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10/2/2012 1
a milestone in the journey from
Nonlinear Optics ---
10/2/2012 2
The technology of
generating and harnessing light
and other forms of energy
whose quantum is the Photon
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The Technology of Photonics : control, communications, computing
Control a large current
using a small current
Nonlinearity is required for light to control light
???
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Linear vs nonlinear
Stimulus vs response, Extreme stimulus
Linear response theory
Transport properties, mass, charge, heat
Stress vs starin
Linear regime NonLinear regime
Electric field
Polarization
We are nonlinear!
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Nonlinear optical properties (NLO)
Linear optical properties
intensity independent (eg., reflection, refraction and
absorption)
Nonlinear optical properties
depend on the intensity of incident light
eg., nonlinear absorption, nonlinear refractive index
Large optical intensity stronger perturbation of the Coulomb field in the medium nonlinear interaction optoelectronic applications
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NL medium
2
SHG : Second harmonic generation
A simple example for NLO effects: Harmonic Generation
e.g. 694 nm (red) 347 nm (violet)
How do we understand this?
physical picture…an analogy
A small signal electronic amplifier produces higher harmonics
of the input signal is not centered around the linear region of the
transistor characteristic curve.
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Examples of nonlinear systems
2
20
d g
dt l
Linearised pendulum
Actual (= nonlinear) pendulum
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0
0P E
0x xx x xy y xz zP E E E
0
0
y yx x yy y yz z
z zx x zy y zz z
P E E E
and
P E E E
What exactly is NON LINEAR? Nonlinear dependence of polarization
on optical field
Physical meaning, mathematical features
Polarization: dipole moment per unit volume of the medium.
Susceptibility : a characteristic property of the medium.
This is
linear!
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1
0
0
y yx x yy y yz z
z zx x zy y zz z
P E E E
and
P E E E
x xx xy xz x
y yx yy xy y
z zx zy zz z
P E
P E
P E
0x xx x xy y xz zP E E E
0
z
i ij j
x
P E
0i ij jP E
Einstein’s summation notation: Summation over repeated/dummy variable
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2
Linear optics : superposition
No energy transfer among waves
Nonlinearity Energy transfer; wave mixing
n th order, (n+1) wave mixing
(n) : susceptibility of n th order is an
(n+1) th rank tensor with [3(n+1)] components
(1) (2) (3)
0 ...i ij j ijk j k ijkl j k lP E E E E E E
• a tensor quantity • a complex quantity • a frequency-dependent quantity
( )n
What exactly is NON LINEAR? Nonlinear dependence of polarization on optical field
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3
Second Order Nonlinear Optical Processes
• Second harmonic generation
• Linear electro-optic effect : Pockel’s effect
Large and fast nonlinearity: A materials problem
Third order Nonlinear Optical Effects
• Phase conjugation
• Stimulated Raman scattering
• Self focusing
• Bistability
• Quadratic electro-optic effect : Kerr Effect
(1) (2) (3)
0 ...i ij j ijk j k ijkl j k lP E E E E E E
Second order NLO effects
(2) 2
SHG : Second harmonic generation
(2) 1
Sum and difference frequency generation
2
1+2
12
• Optical parametric oscillation • Applications of wave mixing
Latest solid state tunable lasers commercially available today are based on wave-mixing
e.g. Ti:Saphire
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5
The first ever experiment on Nonlinear optics
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6
Second Harmonic Generation
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7
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8
Optical Phase Conjugation : idea
The phase of wave 4 is conjugated w.r.t that of wave 3 i.e. 4 is a time-reversed replica of 3
1 2
3
4
beam 1 beam 2
beam 3
beam 4
Scheme of DWFM
beam 1 beam 2
beam 3
beam 4
Scheme of DWFM
Three input waves inside a medium
generate a fourth wave as output
(3)
(3)
(3)
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9
Optical Phase Conjugation : implementation
Plane wave distorter ord. mirror
Reflection of a distorted wave from an ordinary mirror
distorted
distorted,
reflected further
distorted
incident
Reflection of a distorted wave from a OPC mirror
Plane wave distorter OPC mirror
distorted
distorted,
‘reflected’ from OPCM distortion-corrected
incident
Remember:
‘OPC mirror’ is not a
mirror,
but an OPC setup
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2
A picture from Wikipedia
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3
Ordinary mirror vs. “OPC mirror” i.e. linear reflection versus nonlinear reflection
Ordinary mirror
Optical Phase conjugate mirror Note: OPC mirror is not actually any mirror, but an OPC set up; with beam 3 as input and beam 4 as output. Beam 4 results from NL wave mixing and emerges out in a direction exactly
opposite to that of beam 3.
beam 1 beam 2
beam 3
beam 4
Scheme of DWFM
beam 1 beam 2
beam 3
beam 4
Scheme of DWFM
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4
Optical Phase Conjugation: Applications
Apart from measurement of chi-3 to characterize the NL material, wave front reversal (time-reversal) and distortion-healing properties of OPC are used in Adaptive Optics applications such as
Precise targeting of a beam,
Precise beam control in lithography,
Aberration-correction in amplifiers in fiber-optic communications etc
Optical data and image processing
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5
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6
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7
Guassian laser beam
Nonlinear medium
Self focusing n(I) = n0 + n2I
IIIIIIII ((((((
Applications :
•Beam shaping •Pulse shaping – soliton propagation •Optical limiting •Measurement of n2
An NLO phenomenon of the third order
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9
Implications of self focusing: a) The beam gets focused into one or more extremely narrow filaments with high intensity, sometime damaging the medium. b) The focusing effect can be used to compensate for the
beam spreading effect due to diffraction over large
distances, e.g. in fiber optic communications.
Thus a shape-maintaining beam (spatial soliton) can be
obtained.
c) By measuring the changes in beam profile in a self focusing experiment, it is possible to measure
(3)
An NLO phenomenon of the third order
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0
An NLO phenomenon of the third order:
Self focusing: A medium behaves like a lens
and a parallel beam gets focused (without any lens)
medium (3)
Refractive index becomes dependent on intensity I for large I
n(I) = n0 + n2I
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1
Conventional Materials
•Inorganic salts KDP, ADP, BaTiO3, BBO
•Semiconductors GaAs, Si, Ge, InSb
•Organic Materials Polymers, dyes, urea
Figure of Merit Large and Fast nonlinearity
Novel Materials QD, CNT, PBG
Materials for Nonlinear Optics
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