We show numerically and analytically that an optical pulse that crosses over a temporal boundary in a dispersive medium acts as a temporal analog of the spatial reflection and refraction at a dielectric interface.
We develop an analytic approach for reflection of light at a temporal boundary inside a dispersive medium and derive frequency-dependent expressions for the reflection and transmission coefficients. Using the analytic results, we study the temporal reflection of an optical pulse and show that our results agree fully with a numerical approach used earlier. Our approach provides approximate analytic expressions for the electric fields of the reflected and transmitted pulses. Whereas the width of the transmitted pulse is modified, the reflected pulse is a mirrored version of the incident pulse. When a part of the incident spectrum lies in the region of total internal reflection, both the reflected and transmitted pulses are distorted considerably.
Energy rays ('photon trajectories') based upon the hydrodynamic formulation of electrodynamics are presented for time-dependent electromagnetic wave propagation. We derive Cauchy's equation of motion for the electromagnetic effective force governing the dynamics of energy rays. The effective force generated by the electromagnetic effective stress provides a surface force acting on the energy fluid element. For the head-on collision of two electromagnetic Gaussian pulses, the electromagnetic effective force, analogous to the role played by the quantum force in Bohmian mechanics, guides these non-crossing energy rays. For an electromagnetic pulse traveling from free space to a dielectric medium, the energy rays guided by the electromagnetic effective stress display reflection and refraction at the interface.