nonlinear optical materials

Nonlinear optics

Prof. V. KrishnakumarProfessor and Head

Department of PhysicsPeriyar University

Salem – 636 011, India

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

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.

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

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”.

In Non-Linear Optics

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

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

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.

Nonlinear polarization• Linear medium: low field intensity

• Nonlinear medium: high field intensity

PED += 0ε EED r 0εεε =⋅=

Linear polarization

PED += 0ε

Nonlinear polarization

EP ⋅= χε0

NLL PPEEEP +=+⋅+⋅+⋅= ...3)3(2)2(0 χχχε

NLLlkjijklkjijkjiji PPEEEEEDEP +=++⋅+⋅= ...420 χχε

Linear susceptibility

tensor

2nd order nonlinear

susceptibility tensor

3rd order nonlinear

susceptibility tensor

Summation over repeated indices

χε += 1r

i, j, k = x, y, z

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

Sum frequency Pump laser

Laser emissionSHG

Image courtesy of Institut für Angewandte Physik

Nonlinear optics is a colorful discipline!

Introduction to nonlinear optics…Sum frequency generation

Example of second order nonlinear optical effects

1ω3ω2ω = ω1+ω2

SHG, THG and higher harmonic generation

Second harmonic generation (SHG): two photons of frequency ω yield one of frequency 2ω.

∑=γβ

γβαβγα ωωωωωχω,

)2(0 )()(),;2(ε)2( EEP

),;2()2( ωωωχαβγ : symmetric under interchange of β and γ.

A Chemist view of nonlinear optics

Chemist

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

Light polarized normal to c-axis: high refractive index

⇒ can choose any angle θ , still same index

nθ

k

c-axis

Phase matching

Light polarized along c-axis: low refractive index

⇒ different index for different angles θ

nθ

k

c-axis

Suppose n2ω > nω

Field normal to c-axis

nω

θ

k

c-axis

n2ω

θ

k

c-axis

nω

n2ω θ

k

c-axis

Field partially parallel to c-axis

If 2ω light hascomponent // c-axis

⇒ phase matching possible

Phase matching condition

• Only when 2k1 = k2 will SHG be efficient– n(λ1) = n(λ2)

• General rule for parametric processes– SHG, SFG/DFG, THG, FWM– momentum conservation

2k1 = k2

2k1 ≠ k2

~ 100% SHG conversion efficiency is possible by optimizing phase matching!

Applications:

• Optical phase conjugation

• Optical parametric oscillators

• Optical computing

• Optical switching

• Optical data storage