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a milestone in the journey from

Nonlinear Optics ---

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The technology of

generating and harnessing light

and other forms of energy

whose quantum is the Photon

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The Technology of Photonics : control, communications, computing

Control a large current

using a small current

Nonlinearity is required for light to control light

???

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Linear vs nonlinear

Stimulus vs response, Extreme stimulus

Linear response theory

Transport properties, mass, charge, heat

Stress vs starin

Linear regime NonLinear regime

Electric field

Polarization

We are nonlinear!

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Nonlinear optical properties (NLO)

Linear optical properties

intensity independent (eg., reflection, refraction and

absorption)

Nonlinear optical properties

depend on the intensity of incident light

eg., nonlinear absorption, nonlinear refractive index

Large optical intensity stronger perturbation of the Coulomb field in the medium nonlinear interaction optoelectronic applications

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NL medium

2

SHG : Second harmonic generation

A simple example for NLO effects: Harmonic Generation

e.g. 694 nm (red) 347 nm (violet)

How do we understand this?

physical picture…an analogy

A small signal electronic amplifier produces higher harmonics

of the input signal is not centered around the linear region of the

transistor characteristic curve.

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Examples of nonlinear systems

2

20

d g

dt l

Linearised pendulum

Actual (= nonlinear) pendulum

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0

0P E

0x xx x xy y xz zP E E E

0

0

y yx x yy y yz z

z zx x zy y zz z

P E E E

and

P E E E

What exactly is NON LINEAR? Nonlinear dependence of polarization

on optical field

Physical meaning, mathematical features

Polarization: dipole moment per unit volume of the medium.

Susceptibility : a characteristic property of the medium.

This is

linear!

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1

0

0

y yx x yy y yz z

z zx x zy y zz z

P E E E

and

P E E E

x xx xy xz x

y yx yy xy y

z zx zy zz z

P E

P E

P E

0x xx x xy y xz zP E E E

0

z

i ij j

x

P E

0i ij jP E

Einstein’s summation notation: Summation over repeated/dummy variable

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Linear optics : superposition

No energy transfer among waves

Nonlinearity Energy transfer; wave mixing

n th order, (n+1) wave mixing

(n) : susceptibility of n th order is an

(n+1) th rank tensor with [3(n+1)] components

(1) (2) (3)

0 ...i ij j ijk j k ijkl j k lP E E E E E E

• a tensor quantity • a complex quantity • a frequency-dependent quantity

( )n

What exactly is NON LINEAR? Nonlinear dependence of polarization on optical field

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Second Order Nonlinear Optical Processes

• Second harmonic generation

• Linear electro-optic effect : Pockel’s effect

Large and fast nonlinearity: A materials problem

Third order Nonlinear Optical Effects

• Phase conjugation

• Stimulated Raman scattering

• Self focusing

• Bistability

• Quadratic electro-optic effect : Kerr Effect

(1) (2) (3)

0 ...i ij j ijk j k ijkl j k lP E E E E E E

Second order NLO effects

(2) 2

SHG : Second harmonic generation

(2) 1

Sum and difference frequency generation

2

1+2

12

• Optical parametric oscillation • Applications of wave mixing

Latest solid state tunable lasers commercially available today are based on wave-mixing

e.g. Ti:Saphire

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The first ever experiment on Nonlinear optics

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Second Harmonic Generation

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Optical Phase Conjugation : idea

The phase of wave 4 is conjugated w.r.t that of wave 3 i.e. 4 is a time-reversed replica of 3

1 2

3

4

beam 1 beam 2

beam 3

beam 4

Scheme of DWFM

beam 1 beam 2

beam 3

beam 4

Scheme of DWFM

Three input waves inside a medium

generate a fourth wave as output

(3)

(3)

(3)

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Optical Phase Conjugation : implementation

Plane wave distorter ord. mirror

Reflection of a distorted wave from an ordinary mirror

distorted

distorted,

reflected further

distorted

incident

Reflection of a distorted wave from a OPC mirror

Plane wave distorter OPC mirror

distorted

distorted,

‘reflected’ from OPCM distortion-corrected

incident

Remember:

‘OPC mirror’ is not a

mirror,

but an OPC setup

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2

A picture from Wikipedia

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3

Ordinary mirror vs. “OPC mirror” i.e. linear reflection versus nonlinear reflection

Ordinary mirror

Optical Phase conjugate mirror Note: OPC mirror is not actually any mirror, but an OPC set up; with beam 3 as input and beam 4 as output. Beam 4 results from NL wave mixing and emerges out in a direction exactly

opposite to that of beam 3.

beam 1 beam 2

beam 3

beam 4

Scheme of DWFM

beam 1 beam 2

beam 3

beam 4

Scheme of DWFM

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Optical Phase Conjugation: Applications

Apart from measurement of chi-3 to characterize the NL material, wave front reversal (time-reversal) and distortion-healing properties of OPC are used in Adaptive Optics applications such as

Precise targeting of a beam,

Precise beam control in lithography,

Aberration-correction in amplifiers in fiber-optic communications etc

Optical data and image processing

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Guassian laser beam

Nonlinear medium

Self focusing n(I) = n0 + n2I

IIIIIIII ((((((

Applications :

•Beam shaping •Pulse shaping – soliton propagation •Optical limiting •Measurement of n2

An NLO phenomenon of the third order

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Implications of self focusing: a) The beam gets focused into one or more extremely narrow filaments with high intensity, sometime damaging the medium. b) The focusing effect can be used to compensate for the

beam spreading effect due to diffraction over large

distances, e.g. in fiber optic communications.

Thus a shape-maintaining beam (spatial soliton) can be

obtained.

c) By measuring the changes in beam profile in a self focusing experiment, it is possible to measure

(3)

An NLO phenomenon of the third order

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0

An NLO phenomenon of the third order:

Self focusing: A medium behaves like a lens

and a parallel beam gets focused (without any lens)

medium (3)

Refractive index becomes dependent on intensity I for large I

n(I) = n0 + n2I

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1

Conventional Materials

•Inorganic salts KDP, ADP, BaTiO3, BBO

•Semiconductors GaAs, Si, Ge, InSb

•Organic Materials Polymers, dyes, urea

Figure of Merit Large and Fast nonlinearity

Novel Materials QD, CNT, PBG

Materials for Nonlinear Optics