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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 9, Iss. 12 — Dec. 1, 1992
  • pp: 2258–2264

Modified theory of three-channel Kerr-type nonlinear directional coupler

Chula Mapalagama and R. T. Deck  »View Author Affiliations

JOSA B, Vol. 9, Issue 12, pp. 2258-2264 (1992)

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We point out inconsistencies in previous analyses of multiple-channel nonlinear directional couplers based on Kerr-type media and present a modified set of coupled-mode equations for a three-channel nonlinear coupler that indicate a mode of power switching between channels with increased input power that is both qualitatively and quantitatively different from that predicted previously.

© 1992 Optical Society of America

Original Manuscript: January 13, 1992
Revised Manuscript: March 25, 1992
Published: December 1, 1992

Chula Mapalagama and R. T. Deck, "Modified theory of three-channel Kerr-type nonlinear directional coupler," J. Opt. Soc. Am. B 9, 2258-2264 (1992)

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  12. After adjustment of notational differences it is easily shown that in the simpler case of a two-channel coupler Eqs. (9) and (10) reduce identically to the equations of Ref. 9.
  13. This approximation can be eliminated by expansion of the coupler field E in terms of the supermodes of the total structure rather than in terms of the fields of the separate channels as in Eq. (2). On the other hand, it is shown in Ref. 5 for the case of a two-channel coupler that the nonlinear power switching curves obtained with and without this approximation are in reasonably good agreement.
  14. The two conditions are not identical because of the differences in the regions of integration in the definitions of the coefficients where the integrands of the defining integrals are large. As a consequence of these differences it is possible for the coefficient Q∼n to exceed the coefficient kn while the coefficients R∼n,n′ and T∼n,n′ remain less than the coefficient kn,n′.
  15. These parameter values approximately correspond to the values that characterize the two-channel coupler described in Ref. 4.
  16. This conclusion is consistent with the above analysis of Eqs. (9) and with the conclusions arrived at in Ref. 9.
  17. Further decrease in the coupling between the channels can cause the coupling length L to exceed the limits allowed in the design of a practical coupler.

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