July 2003 Chuck DiMarzio, Northeastern University 11140b-06-1 ECEG105 Optics for Engineers Course Notes Part 6: Interference Prof. Charles A. DiMarzio.

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


Basic Equations of Interference

Re E

Im E


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


Mach Zehnder (2)

Straight-Line Layout: Transit Time

s BS1 BS2

s BS1 M2 BS2

M1

Diffuser


Mach Zehnder (3)


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


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.


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


Fabry-Perot Interferometer (1)I1 I4

Straight Line Model

Multiple Sources, with decreasing amplitudes (usually) and increasing distances (and

thus phases).


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


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


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


Interference Magnitudes


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


Amplitude Modulator

Fiber Splitters

E/O Modulator

Input Output

Unused Alt.Output


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


Thin Films: Fresnel Coefficients


Coherence Issues


Etalon Transmission

Only Coherent Sourcescontribute to the fringes

Re (1/ )

Im (1/)


Thin Film Matrices (1)


Thin Film Matrices (2)

M=M1M2M3M4

M1M4

November 2007


High Reflection Stack (1)

November 2007


High Reflection Stack (2)

Phase=0

Sign of Reflectivity is invertedon going from High to Low Index.

LH H L

November 2007


Anti-Reflection Coatings

nnQuarter-Wave Coating

Magnesium Flouride n=1.35is a close match, low cost and durable.

Phase=0

R

4%

Examples

Uncoated Glass

Violet Red

OneLayer

TwoLayers

ThreeLayers

July 2003 Chuck DiMarzio, Northeastern University 11140b-06-1 ECEG105 Optics for Engineers Course Notes Part 6: Interference Prof. Charles A. DiMarzio.

Documents

chuck dimarzio

s bs s m2 m1 bs slide

denominator slide

wave bump slide

power c c c cc m1 m2

optical testing bs m1

e im e slide

fabryperot interferometer