Multi-beam Interference Flashcards
What is a multi-beam interferometer
a spectroscopic device of extremely high resolving power, also serving as a basic laser resonator cavity
What are the priciple components of the Fabry-Perot Interferometer
two plane parallel, highly reflecting surfaces, separated by some distance d.
When the refractive index outside the fabry-perot slab is different from that inside what is the path difference
2nd cosπ, but due to one of the reflections happening at a denser medium, there is an additional pi phase change so overall pd between 2 rays is 2nd cosπ - Ξ»/2
(in words) what is the fraction of intensity reflected of a fabry perot interferometer
energy carried by reflected [transmitted] wave/energy carried by incident wave
How does a Fabry-Perot etalon work?
By constructive interference of radiation from multiple reflections between two exactly parallel surfaces with a gap between them. The plates are coated with a reflective inner surface.
Mechanically varying the gap by moving the mirrors makes it an interferometer
Describe the optical set up to observe interference from a Fabry-Perot Interferometer
- incident beam goes into the slab
- each ray, reflected or transmitted bears a fixed phase relationship to all the other rays
- phase differences arise from optical path length differences and phase shifts at certain reflections
- coherent waves are brought to a focus by lenses on either side of the slab where they interfere
For a Fabry-Perot interferometer what are the optical path length differences and phase differences between adjacent rays
Ξ = 2ππ cos π
πΏ = 2π (2ππ cos π)/π
What type of fringes does the Fabry-perot form
- fringes of equal inclination
- formed at infinity and observed using a converging lens
What function describes the ratio of transmitted intensity to the incident intensity
the Airy Function
What formula defines the contrast/coefficient of finesse
F = 4R/(1-R)^2
What is the condition for interference peaks?
mπ =2nd cosπ
Define the free spectral range
the frequency spacing between orders of the Fabry-Perot cavity
the repetition frequency of the spectrum
What is the formula for the FSR or the frequency spacing?
c/2nd
What is the Finesse of a cavity
the finesse of a cavity defines the fringe sharpness and depends on the reflectivity of the cavity mirrors
what is the formula for the finesse
pi*sqrt(F)/2
How is the FWHM bandwidth related to the finesse and what does this imply
it is inversely proportional
implies that high finesse = sharper fringes
How does multibeam compare to 2 beam interference
multibeam redistributes the energy density
How does multibeam interference allow us to see closely spaced wavelengths
high resolution can be achieved by adding together radiation from many coherent sources
sharper fringes give a higher resolution so we can see closely spaced wavelengths in the interference pattern
How can you achieve a higher resolution of the fabry perot
By operating at a higher order number at the expense of smaller fsr
what is the ultimate limit on finesse
the flatness of the mirrors
What is one of the main challenges of the F-P
it is very difficult to change mirror separation while maintaining parallelism of plates
What are the commercial uses of the F-P
- mode analysis of diode lasers
- optical cavities or resonators for lasers
Uses of thin dielectric film coatings
- elimination of unwanted reflections from glass surfaces
- multiplayer, nonabsorbing beamsplitters
Describe how antireflection coatings work
- using the boundary conditions at the interface, we can show that at very close to normal incidence, the reflectance formula simplifies for a particulat film thickness and refractive index relationship
How do interference filters work
- like a thin F-P etalon
- if plate separation in order of a wavelength, peaks are widely separated
- all but one peak can be blocked using an absorbing filter
- transmitted light corresponds to a single sharp peak
- etalon serves as a narrow band-pass filter
What are the conditions for interference to occur
- waves have the same wavelength and polarisation
If wavelengths and polarisations are the same, what is the irradiance of the interference of 2 waves
πΌ = πΌ1 + πΌ2 + ππRe{π¬π β π¬πβ }
If two waves combine but cannot interfere, what is the irradiance
I = I1 + I2
What are the Fresnel-Arago Laws for Interference of polarised light
- orthogonal coherent polarisation states cannot interfere
- parallel coherent polarisations will interfere like natural light
- 2 constituent orthogonal polarisation states of natural light cannot interfere to form a readily observable fringe pattern even if rotated into alignment because they are incoherent
