Search

We present a theoretical analysis of highly elliptical optical fibers by expanding the vector fields as a series of orthogonal functions. Higher-order cutoff values of the normalized frequencies (V numbers) are evaluated for step-index fibers of varying ellipticities. The effect of different refractive-index profiles on the birefringence of the fiber is presented. For fibers operated in the two-mode regime, we discuss the effect of ellipticity and refractive-index profile on the differential propagation constant (Deltab) related to the scalar equivalent of LP(0l) and LP(11)(even)modes.

A numerical parametric study is used to gain insight into how the shapes of dispersion and bandwidth spectra are influenced by dimensions and index differences of light-guide structures with two claddings. Computer-simulated fibers are demonstrated to have bandwidths greater than 25 GHz-km across the entire 1.3-1.55-microm wavelength region.

Using an exact waveguide analysis and measured stress profiles, we show that a delicate interplay between form-induced and stress-induced contributions to polarization mode dispersion in dispersion-shifted fibers can significantly reduce intrinsic short-length polarization mode dispersions. Our observations also indicate that the ovality of fibers is not a true indicator of long-length polarization mode dispersion in production-quality cabled fibers.

We study propagation characteristics of double-mode fibers by measuring group delay differences of time-resolved discrete pulses of the LP(01) and LP(11) modes as a function of wavelength in the 1.06- to 1.6-μm region. The technique has been used to make the first measurements of zero intermodal dispersion in the zero material dispersion region of graded-index double-mode fiberguides that can have larger diameters than standard single-mode fibers. The results can also be used to deduce information about the fiber's refractive-index profile, such as δ, the normalized peak refractive index difference.

Loss and bandwidth spectra were measured in the longest length of single-mode MCVD fiber drawn to date. The 21.7-km-long fiber guide has a 0.5 percent index difference between its 7-μm-diameter core and cladding. Chromatic dispersion effects resulted in a minimum dispersion at a wavelength near 1.35 μm. At 1.30 μm, the fiber loss and bandwidth were measured at 1 dB/km and 21 GHz km (source linewidth = 4 nm), respectively. Potential system performance was estimated from calculations of dispersion power penalties and chromatic-dispersion-limited repeater spacings for 274- and 548-Mb/s data transmission rates. A new numerical parametric study was used to show how the bandwidth of a fiber can be optimized by properly choosing its core diameter and core-to-cladding index difference.

We present counting formulas for the number of different ways to grow a given rooted tree, over a specified number of intervals. We call these growth plans, or simply plans. This problem arises, for example, in analog toll-connect networks in which it is desired to introduce digital technology to serve increasing circuit requirements, in the cheapest way. Each circuit in such a network extends from a particular node called the toll center to one of the other nodes. The toll center corresponds to the root, and the portion of the network containing digital equipment corresponds to the rooted subtree whose growth we study. Even for networks of modest size and few growth intervals, the number of plans is too large to permit finding the cheapest by an exhaustive search. We observe that plans differing only in their growth pattern in the neighborhood of some particular node have cost differences that depend principally on their local growth patterns. It is therefore often possible to eliminate at a single stroke a large class of plans having a specified local growth plan at a particular node. By repetition, the number of remaining plans that must have their individual total costs computed can often be reduced to a number sufficiently small for an exhaustive search. We describe two types of local growth behavior appropriate for eliminating classes of plans in this network problem, and give corresponding counting formulas for the number of tree growth plans under these restrictions. A generalized counting formula with arbitrary local restrictions at each node is presented; this general formula contains the prior results as special cases. Finally, an example illustrates the great reduction in number of plans that can sometimes be obtained.

Bandwidth spectra of single-mode fibers are calculated from experimentally obtained chromatic-dispersion-versus-wavelength curves. Results include second-order effects on bandwidth which depend on the curvature of the dispersion curves. Examples illustrate how bandwidth spectra change as a function of source power spectra. They also show how small changes in fiber dimensions and refractive-index differences can cause significant bandwidth changes at 1.3 μm wavelength.

We consider the range of validity of a Hilbert-transform approach in which the measured magnitude of the modulation-transfer-function of an optical fiber is used to compute the fiber's impulse response. It is argued that a key “minimum-phase assumption” can fail to be satisfied in important cases, and a few closely related experimental and analytical results are presented.

Cutoff characteristics are calculated for the fundamental mode in a single-mode double-clad lightguide structure whose refractive index in the inner cladding is less than the index of the outer cladding. Results of this study indicate how to choose the proper depressed cladding width and depth in order to reduce long-wavelength losses that have been observed in experimental MCVD fibers with fluorine-doped phosphosilicate claddings.

The low-loss and low-dispersion properties of single-mode fibers make them obvious choices for wide bandwidth system applications with very long repeater spans. This brief describes the fabrication procedure and transmission properties of a double-clad single-mode fiber which is capable of wide bandwidth (greater than 100 GHz-km for laser sources with 4-nm emission bandwidths) transmission over the widest wavelength range (1.45 μm to 1.73 μm) thus far reported in the literature. This range completely covers the lowest-loss wavelength window for fused-silica optical fibers. Double-clad lightguides1–4 were formed by using an inner cladding to form an index well between the core and a pure silica outer cladding. A computer-aided analytical procedure was used to choose the proper fiber diameter so that waveguide dispersion effects could be used to cancel material dispersion at predetermined wavelengths.5

The yield equation of a slip or twinning system is represented by a surface in five dimensional stress coordinates. Because of crystallographic symmetry, the yield surfaces of the twelve {111}〈112〉 twin systems can be arranged as faces of three separate tetrahedra in three-dimensional shear stress coordinates σ23, σ31, σ12. The other two stress components then determine the size of the tetrahedra. For {111}〈112〉 (or {112}〈111〉) slip, three additional tetrahedra are needed for slip in the reverse direction. A general shape change requirement of five or more active twin (or slip) systems may be found as intersections of five or more faces among the tetrahedra with the requirement that the stresses at the intersections do not exceed the yield value for the nonactive systems. These intersections have been obtained systematically. It is verified that the lists of stress states previously reported by Hosford and Chin for {111}〈112〉 multiple slip and twinning are complete.

The dielectric optical waveguide described in this paper has an annular cross section, the refractive index of which is higher than the indices of the material inside and outside of the ring. The solution of the eigenvalue problem is an approximation which is valid for small refractive index differences of the three media. The resulting approximate eigenvalue equation is far simpler than its exact counterpart. The cutoff conditions of the first three modes and the eigenvalue of the lowest-order mode are presented graphically.

Numerical calculations of the Taylor factor and of lattice rotation have been performed for composite slip on {110} 〈110〉 and {110} 〈110〉 slip systems. Two types of deformation were considered: uniaxial deformation which requires single slip only, and axisymmetric flow which requires the activation of five independent slip systems. For lattice rotation, calculations were made for both tension and compression. A variable in these calculations is the ratio of the critical resolved shear stress for slip between the two slip modes. The implications of the theoretical results to deformation texture development and texture hardening in polycrystalline ionic materials are discussed.

Analysis and computations made here, corroborated by experiment, determine the effects of axial displacement and angular misalignment on the power coupled between butt-joined, single-mode optical fibers. The absolute accuracy with which fibers must be joined on-centers is reduced for fibers with relatively smaller core; the angular accuracy is increased.

If a system of communications satellites is uncontrolled after launching, service interruptions are inevitable. The amount of interruption depends on the number of satellites, their altitude, the orbit inclinations, the distance between ground stations, the acceptable signal-to-noise ratio, and other parameters. Various relations between these quantities are presented in tables and graphs, and are illustrated by examples.

Tables and plots are given of certain definite integrals which facilitate the calculation of an upper bound on the field attainable with a given configuration of magnetic material, when the volume occupied by magnetic material consists of a combination of solid and hollow circular cylinders. Such estimates are useful in the design of powerful electromagnets.

The normalized scalar wave equation is solved for propagation parameters which depend on only the normalized frequency V and an arbitrary refractive-index profile. Analytic expressions relate these parameters to the optical fiber diameter, materials, and wavelengths of interest. These expressions are used to find dispersion and bandwidth. In this way it is possible to determine fiber parameters so that minimum dispersion occurs at preferred operating wavelengths. Then refractive-index profiles may be modified to improve bandwidth over desirable ranges.© (1982) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Single-mode fibers serve as transmission highways for lightwave systems that transmit data at high rates over long distances. Fibers are currently being deployed with low losses and near-zero dispersion for lightwave systems applications at wavelengths near 1.3 μn. However, systems of the next generation will undoubtedly include 1.55-μm wavelength applications because intrinsic scattering losses in fused silica glasses are minimized there.

Necessary conditions that a switching function be, in particular, a threshold function have been introduced by Paull and McCluskey [11]; named and studied at some length by Winder [13], [14], [15] and Muroga, et al. [8]; and generalized by Elgot [3], Winder [14], [15] and Gabelman [4]. The basic conditions are the k-monotonicities and have been used not only to recognize threshold functions but also to determine realizing weights and threshold.

Low-loss fibres with dispersion below 2 ps/km nm over the spectral range between 1.28 μm and 1.65 μm have been designed and fabricated. These fibres were achieved by the use of quadruple cladding and designed with the use of a computer analysis program. They should be desirable for future wavelength-division-multiplexing applications.

Exact numerical solutions for the LP(01) propagating mode of the scalar wave equation are used to calculate propagation constants in single-mode fibers with arbitrary refractive-index profiles. The procedure is used to correlate predicted chromatic dispersion properties of single-mode fibers based on interferometrically measured profiles with direct transmission measurements vs wavelength. Resulting waveguide dispersion effects are used to design single-mode fibers that have minimum chromatic dispersion at desired wavelengths within the 1.3-1.6-microm region.

Chromatic dispersion effects have been calculated for light-guides containing germania-doped silica in the core and fluorine-doped phosphosilicate in the cladding. Numerical results show how to partition core and cladding refractive-index levels in order to control the minimum dispersion wavelength.

Planar optical waveguides consisting of thin dielectric films with metal cladding have been investigated theoretically and experimentally. A computer program was devised to provide the phase and attenuation constants and wavefunctions for TE and TM modes in symmetric and asymmetric guides. Approximate expressions suitable for slide-rule calculation were also derived. Numerical results and illustrations are given for films of photoresist with Al, Ag, and Au cladding. Direct measurements of the attenuation and phase constants at 0.633 microm of numerous experimental waveguides are in reasonable agreement with theory. Attenuations