Linear Optics vs Non Linear Optics

Linear optics- ‘Optics of weak light’: Light is deflected or delayed but its frequency is

unchanged. Superposition principle holds

Non-Linear optics-‘Optics of intense light’: We are concerned with the effects that light itself induces

as it propagates through the medium.

Superposition principle not valid

In Linear optics

A light wave acts on a molecule, which vibrates and then emits its own light wave that interferes with the original light wave.

In Non-Linear Optics

If irradiance is high enough vibrations at all frequencies corresponding to all energy differences between populated states are produced.

OPTICS – A LIGHT MATTER INTERACTION

Nonlinear optics (NLO) is the study of interaction of intense laser light with matter.

output

NLO

samp

le

input

νh

E1

E2

Absorption

E1

E2νh

Spontaneous Emission

Light Matter interaction

E1

E2νhνh νh

Stimulated Emission

Stimulated Emission

m

Properties of Laser Beam

A laser beam •Is intense•Is Coherent•Has a very low divergence

Optical power density

Focused laser beam E ~ 1010 V/m

How does optical nonlinearity arise

The strength of the electric

field of the light wave should be in the range of atomic fields N

a0

e

νh

20/ aeEat =

220 / mea =

V/m102 10×≈atE

Applied Electric field distorts the cloud and displace the electron

Compare this with mass on a spring Separation of charges gives rise to a dipole moment Dipole moment per unit volume is called the

polarisation

++=+ --

E

Optical Nonlinearity

F= - kx

When electromagnetic waves propagate in a material, the atoms and molecules oscillate at the frequencies of the electric field associated with waves. The field associated with these EM waves polarizes the molecules in the medium, displacing them from their equilibrium positions and induces a dipole moment, p, given by

p=qd q is the electric charge and d is the field induced displacement. The polarization P, i.e. the dipole moment per unit volume, resulting from this induced dipole is given by

P=Nqd N is the electron density in the medium.

The polarizing effect of the field on the molecular dipoles depends both on the properties of the medium and on the field strength E.

P= ϵ0 χ E

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

Input intensity

Output

P=Nqd

?

Like loaded spring

m

F= -kx

P= ϵ0 χ E

E = Eo cosωt

(1) (2) 2 (3) 30 ...P E E Eε χ χ χ = + + +

1.Permanent Polarization

2.First order Polarization

3.Second order Polarization

4.Third Order Polarization

Second Harmonic Generation

ωω

ω2)2(χ

Third Harmonic generation

ω )3(χω3

ω

E = E1 cosω1t +E2 cosω2t

OPTICAL MIXING

22211

)2()2( )coscos( tEtEP ωωχ +=

)cos(&)cos( 2121 ωωωω −+

1ω

2ω)2(χ

1ω

2ω213 ωωω +=

Sum Frequency Generation

1ω3ω2ω

1ω

2ω)2(χ

2ω

1ω213 ωωω −=

Difference Frequency GenerationDifference Frequency Generation

1ω3ω2ω

FOCUSING OF LIGHT BY LENS

focus

Refractive Index with Intensity 3 3

0 0LP E E=εχ +εχ

0

nε

=ε

0D E E P= ε = ε +

3 20 01 L ( )( ( ) E )E= ε +χ +ε χ

3 20 01 L( ) Eε = ε + χ + ε χ

31 2 2 1 21 1

1L / /

Ln ( ) ( E )χ= +χ ++χ

20 2 0n n E≈ +

Nonlinear Refractive Index

Innn 20 +=

where 20 |)(|2

ωπ

Ecn

I = )3(20

2

2

12 χπcn

n =

Self focusing and self defocusing

The laser beam has Gaussian intensity profile. It can induce a Gaussian refractive index profile

inside the NLO sample.

)3(χ

Nd:YAGLaser

DetectorD2

Computer

Lens Aperture

+Z

Sample Cell

-ZDetector

D1 Power Meter

Z-scan Set-upZ-scan Set-up

z.swf

Z- Scan Signature

0.4

0.6

0.8

1

1.2

-20 -10 0 10 20

Z mm

No

rma

lise

d T

ran

smitt

an

ce

0.2

0.4

0.6

0.8

1

1.2

-20 -10 0 10 20

Z (mm)

Nor

mal

ised

Tra

nsm

ittan

ce

Different Class of NLO Materials

Inorganic Lithium niobium oxide, Potassium titanile Phosphate Ammonium dihydrogen phosphate, Potassium dihydrogen phosphate, Barium Metaborate

Organics Materials

Low cost Ease of fabrication Integrating in to a single devicesEasy to do fine tuning of its NLO properties by

turning its Chemical structure Low dielectric constant Inherent synthetic flexibilityHigh optical damage threshold

Structural requirement

++= +

-

D A D A

Enhancement of NLO response Science 281 (1998) 1653

TNLO enhancement by

Increase conjugation length Create D-π-A- π -D structure A- π -D- π –A structure

•New Frequency Generations

•Different Wavelength lasers from the same Laser Source

•Optical limiting

Input fluence

Output fluence

Applications:

Waveguide Inscriptions Lab on a Chip

Optical Signal Processing

1. Switching and routing are carried out electronically and processing in the electronic domain

2. Optical transmission in optical domain 3. Detection and processing in the electronic domain

again 1 2 3 to a single Unit