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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),
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