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Conference on Lasers and Electro-Optics

Optical bi- and tri-stability by excitation of surface electromagnetic waves at boundaries of one- and two-photon resonant media

L. M. Kocharyan

Published Aug 29, 2005• 0 citations

Abstract

Summary form only given. The resonant nature of the excitation of surface electromagnetic waves (SEWs), i.e. the resonant dependence of the reflectivity on the incident radiation wavevector component parallel to the interface (surface), k, leads to the nonlinear phenomena arising and particularly optical bi- and multi-stability appearance at relatively small nonlinearities. At such nonlinearities the field induced variation of the SEW wavevector, K, becomes comparable with the width, Im(K), of the mentioned geometrical (angular) resonance. In the paper the theory of optical bi- and multistability at the excitation of TM-polarized SEWs via the Kretschmann attenuated total reflection (ATR) scheme (glass prism-metal film-dielectric) in which the dielectric exhibits a relatively small one- or two-photon resonant nonlinearity is presented. The system of equations describing the excitation of nonlinear SEWs is presented in general form for arbitrary type of nonlinearity by means of the SEW wavevector nonlinear term, K/sup NL/.

DOI: 10.1109/iqec.2000.908003

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Summary form only given. The resonant nature of the excitation of surface electromagnetic waves (SEWs), i.e. the resonant dependence of the reflectivity on the incident radiation wavevector component parallel to the interface (surface), k, leads to the nonlinear phenomena arising and particularly optical bi- and multi-stability appearance at relatively small nonlinearities. At such nonlinearities the field induced variation of the SEW wavevector, K, becomes comparable with the width, Im(K), of the mentioned geometrical (angular) resonance. In the paper the theory of optical bi- and multistability at the excitation of TM-polarized SEWs via the Kretschmann attenuated total reflection (ATR) scheme (glass prism-metal film-dielectric) in which the dielectric exhibits a relatively small one- or two-photon resonant nonlinearity is presented. The system of equations describing the excitation of nonlinear SEWs is presented in general form for arbitrary type of nonlinearity by means of the SEW wavevector nonlinear term, K/sup NL/.

We consider an attenuated total reflection prism-coupling geometry used to excite surface-plasmon waves along a metal film, bounded by a substrate with an intensity-dependent dielectric constant. Nonlinear wave theory is developed in the infinite incident plane-wave approximation, assuming a dielectric constant proportional to the square of the electric field normal to the film. We calculate the intensity required to observe bistability in the reflected intensity by excitation of the nonlinear, long-range surface plasmon and find it to be 2 orders of magnitude less than that required for the nonlinear, single-surface plasmon. We compare the nonlinear wave analysis with other approaches and illustrate the effects of the sign of the nonlinearity and of a nonlinear coupling layer.

Wysin et al1 suggested that the local field enhancement near a metal surface which occurs if surface plasmons are excited in a metal film, can be useful for observing optical bistability arising from the nonlinearity of the Kerr medium. Other geometrical arrangements2 have also been suggested. These studies assume plane waves in the nonlinear medium and use the Fresnel formulae for reflection and refraction from a layered medium but with linear refractive index replaced by the nonlinear refractive index. This assumes that the fields in the medium are homogeneous. However if surface plasmons are excited, then the fields are inhomogeneous and one has the problem of reflection and refraction from an inhomogeneous layered medium. The inhomogeneity is to be determined self consistently. Thus a proper treatment of optical bistability with surface plasmons should use the nonlinear solutions of the wave equation in Kerr medium. This is what we do in this paper.

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In this study, we investigate the optical bistability and multistability in a pure single Kerr nonlinear layer of dielectric material using the Maxwell-Duffing approach. We employ the Duffing anharmonic oscillator as an alternative constitutive relation to express the electric field as a nonlinear function of the induced polarization. Utilizing both the electromagnetic wave equation and the Duffing constitutive relation, we obtain a nonlinear polarization equation propagates through the nonlinear layer under the slowly varying envelope approximation. With the application of boundary conditions at both interfaces, expressions for the incident, reflected, and transmitted intensities of the light wave are obtained as nonlinear functions of the polarization and other controlling parameters. For realistic input parameters, our numerical results demonstrated the existence of an intrinsic optical bistability (IOB) in a pure single dielectric layer. Furthermore, the threshold value of the observed IOB depends essentially on the value Eth, i.e., the minimum value required to invoke the third-order nonlinearity inside the material. For operating frequency near the sharp resonance region, Eth was found to be ≈105 V/cm; this is equivalent to a threshold value of the optical intensity ≈1010 W/cm2. With the developments in THz sources, it is nowadays possible to observe this IOB experimentally by tuning the operating frequency near the sharp resonance region of the material. Steps to get the threshold value of Eth are also advised.