1. More Interference Michelson Interferometer (cont'd) Unbalanced
Prof. Rick Trebino
Georgia Tech
Michelson Interferometer (cont'd)
Unbalanced
Other interferometers
Mach-Zehnder
Sagnac
Fizeau Wedge
Newton's Rings
The Fabry-Perot Interferometer
Anti-Reflection Coatings
Single- and Multi-layer
Photonic Crystals

2. The Unbalanced Michelson Interferometer
Misalign mirrors, so beams cross at an angle.
The Unbalanced Michelson Interferometer z x
Input
beam
Now, suppose an object is placed in one arm. Now, one beam will have an extra spatially varying phase, exp[2if(x,y)].
The cross term becomes:
Re{ exp[2if(x,y)] exp[-2ikx sinq] }
Mirror
Beam-
splitter
Fringes
exp[if(x,y)]
Place an
object in
this path
Mirror
Distorted fringes
(in position)
Iout(x) x

3. Spatial fringes distorted by a soldering iron tip in one path
The Unbalanced Michelson Interferometer can sensitively measure phase vs. position.
Placing an object in one arm of a misaligned Michelson interferometer will distort the spatial fringes.
Spatial fringes distorted by a soldering iron tip in one path
Beam-
splitter
Input
beam
Mirror
Fringes
Phase variations of a small fraction of a wavelength can be measured.

4. The Mach-Zehnder Interferometer
Beam-
splitter
Input
beam
Mirror
Output beam
Object
The Mach-Zehnder interferometer is usually operated misaligned and with something of interest in one arm.

5. Mach-Zehnder Interferogram
Nothing in either path
Plasma in one path

6. The Sagnac Interferometer
The two beams take the same path around the interferometer and the output light can either exit or return to the source.
Mirror
Not only do both beams take the same path through the device, they also pass through the same amount of glass in the beam splitter!
Beam-
splitter
Mirror
Input
beam
It turns out that no light exits! It all returns to the source!

7. Why all the light returns to the source in a Sagnac interferometer
Reflection off a front-surface mirror yields a phase shift of p (180 degrees).
Since the paths are the same, all that matters are the phase shifts on the reflections.
Mirror
For the exit beam:
Clockwise path has phase shifts of p, p, p, and 0.
Beam-
splitter
Input
beam
Return beam
Counterclockwise path has phase shifts of 0, p, p, and 0.
Perfect cancellation!!
Reflection off a back-surface mirror yields no phase shift.
Mirror
Reflective surface
Exit beam
For the return beam: Clockwise path has phase shifts of p, p, p, and 0. Counterclockwise path has phase shifts of 0, p, p, and p.
Constructive interference!

8. The Sagnac Interferometer senses rotation.
Suppose that the beam splitter moves by a distance, d, in the time, T, it takes light to circumnavigate the Sagnac interferometer.
So one beam will travel more (d), and the other less distance (-d).
If R = the interferometer radius,
and W = its angular velocity:
Thus, the Sagnac Interferometer's sensitivity to rotation depends on its area. And it need not be round!
Sagnac
Interfer-
ometer
(fiber) q R
q = WT d
d = Rq

9. Newton's Rings

10. You see the color l when constructive interference occurs.
Newton's Rings
Get constructive interference when an integral number of half wavelengths occurs between the two surfaces (that is, when an integral number of full wavelengths occur between the path of the transmitted beam and the twice reflected beam).
You see the color l when constructive interference occurs.
You only see bold colors when m = 1 (possibly 2). Otherwise the variation with l is too fast for the eye to resolve. L
This effect also causes the colors in bubbles and oil films on puddles.