DOI 10.1515/joc-2013-0061 J. Opt. Commun. 2014; 35(1): 17 – 22 Bishuddhananda Das, Anup Kumar Maiti and Sankar Gangopadhyay* Simple Method for Prediction of Far-Field Patterns of Single-mode Dispersion-shifted and Dispersion-flattened Fibers Abstract: Based on the simple series expression of funda- mental mode in dispersion-shifted and dispersion- flattened fibers, we formulate analytical expressions for far-field pattern of such fibers and evaluate them. The concerned calculations require much less computations. Taking three typical trapezoidal fibers as example of dispersion-shifted fiber, we show that our results match excellently with the exact numerical results. As example of dispersion-flattened fiber, we choose two parabolic profile W and two step profile W fibers for our study and here also, our estimations agree excellently with the exact numerical results. The present formalism can also be used for predicting different propagation characteristics associ- ated with the far-field. Further, one can also predict the fundamental modal field from the knowledge of far-field pattern. This simple but accurate formalism developed will benefit the system engineers working in the field of optical technology. Keywords: dispersion-shifted fiber, dispersion-flattened fiber, fundamental mode, far-field pattern PACS ® (2010). 42.81.-i, 42.82.-m *Corresponding author: Sankar Gangopadhyay: Department of Physics, SDET-Brainware Group of Institutions, Barasat, Kolkata 700124, West Bengal, India. E-mail: sankar.gangopadhyay@yahoo.co.in Bishuddhananda Das, Anup Kumar Maiti: Department of Physics, SDET-Brainware Group of Institutions, Barasat, Kolkata 700124, West Bengal, India 1 Introduction Single-mode optical fiber has emerged as the most effec- tive broad band transmission medium of present commu- nication system comprising the wave length division mul- tiplexing optical networks. The operating wavelength for such system ranges from 1.3 to 1.6 µm since the fiber mate- rial silica has negligible attenuation loss (0.2 dB/km approximately) at the wavelength 1.55 µm while material dispersion vanishes at the wavelength 1.3 µm. Thus if the zero dispersion wavelength is shifted to 1.55 µm region, one can obtain minimum attenuation loss and extremely low dispersion simultaneously and consequently large bandwidth system along with long repeater less transmis- sion can be realized. Such fibers, known as dispersion- shifted fiber, can be obtained by monitoring suitable change of the parameters of the fiber [1–3]. Further, the operating wavelength of Erbium-doped fiber amplifier being 1.55 µm, the dispersion-shifted fiber emerges as a potential device in the field of all optical technology [4–5]. Side by side, there is another type of fiber, termed as dispersion-flattened fiber, in which almost zero disper- sion is obtained over a range of wavelengths. This type of fiber is used for the purpose of enhancing the information carrying capacity by wavelength division multiplexing [6]. In this context, the derivation of simple but accurate expressions for modal field of single-mode dispersion- shifted and dispersion- flattened fibers is of tremendous importance for estimation of various propagation parame- ters of such fibers. The application of two parameter vari- ational technique [7] can predict the fundamental mode and the associated propagation parameters accurately but the evaluations by this formalism require complicated computations. A simple power series expression of funda- mental mode of graded index fiber based on Chebyshev technique has already been reported [8]. This suitable form of fundamental mode has been shown to have esti- mated the propagation parameters of single-mode graded index fibers excellently [8–11]. This method is based on formulation of linear relation of 1 0 ( )/ ( ) K W K W with 1/W in the wide single-mode range ≤ ≤ 0.60 2.5 W . In accor- dance with this simple formalism, analytical expressions of fundamental mode of dispersion-shifted as well as dispersion-flattened fibers have been formulated [12]. It has been also shown that using this formalism, one can evaluate the cladding decay parameters of such fibers accurately but in a simple fashion [12]. For such fibers it is relevant to mention that detailed analysis of far-field pattern is of tremendous importance since its knowledge enables one to predict the normalized frequency and core radius and thereby the important fiber parameter namely Brought to you by | Purdue University Libraries Authenticated Download Date | 6/7/15 5:06 PM