Multi-beam Interference

Question 1

What is a multi-beam interferometer

Answer 1

a spectroscopic device of extremely high resolving power, also serving as a basic laser resonator cavity

Question 2

What are the priciple components of the Fabry-Perot Interferometer

Answer 2

two plane parallel, highly reflecting surfaces, separated by some distance d.

Question 3

When the refractive index outside the fabry-perot slab is different from that inside what is the path difference

Answer 3

2nd cos𝜃, 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 cos𝜃 - λ/2

Question 4

(in words) what is the fraction of intensity reflected of a fabry perot interferometer

Answer 4

energy carried by reflected [transmitted] wave/energy carried by incident wave

Question 5

How does a Fabry-Perot etalon work?

Answer 5

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

Question 6

Describe the optical set up to observe interference from a Fabry-Perot Interferometer

Answer 6

• 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

Question 7

For a Fabry-Perot interferometer what are the optical path length differences and phase differences between adjacent rays

Answer 7

Λ = 2𝑛𝑑 cos 𝜃
𝛿 = 2𝜋 (2𝑛𝑑 cos 𝜃)/𝜆

Question 8

What type of fringes does the Fabry-perot form

Answer 8

• fringes of equal inclination
• formed at infinity and observed using a converging lens

Question 9

What function describes the ratio of transmitted intensity to the incident intensity

Answer 9

the Airy Function

Question 10

What formula defines the contrast/coefficient of finesse

Answer 10

F = 4R/(1-R)^2

Question 11

What is the condition for interference peaks?

Answer 11

m𝜆 =2nd cos𝜃

Question 12

Define the free spectral range

Answer 12

the frequency spacing between orders of the Fabry-Perot cavity
the repetition frequency of the spectrum

Question 13

What is the formula for the FSR or the frequency spacing?

Answer 13

c/2nd

Question 14

What is the Finesse of a cavity

Answer 14

the finesse of a cavity defines the fringe sharpness and depends on the reflectivity of the cavity mirrors

Question 15

what is the formula for the finesse

Answer 15

pi*sqrt(F)/2

Question 16

How is the FWHM bandwidth related to the finesse and what does this imply

Answer 16

it is inversely proportional
implies that high finesse = sharper fringes

Question 17

How does multibeam compare to 2 beam interference

Answer 17

multibeam redistributes the energy density

Question 18

How does multibeam interference allow us to see closely spaced wavelengths

Answer 18

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

Question 19

How can you achieve a higher resolution of the fabry perot

Answer 19

By operating at a higher order number at the expense of smaller fsr

Question 20

what is the ultimate limit on finesse

Answer 20

the flatness of the mirrors

Question 21

What is one of the main challenges of the F-P

Answer 21

it is very difficult to change mirror separation while maintaining parallelism of plates

Question 22

What are the commercial uses of the F-P

Answer 22

• mode analysis of diode lasers
• optical cavities or resonators for lasers

Question 23

Uses of thin dielectric film coatings

Answer 23

• elimination of unwanted reflections from glass surfaces
• multiplayer, nonabsorbing beamsplitters

Question 24

Describe how antireflection coatings work

Answer 24

• 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

Question 25

How do interference filters work

Answer 25

• 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

Question 26

What are the conditions for interference to occur

Answer 26

• waves have the same wavelength and polarisation

Question 27

If wavelengths and polarisations are the same, what is the irradiance of the interference of 2 waves

Answer 27

𝐼 = 𝐼1 + 𝐼2 + 𝑐𝜖Re{𝑬𝟏 ∙ 𝑬𝟐∗ }

Question 28

If two waves combine but cannot interfere, what is the irradiance

Answer 28

I = I1 + I2

Question 29

What are the Fresnel-Arago Laws for Interference of polarised light

Answer 29

• 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