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## Introduction to Nonlinear Optics

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### Nonlinear Optics: Study of interaction of ... energy coupling between the two beams. ... Generation of a time-reversed replica of the wave, like a mirror. E ... – PowerPoint PPT presentation

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Title: Introduction to Nonlinear Optics

1
Introduction to Nonlinear Optics
• Azita Emami
• May 2002

2
Outline
• General Introduction
• Photorefractive Effect
• Wave Mixing
• Phase Conjugation
• Stimulated Back Scattering
• Other Applications

3
Introduction
• What does the index of refraction mean?
• Linear Region Efield ltlt Intra-Atomic field. n
is independent from the light intensity, I.
• Nonlinear Region Efield Intra-Atomic field.
Modified electron distribution, n depends on
I.

4
Introduction (2)
• Nonlinear Optics Study of interaction of light
in matter
• We can control n by the light itself or
manipulate one beam with the other.
• Leads to a Great variety of technical
innovations.

5
Material Response to the Light
• P e0 c(1)E e0 c(2)EE e0 c(3)EEE
• P induced polarization of medium
• e0 dielectric constant of vacuum
• E electric field
• c(i) constant
• D e0E P eE
• In linear optics n2 1 c(1)

6
Nonlinear Terms
• Second-order term, c(2)EE
• frequency doubling
• sum/difference generation
• Third-order term, c(3)EEE
• 3rd harmonic generation
• Raman Brillouin Scattering
• Self focusing
• Optical Phase Conj.

7
Nonlinear terms (2)
• Now consider an optical beam with frequency w and
a DC field
• EE0 Ewcos(wt)
• c(2) E0 Ewcos(wt)
• linear electro-optic effect discovered by
Pockels in 1883, modifying n with a DC field
• used for optical switching
• used for phase modulation of light

8
More Terms
• c(2)Ew2
• static voltage appears across the sample
• c(2)Ew2 cos(2wt)
• c(3) E02 Ew cos(wt)
• quadratic electro-optic effect (DC Kerr
effect)
• c(3) E0 Ew2 cos(2wt)
• c(3) Ew3 cos(3wt)

9
Last term Kerr effect
• c(3) Ew3 cos(wt) c(3) Ew2 (Ewcos(wt))
• optical (or AC) Kerr effect
• looks like a refractive index which depends
on the optical field strength
• n n0n2I
• self-focusing and self-phase modulation

10
Photorefractive Effect
• Change of the local index of refraction by
illumination of a beam with spatial variation of
Intensity.
• First discovered in 1966, study of laser beams
through electro-optic crystals
• LiNbO3, BaTiO3, KNbO3, LiT aO3,

11
Simple Model for Photorefractive effect
• There are impurities with energy levels around
the middle of band gap (donors).
• With enough photon energy, electrons get excited.
• Electrons migrate and get trapped at nearby sites
in the dark side
• Space charge separation, E field, change in n.

12
Periodic Media
• A periodic media can be created using the
photorefractive effect
• Many important phenomena involve the scattering
of light from gratings or holograms
• Wave mixing, phase conj., dynamic holography, etc.

13
Wave in Periodic Media
• Grating, when dielectric constant is a periodic
function of position.

14
Two Wave Mixing
• Two beams with same frequency create a stationary
interference pattern.
• There will be energy coupling between the two
beams.
• Can be used for beam amplification, one beam
pumps the energy in to the other

15
Photorefractive Resonators
16
Optical Phase Conjugation
• Generation of a time-reversed replica of the
wave, like a mirror
• E A cos(wt-kz-f)
• Ec A cos(wtkzf)
• Lensless imaging, distortion correction,
associated with a frequency shift
• With nonlinear techniques this can be done
real-time

17
Phase Conjugation
18
Generation of Phase-Conj. waves
• FWM
• Degenerate Four-Wave Mixing (similar to
holography)
• Nondegenerate FWM, gives large freq shift
• Stimulated Scattering processes
• Brillouin scattering involves acoustic
waves, small freq shift
• Raman Scattering molecular vibration or
optical phonons, larger shift

19
DFWM
• A 3rd order nonlinear optical process
• The induced grating by 2 input waves scatters the
3rd and generates the 4th
• Inputs are 2 antiparallel, high-power pumps and a
weaker probe wave, the output could be amplified
besides being conjugated
• In conventional holography gratings are recorded
in a photographic emulsion

20
Holography
• Record object beam A1 with the reference beam A2
• Read out by A3 which is A2s phase conj.

21
Raman Brellouin Processes
• Mixing of mechanical oscillations with a light
beam in a nonlinear media
• Mechanical var. intra-atomic dis in a molecule
or density in a solid or liquid
• Freq spectrum of light is modified while phonons
are emitted or absorbed

22
Brillouin Scattering
• n is a function of density, Debye-Sears effect
(acoustic wave scatters light with a Doppler
shift)
• In turn electronic polarization creates pressure
variations
• Light can pump a sound wave
• Then it is scattered back with slightly different
freq.

23
Raman Scattering
• Intra-atomic distance within the molecule is
changed when the electron cloud is displaced
• Involves the vibration state of molecules
• Here variables are microscopic while in Brillouin
macroscopic

24
More
• Optical Computing
• Fourier Optics using FWM, Image Subtraction
• Optical Interconnection
• Amplification, Dispersion cancellation,
Optical switches with dynamic holography (1 ms
recording time),