Based on the transfer matrix method, the recursion of an electromagnetic wave propagating in an asymmetric Kerr nonlinear medium is analytically formulated, from which the rectification effect is clearly presented. The effects on the rectification region of the linear part and nonlinear coefficient of permittivity are both studied, and the energy densities before and after rectification are discussed. We use a rectifying factor to describe the intensity of the rectification effect.The result shows that every transmission peak is divided into two parts when the symmetry is broken, and nonlinear asymmetry has a more significant effect on the rectification effect than the linear asymmetry. The rectification intensity and area will be enlarged when the asymmetry factor is increased in a certain range.
With the Coulomb gauge, the Chern-Simons-Georgi-Glashow (CSGG) model is quantized in the Dirac formalism for the constrained system. Combining the Gauss law and Coulomb gauge consistency condition, the difference between the Schwinger angular momentum and canonical angular momentum of the system is found to be an anomalous spin. The reason for this result lies in the fact that the Schwinger energy momentum tensor and the canonical one have different symmetry properties in the presence of the Chern-Simons term.
