Retrieval of all effective susceptibilities in nonlinear metamaterials

Electromagnetic metamaterials can be designed so their structure controls both linear and nonlinear electromagnetic behavior. The paper notes that nonlinear properties are usually anisotropic and that existing ways to extract (retrieve) nonlinear material parameters have limitations. The authors generalize a nonlinear transfer-matrix approach to include all nonlinear susceptibility terms. This lets them retrieve the full set of effective nonlinear susceptibilities for metamaterial elements rather than only partial information. They demonstrate the method using sum frequency generation, and state that the same approach can be used for other second-order or higher-order nonlinear processes.