In the linear regime, electromagnetic waves at different frequencies do not directly interfere with each other. Interference typically refers to the phenomenon where two or more waves combine and produce a resulting wave that has regions of constructive and destructive interference.
In the linear regime, the electric field of an electromagnetic wave is typically much weaker compared to the interatomic electric field within a material. Under these conditions, the response of the material to the electromagnetic wave is considered linear, meaning that the polarization of the material is directly proportional to the applied electric field.
Since the electric field of an electromagnetic wave is negligible compared to the interatomic field, the interaction between waves of different frequencies will primarily occur through their independent interactions with the material. Each frequency component will induce its own polarization in the material based on its specific characteristics, without directly influencing the other frequencies.
However, it's important to note that if the waves are non-linear in nature or interact with a non-linear medium, higher-order effects such as harmonic generation or mixing may occur, leading to interactions between different frequencies. Additionally, when waves of different frequencies propagate through a medium, dispersion effects can cause frequency-dependent phase shifts that can indirectly affect their interaction.