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
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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….. Slide30Slide31
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 0.35m<<1.55m
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