developed technique for directly measuring fiber dispersion in the frequency domain as a function of wavelength is described Spectrally filtered white light from a xenon arc lamp is sinusoidally modulated in the range 0 to 1 GHz by an electrooptic modulator and injected into a fiber The procedure is to vary the modulation frequency and measure the corresponding sideband output power with a photomultiplier and spectrum analyzer Ratio measurements between the test fiber and a short reference fiber give the baseband frequency response A number of germanium- and boron-doped fibers have been examined The least dispersive borosilicate graded-index fiber has a 1 dB bandwidth of 1 GHz, after 107 km of propagation at λ = 908 nm The width broadens gradually with increasing wavelengths up to λ = 1100 nm

Mode conversion losses of randomly bent, singly and doubly clad waveguides for single mode transmission

Abstract: Mode conversion effects take place when a dielectric optical guide is bent and its curvature varies along the guide. This paper considers and compares such conversion losses of singly and doubly clad slabs (adopted as analogs of corresponding fibers) for single mode transmission. It is shown that the conversion loss of a W-type slab is much smaller than that of a singly clad slab, provided that the beamwidths of both guides are equal. This property is the consequence of the wider mode spacing of the W-guide.

Mode mixing with reduced losses in parabolic-index fibers

Abstract: We present design criteria for the construction of a modified parabolic-index fiber with intentional mode coupling. Mode coupling serves the purpose of reducing multimode pulse dispersion and is accomplished by introducing carefully designed index fluctuations into the fiber core or by controlled “random” bends of the fiber axis. Radiation losses due to mode coupling can be minimized by terminating the parabolic-index fiber core in an abrupt index discontinuity. The additional modes introduced by this step must be filtered out by periodic mode filters that consist of parabolic-index fiber sections without the refractive-index step.

Microbending loss in single-mode W-fibres

Abstract: The microbending loss in single-mode W-fibres has been determined by calculating the coupling coefficients between the fundamental mode and the radiation modes. It is shown that the microbending loss is of the same order of magnitude, or even larger than, the microbending loss in comparable single-mode cladded-core fibres.

A large-tolerant single-mode optical fiber coupler with a tapered structure

Abstract: An efficient and large-tolerant single-mode optical fiber coupler with a tapered structure is fabricated and studied experimentally. The maximum coupling efficiency of 95 percent and the tolerance in the coupling length of 2.5 mm permitting the coupling efficiency of more than 90 percent are obtained experimentally. The approximate analysis based upon a coupled mode equation is developed using a step transition model in order to describe the basic principle of this coupler.

W fiber design considerations

Abstract: The baseband frequency characteristics and the average confinement of light to core properties of a W fiber are analyzed in conjunction with corresponding singly clad (SC) fibers under some ideal assumptions It is found that the bandwidth of a W fiber is almost equal to that of the SC fiber that has no intermediate layer and is much wider than that of the other SC fiber in which the intermediate layer extends to infinity. The average fractional power flow outside the core in a W fiber is drastically reduced in comparison with both SC fibers. Practical design considerations are deduced from a typical example.

Single mode laser multiterminal optical data communication system

Abstract: A multiterminal single mode communication system using single mode fibers d a single centrally located laser source. An electro-optical switch at the terminal switches pulses of light from the communication channel to a distribution channel comprising a single mode fiber. Information is switched on by an electrical modulator which controls the light switching of the switches and information is taken off by light detectors.

Input and output devices for optical fiber

Abstract: Input and output devices for an optical fiber include an acoustic transducer for generating a planar acoustic wave tilted at an angle with respect to the axis of an optical fiber embraced by a quartz block. The gap between the optical fiber and the quartz block is filled with a liquid, such as water, to obtain acoustic impedance matching. A desired mode of propagating light can be extracted from the fiber or injected therein by reflection under Bragg's condition through a glass block and optical system without cutting or damaging the optical fiber.

Steady-state losses of optical fibers and fiber resonators

Abstract: We study the steady-state loss of a fiber with random, nearest-neighbor coupling and compare it with the mode with the lowest loss of a cavity formed from a section of the same type of fiber. We find that the loss of the cavity is not identical with the loss of the steady-state distribution of the fiber with random coupling. In fact, fiber and fiber resonator behave very differently if the fiber mode of highest order is made very lossy. The loss of the steady-state distribution of the fiber with random, nearest-neighbor coupling approaches a weighted average of the losses of its individual modes plus a contribution from the coupling coefficient that couples the highest-order mode to its neighbors. The cavity loss, on the other hand, becomes independent of the coupling coefficients and of the loss of the highest-order mode, provided this loss becomes much higher than the coupling strength. This behavior leads us to conclude that the loss of the cavity is a weighted average of the losses of all those modes whose coupling strength exceeds their (individual, uncoupled) loss coefficients. Two resonator modes with propagation constants β 1 and β 2 remain uncoupled unless they satisfy the condition β 1 − β 2 = 2πn/L, where n is an integer and L is twice the length of the resonator.

Scattering from a localized inhomogeneity in a cladded fiber optical waveguide. 1:radiation loss.

Abstract: An exact analysis using the Green’s function formulation of the problem of scattering from a localized inhomogeneity inside a cladded fiber optical waveguide is carried out. The analysis yields radiation loss that agrees well with that evaluated from the infinite-medium approximation. However, the spatial distribution of the radiation loss, i.e., the radiation pattern, differs markedly from that predicted by the infinite-medium approximation. The same analysis also permits the study of mode conversion due to scattering to be reported separately.