Uncertainty relation for the optimization of optical-fiber transmission systems simulations

Optics Express

Volumn 13, Issue 10, 2005, Pages 3822-3834

  Rieznik, A A ^a,b   Tolisano, T ^a   Callegari, F A ^a   Grosz, D F ^c   Fragnito, H L ^a  

^a UNIVERSITY OF CAMPINAS   (Brazil)

^b PADTEC   (Brazil)

^c INSTITUTO TECNOLÓGICO DE BUENOS AIRES   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; LIGHT TRANSMISSION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; OPTIMIZATION;

MATHEMATICAL INEQUALITY; OPTICAL-FIBER COMMUNICATIONS SYSTEM; SPLIT-STEP FOURIER METHOD (SSFM); UNCERTAINTY PRINCIPLE;

OPTICAL FIBERS;

EID: 21244494811     PISSN: 10944087     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OPEX.13.003822     Document Type: Article

References (14)

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3. G.M. Muslu and H.A. Erbay, "Higher-order split-step Fourier schemes for generalized nonlinear Schrödinger equation" Mathematics and Computers in Simulation (In press).
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5. Xueming Liu and Byoungho Lee, "A Fast Method for Nonlinear Schrödinger Equation," IEEE Photon. Technol. Lett. 15, 1549-1551 (2003).
6. See also Xueming Liu and Byoungho Lee, "Effective Algorithms and Their Applications in Fiber Transmission Systems" Japanese Journal of Applied Physics, 43, 2492-2500, (2004).
7. Eq. (6) is a variant of the so-called Baker-Hausdorff formula. See, for example, G.H. Weiss and A.A. Maraudin, J. Math. Phys, 3, 771-777 (1962).
8. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970).
9. 2, the "quantum covariance," is given by 〈C〉≤1/ 2〈DN+ND〉-〈D〉〈N〉.
10. This is a straightforward consequence of Parseval's theorem. In quantum mechanics the Fourier transform of an operator is nothing but the same operator expressed in the conjugate representation. Of course, the QM average value of an observable operator can not depend on the representation.
11. J. Van Roey, J. van der Donk, and P.E. Lagasse, "Beam propagation method: analysis and assessment" J. Opt. Soc. Am., 71, 808-810 (1981).
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