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Journal of the Optical Society of America B

Optical bistability with surface plasmons beyond plane waves in a nonlinear dielectric

Subhasish Dutta Gupta, G. S. Agarwal

Published Feb 1, 1986• 31 citations
Publisher

Abstract

Optical bistability with surface plasmons is studied assuming nonlinear polaritons in a Kerr medium. Significant departures from the plane-wave results for the switching intensities and hysteresis curves are predicted.
DOI
10.1364/josab.3.000236

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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.
Optical bistability based on surface plasmon polaritons in the Kretschmann configuration involving a Kerr nonlinear medium is described by analytical solutions. The conditions of forming the optical bistability with different parameters are explored. The resonant angle of surface plasmon polaritons varying with the incident light intensity also generates the phenomenon of bistability. The system could form optical bistability with the special thickness of the metal film and incident angle. This kind of system has potential application in all-optical networks.
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.
We have theoretically analysed the optical bistability due to the excitation of surface plasmon polaritons (SP's) in samples, prism/metal film/nonlinear optic medium and prism/gap material/metal film/non-linear optic medium, where the non-linear optic medium has an intensity-dependent refractive index. We considered two cases, i.e. non-linearity along the propagation direction of SP's and along the normal to the interface. In the former case, the critical input power for the optical bistability was too high to allow experimental observation, while it was reasonably low for the latter case.