Fig. 1. (a) Electric (E) and magnetic (H) fields due to a radiating polarization sheet PS(ω) at the boundary I on top of a thin film of thickness d2. kR and kT are beam wave vectors along the reflected and transmitted directions. Inset: Schematics of a typical experimental setup. (b), (c) Two-layer systems with PS(ω) at different boundaries. (d) An N-layer system with PS(ω) at the ith boundary between the ith and (i+1)th media. (e) An N-layer system with multiple interfacial polarization sheets.

Fig. 2. (a) Schematics of SHG from a nonlinear thin film on a substrate. (b) The calculated ratio between the SH signal from the thin film and that from a bulk nonlinear crystal versus the film thickness, detected along the reflected (solid line) or transmitted directions (dashed curve). The incident beam is centered at 800 nm with a bandwidth of 60 nm. All beams are TE waves.

Fig. 3. (Color online) (a) Schematic of SFG from substrate/SiO2/water system. (b), (c) The calculated ratio between the SF signals from the thin film SiO2/H2O interface to that from a bulk SiO2/H2O interface, versus the SiO2 film thickness (solid lines). The signal ratio from the substrate/SiO2 interface is shown for comparison (dashed lines, magnified for clarity). The substrate material is assumed to be (b) silicon or (c) cubic zirconia. The infrared wavenumber is at 3300cm−1. (d) The spectral dependence of SF signals from a 140 nm thick SiO2/H2O interface, deposited on silicon (black) or cubic zirconia (red). The inset shows that from the substrate/SiO2 interfaces.