Introduction to Nonlinear Optics

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Introduction to Nonlinear Optics

• H. R. Khalesifard
• Institute for Advanced Studies in Basic Sciences
• Email khalesi_at_iasbs.ac.ir

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Contents

1. Introduction
2. The essence of nonlinear optics
3. Second order nonlinear phenomena
4. Third order nonlinear phenomena
5. Nonlinear optical materials
6. Applications of nonlinear optics

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Introduction

• Question
• Is it possible to change the color of a
  monochromatic light?
• Answer
• Not without a laser light

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Stimulated emission, The MASER and The LASER

• (1916) The concept of stimulated emission Albert
  Einstein
• (1928) Observation of negative absorption or
  stimulated emission near to resonant wavelengths,
  Rudolf Walther Ladenburg
• (1930) There is no need for a physical system to
  always be in thermal equilibrium, Artur L.
  Schawlow

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LASER (MASER)
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The Maser

• Two groups were working on Maser in 50s
• Alexander M. Prokhorov and Nikolai G. Bassov
  (Lebedev institute of Moscow)
• Charles H. Townes, James P. Gordon and Herbert J.
  Zeiger (Colombia University)

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• Left to right Prokhorov, Townes and Basov at
  the Lebede institute (1964 Nobel prize in Physics
  for developing the Maser-Laser principle)

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• Townes (left) and Gordon (right) and the
  ammonia maser they had built at Colombia
  University

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The LASER

• (1951) V. A. Fabrikant A method for the
  application of electromagnetic radiation
  (ultraviolet, visible, infrared, and radio
  waves) patented in Soviet Union.
• (1958) Townes and Arthur L. Schawlow, Infrared
  and Optical Masers, Physical Review
• (1958) Gordon Gould definition of Laser as
  Light Amplification by Stimulated Emission of
  Radiation
• (1960) Schawlow and Townes
  U. S. Patent
  No. 2,929,922
• (1960) Theodore Maiman Invention of the first
  Ruby Laser
• (1960) Ali Javan The first He-Ne Laser

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• Maiman and the first ruby laser

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• Ali Javan and the first He-Ne Laser

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Properties of Laser Beam

• A laser beam
• Is intense
• Is Coherent
• Has a very low divergence
• Can be compressed in time up to few femto second
  

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Applications of Laser

• (1960s) A solution looking for a problem
• (Present time) Medicine, Research, Supermarkets,
  Entertainment, Industry, Military, Communication,
  Art, Information technology,

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Start of Nonlinear Optics

• Nonlinear optics started by the discovery of
  Second Harmonic generation shortly after
  demonstration of the first laser.
• (Peter Franken et al 1961)

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2. The Essence of Nonlinear Optics

• When the intensity of the incident light to a
  material system increases the response of medium
  is no longer linear

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Response of an optical Medium

• The response of an optical medium to the incident
  electro magnetic field is the induced dipole
  moments inside the medium

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Nonlinear Susceptibility
Dipole moment per unit volume or polarization

• The general form of polarization

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Nonlinear Polarization

• Permanent Polarization
• First order polarization
• Second order Polarization
• Third Order Polarization

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How does optical nonlinearity appear

• The strength of the electric field of the
  light wave should be in the range of atomic fields

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Nonlinear Optical Interactions

• The E-field of a laser beam
• 2nd order nonlinear polarization

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2nd Order Nonlinearities

• The incident optical field
• Nonlinear polarization contains the following
  terms

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Sum Frequency Generation
Application Tunable radiation in the UV
Spectral region.
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Difference Frequency Generation
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Phase Matching

• Since the optical (NLO) media are dispersive,
• The fundamental and the harmonic signals have
• different propagation speeds inside the media.
• The harmonic signals generated at different
  points
• interfere destructively with each other.

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SHG Experiments

• We can use a resonator to increase the efficiency
  of SHG.

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Third Order Nonlinearities

• When the general form of the incident electric
  field is in the following form,
• The third order polarization will have 22
  components which their frequency dependent are

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The Intensity Dependent Refractive Index

• The incident optical field
• Third order nonlinear polarization

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The total polarization can be written as
One can define an effective susceptibility
The refractive index can be defined as usual
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By definition
where
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Typical values of nonlinear refractive index
Mechanism n2 (cm2/W) (esu) Response time (sec)
Electronic Polarization 10-16 10-14 10-15
Molecular Orientation 10-14 10-12 10-12
Electrostriction 10-14 10-12 10-9
Saturated Atomic Absorption 10-10 10-8 10-8
Thermal effects 10-6 10-4 10-3
Photorefractive Effect large large Intensity dependent
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Third order nonlinear susceptibility of some
material
Material ? 1111 Response time
Air 1.210-17
CO2 1.910-12 2 Ps
GaAs (bulk room temperature) 6.510-4 20 ns
CdSxSe1-x doped glass 10-8 30 ps
GaAs/GaAlAs (MQW) 0.04 20 ns
Optical glass (1-100)10-14 Very fast
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Processes due to intensity dependent refractive
index

1. Self focusing and self defocusing
2. Wave mixing
3. Degenerate four wave mixing and optical phase
   conjugation

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Self focusing and self defocusing

• The laser beam has Gaussian intensity profile. It
  can induce a Gaussian refractive index profile
  inside the NLO sample.

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Wave mixing
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Optical Phase Conjugation

• Phase conjugation mirror

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Aberration correction by PCM
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What is the phase conjugation
The signal wave
The phase conjugated wave
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Degenerate Four Wave Mixing

• All of the three incoming beams A1, A2 and A3
  should be originated
• from a coherent source.
• The fourth beam A4, will have the same Phase,
  Polarization, and
• Path as A3.
• It is possible that the intensity of A4 be more
  than that of A3

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Mathematical Basis
The four interacting waves
The nonlinear polarization
The same form as the phase conjugate of A3
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Holographic interpretation of DFWM
Bragg diffraction from induced dynamic gratings