Accurate Estimate of Some Propagation Characteristics for the First Higher Order Mode in Graded Index Fiber with Simple Analytic Chebyshev Method

Abstract

Using Chebyshev power series approach, accurate description for the first higher order (LP 11 ) mode of graded index fibers having three different profile shape functions are presented in this paper and applied to predict their propagation characteristics. These characteristics include fractional power guided through the core, excitation efficiency and Petermann I and II spot sizes with their approximate analytic formulations. We have shown that where two and three Chebyshev points in LP 11 mode approximation present fairly accurate re sults, the values based on our calculations involving four Chebyshev points match excellently with available exact numerical results.

An Exact Analysis of the Fundamental and First Higher Order Mode in Graded Index Fibers with Direct Power Series Method

“… . We have compared our results with those obtained by Chebyshev method already reported in our earlier paper [15]. It was shown there that the values of propagation characteristics of LP 11 mode in parabolic and triangular index fibers obtained by CPS technique using four Chebyshev points closely matched with standard numerical values.…”

“…Since the current interest is in Two Mode Fibers where LP 01 and LP 11 modes both exist, it is important to find the range within which these modes can exist. We have compared our data with one analytic method like Chebyshev Power Series (CPS) technique, as it is already established as an approximate analytic method for the calculation of different propagation characteristics of graded index fiber in LP 01 and LP 11 mode [14,15]. We found that Chebyshev technique results are in close accordance with our values.…”

“…to convert the series to Bessel function. 0 V  Petermann-2 spot size was determined with Chebyshev Power Series technique in [15] for LP 11 mode; it was also compared with an accurate numerical calculation. Those results are very close to our results with Power Series technique in this paper.…”

“…Matrix methods are problematic for profiles with sharp index difference. In the literature, there are some approximate analytic methods also like variational analysis [12,13], Chebyshev power series method [14,15] etc. The analytic methods involve cumbersome algebraic calculations followed by some computation; due to approximations these methods are not so accurate.…”