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Introduction to Nonlinear Optics. H. R. Khalesifard Institute for Advanced Studies in Basic Sciences Email: khalesi@iasbs.ac.ir. Contents. Introduction The essence of nonlinear optics Second order nonlinear phenomena Third order nonlinear phenomena Nonlinear optical materials

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introduction to nonlinear optics

Introduction to Nonlinear Optics

H. R. Khalesifard

Institute for Advanced Studies in Basic Sciences

Email: khalesi@iasbs.ac.ir

contents
Contents
  • Introduction
  • The essence of nonlinear optics
  • Second order nonlinear phenomena
  • Third order nonlinear phenomena
  • Nonlinear optical materials
  • Applications of nonlinear optics
introduction

NLO sample

output

input

Introduction

Question:

Is it possible to change the color of a monochromatic light?

Answer:

Not without a laser light

stimulated emission the maser and the laser
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
slide5

E2

E2

E2

E1

E1

E1

Absorption

Spontaneous

Emission

Stimulated

Emission

slide6

Light (Microwave) Amplification

by

Stimulated

Emission of Radiation

LASER

(MASER)

the maser
The Maser

Two groups were working on Maser in 50s

  • AlexanderM. Prokhorov and Nikolai G. Bassov (Lebedev institute of Moscow)
  • Charles H. Townes, James P. Gordon and Herbert J. Zeiger (Colombia University)
slide8
Left to right: Prokhorov, Townes and Basov at the Lebede institute (1964 Nobel prize in Physics for developing the “Maser-Laser principle”)
slide9
Townes (left) and Gordon (right) and the ammonia maser they had built at Colombia University
the laser
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
properties of laser beam
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
applications of laser
Applications of Laser
  • (1960s) “A solution looking for a problem”
  • (Present time) Medicine, Research, Supermarkets, Entertainment, Industry, Military, Communication, Art, Information technology, …
start of nonlinear optics
Start of Nonlinear Optics

Nonlinear optics started by the discovery of Second Harmonic generation shortly after demonstration of the first laser.

(Peter Frankenet al 1961)

2 the essence of nonlinear optics
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

Output

Input intensity

response of an optical medium
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

nonlinear susceptibility
Nonlinear Susceptibility

Dipole moment per unit volume or polarization

The general form of polarization

nonlinear polarization
Nonlinear Polarization
  • Permanent Polarization
  • First order polarization:
  • Second order Polarization
  • Third Order Polarization
how does optical nonlinearity appear

e

a0

N

How does optical nonlinearity appear

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

nonlinear optical interactions
Nonlinear Optical Interactions
  • The E-field of a laser beam
  • 2nd order nonlinear polarization
2 nd order nonlinearities
2nd Order Nonlinearities
  • The incident optical field
  • Nonlinear polarization contains the following terms
sum frequency generation
Sum Frequency Generation

Application:

Tunable radiation in the

UV Spectral region.

slide24

Application:

The low frequency photon, amplifies in the presence of high frequency beam . This is known as parametric amplification.

Difference Frequency Generation

phase matching
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.
shg experiments
SHG Experiments
  • We can use a resonator to increase the efficiency of SHG.
third order nonlinearities
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

the intensity dependent refractive index
The Intensity Dependent Refractive Index
  • The incident optical field
  • Third order nonlinear polarization
slide30

The total polarization can be written as

One can define an effective susceptibility

The refractive index can be defined as usual

processes due to intensity dependent refractive index
Processes due to intensity dependent refractive index
  • Self focusing and self defocusing
  • Wave mixing
  • Degenerate four wave mixing and optical phase conjugation
self focusing and self defocusing
Self focusing and self defocusing
  • The laser beam has Gaussian intensity profile. It can induce a Gaussian refractive index profile inside the NLO sample.
optical phase conjugation

PCM

M

PCM

s

M

Optical Phase Conjugation
  • Phase conjugation mirror
aberration correction by pcm

PCM

Aberrating

medium

Aberrating

medium

PCM

s

Aberration correction by PCM
what is the phase conjugation
What is the phase conjugation

The signal wave

The phase conjugated wave

degenerate four wave mixing

A1

A2

A3

A4

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 morethan that of A3
mathematical basis
Mathematical Basis

The four interacting waves

The nonlinear polarization

The same form as the phase conjugate of A3

holographic interpretation of dfwm

A1

A2

A3

A4

Holographic interpretation of DFWM

Bragg diffraction from

induced dynamic gratings