Basic Theory of Surface Sum-Frequency Generation

A detailed description on the basic theory of optical sum-frequency generation from an interfacial system is presented. Both the interface and the bulk generally contribute to the sum-frequency output. Two seemingly different approaches to specify bulk nonlinearity that includes electric-quadrupole and magnetic-dipole contributions are shown to yield the same sum-frequency output if surface nonlinearity is properly taken into account. The question of whether surface and bulk nonlinearities can be uniquely defined and separately measured is discussed. It is shown that the answer is affirmative. Truly bulk and truly surface nonlinear susceptibilities can be uniquely defined and separately deduced from measurements of transmitted and reflected sum-frequency generation.