Transcript NonlinearOpt_MIT(Garmire)

Charles Townes at MIT
Nonlinear Optics
Elsa Garmire
Thayer School of Engineering
Dartmouth College
[email protected]
Townes: 1958-1961
• 1958: Schawlow-Townes paper “Infrared and Optical
Masers”
• Cold War: Technical advice to the military
– Chaired Committee to create interest in mm waves.
– Chaired Committee to continue support in infrared.
• 1959-61: Vice President and Director of Research for the
Institute for Defense Analysis in Washington
“I felt that there just were not enough good scientists in
Washington, and we had a pressing problem with the
Russian missiles and other things coming on, and it was
just a part of my duty”
1961-1967: Townes at MIT
• Responsibilities: Provost
Research: Nonlinear Optics
• “We were in the early stages of non-linear optics. I was
working on non-linear optics, and various new effects that
were being found there.
• “I had also invited Ali Javan, who had been at Bell Telephone
Laboratories, to come to MIT as a professor, and the physics
department accepted that.
• “So it was quite a group working, and I
could come and go and do little parts of it
when I had time, and that kept me busy,
and I did some moderately important work
in non-linear optics at that time.”
Second Commercially Sold Laser
Flash Lamp
Partial reflection
on rod
Laser
Beam
Out
Ruby
Rod
100% reflective
coating
Capacitor
Power Supply
MIT Laser Laboratory (1961-1966)
Stimulated Raman Scattering in Liquids
Elsa’s Father
Ruby Laser
Oscilloscope
Townes and Nonlinear Optics at MIT
1) Explained important aspects of Stimulated Raman Scattering
(SRS): coherent molecular vibrations
2) Introduced Stimulated Brillouin Scattering (SBS)
3) Introduced Spatial Solitons
(self-trapped optical beams)
4) Demonstrated filament-formation and instabilities.
5) Introduced Self-steepening of Pulses
(change in pulse shape from Self-Phase Modulation)
1) Raman Scattering
• Raman Scattering: Inelastic scattering from molecules with
natural resonance frequencies Wr.
• Stokes light: Scattered light is at frequency lower by Wr
because molecule begins vibrating at frequency Wr
• Anti-Stokes light: Scattered light from vibrating molecules.
Scattered light is at frequency higher by Wr because molecule
loses vibrational energy at frequency Wr.
• Ordinary Anti-Stokes Raman Scattering
– Vibration thermally induced
– Small fraction of molecules
– Weak anti-Stokes
Light
beam
Molecule
Wr
Stokes
AntiStokes
Stimulated Raman Scattering
• SRS: A coherent laser beam at frequency ωL causes gain for
the Stokes wave at frequency ωL - Wr.  Intense Stokes.
• Observed up to n = 3 in frequency: ωL - nWr.
• Anti-Stokes light: Comparable intensity to Stokes.
• Observed frequencies ωL + nWr with n up to 2.
• Anti-Stokes emitted in cones, observed as rings on film. Why?
Anti-Stokes from Ruby Laser in Benzene
2
Q-switched  10 ns pulses
1
ωL
Laser, ωL
Molecule
Wr
Stokes
AntiStokes
Townes’ Inspiration for
Coherent Molecular Oscillations
• 3rd Quantum Electronics Conference, Paris; 1963
– Lincoln Laboratories theoretical paper on optical phonons.
• Experiments:
– Hughes Research Laboratories: Stokes n = 3
– Terhune and Stoicheff: Intense anti-Stokes emission
• Stoicheff visited MIT, so we had early access to his data.
• Townes realized that coherent laser light could drive
coherent optical phonons (molecular oscillations).
Stokes
Phonon
Laser
Anti-Stokes
K = kL – kS
Laser
Anti-Stokes as a Parametric Process
Requires phase coherence over interacting length: Phase Matching
kS = nS (w L – W o )/c
Stokes
Laser kL = nLw L/c
ka = na (w L + W o )/c
Anti-Stokes
K = kL – kS
kL = nLw L/c
Laser
• Molecular vibration K, driven by Stokes generation.
• Second laser photon scatters off K to produce anti-Stokes
• Phase-matching means conical anti-Stokes generation
"Coherently Driven Molecular Vibrations and Light Modulation"
(Garmire, Pandarese, Townes) Phys. Rev. Lett. 11, 160 (1963).
Coherent Molecular Oscillations
• Laser light photons become intense Stokes forward-directed
photons at frequency ω - Wr.
• Missing photon energy creates molecular oscillation.
• Coherent light transfers its phase coherence to molecular
vibrations: Km = kL - ks.
• Periodic vibrations can subsequently be transferred back to
the light wave as coherent anti-Stokes emission
ks
• Classic resonant parametric process.
Km
Stokes
Molecule
• Stokes process begins the vibration
A.S.
• Stokes photon used up
Laser
in creating anti-Stokes
• kAS = kL + Km = 2kL - ks
kL
kAS
Experimental Proof: SRS in Calcite
Black = Diffuse Forward Stokes
White = anti-Stokes cone
Cone of missing Stokes
due to generation of anti-Stokes
White = Laser Light
Cone angles agree with theory
“Angular Dependence of Maser-Stimulated Raman Radiation in Calcite,”
R. Chiao and B. P. Stoicheff, Phys. Rev. Lett. 12, #11, 290 (1964).
Anti-Stokes from Benzene
Stimulated Raman Scattering
Liquids: Anti-Stokes in Acetone
Successively
higher power
pump.
Forward-directed
a) Forward-directed
b) Filament-emitted
(Cerenkov)
c) Volume and forward
Phase-Match
Filament-emitted
Too Big for Phase-Match
d) All three
Filaments conserve momentum only along laser beam: kL = kAScos
Explanation: Mis-aligned Cell
Cell Facets
act as
mirrors to
increase
off-axis
Stokes.
Stokes
Enough to
generate
Anti-Stokes
Volumematched.
FILTER
Anti-Stokes
Misaligned Cell at Higher Power
 = volume
phase-match
S
AS
L
L
 = filament
phase-match
L
S
AS
L
L
Evidence of Filaments
The first evidence of self-trapping of laser beams
Anti-Stokes spatial distribution (no camera lens)
(a) Acetone and (b) Cyclohexane
(b) Many filaments + Volume
(a) Two side-by-side Filaments
Cylindrical Lens: More Proof
of A.S. Generation from Filaments
Calcite: Cylindrical lens with vertical
axis forms volume phase-matched
anti-Stokes ellipses.
Benzene: Same Geometry.
Circular anti-Stokes proves surfaceemission generated from filaments.
Weak signs of elliptical volume
emission.
Single Frequency Mode Excitation
Imaging Spectrograph
 LASER frequency
Single frequency generated at each anti-Stokes Raman order.
Multi-mode excitation: slit inserted in
spectrograph: (self-phase modulation)
2) Brillouin Scattering
• Inelastic scattering of light beam from acoustic phonons
• Analogous to Raman scattering, but molecular vibration
replaced by acoustic wave with frequency near 30 GHz.
• Acoustic wave and scattered light wave are emitted in
specific directions, obeying phase-match.
• Brillouin frequency shift depends on angle:
Ws = 2wo(vac /vph) sin(/2)
vac << vph   large
ωL
ωL - ΩS
kS
kL
phonon = kL - kS
Stimulated Brillouin Scattering
• “Stimulated Brillouin scattering of an intense optical maser
beam involves coherent amplification of a hypersonic lattice
vibration and a scattered light wave”
• “Analogous to Raman maser action, but with molecular vibration
replaced by an acoustic wave with frequency near 30 GHz.”
• “Both the acoustic and scattered light waves are emitted in
specific directions.”
• The largest SBS signal is retro-reflected with frequency shift
Ws = 2wo(vac /vph)
ωL
Retro-reflected Signal ωL - ΩS
R. Y. Chiao, E. Garmire, C. H. Townes, Proc. Enrico Fermi Summer School of Physics, 1963
Stimulated Brillouin Scattering
Fabry-Perot rings
M = OPTICAL MASER
B = BRILLOUIN
Brillouin frequency
offset agrees with
theory (~30 GHz)
“Stimulated Brillouin
Scattering and generation
of intense hypersonic
waves” R . Y. Chiao, C. H.
Townes, and B. P. Stoicheff,
Phys. Rev. Lett. 12, 592
(1964).
SBS was detected in quartz and sapphire.
Stimulated Brillouin Scattering in Liquids
first demonstration of Phase Conjugation (unrecognized)
Q-switch
gain
mirror
SBS
Note: drawing
did not include
phaseconjugation
Multiple orders by ruby amplification
Fabry-Perot
Interferogram
Laser
SBS1; SBS2
"Stimulated Brillouin
Scattering in Liquids"
(Garmire, Townes)
Appl. Phys. Lett. 5, 84
(1964).
Early Observation of SBS
Beam
Block
“A” reads 10 X power out. Why?
First realized in 1972: Zeldovich
Detector
Detector
3) Townes’ Inspiration for “Spatial Solitons”
Michael Hercher’s photographs of damage in glass block:
University of Rochester, New York
Focal spot size = 0.04 cm
Direction of laser beam
Self-Trapping of Optical Beams
“An electro-magnetic beam can produce its own dielectric
waveguide and propagate without spreading.
This may occur in materials whose dielectric constant increases
with field intensity, but which are homogeneous in the absence
of the electromagnetic wave.”
“A crude description can be obtained by considering diffraction of a
circular optical beam of uniform intensity across diameter D in material
for which the index of refraction may be quadratic in field.”
Divergence angle = 1.22 l/nD set equal to critical angle for TIR.
Threshold power P = (1.22l)2c/64n2, independent of diameter.
P ~ 106 W.
Divergence by diffraction
Total internal reflection
R. Y. Chiao, E. Garmire and C. H. Townes, Phys. Rev. Lett. 13, (1964)
Slab-Shaped Beam (1D confinement)
1D Spatial Soliton
Solution is
E(y) = Eosech(Gy).
where G =
Solution is stable
2D Confinement (cylindrical beam)
Solution
turned out
to be
unstable
in typical
nonlinear
media
Integration gives the critical power
P =
which equals that given before.
“The Townes profile”
Spatial Soliton exists in Photorefractive
Materials with Electric Field
With Field
Bismuth titanate
crystal 5 mm
long
Without
Field
Experimental demonstration of optical spatial soliton propagating through
5 mm long nonlinear photorefractive crystal. Top: side-view of the soliton
beam from scattered light; bottom: normal diffraction of the same beam
when the nonlinearity is 'turned off'
Formation of Self-trapping Filaments
Laser
With Pinhole
Increasing
Laser
Power
No Pinhole
“Dynamics and Characteristics of the Self-Trapping of Intense Light Beams,”
E. Garmire, R. Y. Chiao, and C. H. Townes, Phys. Rev. Lett. 16, (1966)
Townes and Technical Errors
Divided Loyalties
(MIT administration, NASA, Research, Nobel Prize)
• Creative (and busy) people have to be willing to be wrong.
• Be as sure as you can be.
• It’s acceptable to make errors when a field is new.
– Initial Laser paper
– Self-trapping paper
– Instabilities in self-trapping
– Single mode needed to see self-focusing
– Phase Conjugation
4) "A New Class of Trapped Light
Filaments"
Simultaneous presence of SRS
and SBS. Lots still to explain!
R. Y. Chiao, M. A. Johnson, S. Krinsky, H. A. Smith C. H. Townes,
E. Garmire, IEEE J. Quantum Electr. QE-2, 467 (1966).
5) Self-Steepening of Light Pulses
• Change in temporal shape of light pulses due to propagation in
medium with intensity-dependent refractive index
• Phase varies with time: Broadens frequency spectrum
• Equation for pulse energy:
• (Self-phase modulation)
Gaussian input pulse in nonlinear medium
zo = 0
z1 = zs/2
z2 = zs
Transforms into
Optical Shock
Trailing edge
Pulse slows down
Phys. Rev., 164, 1967, F. Demartini, C. H. Townes, T. K. Gustafson, P. L. Kelley
Spectrum of Modulated Gaussian Pulse
Self-phase Modulation
ΩM = ωo/100
ΩM = ωo/500
2000 cm-1
z2 = 2z1
Phys. Rev., 164, 1967, F. Demartini, C.
H. Townes, T. K. Gustafson, P. L. Kelley
z2 = 2z1
Townes’ Technical Contributions to
Nonlinear Optics
1) Explained important aspects of Stimulated Raman Scattering
(SRS): coherent molecular vibrations
2) Introduced Stimulated Brillouin Scattering (SBS)
3) Introduced Spatial Solitons
(self-trapped optical beams)
4) Demonstrated filament-formation and instabilities.
5) Introduced Self-steepening of Pulses
(equation for calculation; self-phase modulation)
Elsa’s Personal Comments
Townes Relaxing at his Farm
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Finding an Advisor
Ray Chiao
Beer in the MIT pub
Paul Fleury
Religion
Pregnancy
Post-doc at NASA
Advising Style
On being a woman
PhD Students: Elsa Garmire, Ray Chiao (and Paul Fleury)
Also Javan’s group; visitors: Boris Stoicheff, Francesco deMartini
Also Paul Kelley from Lincoln Labs; also undergraduates
Garmire and Townes, 2007
Tony Siegman
END