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The following paper is aimed at such formulas and functions. Recent efforts in simplifying the theory for weakly guided modes had promising results, but in the region of interest, they did not lead to the kind of simple formulas one would wish to have for fiber design work. Maxwell’s equations have exact solutions for the dielectric cylinder, but even with the simplifying assumption that the cladding be infinitely thick these solutions are too complicated to be evaluated without computer. The modes that do propagate are weakly guided, but in general the guidance is sufficient to negotiate bends with radii of tens of centimeters. Typically, a difference of a few parts in a thousand is feasible. Most modes can be suppressed by making the core thin and the index different between core and cladding small.
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A fiber waveguide consists of a thin central glass core surrounded by a glass cladding of slightly lower refractive index. Since this causes signal distortion over long distances, fibers that transmit only a limited number of modes are of special interest.
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In general, these fibers support many modes, which propagate at different velocities. Recently, glass fibers have been produced that permit the transmission of optical signals over several kilometers. Plots vs frequency of these parameters are given for 70 modes It considers the propagation constant, mode delay, the cladding field depth, and the power distribution in the fiber cross section. This article presents simple formulas and functions for the fiber parameters as a help for practical design work. Thin glass fibers imbedded into a glass cladding of slightly lower refractive index represent a promising medium for optical communication.
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Note: Author names will be searched in the keywords field, also, but that may find papers where the person is mentioned, rather than papers they authored.Use a comma to separate multiple people: J Smith, RL Jones, Macarthur.Use these formats for best results: Smith or J Smith.For best results, use the separate Authors field to search for author names.Use quotation marks " " around specific phrases where you want the entire phrase only.Question mark (?) - Example: "gr?y" retrieves documents containing "grey" or "gray".Asterisk ( * ) - Example: "elect*" retrieves documents containing "electron," "electronic," and "electricity".Improve efficiency in your search by using wildcards.Example: (photons AND downconversion) - pump.Example: (diode OR solid-state) AND laser.Note the Boolean sign must be in upper-case. Separate search groups with parentheses and Booleans.Keep it simple - don't use too many different parameters.For this reason we feel that these methods are preferable to those based on the Kirchhoff formula. The calculations of diffracted fields and radiation fields, based either on the Equivalence Principle or on the more general Induction Theorem, depend upon a priori verifiable approximations to the actual fields in the neighborhoods of the sources of the diffracted and radiated waves. If, on the other hand, this formula is applied to some auxiliary vector potential from which the diffracted field is subsequently deduced by differentiation, the result (although consistent with Maxwell's equations) depends on the particular choice of the auxiliary vector and in some instances, at least, is obviously unreasonable (Appendix III). If the Kirchhoff formula is applied directly to the field intensities of the incident wave over the aperture, the diffracted field is found to be inconsistent with Maxwell's equations. Inasmuch as it is rarely possible to treat diffraction of electromagnetic waves exactly, the Kirchhoff formulation of Huygens' Principle has been frequently used in approximate calculations.