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New Era of Discreteness and Periodicity in New Era of Discreteness and Periodicity in

New Era of Discreteness and Periodicity in - PowerPoint Presentation

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New Era of Discreteness and Periodicity in - PPT Presentation

Optics   George Stegeman KFUPM Chair Professor   Professor Emeritus College of Optics and PhotonicsCREOL University of Central Florida USA 1887 1D Periodic in 1D Bragg grating ID: 536512

dispersion photonic diffraction optical photonic dispersion optical diffraction wavelength negative band index crystal properties waveguide periodic normal single optics

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Slide1

New Era of Discreteness and Periodicity in

Optics

 

George

Stegeman

, KFUPM Chair Professor

 

Professor Emeritus

College of Optics and Photonics/CREOL

University of Central Florida, USASlide2

1887

1-D

Periodic

in 1D

“Bragg grating”

What Is Meant By Discreteness and Periodicity?

Collection of

similar, discrete optical structures, materials, devices etc

. which as an

ensemble

create new phenomena, functionalities or applications.

Frequently periodicities are involved in discreteness, i.e. the structure arrangement is (quasi-) periodic in space.

Periodic

in

2D “Photonic crystal fiber”

Periodic in 1D “Waveguide array”

1990sSlide3

White Light

Incidence

Classic example of

periodicity

involving interference – dielectric mirror (frequency filter)

n

1

n

2

n

1

Single large (many optical wavelengths

in size) block of material (e.g. glass)

 Essentially nothing happens

Multi-layer structure

- different refractive indices (optical impedances) in each layer, layer thicknesses

/2

n

1

n

2

- Periodicities of order a few wavelengths

Analogy to solid state physics, but now with complete control over band structure

Multiple bands for propagation, i.e.

Floquet

-Bloch analysis of modes and dispersion

Guiding of radiation requires introducing

defects

into regular structures

Fabrication tolerances can be very

demanding but technology available

For an excellent discussion, see http://ab-initio.mit.edu/photons/Slide4

Where Did Awareness of New Optics From

Discreteness

Start?

Pioneering paper: E. Yablanovitch, “Inhibited Spontaneous Emission in

Solid-State Physics and Electronics”, Phys. Rev. Lett.,

58, 2059 (1987)

Atom in infinite medium radiates in all

directions at

at when electron in an excitedstate (lifetime

gm) drops to ground state viaspontaneous emission (fundamental process

)

Inside a cavity, only radiation in

cavity modes

cav

=

m

d/2

is allowed

n=1, 2, 3

…, i.e.

standing waves

d

-

|

g

>

|

m

>Slide5

Discreteness

New Science

at

cav

=

m

d/2

at



cav

Lifetime of excited state altered

Fundamental process inhibited!

at



cav

-

|

g

>

|

m

>

-

|

g

>

|

m

>Slide6

Length

Scales of Periodicity and Consequences

1. 

Optical Wavelength

- periodically modulated (in space) dispersion relations - prime examples are photonic crystals and waveguide arrays

- many new wavevectors available for wavevector-conserving interactions - control of anomalous diffraction (space) and dispersion (time) possible

- many new solitons - basic concepts closely related to solid state physics

2. Sub-optical Wavelength - modified optical properties when averaged over a wavelength - prime example is “meta-materials”

 unique optical properties - negative refractive index - novel dispersion relations and propagation properties - etc.

- effective medium theories important

Photonic Crystals

Photonic Crystal

Fibers

Waveguide Arrays

Negative IndexSlide7

1 D “Photonic Crystal”

n

1

n

2

White Light

Incidence

Constructive interference on reflection at

gap

!

band gap

k

0

–π/

a

irreducible Brillouin zone

d

Frequency

Gap

d=

/2

w

Slide8

1887

1987

1-D

2-D

3-D

Periodic

in 1D

“Bragg grating”

Periodic in

two dimensions

Periodic in

three dimensionsSlide9

3D Photonic Crystal: MIT

“Super-prism” Effect

Lasers

“Negative Refraction”

I.

II.

U

Õ

L

G

X

W

K

0

.

2

0

.

4

0

.

6

0

.

8

0

2

1

%

g

a

p

L'

L

K'

G

W

U'

X

U''

U

W'

K

zSlide10

Prisms: Bulk

Optics

Snells

Law:

n

1sin(

1)=n2

sin(2)

n

1

n

2

1

2

Refractive Index Dispersion in Visible

Angular Dispersion

Slide11

“Super” Prism: Photonic Crystal

Bulk

G

X

gap

Photonic

Crystal

Angular Dispersion

L'

L

K'

G

W

U'

X

U''

U

W'

K

zSlide12

Super Prism Effect:

Control Both Magnitude and Sign of Angular Dispersion

Input Guides

Output Guides

PC

SOI Planar Photonic Lattice

Near

-K direction

0.4

o

/nm

Near

-M direction

1.3o

/nm(100x normal glass prism)

A. Lupu, E. Cassan, S. Laval, et. al., Opt. Expr. 12, 5690 (2004)Slide13

“2D Optical Circuits in Quasi-3D” Photonic Crystals

Note:

– This 2D circuit

must

be imbedded in a 3D photonic crystal

to avoid radiation loss along the z-axis!

y

x

z

Guided Wave Planar Device Concept

“Light Channels” introduced by eliminating one row and/or columnSlide14

“2D Optical Circuits in Quasi-3D” Photonic Crystals

z

k

z

If height

z

is

finite

,

we must couple to

out-of-plane wavevectors…

Make it as tall as possible!!Slide15

Reducing Bending

Losses: Technical University of Denmark

Two Bend Loss/Loss of Straight Guide

Optimized

Un-optimized

Optimized

L.H. Frandsen, A. Harpøth, P.I. Borel, M. Kristensen, J.S. Jensen

and O. Sigmund, Opt. Expr.,

12

, 5916 (2004)Slide16

Photonic Crystal

Fibres

: Cylindrical 1D Photonic Crystals

Defect Necessary for Guiding

geometry, shape and filling material can be varied

fabrication improved to loss of 0.58dB/km at 1550nm

exquisite

control

of dispersion in effective index

- zero group velocity dispersion (GVD) wavelength - multiple zero GVD wavelengths - phase-matching of nonlinear interactions

photonic band gaps fibers wavelength size modal areas  enhanced NLO

Courtesy of Phillip Russell, Bath UniversitySlide17

wavelength (

m

m)

0.5

0.6

0.7

0.8

0.9

1.0

-

300

-

- 200

100

0

100

200

300

(

/

n

.

k

p

s

m

m

)

anomalous

normal

bulk silica

silica strand

(computed)

silica webs reduce

GVD in PCF

GVD (ps/nm-km)

Wavelength (

m)

Group Velocity Dispersion (GVD) Control: Bath University

Fiber Transmission Line

Temporal

PulseSlide18

wavelength (

m)

dispersion (ps/nm.km)

2

0

2

4

6

8

10

1.6

1.4

1.2

1

normal

anomalous

d = 0.57

m

Λ = 2.47

m

d = 0.58

m

Λ = 2.59

m

Control of dimensions

to better than 1% required

PCF With Ultra-Flat and Ultra-Small Dispersion (GVD): Bath

d = hole size

= hole separation

11 periodsSlide19

Supercontinuum Generation: Opt. Expr. May 2006, Bath Fiber

pump

=1550nm

100fs pulses

A nonlinear optics feast of effects!!

Self- and cross-phase modulation

Multi-wave mixing

Stimulated Raman, Anti-stokes Raman

Raman Self-Frequency ShiftThird Harmonic GenerationEtc.

From

<350nm to >3000 nm!Slide20

a

n

is field at n-

th

channel center

β

is propagation constant of single isolated channel

E(x) is the transverse channel waveguide field.

c is coupling constant due to field overlap

n

n+1Waveguide Arrays: Coupling

Between Waveguides

a

n+1

n

n+1

E(x)

a

nSlide21

Arrays of Weakly Coupled Waveguides: “Discrete” Diffraction

Discrete diffraction

Light

spreads (diffracts) through array by “discrete diffraction”, via coupling c

1D or 2D lattices of waveguides

feature dimensions of order of the wavelength of light

periodicity

 multiple (

Floquet

-Bloch) bands for propagation

- negative refraction - normal, zero or anomalous diffraction

- discrete Talbot effect - photonic Bloch oscillations

Many novel “discrete” spatial

solitons

-

solitons

with fields in-phase or out-of-phase in

adjacent

channels

- “interface “

solitons

at edges, corners and between dissimilar

arrays

Distance

Waveguide Number

20

-20Slide22

1D

Diffraction

in Waveguide Arrays

k

z

k

x

d

-

Normal diffraction

“Anomalous” diffraction

Zero diffraction

D

< 0 “normal” diffraction

D

> 0 “anomalous” diffraction

k

x

Bloch

wavevector

(momentum)

Homogeneous Medium

Normal diffraction

1-3 degreesSlide23

Finite Beam Excitation

Distance

Waveguide Number

0

20

-20

W

z

Diffraction in Bulk MediaSlide24

Length

Scales of Periodicity and Consequences

2. Sub-optical Wavelength

- modified optical properties when averaged over a wavelength

- prime example is “meta-materials”

 unique optical properties - negative refractive index - novel dispersion relations and propagation properties

- etc. - effective medium theories important - basic concepts closely related to solid state physics

Slide25

Negative Index Materials: Problem in Materials Science

Negative Dielectric Constant

Found in nature (metals)

due to electron plasma resonances

Negative Magnetic Permiability

Not found in nature

Composite Materials with Metals

For metallic (sub-wavelength) inclusions

Plasmon (collective electron) resonances

with resonant frequencies

depending

on shape and size both electric and magnetic properties changed

Pioneer:

V. G. Veselago, Soviet Physics USPEKI 10, 509 (1968).Slide26

Negative Index Materials in the Near Infrared

Al

2

O

3

Au

=2000nm

Shuang Zhang, Wenjun Fan, N. C. Panoiu,K. J. Malloy, R. M. Osgood and S. R. J. Brueck,

Phys. Rev. Lett.,

95, 137404 (2005)Slide27

Examples of Repercussions and Possible Applications:

Contra-directional Energy and Phase Velocity

Wave vectors

Poynting vectors

(energy flow)

Maxwell’s Equation predict:

Courtesy of Allan Boardman, Salford University

Wave vectors

Poynting vectors

(energy flow)Slide28

“Cloaking”

J. B. Pendry, D. Schurig, D. R. Smith, Science,

312

, 1780 (2006)

Quote: “it is now conceivable that a material can be constructed whose permittivity and permeability values may be designed to vary independently and arbitrarily throughout a material, taking positive or negative values as desired.”

“Each of the rays intersecting the large sphere is required to follow a curved, and therefore longer, trajectory than it would have done in free space, and yet we are requiring the ray to arrive on the far side of the sphere with the same phase.”

 Works over a narrow spectral bandwidthSlide29

Summary

Discreteness with periodicity introduces new paradigms into optics

F

undamental wave properties, namely refractive index, dispersion,

scattering and interference, and diffraction can be controlled

and/or eliminated

3. New physical phenomena are introduced and well-known effects

are changed. New ultra-compact optical devices possible

And much, much more….. Slide30
Slide31

Negative Index Materials: Martin Wegeners Group

Optics Letters,

31

, 1800, (2006)

 = 1500nmSlide32

d

G

X

M

irreducible Brillouin zone

2-D Photonic Crystals - Array of Pillars: MIT

frequency

w

(2πc/d) =

d

/

l

G

X

M

G

0

0.2

0.4

0.6

0.8

1

TM Photonic Band Gap

TM bands

n

2

/

n

1

=3.5

E

H

E

H

TM

TE

Orthogonal Field Distributions

E

z

(+ 90° rotated version)

E

z

+Slide33

Electrically Pumped

, Semiconductor Photonic Crystal Laser:

Park et. al. Science Sept 3, 2004

2007 – 100

A and 0.9V thresholdSlide34

0.3

0.2

0.1

0.0

10

20

30

40

50

60

70

80

fibre length (cm)

relative coupled power

P

coupled energy 5.6

J

pulse duration 6 nsec

S

AS

0.000

0.010

0.020

Highly Efficient Raman Shifter: Bath Un. Science 2002

Stokes

(683 nm)

anti-Stokes

(435 nm)

hydrogen

filled

pump

(532 nm)Slide35

k

z

(1/

m)

=k

x

d (units of )

Band 1:

Band 2:

Band 3:

Band 4:

Floquet-Bloch BandsSlide36

G

X

M

(k not conserved)

2D Photonic Crystal Cavity Modes: MIT

G

X

M

G

frequency (c/a)

Bulk Crystal Band Diagram

0

0.2

0.4

0.6

Photonic Band Gap

A

point defect

can

push up

a

single

mode

from the

band edge

High Q cavitiesSlide37

“Endlessly” Single Mode Fibres

Normal fibers: single mode for

2a

endlessly single-mode

The smaller the

, the smaller the influence

of the air holes

 the larger the effective

n

cl

the smaller

with proper design

V

<2.405

- Measured single mode for 0.35m<<1.55m

T. A. Birks, J. C. Knight, and P. St. J. Russell,

Opt. Expr.,

22

, 961 (1997)Slide38

Example of Shape Dependence

Zahyun Ku and S. R. J. Brueck, Opt. Expr.,

15,

4515 (2007)

3

2

1

0

FOM

0

-4

4

Effective Index