2. 3.46/3.156
Fall
2015
Class
Organiza4on
n Instructor:
§ Prof.
Polina
Anikeeva
(8-‐425)
[anikeeva@mit.edu]
§ Office
Hours:
Monday
6:30-‐7:30
pm
n Guest
Lectures:
§ Prof.
Lionel
Kimerling
(13-‐4118)
[lckim@mit.edu]
§ Dr.
Chris
Doerr
(?)
[doerrcr@gmail.com]
n Class
Format:
¨ Monday
9:30-‐11
am
§ Quiz
(10
min):
aZendance
mandatory
§ Review
of
last
class/student
ques4ons
§ Lecture
¨ Wednesday
9:30-‐11
am
§ Review
of
last
class/student
ques4ons
§ Lecture
n Grading:
G
UG
§ Problem
Sets
(4)
20%
0%
§ Quizes
(7-‐8)
30%
25%
§ Design
Reviews
(3)
40%
50%
§ Final
Exam
–
DR4,
oral
10%
25%
2
3. 3.46/3.156
Fall
2015
Schedule
and
Topics
3
Op4cs
Optoelectronics
Special
topics
Integra4on
§ Intro:
Photonic
Materials
Design
×2
(PA)
§ Photon
Op4cs
&
EM
Wave
Op4cs
§ Periodic
Media
&
Photonic
Crystals
§ Op4cal
Resonators
§ Guided
Wave
Op4cs
§ Microphotonic
Numerical
Simula4on
1
(CD-‐?)
§ Electrons
and
Photons
in
Semiconductors
§ Materials
Processing
(LCK)
§ Solar
Cells
§ Photodetectors
§ LEDs
§ Op4cal
Amplifiers
and
Lasers
§ Semiconductor
Lasers
§ Organic
Optoelectronics
§ Nanostructured
Optoelectronics
×2
§ Non-‐Linear
Op4cs
§ Biophotonics
4. 3.46/3.156
Fall
2015
Class
Organiza4on
n Course
Website
¨ Stellar:
h"p://stellar.mit.edu/S/course/3/fa15/3.46/
¨ Access:
registered
students
and
authorized
auditors
n Lecture
Content
(on
Materials
link)
1. Lecture
Slides
n Posted
to
website
within
24
hrs
of
presenta4on
2. Lecture
Materials:
resources,
readings,
tools
n Posted
to
website
4
5. 3.46/3.156
Fall
2015
Class
Organiza4on
n Student
data
¨ Submit
to
Ayn
Inserto
(ainserto@mit.edu)
1. Full
Name
2. Undergraduate/graduate
status
(UG/G)
3. Research/UROP
advisor
and
thesis
topic
(if
applicable)
4. Status:
class-‐registered
or
auditor
n Work
Groups
¨ For
doing
weekly
Problem
Sets
(G)
and
Design
Review
projects
(All)
¨ 2-‐3
Graduate
or
4-‐5
Undergraduate
students
¨ Groups
will
be
assigned
by
Polina
Anikeeva
5
6. 3.46/3.156
Fall
2015
Class
Organiza4on
Problem
Sets
and
Design
Reviews:
n Weekly
Problem
Set
and
Monthly
Design
Review
assignment
n Problem
Sets
and
Design
Reviews
will
be
done
by
Work
Groups
n One
PSet/DR
per
group
uploaded
(MSWord,
Pages,
PDF)
to
Homework
link
n Electronic
Signature:
name
entry
on
top
of
page
1
aZes4ng:
a) Your
contribu4on
b) Agreement
that
all
Group
members
have
contributed
n All
members
of
a
given
Group
receive
same
PSet/DR
grade
n Group
members
may
pick-‐up
graded
hard-‐copy
from
PA
n Problem
Set
1
and
Design
Review
1
are
assigned
today
(Wednesday,
Sep.
9)
¨ Grad
students:
PSet
due
09/16/15
¨ DR
1
due
10/07/15
¨ Download
from
course
website
6
7. 3.46/3.156
Fall
2015
Class
Organiza4on
n Design
Review
project
¨ In-‐class
introduc4on
and
discussion
¨ 20
min
(5-‐10
slide)
presenta4on,
all
Group
members
speak
¨ Corrected
slides
+
final
2-‐3-‐page
report
due
two
days
later
(email
to
PA)
n Weekly
Quiz
and
Final
Exam
¨ Weekly
Quiz
test
student
aZen4veness,
covers
two
lectures
from
previous
week
¨ Skipping
a
weekly
Quiz
without
advance
no4fica4on
=
0
grade
for
that
Quiz
¨ Final
Exam
-‐
Oral
on
Friday
12/05
evening
¨ Quiz
1
is
on
Monday
Sep.
14
§ Tes4ng
Lecture
1
content
7
8. 3.46/3.156
Fall
2015
Resources
n 3.23
or
3.024
Notes
if
you
already
took
the
class.
n “Fundamentals
of
Photonics”
B.
E.
A.
Saleh
and
M.
C.
Teich
¨ Chs.
5,
6
n “Op4cal
Materials”
reading
by
A.
M.
Glass
n “Bands
and
Bonds”
reading
by
L.
C.
Kimerling
n “Hardness
of
Covalent
and
Ionic
Crystals:
First-‐Principle
Calcula4ons”,
Antonín
Šimůnek
and
Jiří
Vackář,
PRL
96
(2006)
8
9. 3.46/3.156
Fall
2015
Op4cal
Fiber:
How
It’s
Made?
9
SiO2:
GeO2
SiO2:
SixOyFz
Germania
doped
silica
n
>
n(SiO2)
Fluorosilicate
doped
silica
n
<
n(SiO2)
§ The
fiber
geometry
is
defined
on
a
macroscale:
Preform
fabrica4on
§ Fiber
dimensions
are
reduced
to
microscale:
Thermal
drawing
11. 3.46/3.156
Fall
2015
Op4cal
Loss
in
Silica
Fiber
11
Rayleigh
scaZering:
Density
varia4on
on
the
length
scale
shorter
than
the
light
wavelength
Intrinsic
electronic
absorp4on
of
silica
is
in
the
UV
~
140
nm.
Silica
is
an
insulator,
i.e.
wide
bandgap.
Mie
scaZering:
Density,
geometry
varia4on
on
the
length
scale
longer
than
the
light
wavelength
Intrinsic
absorp4on
of
silica
vibra4onal
modes
and
mul4photon
absorp4on
extends
into
the
near
IR.
Vibra4onal
peaks
are
>
7
µm.
Extrinsic
absorp4on:
water
vapor
OH
and
combina4on
OH-‐silica
vibra4onal
modes
at
0.95,
1.24
and
1.29
µm.
12. 3.46/3.156
Fall
2015
Op4cal
Loss
in
Silica
Fiber:
Why
Silica?
12
Fiber
Material
Op4cal
loss
(dB/km)
Experimental
Theore4cal
SiO2
0.16
(1.55
µm)
~0.1
(1.55
µm)
GeO2
4
(2.0
µm)
0.1
(2.5
µm)
Fluorides
0.9
(2.5
µm)
0.001
(3.5
µm)
Chalcogenides
35
(2.5
µm)
0.05
(5
µm)
Polymers
20
(0.7
µm)
Theore4cal
Loss
Plot
13. 3.46/3.156
Fall
2015
Op4cal
Loss
in
Silica
Fiber:
Why
Silica?
13
Fiber
Material
Op4cal
loss
(dB/km)
Experimental
Theore4cal
SiO2
0.16
(1.55
µm)
~0.1
(1.55
µm)
GeO2
4
(2.0
µm)
0.1
(2.5
µm)
Fluorides
0.9
(2.5
µm)
0.001
(3.5
µm)
Chalcogenides
35
(2.5
µm)
0.05
(5
µm)
Polymers
20
(0.7
µm)
§ Fluorides,
chlorides,
chalcogenides:
Unstable
in
moisture,
toxic,
crystalize
§ Silica:
Cheap,
stable,
easy
to
fabricate
Theore4cal
Loss
Plot
14. 3.46/3.156
Fall
2015
Light
Propaga4on:
Wave
Equa4on
14
∇×
E +
∂
B
∂t
= 0
∇×
H −
∂
D
∂t
=
J
∇⋅
B = 0
∇⋅
D = ρ
Maxwell’s
Equa4ons:
∇2
E −
1
c2
∂2
E
∂t2
= 0
∇2
H −
1
c2
∂2
H
∂t2
= 0
Wave
equa4on:
(absence
of
charges
and
currents)
c =
c0
n
=
1
µε
speed
of
light
in
media:
speed
of
light
in
vacuum:
n =
c0
c
=
µε
µ0ε0
= µrεr
refrac4ve
index:
c0 =
1
µ0ε0
= 3×108
m s
ε0 =
10−9
36π
F m
µ0 = 4π ×10−7
H m
permi•vity
of
free
space:
permeability
of
free
space:
Simplest
solu4on
to
wave
equa4on:
plane
waves
E = Re
E0ei
k
r−iωt
+C.C.
"
#
$
%
H = Re
H0ei
k
r−iωt
+C.C.
"
#
$
%
15. 3.46/3.156
Fall
2015
Interac4on
of
Light
and
MaZer
Damped
Driven
Harmonic
Oscillator
Analogy:
15
d2 !
x
dt2
+σ
d
!
x
dt
+ω0
2 !
x =
!
F
m
!
P = N
!
p = Nex
d2
!
P
dt2
+σ
d
!
P
dt
+ω0
2
!
P =ω0
2
ε0 χ0
!
E
!
F = e
!
E
e2
N
m
=ω0
2
ε0 χ0
P =
ω0
2
ε0 χ0
ω0
2
−ω2
−iσω
E =ε0 χ ω
( )
E
!
E =
!
E0ei
!
k
!
r−iωt
⇒ P
!
"
= P0
!"
!
ei
"
k
"
r−iωt
B =σm
k =ω0
2
m
x
18. 3.46/3.156
Fall
2015
Dispersion
and
Pulse
Propaga4on
18
n = n λ
( )⇒ c = c λ
( )
§ Normal
dispersion:
in
the
medium
blue
light
has
lower
velocity
than
red
§ Light
pulses
get
broadened
due
to
shorter
wavelengths
“falling
behind”
Larger
dispersion
implies
longer
spacing
between
the
pulses
and
hence
lower
bit
rate
19. 3.46/3.156
Fall
2015
La•ce
Proper4es
La•ce
parameter,
Bond
s4ffness
19
k =
dF
dr
LaAce
parameter
a:
Balance
between
aZrac4ve
and
repulsive
forces
Bond
sDffness
is
constant
and
the
force
is
linear
for
small
devia4ons
from
equilibrium
la•ce
parameter:
20. 3.46/3.156
Fall
2015
La•ce
Proper4es:
Structure
vs.
Func4on
La•ce
parameter,
Bond
s4ffness
20
II III IV V VI
Size
of
the
atom
vs.
bond
s4ffness?
21. 3.46/3.156
Fall
2015
La•ce
Proper4es:
Structure
vs.
Func4on
La•ce
parameter,
Bond
s4ffness
21
Shielding
of
the
poten4al
with
many
electrons
⇒
Lower
bond
strength
II III IV V VI
Size
of
the
atom
vs.
bond
s4ffness?
Large
atom
Small
atom
Minimal
screening
with
none
or
few
electrons
⇒
Higher
bond
strength
Higher
bond
s4ffness
⇒
higher
elas4c
modulus
Shorter
bonds
⇒
higher
elas4c
modulus
E =
K
a
22. 3.46/3.156
Fall
2015
Bands
and
Bandgaps:
Metal,
Semiconductor,
Insulator
Periodicity
of
the
la•ce
=>
Bands
22
allowed
forbidden
allowed
forbidden
allowed
allowed
forbidden
EF EF
valence band
conduction band
Eg
Eg
Metal Semiconductor Insulator
23. 3.46/3.156
Fall
2015
Bands
and
Bandgaps:
Periodic
Poten4al
23
E1 =
2
2m
g
2
!
"
#
$
%
&
2
−V
E2 =
2
2m
g
2
!
"
#
$
%
&
2
+V
2V
For
simple
1D
periodic
poten4al:
V = 2Vo cosgx, g =
2π
a
Eg = E2 − E1 ≈ 2V0
2
2m
k2
− E
"
#
$
%
&
'Ck
+ VG
Ck−G
G
∑ = 0
Solu4on
to
central
equa4on:
Simplified
representa4on
of
band
diagram:
24. 3.46/3.156
Fall
2015
24
For
simple
1D
periodic
poten4al:
V = 2Vo cosgx, g =
2π
a
Eg = E2 − E1 ≈ 2V0
Size
of
the
atom
vs.
band
gap?
Bands
and
Bandgaps:
Periodic
Poten4al
25. 3.46/3.156
Fall
2015
25
For
simple
1D
periodic
poten4al:
V = 2Vo cosgx, g =
2π
a
Eg = E2 − E1 ≈ 2V0
Large
atom
Small
atom
Shielding
of
the
poten4al
with
many
electrons
⇒
Lower
band
gap
Minimal
screening
of
the
poten4al
⇒
Higher
band
gap
Bands
and
Bandgaps:
Periodic
Poten4al
Size
of
the
atom
vs.
band
gap?
26. 3.46/3.156
Fall
2015
Structure-‐Property
Rela4ons
Material:
V/III-‐V
Ionicity
Eg, eV a, Å Hardness,
GPa
Cdia/BNzb
0/0.18
5.5/6.5
3.56/3.16
96/31
Si/AlP/NaCl
0/0.31/0.94
1.12/2.45/8.97
5.42/5.46/5.65
11.3/9.4/0.2
Ge/GaAs
0/0.31
0.67/1.42
5.66/5.65
8.8/7.5
Sn/InSb
0/0.32
0.08/0.17
6.45/6.09
2.2
26
II III IV V VI
Eg, K
Large
atoms
⇒
poten4al
shielding
⇒
lower
bandgap
and
bond
s4ffness
Eg, K:
BN
>
AlP
>
GaAs
>
InSb
GaN
>
GaP
>
GaAs
>
GaSb
C
>
Si
>
Ge
>
Sn
Zn(O,
S,
Se,Te)
>
Cd(O,
S,
Se,Te)
In
addi4on
to
the
bond
length
bond
type
influences
the
material
proper4es:
§ Higher
ionicity
leads
to
higher
poten4al
experienced
by
electrons
⇒
increased
band
gap
§ Higher
ionicity
⇒
reduced
hardness
27. 3.46/3.156
Fall
2015
Materials
Design
by
Property
Maps
27
Rules
of
Structure
§ Covalent
solids:
Ionic
charge
(e)
÷
Ionic
Radius
(nm)
>
7
§ Structure
of
covalent
solids:
“8-‐N”
Rule:
Coordina4on
number
of
a
covalent
solid
is
CN=8-‐N
N=number
of
outer
electrons
Material
CN,
crystal
structure
C,
Si,
Ge,
α-‐Sn
8-‐4=4,
tetrahedral
P,
As
8-‐5=3,
hexagonal
S,
Se,
Te
8-‐6=2,
rings,
chains
Property
Maps:
(courtesy
of
Prof.
Kimerling)
![3.46/3.156
Fall
2015
Class
Organiza4on
n Instructor:
§ Prof.
Polina
Anikeeva
(8-‐425)
[anikeeva@mit.edu]
§ Office
Hours:
Monday
6:30-‐7:30
pm
n Guest
Lectures:
§ Prof.
Lionel
Kimerling
(13-‐4118)
[lckim@mit.edu]
§ Dr.
Chris
Doerr
(?)
[doerrcr@gmail.com]
n Class
Format:
¨ Monday
9:30-‐11
am
§ Quiz
(10
min):
aZendance
mandatory
§ Review
of
last
class/student
ques4ons
§ Lecture
¨ Wednesday
9:30-‐11
am
§ Review
of
last
class/student
ques4ons
§ Lecture
n Grading:
G
UG
§ Problem
Sets
(4)
20%
0%
§ Quizes
(7-‐8)
30%
25%
§ Design
Reviews
(3)
40%
50%
§ Final
Exam
–
DR4,
oral
10%
25%
2](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)