Sum-frequency generation at interfaces: A Fresnel story. II. Analytical expressions for multilayer systems

Area of Science:

• Nonlinear Optics
• Spectroscopy
• Materials Science

Background:

• Sum-Frequency Generation (SFG) spectroscopy is a powerful surface-sensitive technique.
• Existing SFG formalism is limited to three-layer systems.
• Analyzing complex multilayered systems requires a more generalized approach.

Purpose of the Study:

• To generalize the Sum-Frequency Generation (SFG) formalism for multilayered systems.
• To develop universal Fresnel factors applicable to N-layer systems.
• To simplify the analysis of light propagation and interference in complex SFG experiments.

Main Methods:

• Generalization of the existing three-layer SFG formalism to an N-layer system.
• Development of universal Fresnel factors that account for all optical complexities.
• Derivation of explicit equations for four- and five-layer systems.
• Simulations to validate the generalized formalism against the transfer matrix method.

Main Results:

• A generalized SFG formalism for N-layer systems is presented, with only Fresnel factors modified.
• Universal Fresnel factors analytically describe light propagation and interference in any layer.
• The method simplifies analysis and reduces computational cost compared to transfer matrix methods.
• Demonstrated ability to selectively probe buried interfaces by canceling SFG signals from outer layers.

Conclusions:

• The generalized N-layer formalism provides a more versatile tool for SFG spectroscopy.
• The universal Fresnel factors offer a simplified yet comprehensive approach to optical analysis.
• This work enables advanced studies of complex interfaces and multilayered materials using SFG.