p7 photonic crystal optics

7/27/2019 P7 Photonic Crystal Optics

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7-2E. Photonic crystals

Purdue Univ, Prof. Shalaev, http://cobweb.ecn.purdue.edu/~shalaev/

Univ Central Flor ida, CREOL, Prof Kik, http://sharepoint.optics.ucf.edu/kik/OSE6938I/Handouts/Forms/Al lItems.aspx


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3-D

2-D

1-D


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Consider a two-dimensional hotonic cr stal


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Bloch theorem


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Bloch theorem


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Bloch theorem


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Bloch theorem


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Bloch theorem


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Bloch theorem


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Dispersion curve = Photonic band structure

an gap

Bandgap (no transmission) tan ng wave

vgroup=0

Long wavelength


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Remind the Dis ersion Curve of Slab Wave uide


Because guiding modesredistribute themselves with

Band structure

frequency, for small , the

dispersion curve of guiding

modes approaches the cladding

line;

For lar e it a roaches thecore line.


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Photonic band gap

Light in 1-D photonic crystal

H L H L H L


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Photonic band gap


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Photonic band gap

ragg e ec on

2 ( )B B

nd Sin =

2 ~ 2

Bd B

Bd

= =

Ph t i b d


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Photonic band gap

ragg rac on

Wavelength does not correspond to the

period

Wavelength corresponds to the

period.

.

Wave propagates through.

e ec e waves are n p ase.

Wave does not propagate inside.

Ph t i b d


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Photonic band gap

22

2E k

m=

Photonic band gap


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PBG formationPhotonic band gap

1. Dispersion curve forfree space 3. At the band edges, standing wavesform, with the energy being either in

the high or the low index regions

2. In a periodic system, when half the

aka ==2

wavelength corresponds to the periodicity

4. Standing waves transport no energy

propagation.with zero group velocity



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n1: g n ex ma er a

n2: low index material4. Standing waves transport no energy

with zero group velocity

n1 n2 n1 n1 n1n2 n2standing wave in n2Air band

Sto band

standing wave in n

0

k



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Plot the dispersion curves for both the positive and the negative sides,|>/ |>/ one reciprocal lattice vectors.


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2-D Photonic Crystals

1. In 2-D PBG, different layer spacing, a, can be met along different =

2. PBG Photonic band a = sto bands overla in all directions

2D Photonic band structure


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an agram

Air band

Stop band

Dielectric band



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1. Stop band


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Four Possible Functionalities of PBG

1. Use of Stop Band

1. Stop Band:

Stop bandomni-directional mirror

PBG wave uides

2. Dielectric band


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.

2. Dielectric Band: Uses the

strong dispersion availablen a p o on c crys a

(dispersion engineeringDielectric band

2. Dielectric band


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2. Dielectric band


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Remind the dispersion relation in bulk media

1. In a homogeneous material in absence of

material dispersion n()=constant =n, thespers on agram s s mp y a s ra g ne:=kc/n.

2. In 2D systems, one can think of this line as a cone.

For a given frequency , this cone becomes a constant frequency circle.

2. Dielectric band


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ky

kx

W ti i k

2. Dielectric band


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Wave propagation in k-space

Real s ace

The wave vector diagram tells us the direction and magnitude of the refracted

and reflected beams. Their direction is normal to the iso-frequency curve and

corresponds to Snells law.

2. Dielectric band


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2. Dielectric band


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2. Dielectric band


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2. Dielectric band


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3. Air band


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3. Use of Air Band

3. Air Band : Couples to radiative

modes for light extraction

- Air bandand fiber coupling.

3. Air band


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4. Defect band


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.

4. Defect Band : Couples to

waveguide/cavity modes forDefect band

spectral control such as PBGpoint defect laser or PBG linedefect filter, etc.


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Line Defect PBG Waveguide4. Defect band


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Line Defect PBG Waveguide

Defect modes

in stop band

Dispersion diagram of W1 line-defect

photonic crystal waveguide:

.

Photons are prohibited in the 2D PBG,

which lead to lossless confinement of

photons in the line defect area.

Defects in PBG4. Defect band


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Defects in PBG

4. Defect band


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4. Defect band


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4. Defect band


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4. Defect band


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3D Photonic materialsS.Noda, Nature (1999) K. Robbie, Nature (1996)

E. Yablonovitch, PRL(1989)

Artificial Phonic Structure



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Artificial Phonic Structure

E.Yablonovitch et al., PRL (1987, 1991)

Fabrication of artificial fcc material

material.


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Natural Opals


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Artificial opal sample (SEM Image)

Several cleaved planes of fcc structure are shown



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There are 3 in-layer position

Silica spheres settle in

close acked hexa onal

A red; B blue; C green;

Layers could pack in

layerscc a ce: or

hcp lattice: ABABAB



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Inversed opals obtain greater dielectric contrast than opals.

Band structure of diamond lattice3D Photonic band structure


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oton c an structure o amon att ce re ract ve n ex ~ .

John et. al. PRE (1998)

PCF


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PCF


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PCF


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The fiber supports a single mode over the range of at least 458-1550nm!

PCF


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PCF


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PCF


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PCF


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PCF


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p7 photonic crystal optics

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