Fermi Resonance Nonlinear Waves and Solitons in Organic Superlattices

Abstract

Fermi resonance is a phenomenon which takes place in vibrational or electronic spectra of molecules. For example, let a molecule have two vibrational modes with frequencies ω_a and ω_b. If the second order resonance condition 2ω _α ≃ ω _b is fulfilled, then the ħω_b, transition in infrared spectrum can be split into two lines of comparable intensity and the second line cannot be explained as a result of interaction of light with the vibrational a mode because the transitions with excitation of two ħω _a quanta are forbidden due to well-known n→n±1 selection rule for harmonic oscillator. E. Fermi explained [1]–[2] this experimental observation as a result of nonlinear resonance interaction of two vibrational modes with each other. Since that time the notion of Fermi resonance has been generalized to the processes with participation of different types of quanta (e.g., ω₁+ω₂≃ω₃, ω₁+ω₂≃ω₃−ω₄, and so on) and to electronic types of excitations as well. Further generalizations were suggested for Fermi resonance interactions of collective modes in molecular crystals and other macroscopic systems, so that Fermi resonance phenomenon became a part of not only molecular physics but solid state physics also (see, e.g., review articles [3]–[5]). Recent progress in molecular beam deposition method permitted one to obtain molecular multilayer structures [6] analogous to inorganic superlattice and quantum well structures.