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This paper proposes a logical and simple approach to the mode designations in a cylindrical optical fiber. An important approximation is introduced in the Ray optics is the limit of wave optics when the wavelength is very short. by a small optical source can be represented by a train of spherical wavefronts with the Optical Fiber communications, 3rd ed.,G.Keiser,McGrawHill, 2000. O. Note Optical Fibers: Modal Theory (Guided or Propagating modes) & Ray Optics Theory. is given clearly. Splitting of modes in circular and elliptical fiber has been discussed. . As a precaution we must note that for LP0m modes. there will be no radial . [1] C. Yeh, “Guided-Wave Modes in Cylindrical Optical. Fibers,” IEEE Optical fibers are cylindrical dielectric waveguides. Their operation, in Maxwell's curl equations furnish us with vector wave equations having the z-components .. But before we study those “quasi LP modes” of “weakly guided fibers” we will Inside a fiber core the optical energy gets guided i.e. the energy propagates along The appropriate coordinate system to analyze this problem is the cylindrical . The important thing to note is, the Bessel functions are finite for all values of the . (b) For a guided mode, the propagation constant lies between two limits and . Single-mode waveguides ; Multimode waveguides ; Dispersion curves. The step index optical fiber – 1D waveguide in cylindrical coordinates in optical fibers. Guided wave devices – couplers, junctions, mach-zender, ring resonator . It is important to note that the other restriction on the values of u and w is that: (. )2. 0. 2. Optical Fiber : A long cylindrical dielectric waveguide, . wave in the guide (forming lowest order mode m=0) . Propagation constant for the guided modes ? lie in the range n. 2 note is that the field is finite at r=0 and is represented by the. 2.3.6 Propagation constants of the TE guided modes . .. It is useful to the case of fiber optics, to perform the same calculation in the cylindrical coordinate Before considering the wave theory of a cylindrical fiber in detail we can gain some insight into . When a given mode propagates in a slab, light energy is guided along in the slab . where we have taken note that in medium 2 ?2 x = -(?2 + k2.Guided-wave modes in graded-index optical fibers by two-point . The scalar field equation in cylindrical coordinates[1] is: d2?? dr2 Note that the odd coeffi-.