Optical bistability in reflection from multilayer metal-dielectric structure with Kerr nonlinearity

Both static and dynamic characteristics of light reflected from a specially designed multilayer metal-dielectric structure with Kerr nonlinearity have been studied in this work. Various regimes of nonlinear reflection from the structure have been demonstrated, including bistable switching between low and high reflection states, which occurs at low intensity of the incident light due to a significant enhancement in the optical field in the nonlinear layer under conditions of total internal reflection. This nonlinear structure has been proposed to use as an optically controlled intracavity laser modulator.

The analytic structure of the BFKL equation and reflection identities of harmonic sums at weight five

We analyze the structure of the eigenvalue of the color-singlet Balitsky–Fadin–Kuraev–Lipatov (BFKL) equation in N[Formula: see text]=[Formula: see text]4 SYM in terms of the meromorphic functions obtained by the analytic continuation of harmonic sums from positive even integer values of the argument to the complex plane. The meromorphic functions we discuss have pole singularities at negative integers and take finite values at all other points. We derive the reflection identities for harmonic sums at weight five decomposing a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a pole at either negative or non-negative values of the argument. The pole decomposition demonstrates how the product of two simpler harmonic sums can build more complicated harmonic sums at higher weight. We list a minimal irreducible set of bilinear reflection identities at weight five which presents the main result of the paper. We show how the reflection identities can be used to restore the functional form of the next-to-leading eigenvalue of the color-singlet BFKL equation in N[Formula: see text]=4[Formula: see text]SYM, i.e. we argue that it is possible to restore the full functional form on the entire complex plane provided one has information how the function looks like on just two lines on the complex plane. Finally we discuss how nonlinear reflection identities can be constructed from our result with the use of well known quasi-shuffle relations for harmonic sums.