Introduction to Nonlinear Optics

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Introduction to Nonlinear Optics

• Azita Emami
• May 2002

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Outline

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

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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.

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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.

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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)

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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.

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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

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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)

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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

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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,

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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.

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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.

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Wave in Periodic Media

• Grating, when dielectric constant is a periodic
  function of position.

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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

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Photorefractive Resonators
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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

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Phase Conjugation
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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

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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

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Holography

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

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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

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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.

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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

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More

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