Lecture 33: Interference in Thin Films

Readings: Textbook pages 1218-1223

Thin refractive medium - "oil films"

Appearence of stable interference pattern rely on coherency of light, most importantly for us temporal coherency .
temporal coherency of EM wave is an ability to predict the value of E-field (at a given place) at time t + Δ t if we measured its value at time t
It is characterized by coherence time τ_c - time interval over which there is a correlation between the ampltiudes of the wave
Coherence time is related to the frequency spectrum of the light - more monochromatic the spectrum further we know the amplitude. Indeed, how long in time the light can be considered coherent is determined by how spread its frequency spectrum is τ_c ≈ 1/Δ f
Coherence is characterized by coherence length, where you multiple the coherence time by the speed of light. Coherence length depends on refractive index of the medium L_c = v τ_c
One can also calculate over how many wavelegths (or periods) the light is coherent. This does not depend ot refractive index. L_c / λ = v τ_c / λ ≈ f / Δ f

Strictly monochromatic light has exactly one frequency in its spectrum. The widths of the spectrum is zero Its coherence time is infinite - we know exactly value of the field at every time moments if we measured it once Lasers aim to be as monochromatic as possible, and thus to have very high coherence of light. But in practice it is limited by quantum processes.
In the opposite regime is the white noise - light where all frequencies are represented with the same power. White noise has width of frequency spectrum Hence it has vanishing temporal coherence
The light emitted by the Sun, light bulbs, etc. is said to be emitted by thermal source It has thermal spectrum described by Planck curve Thermal spectrum is very wide, but still have finite widths Hence there is some, albeit small, coherence in solar light, which make observations of interference possible. Coherence length of the Sun is few microns - just several (of order of 10) wavelengths. I.e after 10 or so periods of oscillations of solar light, we can't be certain what phase is.