Abstract
TE-polarized electromagnetic waves guided by a three-layer structure consisting of a film surrounded by semi-infinite media (all media are characterized by a Kerrlike dielectric function) are investigated by expressing the solution of the field equations in terms of Weierstrass' elliptic functions. Evaluation leads to a universal dispersion relation and its solutions and a universal expression for the power flow. Numerical results are presented for the effective wave number as a function of the intensity of the electric field at the lower surface of the nonlinear film, for various profiles of the field intensity, and for the power flow as a function of the effective wave number.
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References
For a review of the field, which contains a number of special references, see Boardman, A.D., Egan, P., Lederer, F., Langbein, U., Mihalache, D.: in: Modern problems in condensed matter sciences, Vol. 29. Ponath, H.-E., Stegeman, E.I. (eds.), Amsterdam: North Holland 1991
Mihalache, D., Bertolotti, M., Sibilia, C.: in: Progress in optics Vol. XXVII, pp. 229–313. E. Wolf (ed.). Amsterdam: North Holland 1989
Chen, W., Maradudin, A.A.: J. Opt. Soc. Am. B5, 529 (1988)
Stuart, C.A., Arch. Rational Mech. Anal.125, 145 (1993)
Weierstrass, K.: Mathematische Werke, Vol. V, New York: Johnson (n.d.)
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Schuermann, H.W., Schmoldt, R.: Z. Phys. B92, 179 (1993)
see [6], p. 652
see [1] p. 126
see [6] p. 630
Okafuji, S., Nakai, Y.: IEE Proc. J.,138, 204 (1991)
see [6] p. 597. Care must be taken with regard to the order and complexity of the rootsI 1,I 2,I 3
A simple way to show this is by plottingE 2i (z) according to (39)–(41) fora i E 20 ≪1 and comparing with\(E_s^2 = E_0^2 e^{q_s k_0 z} \),E 0 f (cosiq f k 0 z −iq s /q f siniq f k 0 z)2,\(E_c^2 = E^2 (d)e^{ - q_c k_0 (z - d)} \), respectively. Forn 2 \(< \bar \varepsilon _f \) and givenk 0 d, the numerical solutionsn of the linear mode condition taniq f k 0 d=−iq f (q s +q c )/(q 2f +q s q c) agree with solutions of (30), ifa f E 20 ≪1
see [1], p. 129
see [6], p. 631, 649
see [6], pp. 651–652
compare [1], p. 160
see [6], p. 631
see [6], p. 650 for evaluation of (61) by expressing χ(w′) by elliptic 522-5 and elliptic integrals
see [6], pp. 649–650
see [1], p. 218
Akhmediev, N.N.: in: Modern problems in condensed matter sciences, Vol. 29. Ponath, H.-E., Stegeman, E.I. (eds.). Amsterdam: North Holland 1991
Mihalache, D., Mazilu, D., Bertolotti, M., Sibilia, C.: J. Opt. Soc. Am. B5, 565 (1988)