Download Introduction to Nonlinear Optics

Introduction to Nonlinear Optics
H. R. Khalesifard
Institute for Advanced Studies in Basic
Sciences
Email: [email protected]
Contents
1.
2.
3.
4.
5.
6.
Introduction
The essence of nonlinear optics
Second order nonlinear phenomena
Third order nonlinear phenomena
Nonlinear optical materials
Applications of nonlinear optics
Introduction
input
Answer:
Not without a laser light
NLO sample
Question:
Is it possible to change the
color of a monochromatic
light?
output
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
E2
h
Absorption
h
h
E1
E2
E1
Spontaneous
Emission
h
E2
E1
Stimulated
Emission
h
Light (Microwave) Amplification
by
Stimulated
Emission of Radiation
LASER
(MASER)
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)
Left to right: Prokhorov, Townes and Basov at the Lebede
institute (1964 Nobel prize in Physics for developing the
“Maser-Laser principle”)
Townes (left) and
Gordon (right) and
the ammonia maser
they had built at
Colombia University
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
Maiman
and the
first ruby
laser
Ali Javan and
the first He-Ne
Laser
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


(1960s) “A solution looking for a
problem”
(Present time) Medicine, Research,
Supermarkets, Entertainment,
Industry, Military, Communication,
Art, Information technology, …
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)
2. The Essence of Nonlinear Optics
Output
When the intensity of
the incident light to
a material system
increases the
response of
medium is no
longer linear
Input intensity
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
h
h


h
h



Nonlinear Susceptibility
Dipole moment per unit volume or polarization
Pi  Pi   ij E j
0
The general form of polarization
Pi  Pi  χ E j  χ
0
(1)
ij
(2)
ijk
E j Ek  χ E j Ek El  
(3)
ijkl
Nonlinear Polarization




Permanent
Polarization
First order
polarization:
Second order
Polarization
Third Order
Polarization
P   Ej
1
i
(1)
ij
Pi   E j Ek
2
( 2)
ijk
Pi   E j Ek El
3
( 3)
ijkl
How does optical nonlinearity
appear
The strength of the
electric field of the light
wave should be in the
range of atomic fields
h
a0
N
Eat  e / a
2
0
a0   / me
2
e
2
7
Eat  2 10 esu
Nonlinear Optical Interactions

The E-field of a laser beam
~
E (t )  Eeit  C.C.

2nd order nonlinear polarization
~ ( 2)
P (t )  2  ( 2) EE*  (  ( 2) E 2e 2it  C.C.)

2

( 2)

2nd Order Nonlinearities

The incident optical field
~
 i1t
 i 2t
E (t )  E1e
 E2e
 C.C.

Nonlinear polarization contains the following terms
2
1
P(21 )   E
(SHG)
P(2 2 )   ( 2 ) E22
(SHG)
( 2)
P(1   2 )  2  E1 E2
(SFG)
P(1   2 )  2  ( 2 ) E1 E2*
(DFG)
( 2)
P(0)  2  ( 2) ( E1 E1*  E2 E2* ) (OR)
Sum Frequency Generation
2
2

( 2)
1
Application:
Tunable radiation in the
UV Spectral region.
1
3  1   2
2
1
3
Difference Frequency
Generation
2
2

1
( 2)
1
Application:
The low frequency
photon, 2 amplifies in
the presence of high
frequency beam  . This
1
is known as parametric
amplification.
3  1   2
1
2
3
Phase Matching


( 2)
2
•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

We can use a
resonator to increase
the efficiency of SHG.
What is the phase conjugation
The signal wave
~
it
Es (r, t )  Es e  C.C.
The phase conjugated wave
Es  ε̂ s As e
iks .r