Computational Materials Science Laboratory

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Theoretical investigation of different structures of photonic band

gap materials with and without defects

by

Theory

What is a photonic band gap?What is a photonic band gap?

The numerical methodsThe numerical methods

Results

The semiconductors multilayers

The 2D hexagonal structures

The cavity concept and defect in 2D structures

The Sc, cfc and inverted opal structures

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What is a photonic crystal?

a Photonic Band Gap Material

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What is the physical origin of the photonic band structure?

What is the physical origin of the photonic band structure?

Electronic

Photonic

The electron wave scatters coherently from the different potential regions

The electromagnetic fields scattercoherently at the interfaces between

different dielectric regions

)()( RrVrV )()( RrVrV

Rrr Rrr

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The crystal periodicity

aa bb aa bb aa bb aa bb

A system of stacking layers of high and low refractive index

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A minimum of the contrast index

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The optical wave is of the same magnitude as the stack periodicity

aa bb aa bb aa bb aa bb a

a

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The symmetry of the lattice structures

1D 2D 3D

The face centered cubic crystal (3D) was considered the best candidate

since this structure has the most spherical Brillouin zone.

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Why it is so important?The spontaneous emission control

L'émission spontanéeL'émission spontanée

Electro nic Dispersion

Electro nic Dispersion

Photo nic Dispersion

Photo nic Dispersion

kk

1 0001 000

Conduc tion

Conduc tion

kk

hvhv

Photo nic Band Gap

Photo nic Band Gap

Valenc

e

Valenc

e

Electro nic Band Gap

Electro nic Band Gap

Le contrôle de l'émission spontanée Le contrôle de l'émission spontanée

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High reflection substrate based on PBGM

trapped radiation

antenna

air

substrate

air

air

photonic crystalsubstrate

air

(a)

(b)

antenna

A simple substrate

A substrate based on photonic crystal

Why it is so important?

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Highly efficient light emitting diodes

LED Spontaneous emission

p-n junction

each e- on 1 photon90-100%2% of light

Redirect the photons

Why it is so important?

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Increase the spontaneous emission

Edward Purcell 1946

Inhibition of the propagationPBGM

Increase the emissioncavity

Why it is so important?

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When we introduce the defect

Introducing a cylinder with different radius

Introducing a cylinder with different dielectric constant

by either adding or removing dielectric material from a chosen unit cell in the crystal.

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Consequences

Have cavities with high quality factors

Show quite narrow transmission spectra leading to high filters

resonant cavities is enhancing the efficiency of lasers

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Metallic waveguide coaxial cables

Optical fibers

Principal: Rely on total internal reflection.

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If a fiber optic cable takes a tight curve, the angle of incidence is too large for total internal reflection

Since they do not relay exclusively on total internal reflection, continue to confine light even around light corners.

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Light that propagates with frequency within the PBG of the crystal is confined, and can be directed

along the waveguide.

Light is forced to bounce around inside the waveguide, so the light is guided

only around corners.

Theory

What is a photonic band gap?What is a photonic band gap?

The The numerical methods

Results

The semiconductors multilayers

The 2D hexagonal structures

The cavity concept and defect in 2D structures

The Sc, cfc and inverted opal structures