This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Goal: Goal: to measure the specimen’s absorption as function offrequency ω
electro-optic(EO) modulator
(controls refr.index n)
MIT 2.71/2.710 Optics10/24/05 wk8-a-14
Spectroscopy using Fabry-Perot cavity
ω
I(ω)
unknownspectrum
Fabry–Perottransmissivity
ω1sample measured:
I(ω1)
8
MIT 2.71/2.710 Optics10/24/05 wk8-a-15
Spectroscopy using Fabry-Perot cavity
ω
I(ω)
unknownspectrum
Fabry–Perottransmissivity
ω2sample measured:
I(ω2)
MIT 2.71/2.710 Optics10/24/05 wk8-a-16
Spectroscopy using Fabry-Perot cavity
ω
I(ω)
unknownspectrum
Fabry–Perottransmissivity
ω3sample measured:
I(ω3)
9
MIT 2.71/2.710 Optics10/24/05 wk8-a-17
Spectroscopy using Fabry-Perot cavity
ω
I(ω)
unknownspectrum
Fabry–Perottransmissivity
ω3sample measured:
I(ω3)
unknown spectrumwidth should not exceed the FSR
MIT 2.71/2.710 Optics10/24/05 wk8-a-18
Spectroscopy using Fabry-Perot cavity
ω
I(ω)
unknownspectrum
Fabry–Perottransmissivity
ω3sample measured:
I(ω3)
spectral resolutionspectral resolutionis determined by thecavity bandwidth
10
MIT 2.71/2.710 Optics10/24/05 wk8-a-19
Lasers
MIT 2.71/2.710 Optics10/24/05 wk8-a-20
Absorption spectra
λ (µm)
Atm
osph
eric
tran
smis
sion
human vision
11
MIT 2.71/2.710 Optics10/24/05 wk8-a-21
Semi-classical view of atom excitationsEnergy
Energy
Atom in ground stateAtom in ground state
Atom in excited stateAtom in excited state
Ze+e-
MIT 2.71/2.710 Optics10/24/05 wk8-a-22
Light generation
ground state
excited state
equilibrium: most atomsin ground state
Energy
12
MIT 2.71/2.710 Optics10/24/05 wk8-a-23
Light generation
ground state
excited state
A pump mechanism (e.g. thermal excitation or gas discharge) ejects some atoms to the excited state
Energy
MIT 2.71/2.710 Optics10/24/05 wk8-a-24
Light generation
ground state
excited state
The excited atoms radiativelydecay, emitting one photon each
Energy
hν
hν
13
MIT 2.71/2.710 Optics10/24/05 wk8-a-25
Light amplification: 3-level system
ground stateequilibrium: most atomsin ground state; note the existenceof a third, “super-excited” state
Energy super-excited state
excited state
MIT 2.71/2.710 Optics10/24/05 wk8-a-26
Light amplification: 3-level system
ground stateUtilizing the super-excited stateas a short-lived “pivot point,” thepump creates a population inversion
Energy super-excited state
excited state
14
MIT 2.71/2.710 Optics10/24/05 wk8-a-27
Light amplification: 3-level system
ground stateWhen a photon enters, ...
Energy super-excited state
excited state
hν
MIT 2.71/2.710 Optics10/24/05 wk8-a-28
Light amplification: 3-level system
ground state
Energy super-excited state
excited state
hν
When a photon enters, it “knocks” an electron from the inverted population down to the ground state, thus creatinga new photon. This amplification process is called stimulated emission
hν
hν
15
MIT 2.71/2.710 Optics10/24/05 wk8-a-29
Light amplifier
Gain medium(e.g. 3-level system
w population inversion)
Pin
Pout =gPin
MIT 2.71/2.710 Optics10/24/05 wk8-a-30
Light amplifier w positive feedback
Gain medium(e.g. 3-level system
w population inversion)
Pin
Pout =gPin
gΣ+
+
When the gain exceeds the roundtrip losses, the system goes into oscillation
Typical sources: • Argon-ion: 488nm (blue) or 514nm (green); power ~1-20W• Helium-Neon (HeNe): 633nm (red), also in green and yellow; ~1-100mW• doubled Nd:YaG: 532nm (green); ~1-10W
Quality of sinusoid maintained over a time duration known as“coherence time” tc
Typical coherence times ~20nsec (HeNe), ~10µsec (doubled Nd:YAG)
21
MIT 2.71/2.710 Optics10/24/05 wk8-a-41
Two types of incoherence
d1 d2
Michelson interferometer Young interferometer
1r1r
2r
spatialspatialincoherenceincoherence
temporaltemporalincoherenceincoherence
pointsource
matchedpaths
poly-chromatic light(=multi-color, broadband)
mono-chromatic light(= single color, narrowband)
MIT 2.71/2.710 Optics10/24/05 wk8-a-42
Two types of incoherence
d1 d2
1r1r
2r
spatialspatialincoherenceincoherence
temporaltemporalincoherenceincoherence
pointsource
matchedpaths
waves from unequal pathswaves from unequal pathsdo not interferedo not interfere
waves with equal pathswaves with equal pathsbut from different pointsbut from different points
on the wavefronton the wavefrontdo not interferedo not interfere
22
MIT 2.71/2.710 Optics10/24/05 wk8-a-43
Coherent vs incoherent beamsMutually coherent: superposition field amplitudeamplitudeis described by sum of complex amplitudessum of complex amplitudes
1e11φiaa =
2e22φiaa =
221
2
212121 ee
aaaI
aaaaa ii
+==
+=+= φφ
Mutually incoherent: superposition field intensityintensityis described by sum of intensitiessum of intensities1I
21 III +=
2I (the phases of the individual beams vary randomly with respect to each other; hence,we would need statistical formulation todescribe them properly — statistical optics)
MIT 2.71/2.710 Optics10/24/05 wk8-a-44
Coherence time and coherence length
incominglaserbeam
l1
l2
Michelson interferometer
Intensity
l1
• l1-l2 much shortershorter than “coherence length” ctc
sharp interference fringes
Intensity
l1
• l1-l2 much longerlonger than “coherence length” ctc
no interference
0
2I0
I0
23
MIT 2.71/2.710 Optics10/24/05 wk8-a-45
Coherent vs incoherent beamsCoherent: superposition field amplitudeamplitudeis described by sum of complex amplitudessum of complex amplitudes
1e11φiaa =
2e22φiaa =
221
2
212121 ee
aaaI
aaaaa ii
+==
+=+= φφ
Incoherent: superposition field intensityintensityis described by sum of intensitiessum of intensities1I
21 III +=
2I (the phases of the individual beams vary randomly with respect to each other; hence,we would need statistical formulation todescribe them properly — statistical optics)
can be doubled to visible wavelengthsor split to visible + mid IR wavelengths using OPOs or OPAs(OPO=optical parametric oscillator;OPA=optical parametric amplifier)
Typical pulse durations: ~psec to few fsec(just a few optical cycles)
Typical pulse repetition rates (“rep rates”): 80-100MHzTypical average power: 1-2W; peak power ~MW-GW