Optics and Lasers Lecture 3

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Optics and Lasers - Lecture 3

• Optical Resonators storage of light

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Optical Rays
r1
r0
Optical Axis
z0
z1 
)
(
)
(
r0
r1
r1-r0
r1-r0
z1-z0
z1-z0
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How to model a resonator?
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Ray Matrix representation
)
(
)
ri
(
ro
ri
ro
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Consider instead a sequence of lenses ( a more
symmetric version of the cavity)
f1
f2
f2
f1
f2
f1/2
f1/2
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g-parameters definition
g1 1 - L/R1
g2 1 - L/R2
We will use to find families of like resonators
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Consider instead a sequence of lenses ( a more
symmetric version of the cavity)
f1
f2
f2
f1
f2
f1/2
f1/2
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(
)
(
)
(
)
2 g1g2 -1
ro
2 g2 L
ri


ro
ri
2 g1 g2 - 1

MTOT
For more than one pass (N passes)

(MTOT)N
What does it mean if ?
How do we find an MTOT and that make this
true?
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Solution must be bounded
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Normal Modes

(MTOT)N


lN
ri
l (2 g1g2-1) v4 g1g2 (g1g2-1)
Eigenvalues
If g1g2 is gt 1 or lt 0 then l is real (else l is
complex)
If 1gtg1g2 gt 0, then with remarkable insight you
might substitute
2 g1 g2 - 1 ? cos q
l cos q j sin q Expj q
and hence lN Expj q N
One can always choose N so that q N 2 p k, k ? ?
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Stable Cavities
Goto http//stwww.weizmann.ac.il/lasers/laserweb
See page 19, 20
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Charles Fabry (1867-1945) Alfred
Perot (1863-1925),
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FP Cavities
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An example Fabry-Pérot Etalon
Ai
B1
B2
B3
B4
q
q
A1
A2
A3
A4
Traditional Plane-parallel plate with reflecting
coatings Modern plane and curved surfaces facing
each other with adj. gap
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Partial waves
d 4 p n l cos q / l
Ai
B1
B2
B3
B4
q
r,t
q
l
r,t
A1
A2
A3
A4
t2Ai
t2r4e2jdAi
t2r2ejdAi
?Ak t2 (1r2ejd r4e2jd..) Ai
t2/(1-r2 ejd) Ai
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Power Transmitted
It/Ii At At
It (1-R)2
Ii
(1-R)2 4R sind/22
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Maxima in Transmission
when d 2 p m i.e. 4 p n l cosq/l 2 p m
nm m c
In frequency terms
2 n l Cosq
Free Spectral Range Or Fundamental mode
spacing Or longitudinal mode spacing Or axial
mode spacing
c
Dv nm1-nm
2 n l Cosq
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Power Transmitted
It/Ii At At
It (1-R)2
Ii
(1-R)2 4R sind/22
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Width of Resonance
when sin(d-2mp/2)2 (1-R)2/4R i.e. Dn1/2
c/(2 p n l cosq) (1-R)/vR Dn/(p)
(1-R)/vR
BW
Rewriting
Finesse
Dn
p vR
F

(1-R)
Dn1/2
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Finesse
FSR (Dn in Notes)
F
Dn1/2
FSR
BW
FREQUENCY
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Sams Cavity the spacer
Measuring the length of space
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The cavity assembled
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Measuring Sams Cavity
10cm long BW 80kHz FSR 1.5GHz Finesse
19, 000 R 99.984 He finds the centre to
10Hz or so
10-14 m equivalent measurement i.e. an atomic
nucleus
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FPs as Spectrum Analyzers the ultimate prisms
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Using a FP cavity to split up light
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FP Cavities
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FP 1
90
DnFSR
p vR
F

(1-R)
Dn1/2
90
DnFSR c/(2 L)
Dn1/2 DnFSR / F c/(2 L F)
99
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FP2
Too Long!
R90
R99
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FPs as OSAs
Choose the FP characteristics for an OSA on the
basis of the following
1. Make it short enough so that the OSA modes are
further apart than the total spectral width of
the incoming signal
2. Make the BW smaller than the smallest
feature of interest