july 2003 chuck dimarzio, northeastern university 11140b-06-1 eceg105 optics for engineers course...
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July 2003 Chuck DiMarzio, Northeastern University 11140b-06-1
ECEG105Optics for Engineers
Course NotesPart 6: Interference
Prof. Charles A. DiMarzio
Northeastern University
Fall 2007
August 2007
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-2
Basic Equations of Interference
Re E
Im E
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-3
Mach Zehnder (1)
Gas Cell n>1
Example
Straight-Line Layouts:
Source, s
M1
M2BS1
BS2
s BS1 BS2
s BS1 M2 BS2
s BS1 M1 BS2
s BS1 M2 BS2
Geometric
M1 Transit Time
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-4
Mach Zehnder (2)
Straight-Line Layout: Transit Time
s BS1 BS2
s BS1 M2 BS2
M1
Diffuser
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-6
Michaelson Interferometer
Front =50% R?
Rear=AR
BS
M1
M2
Straight-Line Layout: Transit Time
s BS
s BS M2
M1 BS
BS
Geometric Optics
Via M2 with Three Passes Through Beamsplitter and M1 with only one
s BS
s BS M2
M1 BS
BS
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-7
Interferometry: Conflicting Goals
• Match Optical Path Lengths (Transit Time)– Pulses must arrive simultaneously for interference, or
– Paths must be within coherence length of the source (more on this later in the course)
• Match Wavefront Curvature (geom. opt.)– Fringes must be few enough to be within resolution of
instrumentation
• Thus we can’t compensate for extra glass with extra path length.
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-8
Compensator Plate
BS
s BS
s BS M2
M1 BS
BS
s BS
s BS M2
M1 BS
BS
Goal: Match Paths in Transit Time and Wavefront Curvature
t
sourcePower received
PowerC
C C
CC
M1
M2
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-9-50 0 50
-50
0
50 0
0.5
1
1.5
2
Optical Testing
BS
M1, Known Reference
-50 0 50
-50
0
50 0
0.5
1
1.5
2
-50 0 50
-50
0
50 0
0.5
1
1.5
-50 0 50
-50
0
50 0
0.5
1
1.5
2
M2,Mirror Under Test
Spheres 4-wave difference Same with 2-wave bump
Flats with 8-wave tilt Same with 2-wave bump
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-10
Fabry-Perot Interferometer (1)I1 I4
Straight Line Model
Multiple Sources, with decreasing amplitudes (usually) and increasing distances (and
thus phases).
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-11
Fabry-Perot: Transmission Peaks
460 470 480 490 5000
0.05
0.1
0.15
0.2
0.25
f, Freq., THz
T, T
ran
smis
sion
600nm650nm
10m
FSR
August 2007
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-12
Fabry-Perot: Resolution
460 470 480 490 5000
0.05
0.1
0.15
0.2
0.25
f, Freq., THz
T, T
ran
smis
sion
600nm650nm
10m
f
FSR
August 2007
Max
1
1
2
0.7 Max
GraphicalAnalysisof I
4/I
1
Denominator
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-13
Fabry-Perot: Extinction
460 470 480 490 5000
0.05
0.1
0.15
0.2
0.25
f, Freq., THz
T, T
ran
smis
sion
August 2007
600nm650nm
10m
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-15
Coherent Detection
0 20 40 60 80 1000
2000
4000
6000
8000
10000
Psig
Signal4kTB
QuantumNoise
0 20 40 60 80 1000
1
2
3
4
5
6x 10
4
Psig
Dotted Lines:Higher LO
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-16
Amplitude Modulator
Fiber Splitters
E/O Modulator
Input Output
Unused Alt.Output
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-17
Thin Films: Three Approaches
Sum the multiple Reflections
EAEB EC ED
Use Wave Equationand BoundaryConditions
E1
Network Approachwith Fresnel Coefficients
E2 E3 E4
E’1 E’2 E’3 E’4
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-20
Etalon Transmission
Only Coherent Sourcescontribute to the fringes
Re (1/ )
Im (1/)
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-22
Thin Film Matrices (2)
M=M1M2M3M4
M1M4
November 2007
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-23
High Reflection Stack (1)
November 2007
July 2003 Chuck DiMarzio, Northeastern University 11140b-06-24
High Reflection Stack (2)
Phase=0
Sign of Reflectivity is invertedon going from High to Low Index.
LH H L
November 2007