Ukrainian Journal of Physical Optics 
Home page
 
 

Other articles 

in this issue
Transformation of sinusoidal electromagnetic and polarization waves into cnoidal waves in an optical fibre
Dzedolik I.V.

Taurida V. Vernadsky National University, 4 Vernadsky Ave., 95007 Simferopol, Ukraine

download full version

It is shown that a sinusoidal signal wave can transform into a cnoidal (periodic) wave in an optical fibre if the power signal propagates in the fibre core. In this case the signal wave period increases, but the wave profile does not almost change. The signal wave gets the form of kink for the high-power signal. The wave transformation is determined by nonlinear effects in the fibre core. The lin-ear modes of the fibre transform into the nonlinear ones under influence of cubic or higher nonlinear interactions of electromagnetic and polarization waves. These changes are described by the equation with sinusoidal nonlinearity for the polari-zation wave. The approximate and exact analytical solutions of the nonlinear equation are obtained. 

Keywords: optical fibre, polariton, cnoidal wave, kink

PACS:  42.65.-k, 42.65.Wi
UDC : 535.3
Ukr. J. Phys. Opt. 9 226-235 
doi: 10.3116/16091833/9/4/226/2008
Received: 04.08.2008
 
REFERENCES
  1. Sukhorukov A P. Nonlinear wave interactions in optics and radio physics. Moscow: Nauka (1988).
  2. Kivshar Yu S and Agrawal G P. Optical Solitons: From Fibres to Photonic Crystals. Academic Press (2003).
  3. Snyder A W and Love J D. Optical waveguide theory. London, New York: Chapman and Hall (1983).
  4. Dzedolik I V and Dzedolik A I, 2002. Nonlinear modes in optical fibres. Technical Physics Letters. 28(5): 403–405. 

    5. doi:10.1134/1.1482749
  5. Zheltikov A, 2005. Gaussian-mode analysis of waveguide-enhanced Kerr-type nonlinearity of optical fibres and photonic wires. J. Opt. Soc. Am. B. 22(5): 1100–1104. 

    6. doi:10.1364/JOSAB.22.001100
  6. Qi X, Zhang X, Wei H and Plant D V, 2006. Linearity of nonlinear pertur-bations in fibre-optic transmission lines and its applications to nonlinear compensations. J. Opt. Soc. Am. B. 23(10): 2032–2039.

    7. doi:10.1364/JOSAB.23.002032
  7. Korneev N and Marroquin F, 2007. Long-distance propagation of periodic patterns in weakly nonlinear Kerr medium. J. Opt. Soc. Am. B. 24(1): 84–89.

    8. doi:10.1364/JOSAB.24.000084
  8. Dzedolik I V. Polaritons in optical fibres and dielectric resonators. Simfer-opol: DIP (2007). 
  9. Nayfeh A H. Perturbation methods. New York-London-Sydney-Toronto: John Wiley and Sons (1973).
(c) Ukrainian Journal of Physical Optics