Download - 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