Long-range surface plasmon polaritons (LRSPPs) are optical surface waves that
 propagate along a thin symmetric metal slab or stripe over an appreciable length
 (centimeters). Vigorous interest in LRSPPs has stimulated a large number of studies
 over three decades spanning a broad topical landscape. Naturally, a good segment of
 the literature covers fundamentals such as modal characteristics, excitation, and
 field enhancement. But a large portion also involves the LRSPP in diverse phenomena,
 including nonlinear interactions, molecular scattering, fluorescence,
 surface-enhanced Raman spectroscopy, transmission through opaque metal films and
 emission extraction, amplification and lasing, surface characterization, metal
 roughness and islandization, optical interconnects and integrated structures,
 gratings, thermo-, electro- and magneto-optics, and (bio)chemical sensing. Despite
 the breadth and depth of the research conducted to date, much remains to be
 uncovered, and the scope for future investigations is broad. We review the properties
 of the LRSPP, survey the literature involving this wave, and discuss the prospects
 for applications. Avenues for further work are suggested.

Long-range surface plasmon polaritons

The authors review progress in the application of nonlinear optical phenomena to integrated optics. Essentially all integrated optics devices such as directional couplers, Mach-Zehnder interferometers, prism couplers, etc., can be used for all-optical signal processing when at least one of the waveguiding media exhibits an intensity-dependent refractive index. Experimental and theoretical results on the operating characteristics and figures of merit of such devices, as well as a new class of phenomena based on large nonlinear changes in waveguide properties will be summarized. Also discussed are measurement techniques for evaluating waveguide nonlinearities. Progress in the implementation of other nonlinear third order interactions, such as degenerate four-wave mixing and nonlinear spectroscopy, will also be reviewed. >

Third order nonlinear integrated optics

Publisher Summary This chapter describes the nonlinear wave propagation in planar structures. The two categories of integrated all-optical devices can be anticipated on the basis of the nonlinear optical phenomena. The first class of optical devices is that in which the nonlinear change in the refractive index is small in comparison with the refractive index difference between the guiding media. The second category of nonlinear optical devices is that in which the optically induced change in refractive index is comparable with, or larger than, the index differences among the guiding media. The chapter discusses the study of electromagnetic waves guided by nonlinear interfaces. The basic concepts and method used to analyze nonlinear guided wave phenomena are also discussed. The nonlinear TE polarized waves guided by thin dielectric films are studied. The chapter explains that very thin metal films (nonlinear surface plasmon polaritons) can also guide nonlinear TE polarized waves. The experiments reported on nonlinear guided wave phenomena are reviewed in the chapter.

IV Nonlinear Wave Propagation in Planar Structures

We derive exact dispersion relations for transverse magnetic polarized guided waves at an interface between either a linear dielectric or a metal and a nonlinear dielectric. The nonlinearity is taken to be a Kerr-type nonlinearity. Numerical results are presented for the dielectric–metal case.

Exact dispersion relations for transverse magnetic polarized guided waves at a nonlinear interface.

We study nonlinear modes in a subwavelength slot waveguide created by a nonlinear dielectric slab sandwiched between two metals. We present the dispersion diagrams of the families of nonlinear guided modes and reveal that the symmetric mode undergoes the symmetry-breaking bifurcation and becomes primarily localized near one of the interfaces. We also find that the antisymmetric mode may split into two brunches giving birth to two families of nonlinear antisymmetric modes.

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Nonlinear plasmonic slot waveguides

Exact calculations are presented of the properties of nonlinear p-polarized waves propagating along the plane boundary between a nonabsorbing, optically self-focusing, nonlinear dielectric and a nonabsorbing positive, or negative, linear dielectric. A nonlinear polarization is used that arises from a number of causes for both Kerr-like and non-Kerr-like saturating media. In the results given here the linear dielectric is a metal, if negative, and is glass if positive. It is found that the variation of the power flow along the guiding surface with effective index, for negative linear dielectrics, will always exhibit a maximum. For data corresponding to copper bounded by, for instance, a self-focusing nonlinear semiconductor, access to this maximum involves such a large change in the refractive index of the nonlinear material, that it is of no practical interest. In the visible better matching of the metal to a nonlinear material can, in principle, be achieved so this maximum may be reached for fairly modest nonlinear changes in the refractive index. A detailed comparison is made with approximations that are based upon a curtailed form of nonlinearity. At low frequencies, for modest nonlinear changes in the refractive index, the dependence of the power flow curve upon the effective guide index is fairly close to several of the earlier published theories. These include a well-known approximation in which the transverse field component is assumed to be dominant. The neighborhood of the maximum, and beyond, becomes accessible at higher operating frequencies and significant differences from earlier approximations may then occur. For positive linear dielectrics the exact theory shows a strong similarity to many more approximate ones, as expected, but the difference between the TM and TE surface wave behavior cannot be discounted. We present several sample calculations of the power flow together with detailed plots of the field components, the magnitude of the nonlinearity, the effect of nonlinearity, and the behavior of the first integral.

Exact theory of nonlinear p-polarized optical waves.

A full theory of the interaction between nonlinear transverse-electric and transverse-magnetic waves is derived. A new form of third-order tensor that accounts for the presence of the two polarizations is described and a mathematical discussion of the first integral is presented. The theory is illustrated by a full set of numerical results both for single-interface and thin-film structures.

Transverse-electric and transverse-magnetic waves in nonlinear isotropic waveguides

The first reported calculations of the eigenstates of surface-guided nonlinear coupled electromagnetic TE–TM waves in Kerr-type nonlinear dielectrics are presented. It is shown that the stationary states exist between loci that define a pure nonlinear TE wave with a zero-amplitude TM wave and a pure nonlinear TM wave with a zero-amplitude TE wave. The relative TE/TM content of the waves is given, together with the field profiles of the waves, for a single interface between a nonlinear and a linear dielectric. For the metal film the coupling possibilities greatly increase, and these are discussed in detail with reference to the familiar long- and short-range plasmons.

T. Twardowski

Papers

Exact dispersion relations for transverse magnetic polarized guided waves at a nonlinear interface.

Exact theory of nonlinear p-polarized optical waves.

Transverse-electric and transverse-magnetic waves in nonlinear isotropic waveguides

Theory of nonlinear interaction between TE and TM waves

The effect of diffusion on surface-guided nonlinear TM waves: A finite element approach