Showing papers on "Step-index profile published in 1976"

Optical waveguide refractive index profiles determined from measurement of mode indices: a simple analysis.

Abstract: The WKB approximation is used to derive simple equations that predict the shape of the index profile from measured mode indices of a planar optical waveguide. This nondestructive test is a useful tool in the study of diffused guides. The index profile is assumed either to decrease monotonically from the surface or to be symmetrical in the case of a buried guide. The approximation uses straight line segments to connect the measured points. Results are compared with mathematical solutions for exponential, Fermi, and step distributions and with other independent experimental observations of the profile in a nickel-diffused LiNbO(3) guide.

Pulse broadening in graded-index optical fibers.

Abstract: This paper reports on some theoretical and experimental investigations of the radial refractive index gradient that maximizes the information-carrying capacity of a multimode optical waveguide. The primary difference between this work and previous studies is that the dispersive nature of core and cladding materials is taken into consideration. This leads to a new expression for the index gradient parameter alpha(c) which characterizes the optimal profile. Using the best available refractive index data, it is found that in high-silica waveguides, the dispersive properties of the glasses significantly influence the pulse broadening of near-parabolic fibers, and that the parameter alpha(c) must be altered by 10-20% to compensate for dispersion differences between core and cladding glasses. These predictions are supported by pulse broadening measurements of two graded-index fibers. A comparison is made between the widths and shapes of measured pulses and pulses calculated using the WKB approximation and the near-field measurement of the index profiles. The good agreement found between theory and experiment not only supports the predictions made for the value of alpha(c), but demonstrates an ability to predict pulse broadening in fibers having general index gradients.

Material and Mode Dispersion in GeO2·B2O3·SiC2 Glasses

Abstract: Material and mode dispersion in fibers made from glasses in the system GeO2-B2O,3-SiO2 have been calculated using refractive index dispersion results for these glasses. Refractive indices were measured on bulk glass specimens using the minimum deviation method at wavelengths from 0.4358 to 1.0830 μm. The resultant data were then fitted to a 3-term Sellmeier dispersion relation for each glass composition. The fitted equations and a recent theory on the relation of the optimum index profile in a graded index optical waveguide to pulse dispersion were used to calculate the exponent α, which characterizes the shape of the profile, for several practical fiber models. The most effective profile shape for reducing pulse dispersion is a function of wavelength, composition, and fictive temperature. The present data were used elsewhere to predict accurately the optimum profile for minimization of pulse dispersion in several fiber systems consisting of germanium borosilicate glasses.

Binary silica optical fibers: refractive index and profile dispersion measurements.

Abstract: The variation of the core-cladding refractive index difference Deltan(lambda) is determined as a function of wavelength for GeO(2)-SiO(2), B(2)O(3)-SiO(2), TiO(2)-SiO(2), P(2)O(5)-SiO(2), Al(2)O(3)-SiO(2), and Cs(2)O-SiO(2) optical fibers. The measurements are obtained by electronically processing the output of an interference microscope illuminated by a monochromatic light source variable over the 0.5-1.1-microm range. The Deltan(lambda) results are utilized to calculate the precise grading of the refractive index profile characterized by an exponent alpha(lambda) required to achieve a minimum modal dispersion. The material dispersion for these compositions is also calculated with the aid of available n(lambda) data for SiO(2).

Determination of optical fiber refractive index profiles by a near‐field scanning technique

Abstract: A simple and rapid method is described for determining the refractive index profile of an optical fiber by observation of the near‐field intensity distribution. It is shown that in many cases the presence of tunnelling leaky modes is unavoidable and that these cause a length‐dependent error in the measurement. A correction factor is developed which may be applied to the measured intensity profile once the fiber length, core diameter, and numerical aperture are known. Examples are given of measurements made on both step and graded‐index fibers.

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

Refractive index profiling of graded index optical fibers

Abstract: Details of a method of determining the refractive index distribution of graded‐index optical fibers based on interference microscopy are discussed. Sample preparation techniques, observational methods, and data reduction and analysis by a computer fitting program are described. Representative data for optical fibers prepared by chemical vapor deposition are shown.

Automatic analysis of interferograms: optical waveguide refractive index profiles.

Abstract: Compensation of mode velocities in optical waveguides can be achieved by fabricating fibers having graded refractive index cores. One technique for measuring these index profiles is interference microscopy. We have developed a machine aided method for analysis of interference micrographs for the rapid determination of optical waveguide refractive index profiles. Our method consists of digitizing the interference micrograph with a scanning microdensitometer, followed by computer determination of the position of the center line of each fringe. The data obtained are then converted into refractive index and fiber radius information, which is used to calculate a best fit power law function.

Novel technique for measuring the index profile of optical fibers

Abstract: A novel technique for measuring the refractive index profile of optical fibers is demonstrated, which offers substantial advantages over alternative methods. The method consists of illuminating a small area of the fiber core and measuring the total transmitted power. The transmission of leaky modes is accounted for in the manner reported previously by other authors. The index profiles of germanium-doped fibers obtained by this technique are compared to interferometric measurements. The resolution is shown to be limited by wave optics effects to about λ o (4n√2Δ)−1, where Δ ≡ Δn/n. The distortion of the index profile as the wavelength varies and wave-optics effects are investigated.

The determination of the refractive index and thickness of a transparent film

Abstract: A method in which the refractive index and thickness of a transparent film are determined simultaneously from measurements of transmittance at normal incidence is presented. This has been applied successfully to films of Ta2O5.

Pulse transmission measurements for determining near optimal profile gradings in multimode borosilicate optical fibers

Abstract: Dispersive differences between B2O3 and SiO2 constituents make nonparabolic profiles optimal equalizers of intermodal group delays in fibers with graded B2O3–SiO2 cores and uniform B2O3–SiO2 cladding. Pulse dispersion measurements were correlated with profile shapes in a systematic study of multimode fibers with near power law gradients. Far field spatial ray filters were used to diagnose impulse response shapes so that new fibers could be fabricated with closer-to-optimal profile gradients. One of the fibers had an α ≈ 1.77 power law exponent that was nearly optimal for λ = 907.5-nm wavelength and caused 2σ = 0.26-nsec/km full rms output pulse spreading. When expected material dispersion effects were deconvolved from the output pulse spreading, the resultant pulse width was approximately 75 times less than the result expected for a comparable step-index fiber. This is the largest pulse width reduction reported yet.

Dispersion in optical fibres with stairlike refractive-index profiles

Abstract: In multimode circularly symmetric fibres whose index distribution is a stairlike approximation of an optimum profile, the modal dispersion increases as the number of steps decreases. For a fibre with Δn/n=0.02 and a core radius of 40 μm, numerical calculations based on wave optics show that the r.m.s. impulse response width at λ=1 μm increases from 0.075 ns/km for the smooth optimum profile to 0.23 ns/km for 40 steps of equal areas. Thus an important conclusion of the analysis is that one should avoid introducing steps in the refractive-index profile of fibres for optimum results.

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.

Correction factors for the determination of optical-fibre refractive-index profiles by the near-field scanning technique

Abstract: Numerical calculations are presented of the correction factor for use with the near-field scanning method of index profile determination. It is shown that a single curve can be applied to a range of possible profiles, and a numerically obtained average curve is given.

Elimination of errors due to sample polishing in refractive index profile measurements by interferometry

Abstract: The surface contouring caused by routine polishing of fibers and preforms in preparation for measurement of the refractive index profile has been studied. By observation of the surface interference fringes the effect of polishing on doped preforms is visualized. It is found that composition‐dependent thickness variations occur which can cause a sizable error in the refractive index variation deduced by interference measurements in performs (several percent) and in fibers (∼50%). The difficulty is eliminated by several minutes of additional polishing on a hard lap.

Optical fiber with compression surface layer

Abstract: A glass dielectric fiber waveguide with a composition profile varying radially from the center to the surface, the composition profile causing a surface layer which is in compression, said composition profile being caused by (a) at least one dopant used substantially to create a stress profile wherein the surface is in compression, and (b) at least one dopant used substantially for the purpose of creating an index of refraction profile.

Mode behaviour in a tapered multimode fibre

Abstract: A derivation based on ray tracing and the local plane-wave approximation is used to show the behaviour of waveguide modes in a linearly tapered multimode fibre having a step-index profile. The azimuthal mode order l is invariant through the taper, and, for suitably designed tapers, the changes in the radial mode order m and the lateral component u are negligible. A formula for designing such tapers is presented.

Multimode optical waveguides with graded refractive index: theory of power launching.

Abstract: The power launching into multimode optical fibers with any profile of refractive index is analyzed by means of the geometrical optics. First two formulas of the numerical aperture are obtained, one including and the other excluding the contribution of leaky skew rays. Each one of these two numerical apertures has a certain domain of application, and the launching efficiencies from incoherent sources into optical fibers are calculated in both cases. Useful formulas and plots of launching efficiency for a few refractive index profiles are given. Finally the power losses due to source-fiber coupling errors (separation, displacement, or misalignment) are evaluated, and an interesting effect of virtual lengthening of the fiber is found.

Measurement of the numerical aperture of a step-index optical fibre

Abstract: We describe a simple method for measuring the numerical aperture of a step-index fibre. The value obtained by this method depends only on the index difference between the core and cladding, and it is then possible deduce the index difference from this measurement.

Determination of diameters and refractive indices of step-index optical fibres

Abstract: A method is given whereby the radii and refractive indices of the core and cladding of a step-index optical fibre can be determined uniquely from the backward-scattered pattern. The technique is based on the analysis of various rays that contribute to the formation of the back-scattered pattern.

Pulse separating in transmission characteristics of multimode graded index optical fibers.

Abstract: The transmission characteristics of multimode graded index optical fibers, whose refractive index profiles were nearly parabolas, were measured. No change of the output pulse waveform could be detected at a 1-km length with a lowest-order mode excitation. In the case of mismatching excitation, output pulse waveforms separated into two pulse peaks. This was caused by the refractive index profile that was not a single function but a combination of two functions.

Scattering and absorption losses of multimode optical fibers and fiber lasers

Abstract: We present an approximate theory of loss coefficients for modes of step-index fibers with various types of distortions and for fibers with lossy claddings. The fiber irregularities are assumed to be sinusoidal and random variations of the core-cladding interface. Formulas for the loss coefficients are presented and plotted for different values of the compound mode number M. For fiber lasers, we plot the loss coefficients as functions of the mirror tilt angles. We consider as an example a Nd-YAG fiber laser with refractive index n 1 = 1.8 and a core radius of a = 40 µm operating at a wavelength of λ = 1.06 µm. For this example, we find that radiation losses are caused by Fourier components of fiber irregularities in the spatial wavelength range between 0.4 and 1.3 µm. Intrinsic losses may be as low as 2α = 10−3 cm−1. It is thus desirable to limit scattering losses to values below 10−3 cm−1. This requirement imposes tolerance restrictions of 0.01 µm on the permissible core radius fluctuations. For core radius fluctuations of this order of magnitude, mirror tilts should not exceed approximately 5 degrees. Cladding losses are not critical, but their influence on laser losses depends on the refractive index ratio of the core and cladding materials. Tolerable cladding losses may range from 10 to 300 cm−1.

Multimode light waveguide for information transmission - has stepped core giving properties of gradient waveguide

Abstract: The waveguide consists of a tubular sheath which is surrounded by a core which has a refractive index higher than the refractive index of the sheath. The core consists of at least two homogenous concentric zones of light-conducting solid material, each having a different refractive index. The radius of the inner core zone is pref. as small as possible in comparison with the thickness of the outer core zone (n). This ensures that the transmittable bit rate is greater by a factor of at least 3/2 than that of a conventional multimode waveguide whose core is not stepped.

Theory of the double heterostructure laser: II. Waveguide model incorporating carrier concentration-dependent refractive index

Abstract: Solutions to charge transport equations are used to illustrate the variation of the active region refractive index of the double-heterostructure GaAs laser. It is shown that a marked asymmetry can arise in the refractive index. In this paper, a suitable waveguide theory is developed to take account of this effect. The necessity for such a waveguide theory is demonstrated by comparing threshold current densities and far-field patterns calculated with this model to those calculated using a simpler waveguide model.

Determination of the parameters of diffused optical microwaveguides

Abstract: A method for the determination of the refractive index profile of single-mode and multimode diffused waveguides is suggested and demonstrated. In this method use is made of the measured values of the effective refractive index of the modes. The parameters of a diffused waveguide in glass are determined experimentally.