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239164DDd01 - 1/100 Self-Phase Modulation in Optical Fiber...

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1/100 JJ II J I Back Close Self-Phase Modulation in Optical Fiber Communications: Good or Bad? Govind P. Agrawal Institute of Optics University of Rochester Rochester, NY 14627 c 2007 G. P. Agrawal
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2/100 JJ II J I Back Close Outline Historical Introduction Self-Phase Modulation and its Applications Modulation Instability and Optical Solitons Optical Switching using Fiber Interferometers Cross-Phase Modulation and its Applications Impact on Optical Communication Systems Concluding Remarks
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3/100 JJ II J I Back Close Historical Introduction Celebrating 40th anniversary of Self-Phase Modulation (SPM): F. Demartini et al., Phys. Rev. 164 , 312 (1967); F. Shimizu, PRL 19 , 1097 (1967). Pulse compression though SPM was suggested by 1969: R. A. Fisher and P. L. Kelley, APL 24 , 140 (1969) First observation of optical Kerr effect inside optical fibers: R. H. Stolen and A. Ashkin, APL 22 , 294 (1973). SPM-induced spectral broadening in optical fibers: R. H. Stolen and C. Lin Phys. Rev. A 17 , 1448 (1978). Prediction and observation of solitons in optical fibers: A. Hasegawa and F. Tappert, APL 23 , 142 (1973); Mollenauer, Stolen, and Gordon, PRL 45 , 1095 (1980).
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4/100 JJ II J I Back Close Self-Phase Modulation Refractive index depends on optical intensity as (Kerr effect) n ( ω , I ) = n 0 ( ω )+ n 2 I ( t ) . Intensity dependence leads to nonlinear phase shift φ NL ( t ) = ( 2 π / λ ) n 2 I ( t ) L . An optical field modifies its own phase (SPM). Phase shift varies with time for pulses. Each optical pulse becomes chirped. As a pulse propagates along the fiber, its spectrum changes because of SPM.
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5/100 JJ II J I Back Close Nonlinear Phase Shift Pulse propagation governed by Nonlinear Schr¨odinger Equation i A z - β 2 2 2 A t 2 + γ | A | 2 A = 0 . Dispersive effects within the fiber included through β 2 . Nonlinear effects included through γ = 2 π n 2 / ( λ A eff ) . If we ignore dispersive effects, solution can be written as A ( L , t ) = A ( 0 , t ) exp ( i φ NL ) , where φ NL ( t ) = γ L | A ( 0 , t ) | 2 . Nonlinear phase shift depends on input pulse shape. Maximum Phase shift: φ max = γ P 0 L = L / L NL . Nonlinear length: L NL = ( γ P 0 ) - 1 .
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6/100 JJ II J I Back Close SPM-Induced Chirp -2 -1 0 1 2 0 0.2 0.4 0.6 0.8 1 Time, T/T 0 Phase, φ NL -2 -1 0 1 2 -2 -1 0 1 2 Time, T/T 0 Chirp, δω T 0 (a) (b) Super-Gaussian pulses: P ( t ) = P 0 exp [ - ( t / T ) 2 m ] . Gaussian pulses correspond to the choice m = 1 . Chirp is related to the phase derivative d φ / dt . SPM creates new frequencies and leads to spectral broadening.
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7/100 JJ II J I Back Close SPM-Induced Spectral Broadening First observed inside fibers by Stolen and Lin (1978).
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