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Optical Solitons in Fibers by Professor Akira Hasegawa, Professor Masayuki Matsumoto

By Professor Akira Hasegawa, Professor Masayuki Matsumoto (auth.)

Optical solitons in fibers are a stunning instance of ways an summary mathematical notion has had an influence on new details transmission applied sciences. the concept that of all-optical info transmission with optical soliton structures is now environment the traditional for the main complicated transmission platforms. The publication bargains with the movement of sunshine waves in optical fibers, the evolution of sunshine wavepackets, optical info move, all-optical soliton transmission structures, the keep watch over of optical solitons, polarization results, dispersion-managed solitons, WDM transmission, soliton lasers, all-optical switching and different functions. This publication is a needs to for all researchers and graduate scholars energetic within the box of optical information transmission.

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In a practical system, the fiber dispersion k often varies in Z. In addition, fiber has amplifiers with gain G(Z) and loss with loss rate Γ per dispersion distance z0 . 18) should be modified to ∂q i ∂2q = d(Z) 2 + i|q|2 q + [G(Z) − Γ ]q . ∂Z 2 ∂T Here d(z) is the group dispersion normalized by its average value. 20) can be easily integrated by means of the Fourier transformation in time ∞ q(Z, T )eiΩT dT . 22) 0 and q(Z, T ) is obtained from the inverse transformation q(Z, T ) = 1 2π ∞ q(Z, Ω)e−iΩT dΩ .

8 Condition of Generation of a Soliton in Optical Fibers 57 Since the Raman process conserves the photon numbers, the cascade process simply shifts the frequency spectrum of the lightwave to longer wavelength. As will be shown in Sect. 2, the major consequence of the shift is the change of the group velocity of solitons throught the group velocity dispersion. Since a soliton exits normally in anomalous dispersion regime where the group dispersion is negative, the Raman effect induces the soliton speed to slow down through the spectrum down shift.

DZ 2 dZ ρ dT Since we cannot accept the solution ρ−2 dρ/dT = const, the only alternative choice is c(Z) = const. 42) or c1 dT + A(Z) . 41), ∂σ/∂Z should also be a function of T . Hence, we take dA/dZ to be constant (= Ω), c1 dT + ΩZ . 45) We now seek a solution of this equation, subject to the conditions 1 to 3. In order to satisfy condition 1, dρ/dT should vanish only at two values of ρ, ρD and ρs . In addition, for the root at ρD to represent an asymptotic value of ρ, it should be a double root.

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