This document discusses nonlinear optics and summarizes key topics covered: - It describes the difference between linear and nonlinear optics, where linear optics involves weak light that is unchanged and nonlinear optics involves intense light that can induce effects and be manipulated. - Nonlinear optics allows changing light properties like color and shape, and has applications in telecommunications and creating ultrashort events. - Phenomena like sum and difference frequency generation are examples of second-order nonlinear optical effects. Phase matching is important for efficient nonlinear optical processes. - Applications of nonlinear optics include optical phase conjugation, optical parametric oscillators, optical computing, optical switching, and optical data storage.

1. Nonlinear optics
Prof. V. Krishnakumar
Professor and Head
Department of Physics
Periyar University
Salem – 636 011, India

2. TOPICS
• Linear optics vs. Non-linear optics
• Importance of Non-linear optics
• Linear & Non-linear polarization.
• Phenomenon associated with NLO
• Materials applied in NLO
• Applications
• Future

3. Linear Optics vs Non Linear Optics
• Linear optics- ‘Optics of weak light’:
Light is deflected or delayed but its frequency is
unchanged.
• Non-Linear optics-‘Optics of intense light’:
We are concerned with the effects that light itself induces
as it propagates through the medium.

4. Non-Linear optics produces many
exotic events
•Nonlinear optics allows us to
change the color of a light beam,
to change its shape in space and
time, to switch telecommunica-tions
systems, and to create the
shortest events ever made by
Man
Ex: Sending infrared light into a
crystal yielded this display of
green light

5. Introduction
• What does the index of refraction
mean?
• Linear Region : Efield << Intra-Atomic
field. “n” is independent from the light
intensity, “I”.
• Nonlinear Region: Efield ~ Intra-Atomic
field. Modified electron distribution, “n”
depends on “I”.

6. In Non-Linear Optics
If irradiance is high
enough vibrations at all
frequencies corresponding to
all energy differences between
populated states are
produced.

7. Introduction
• 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.
1961, Peter Franken, Ruby Laser

8. Importance of ‘NLO’
• Optical wave manipulation is one of the future
technologies for optical processing.
• It has various applications in fiber-optic
communications and optoelectronics which
makes it an increasingly important topic among
electrical engineers.

9. Nonlinear polarization
• Linear medium: low field intensity
D = E + P 0 e D E E r 0 =e × =e e
Linear polarization
e = 1+ c r
• Nonlinear medium: high field intensity
D = E + P 0 e
Nonlinear polarization
P =e c × E 0
L NL P = × E + (2) × E2 + (3) × E3 +... = P + P
0 e c c c
i ij j ijk j k ijkl j k l L NL P = × E + 2D × E E + 4 E E E +... = P + P 0 e c c
Linear
susceptibility
tensor
2nd order
nonlinear
susceptibility
tensor
3rd order
nonlinear
susceptibility
tensor
i, j, k = x, y, z
Summation over
repeated indices

10. Sum frequency generation (SFG)
Difference frequency generation (DFG)
• 2nd order optical nonlinearity
• Start with two beams ω = ω1
and ω = ω2
– SFG: ω3 = ω1 + ω2 , k3 = k1 + k2
– DFG: ω3 = ω1 - ω2 , k3 = k1 - k2
• SFG/DFG for photodetection
– Use a 1060 nm laser to convert 10
μm mid-infrared radiation to 960
nm near-infrared radiation that can
be handled by low-cost detectors
SHG Laser emission
Sum frequency Pump laser
Nonlinear optics is
a colorful discipline!
Image courtesy of Institut
für Angewandte Physik

11. Introduction to nonlinear optics…
Sum frequency generation
Example of second order nonlinear optical effects
3 w 2 w
1 w
= w1+w2
SHG, THG and higher harmonic generation

12.  Second harmonic generation (SHG): two photons of
frequency w yield one of frequency 2w.
=å
a abg b g w c w w w w w
b g
,
(2)
0 P (2 ) ε (2 ; , )E ( )E ( )
c (2) (2w;w,w ) abg : symmetric under interchange of b and g.
A Chemist view of
nonlinear optics
Chemist

13.  Criteria: Absence of centrosymmetry for c(2)
materials; absence of absorptions at inconvenient
frequency: P= eo{ c(1).E +c(2)E.E + c(3)E.E.E+….. }

14. k
Phase matching
c-axis
q n
Light polarized normal to c-axis: high refractive index
Þ can choose any angle q , still same index

15. k
c-axis
q n
Light polarized along c-axis: low refractive index
Þ different index for different angles q

16. Suppose n2w > nw
nw
q
Field normal to c-axis
k
c-axis
n2w
q
k
c-axis
nw
n2w q
k
c-axis
Field partially
parallel to c-axis
If 2w light has
component // c-axis
Þ phase matching possible

17. Phase matching condition
• Only when 2k1 = k2 will SHG be efficient
– n(λ1) = n(λ2)
2k1 = k2
2k1 ≠ k2
~ 100% SHG conversion
efficiency is possible by
optimizing phase matching!
• General rule for parametric processes
– SHG, SFG/DFG, THG, FWM
– momentum conservation

18. Applications:
• Optical phase conjugation
• Optical parametric oscillators
• Optical computing
• Optical switching
• Optical data storage