The transfer of information in fibers with a large dispersion of the first order is accomplished by a temporal analog of the self-imaging effect. The simulation of signal propagation in a single-mode fiber is considered by using the analogous Fresnel diffraction experiment.

Temporal self-imaging effect in single-mode fibers

Theoretical work on dispersion in single-mode fibers sometimes uses the assumption that waveguide dispersion Dw and material dispersion Dm are separate effects that contribute additively to the total amount of dispersion Dm+w. Using Gloge’s LP-mode approximation we compute the dispersion of the LP01 (HE11) mode by solving the eigenvalue equation taking dispersion of core and cladding materials into account. The dispersion of the LP01 mode is computed by numerical differentiation of the solution of the eigenvalue equation. The difference Dm+w − Dm is compared to waveguide dispersion Dw, which is computed by ignoring the dispersive properties of the core and cladding materials. We find large percentage deviations between Dm+w − Dm and Dw. The assumption of additivity of material and waveguide dispersion is thus not quite correct. However, because of the small contribution of waveguide dispersion to the total dispersion of the LP01 mode, even a large percentage error in the waveguide dispersion has little influence on the over-all dispersion of the LP01 mode.

Interdependence of waveguide and material dispersion.

The optical dispersion in singly clad dielectric monomode waveguides is calculated by taking into account the frequency dependence of the refractive indices of the core and the cladding materials. The total dispersion is composed of the material dispersion and the dispersion of the waveguide structure. Fibers can be optimized in such a way that these two portions have opposite signs. The portion due to material dispersion, however, is about 2 orders of magnitude greater than that due to waveguide structure dispersion (considering typical glasses at wavelengths of 0.9 μm and 1.06 μm). Thus, complete compensation of these portions is impossible, and the fibers cannot be made dispersion-free at these wavelengths. The total dispersion at 1.06 μm, however, is smaller than at 0.9 μm by a factor of ⅔.

Dispersion-Optimized Optical Single-Mode Glass Fiber Waveguides

Publisher Summary This chapter focuses on the advances in communication through light fibers. Recent breakthrough in the purification of glass has made it possible to manufacture very low-loss optical fibers. The fibers provide almost all the attractive features of an ideal optical transmission line, such as, low cost, small size, lightweight, flexible, larger bandwidth, high tensile strength, no short circuiting issues, resistant to nuclear radiation, and heat resistance. These optical fibers are used as the communication media for transmitting optical signals. The bandwidth of a single-mode fiber is limited by the dispersion of the normal mode and by the material dispersion effects. One of the unique characteristics of a dielectric fiber waveguide is that below a certain frequency called the cut-off frequency of a particular mode, that mode simply no longer exists. A fiber of a given cross section will support a finite number of guided modes and a continuous spectrum of radiation modes. Any irregularity in the fiber because of diameter variation, bending, interface irregularities, or the presence of scattering centers will produce coupling of the energy of one mode to the others. Mode coupling within an optical fiber may produce the desirable effect of reducing the delay distortion that result from uncoupled multimode operation or may produce the undesirable effect of signal contamination.

Advances in Communication through Light Fibers

An optical amplifier particularly for use in a high data-rate fibre-optics communication link utilizing a body of a dielectric substance transparent to signal light of a given band of wavelengths and transparent also to pumping light of a different band of wavelengths, a smooth continuous surface along the length of the body having as amplifying component a layer of laser material adhered contiguous to the surface. Both signal light and pumping light are introduced into an end face of the body, which may be a passive dielectric fibre core such as glass, or a passive dielectric slab with parallel side walls, utilising mode order converting holograms. By the phenomenon of penetration by light of both frequencies within a thin layer of the adhered material as the light beams undergo multiple total internal reflections at the interface between the body and the laser material, atoms of active material, e.g. Nd.sup.+ 3 or organic dye molecules in the laser medium are optically pumped to a higher energy level, and fluoresce and are stimulated by the evanescent-wave component of the signal light to coherently emit light in a band of wavelengths correlated with the signal band of wavelengths. The amplified signal light is delivered from the other end face, and is launched through further hologram devices in a transmission mode into a succeeding fibre or slab of the link.

Quantum amplifier having passive core and active cladding providing signal gain by interaction of evanescent-wave components of signal and pump beams propagating along the core

The effect of dielectric dispersion on pulse transmission through singly clad, cylindrical fibers is formulated in terms of the effective group index for the waveguide. It is shown that two different solutions are possible for designing guides that give a minimum of distortion due to dispersion. One solution uses fibers with low numerical aperture made from glasses with low dispersion; here for sufficiently long wavelengths minimum distortion is possible while the guide parameters limit conduction to the lowest order mode. It is predicted, for example, that a pulse of radiation in the lowest order mode with a carrier wavelength of 1.06 μ can be conducted with minimum distortion by a fiber made from commercially available, low dispersion glass. In the other solution the fiber is designed so that the HE11 mode provides an anomalous dispersive characteristic; this solution requires a high numerical aperture fiber with a core large enough to support the next higher order group of modes, namely the TE01, TM01, and HE21 modes. For this second solution, it is shown that a dispersionless group index is possible for wavelengths at least as short as 0.77 μ.

Dispersion minimization in dielectric waveguides.

The possibility of being able to separate the effects of waveguide structure from those depending on material dispersion, which we thought we had demonstrated, is true, after all, only when the ratio of indices is kept constant. The data contained in our Figs. 2 and 3 are for the case of constant n1 and n2 as Jürgensen surmised. 1 The curves were used incorrectly for the case of constant r; his final equation states the correct use for that case, and we agree with the value for dng/dλ that he obtained. We agree also with his conclusion that a dispersion-free core/ cladding monomode fiber cannot be made for a wave­ length of 1.06 μm from typical optical glasses. In addition, the case of variable r requires additional partial derivatives not obtainable from Figs. 2 and 3 or other data presented in our paper, so the predictions of dispersionless group index for the HE11 mode when other modes can propagate are without defensible foundation.

Authors’ Reply to Comments on: Dispersion Minimization in Dielectric Waveguides

Holographic method of recording and reconstructing a wavefront, from an array of light spots on a dark field, to propagate the reconstructed wavefront so as to illuminate the light spots to the exclusion of the dark field.

Luther W. Smith

Papers

Dispersion minimization in dielectric waveguides.

Authors’ Reply to Comments on: Dispersion Minimization in Dielectric Waveguides

Efficient illumination of the cores only of a fiber optic bundle using holography