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Photonic Crystals – it’s all about the mirrors

Maksim Skorobogatiy

Canada Research Chair in Photonic Band Gap materials and devices

I would like to thank Prof. Yoel Fink fiber research group at MIT, and Prof. Steven Johnson at MIT for their contributions.

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Low index of refraction

High index of refraction

3D photonic crystal

Periodic electromagnetic media

3

)(~, trkieHE

n

cnk2

/

n

n

Plane-waves in a uniform dielectric

E

H HEfluxEnergy

~

4 Scattering regimes

a

a

a

a>>incoherent scattering

a<<averaging

a~coherent scattering

Photonic crystals

5 Photonic CrystalsPeriodic electromagnetic media

2-D

periodic intwo directions

3-D

periodic inthree directions

1887

1-D

eriodic inone direction

p

1987

quazi-1D

Bragg fibers quazi-2D

microstructured fibers

1977

6 Photonic Crystals Components

periodic electromagnetic media with defects

3D Photonic Crystal with Defectscan trap light in cavities and waveguides (“wires”)

7 1D Photonic Crystal

1 - D

8 Uniform dielectric

k

n

cnk2

/

)(~, trkieHE

n

c

n

ct

22 k

light cone

light line: = c / n

kt

(transverse wavevector)

n(preferred direction) (propagation constant)

Our first band diagram

no light propagation, kt is IMAGINARY

light propagation

22

c

ntk

9 Two uniform dielectrics (intuitive picture)

1k

22

c

niitk

2k

light cone

light line 1: = c / n1

n1

k1t

n2

<

k2t

no light propagation in dielectrics 1,2

light line 2: = c / n2

light propagation in dielectric 2 only

light propagation in dielectric 1,2

2

ii n

c

sin

10 A quest for a perfect mirror

1

190o0 tan-1(n2/n1)

TM

TE 2

21

221

nn

nn

Reflectance

As index contrast increase

As index contrast increase

Dielectric mirror, low loss, but strong angular and polarization dependence

Reflectance is getting more uniform for all polarizations and wider region of angles as index contrast increases

Metallic mirror, low angular and polarization dependence, but very high loss for optical frequencies

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modesin crystal

TE

TM

propagation perpendicular to the layers

1d b

and

gap

Light in the multilayer

conserved

d1 d2

n1n2

d1n1=d2n2=/4

Quaterwave stack condition

Projected Bands of a 1d Crystal(a.k.a. a Bragg mirror)

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modesin crystal

TE

TM

Omnidirectional Reflection[ J. N. Winn et al, Opt. Lett. 23, 1573 (1998) ]

light

line o

f air =

c

in these ranges, there is no overlap between modes of air & crystal

all incident light(any angle, polarization)

is reflectedfrom flat surface

needs: sufficient index contrast & nhi > nlo > 1

conservedAir

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[ Y. Fink et al, Science 282, 1679 (1998) ]

Omnidirectional Mirrors in Practice

/mid

6 9 1 2 1 50

5 0

1 0 0

0

5 0

1 0 0

0

5 0

1 0 0

0

5 0

1 0 0

0

5 0

1 0 0

normal

450 s

450 p

800 p

800 s

Re

flec

tanc

e (

%)

Wavelength (microns)

Te / polystyrene

Ref

lect

ance

(%

)

contours of omnidirectional gap size

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Smaller index, n 1

0%

10%

20%

30%

40%

50%