Matrix formalism for radiating polarization sheets in multilayer structures of arbitrary composition

Abstract

In optical studies on layered structures, quantitative analysis of radiating interfaces is often challenging due to multiple interferences. We present here a general and analytical method for computing the radiation from two-dimensional polarization sheets in multilayer structures of arbitrary compositions. It is based on the standard characteristic matrix formalism of thin films, and incorporates boundary conditions of interfacial polarization sheets. We use the method to evaluate the second harmonic generation from a nonlinear thin film, and the sum-frequency generation from a water/oxide interface, showing that the signal of interest can be strongly enhanced with optimal structural parameters.

Unveiling the structural evolution of oxide surface in liquid water

“…We studied the silicon (Si) /silica/water layer structure, with the near-infrared at 800 nm and broadband infrared centered at 1000 cm − 1 to match the Si-O stretch range. Using the nonlinear optical matrix formalism to calculate the eld distributions across the layer structure 34,36 , we found that despite the strong infrared attenuation in silica, the total SF response from the silica/water interface could be drastically enhanced if the silica lm thickness was near 150 nm (Fig. 1b).…”

“…1b). Meanwhile, the response from the silicon/silica interface remained low, ensuring the SF output to be dominantly from the silica/water interface 34,35 (see Supplementary Section 1.2). We prepared the 150 nm amorphous silica lm on an n-type Si wafer by plasma-enhanced chemical vapor deposition (see Methods).…”

“…Here we report an experimental scheme that can change the scene: a scheme that allows in situ SFVS of oxide surface lattices in liquid water. Using a high refractive index infrared wafer/oxide/water layer structure -a planar cavity -with appropriate oxide lm thickness and excitation geometry, we can speci cally optimize the local optical elds at the oxide/water interface, so that the SF signal from the interface is dominant and readily detectable 34 . The experimental arrangement of our broadband SFVS measurements is sketched in Fig.…”