MIT 2.712.710 Optics

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Todays summary
Multiple beam interferometers Fabry-Perot
resonators Stokes relationships
Transmission and reflection coefficients for a
dielectric slab Optical resonance
Principles of lasers Coherence spatial /
temporal
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Fabry-Perot interferometers
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Relation between r, rand t, t
air
glass
air
glass
Proof algebraic from the Fresnel coefficients or
using the property of preservation of the field
properties upon time reversal
Stokes relationships
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Proof using time reversal
air
glass
air
glass
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Fabry-Perot interferometers
reflected
transmitted
incident
Resonance condition reflected wave 0
? all reflected waves interfere destructively
wavelength in free space
refractive index
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Calculation of the reflected wave
incoming
transmitted
transmitted
reflected
reflected
transmitted
reflected
transmitted
reflected
transmitted
reflected
air
glass
air
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Calculation of the reflected wave
Use Stokes relationships
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Transmission reflection coefficients
reflection
coefficient
transmission
coefficient
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Transmission reflection vs path
Transmission
Reflection
Path delay
Path delay
Reflection
Transmission
Path delay
Path delay
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Fabry-Perot terminology
free Spectral range
band width
Transmission coefficient
resonance frequencies
Frequency v
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Fabry-Perot terminology
FWHM Bandwidth is inversely proportional to the
finesse F (or quality factor) of the cavity
Transmission coefficient
free spectral range
bandwidth
finesse
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Spectroscopy using Fabry-Perot cavity
Goal to measure the specimens absorption as
function of frequency ?
Experimental measurement principle
Scanning stage
(controls cavity length L )
Spectrum of light beam is modified by substance
Light beam of known spectrum
Power meter
Transparent windows
Container with specimen to be measured
Partially-reflecting mirrors (FP cavity)
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Spectroscopy using Fabry-Perot cavity
Goal to measure the specimens absorption as
function of frequency ?
Experimental measurement principle
Spectrum of light beam is modified by substance
Electro-optic (EO) modulator
(controls refr. Index n)
Light beam of known spectrum
Power meter
Transparent windows
Container with specimen to be measured
Partially-reflecting mirrors (FP cavity)
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Spectroscopy using Fabry-Perot cavity
FabryPerot transmissivity
Unknown spectrum
Sample measured
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Spectroscopy using Fabry-Perot cavity
aaaFabryPerot transmissivity
Unknown spectrum
Sample measured
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Spectroscopy using Fabry-Perot cavity
aaaFabryPerot transmissivity
Unknown spectrum
Sample measured
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Spectroscopy using Fabry-Perot cavity
unknown spectrum width should not exceed the FSR
aaaFabryPerot transmissivity
Unknown spectrum
Sample measured
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Spectroscopy using Fabry-Perot cavity
aaaFabryPerot transmissivity
spectral resolution is determined by the cavity
bandwidth
Unknown spectrum
Sample measured
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Lasers
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Absorption spectra
Atmospheric transmission
human vision
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Semi-classical view of atom excitations
Energy
Atom in ground state
Energy
Atom in excited state
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Light generation
Energy
excited state
equilibrium most atoms in ground state
ground state
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Light generation
Energy
excited state
A pump mechanism (e.g. thermal excitation or gas
discharge) ejects some atoms to the excited state
ground state
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Light generation
Energy
excited state
The excited atoms radiatively decay, emitting one
photon each
ground state
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Light amplification 3-level system
Energy
Super-excited state
excited state
ground state
equilibrium most atoms in ground state note the
existence of a third, super-excited state
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Light amplification 3-level system
Energy
Super-excited state
excited state
Utilizing the super-excited state as a
short-lived pivot point, the pump creates a
population inversion
ground state
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Light amplification 3-level system
Energy
Super-excited state
excited state
ground state
When a photon enters, ...
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Light amplification 3-level system
Energy
Super-excited state
excited state
When a photon enters, it knocks an electron
from the inverted population down to the ground
state, thus creating a new photon. This
amplification process is called stimulated
emission
ground state
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Light amplifier
Gain medium (e.g. 3-level system w population
inversion)
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Light amplifier w positive feedback
Gain medium (e.g. 3-level system w population
inversion)
When the gain exceeds the roundtrip losses, the
system goes into oscillation
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Laser
initial photon
Gain medium (e.g. 3-level system w population
inversion)
Partially reflecting mirror
Light Amplification through Stimulated Emission
of Radiation
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Laser
amplified once
initial photon
Gain medium (e.g. 3-level system w population
inversion)
Partially reflecting mirror
Light Amplification through Stimulated Emission
of Radiation
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Laser
amplified once
initial photon
Gain medium (e.g. 3-level system w population
inversion)
reflected
Partially reflecting mirror
Light Amplification through Stimulated Emission
of Radiation
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Laser
amplified once
initial photon
Gain medium (e.g. 3-level system w population
inversion)
reflected
amplified twice
Partially reflecting mirror
Light Amplification through Stimulated Emission
of Radiation
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Laser
amplified once
initial photon
Gain medium (e.g. 3-level system w population
inversion)
reflected
output
amplified twice
reflected
Partially reflecting mirror
Light Amplification through Stimulated Emission
of Radiation
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Laser
amplified once
initial photon
Gain medium (e.g. 3-level system w population
inversion)
reflected
output
amplified twice
reflected
amplified again etc.
Partially reflecting mirror
Light Amplification through Stimulated Emission
of Radiation
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Confocal laser cavities
diffraction angle
waist w0
Beam profile 2D Gaussian function TE00mode
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Other transverse modes
(usually undesirable)
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Types of lasers
Continuous wave (cw) Pulsed
Q-switched mode-locked Gas (Ar-ion,
HeNe, CO2) Solid state (Ruby, NdYAG, TiSa)
Diode (semiconductor) Vertical cavity
surface-emitting lasers VCSEL(also sc)
Excimer(usually ultra-violet)
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CW (continuous wave lasers)
Laser oscillation well approximated by a sinusoid
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 NdYaG 532nm (green) 1-10W
Quality of sinusoid maintained over a time
duration known as coherence
time tc Typical coherence times 20nsec (HeNe),
10µsec (doubled NdYAG)
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Two types of incoherence
temporal incoherence
spatial incoherence
matched paths
point source
Michelson interferometer
Young interferometer
poly-chromatic light (multi-color, broadband)
mono-chromatic light ( single color, narrowband)
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Two types of incoherence
temporal incoherence
spatial incoherence
matched paths
point source
waves with equal paths but from different points
on the wave front do not interfere
waves from unequal paths do not interfere
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Coherent vs incoherent beams
Mutually coherent superposition field amplitude
is described by sum of complex amplitude
Mutually incoherent superposition field
intensity is described by sum of intensities
(the phases of the individual beams vary
randomly with respect to each other hence, we
would need statistical formulation to describe
them properly statistical optics)
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Coherence time and coherence length
? much shorter than coherence length ctc
Sharp interference fringes
Intensity
incoming laser beam
? much longer than coherence length ctc
no interference
Michelson interferometer
Intensity
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Coherent vs incoherent beams
Coherent superposition field amplitude is
described by sum of complex amplitudes
Incoherent superposition field intensity is
described by sum of intensities
(the phases of the individual beams vary
randomly with respect to each other hence, we
would need statistical formulation to describe
them properly statistical optics)
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Mode-locked lasers
Typical sources Ti Sa lasers (major vendors
Coherent, Spectra Phys.) Typical mean
wavelengths 700nm 1.4µm (near IR)
can be doubled to visible wavelengths
or split to visible mid IR wavelengths using
OPOs or OPAs (OPOoptical
parametric oscillator OPAoptical
parametric amplifier) Typical pulse durations
psec to few fsec (just a few
optical cycles) Typical pulse repetition rates
(rep rates) 80-100MHz Typical average power
1-2W peak power MW-GW
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Overview of light sources
non-Laser
Laser
Thermal polychromatic, spatially
incoherent (e.g. light bulb)
Continuous wave (or cw) strictly monochromatic,
spatially coherent (e.g. HeNe, Ar, laser diodes)
Gas discharge monochromatic, spatially
incoherent (e.g. Na lamp)
Pulsed quasi-monochromatic, spatially
coherent (e.g. Q-switched, mode-locked)
Light emitting diodes (LEDs) monochromatic,
spatially incoherent
nsec
psec to few fsec
pulse duration
mono/poly-chromatic single/multi color
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