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The nonlinear Schrödinger equation (NSE) has served as the governing equation of optical soliton in the study of its applications to optical communication and optical switching. Various schemes have been employed for the solution of this nonlinear equation as well as its variants. We report in this paper a relatively simpler new approach for the analytic solution of NSE. In this scheme the equation was first transformed into an arctangent differential equation, which was then separated into the linear and nonlinear parts, with the linear part solved in a straight forward manner. The solution of the nonlinear equation was written in the form of modulation function characterized by its amplitude function A and phase function F(A). Substituting the linear solution for A, the arctangent differential equation was solved for a certain initial value of A. It is shown that this method is applicable to other first-order nonlinear differential equation such as the Korteweg de Vries equation (KdV), which can be transformed into an arctangent differential equation.

I. Introduction

The phenomenon of the solitary wave propagation was observed for the first time by the Scottish scientist John Scott Russell in 1844, when one day he was watching water waves of a certain shape kept on traveling without changing their shape for a distance as far as his eye could see. To explain the behavior of such unusual wave, Korteweg and de Vries governed a model for the wave propagation in shallow water in form a partial differential equation called as KdV differential equation, which its solution appropriates to the features of the solitary wave called as soliton[1]. The existence of solitons in optical fiber was predicted by Zakarov and Zabat (1972) after they derived a differential equation for the light propagating in an optical fiber, that demonstrated later by Hazagawa in 1973 at Bell Laboratory. Next, Mollenauer and Stolen employed the solitons in optical fiber for generating subpicosecond pulses.

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Parameter terpenting untuk menentukan panjang kopling dan formula propagasi medan directional coupler adalah nilai tetapan propagasi efektif medan moda simetri dan moda asimetri. Pada makalah ini dilaporkan formulasi tetapan propagasi efektif dimaksud untuk cahaya modus TE (transverse electric) yang terpandu dalam directional coupler linier dalam bentuk analitis. Formulasi analitis diturunkan dengan menggunakan metode matrik karakteristik pandu gelombang berlapis jamak, dan berlaku untuk kedua moda simetri dan asimetri, baik untuk struktur directional coupler simetri maupun asimetri.

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  1. New Science Future (http://rohedi.blogspot.com)
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pattern-of-normal-modes-for-s3cebcm-and-v2955-and-the-power-transfer-between-the-two-waveguides

pattern-of-normal-modes-for-s3cebcm-and-v2955-and-the-power-transfer-between-the-two-waveguides

This paper presents generalization of the dispersion relation for analysis of optical power transfer of transverse-electric (TE) mode in five-layer of linear symmetrical directional-coupler, which consists of two equal waveguides as guiding layers with a gap material sandwiched between a semi-infinite clad and a substrate. The dispersion equation formulated by normalizing the intensity of normal modes which involve phase-shift due to the internal reflection at each boundary of neighboring layers corresponds to the standing-wave form, i.e, contains the terms of overlapping the normal modes in gap region, the evanescent waves into the superstate regions, and effective lateral width of the directional-coupler. This generalized dispersion equation can overcome disability of coupled–mode approximation when the two waveguides get too close, evenly it can also be used for designing a zero-gap coupler. Simulation of beam propagation and analysis of optical power transfer in the linear directional-coupler are also presented.

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Makalah ini menyajikan prosedur dan hasil perhitungan tenaga gerak partikel yang terperangkap dalam sistem tenaga potensial sumur tanjak dengan pendekatan variasional menggunakan fungsi cobaan Gaussian-Hermite. Unjuk kerja pendekatan variasional ini diujicobakan pada sistem potensial sumur tanjak yang profil distribusi tenaga potensialnya mematuhi fungsi kuadrat secant hyperbolic (Sech2). Semua perhitungan dilakukan secara numerik dan diprogram menggunakan Matlab for Windows. Dari perhitungan normalisasi tenaga partikel untuk dua tingkat terendah (keadaan dasar n=0 dan tereksitasi pertama n=1), diketahui bahwa akurasi pendekatan variasional semakin meningkat untuk nilai normalisasi lebar sumur (L) yang semakin besar.

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A guided wave excited along the boundary between linear and nonlinear media known as initial inspiration for developing devices based on Kerr nonlinear optics, such as the nonlinear directional coupler, etc. Two important parameters for such structure are respectively the minimum amplitude of light required for the excitation, and the location of the peak of guided nonlinear boundary wave. Analytical procedure of derivation the two parameters commonly involved the Jacobi’s elliptic functions based on the numerical integration. In order to simplify the calculation procedure, in this paper we introduce optimization procedure based on applying the solitary wave solution for guided field inside the nonlinear media. The simulation of guided wave excitation at the interface between linear and nonlinear media is also presented.

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Pada makalah ini dilaporkan teknik sederhana dalam menormalisasi bentuk persamaan relasi dispersi pandu gelombang slab untuk cahaya yang dirambatkan pada modus transverse magnetic. Langkah normalisasi dilakukan dengan cara menormalisasi semua komponen transversal tetapan propagasi cahaya terhadap faktor reduksi amplitudo medan magnet cahaya yang ter-evanescent ke daerah substrat. Hasil perumusan sesuai dengan formulaai yang didapatkan dengan teknik lain menggunakan pendekatan sinar optik. Teknik normalisasi ini juga efektif digunakan untuk mendapatkan formulasi medan magnet cahaya terpandu dalam
bentuk ternormalisasi.

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  1. New Science Future (http://rohedi.blogspot.com)
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