Does the spectrum of two-beam interference also show an interference pattern?

Question

I know when you interfere two beams you get an interference pattern with a fringe pattern of λ/(2*sin(θ/2)) in physical space. It seems that there must also be modulation of the spectrum. Is this true, and if so, how do you calculate what it looks like?

As a follow-up if there is spectral interference fringes to observe, would the spectral modulation be observable at any location in the physical pattern, or would it present itself as a change in wavelength across the interference pattern? Practically, would you want to collect a large amount of the physically overlapped beam and send it through a spectrometer to observe the pattern in the spectrum, or perhaps a small probe that would scan across the pattern in physical space?

Thank you!

Answer 1

With monochromatic illumination of a double-slit interferometer, there is no spectral modulation. The resulting fringe pattern is monochromatic.

With white light illumination, the resulting fringe pattern is a superposition of monochromatic fringe patterns, each with fringe spacing that corresponds to its wavelength. So, the resulting fringe pattern has a mixture of wavelengths whose relative intensity varies along the pattern.