The natural oscillation frequency of the photon is equal to the difference in the natural frequencies of the states. The energy and osciallation frequency are related by Planck's constant, that is , where is the photon energy, is the radial frequency and is Planck's constant. Temporal frequency is a natural and fundamental aspect of the electromagnetic field. As discussed in lecture 6, different colors correspond to different temporal frequencies in the field. Objects are different colors because they are formed of materials with different quantum resonance frequencies.
Excited gases tend emit narrow spectral ranges associated with their fundamental resonances.
Spectral ranges emitted by solids tend to be more complex because quantum states broaden in dense arrays of coupled atoms. Since photons are emitted at specific frequencies rather than as arbitrary temporal functions, it is extremely difficult to precisely control the temporal structure of the optical field. This is in sharp contrast to the radio field, which can be determined exactly as a function of time by appropriately modulating the emitting antenna. We will return to these implications a number of times in the course, particularly when discussion detection of the field and optical coherence. For now our goal is simply to motivate our decision to analyze the field in Fourier space.