# Can electromagnetic fields change the frequency of light?

Since light is an electromagnetic wave, can external EM fields change its frequency (through interference perhaps)?

• What do you mean, saying "external"? EM fields in media can change its frequency, if the field intensities are large. Processes of harmonics generation (e.g. you illuminate media with a red laser and get a green beam), and wave mixing are examples of a frequency change. Commented Feb 12, 2020 at 17:06

No this cannot happen. The Maxwell equations are linear in the fields.

• Maxwells equations are linear for the microscopic fields but for macroscopic materials they also need constitutive relations and those can be nonlinear, see any semiconductor junction or ferro/para magnetic materials near saturation. Commented Feb 12, 2020 at 0:10
• @hyportnex I do not read this as a question about devices. Commented Feb 12, 2020 at 6:09
• @hyportnex: If the Maxwell equations are linear than why there is Nonlinear Optics? Electric or magnetic susceptibilities can depend on fields that results in nonlinear dynamics. Commented Feb 12, 2020 at 17:01
• @user2320292 as I wrote above Maxwell's differential equations are linear but the so-called constitutive equations of D = D(E,H) connecting D with E and H, and B= B(E,H) connecting B with E and H can be non-linear. I do not understand your comment as it appears to me that you are saying that the susceptibility of D can be a non-linear function of E, indeed, this is what a constitutive relation is. Commented Feb 12, 2020 at 17:38
• @hyportnex: I think, it is better to consider the Maxwell equations as a set of differential equations (PDEs) and the constitutive equations (CEs), in a sense that one cannot solve PDEs without CEs. In this sense, the MEs are nonlinear, since the CEs are nonlinear, in general. Because of nonlinearity, the field frequency can change. Commented Feb 13, 2020 at 9:01

To answer at the quantum mechanical level, two photon interactions have very low probability, particularly at the low photon energy of visible light. That is why two light beams go through each other without interacting . ( they can show interference patterns, but energies/frequencies do not change).

Static fields are modeled with virtual photons , so the behavior is the same for interactions with real photons which constitute a beam of light: the probability of interaction if calculated will be very small.

Since light is an electromagnetic wave, can external EM fields change its frequency (through interference perhaps)?

Interference is not interaction, it is the superposition of the wavefunctions of the photons that shows the interference in the video linked above. To change the frequency one needs to increase of decrease the energy of the photons, which has very low probability at light frequencies ( at gamma ray frequencies the probabilities are much larger)