communications devices hirohito yamada lecture on 6/23, 6/27, 6/30, 7/7, 7/14, 7/21 in 2015
TRANSCRIPT
Communications Devices
Hirohito YAMADA
Lecture on 6/23, 6/27, 6/30, 7/7, 7/14, 7/21 in 2015
About lecture
1. Schedule 6/23 Basic of semiconductor photonic devices 6/27 Matter-electromagnetic wave interaction based on semi-classical theory 6/30 Electromagnetic field quantization and quantum theory 7/7 Optical transition in semiconductor, Photo diode, Laser diode 7/14 Optical amplifier, Optical modulator, Optical switch,
Optical wavelength filter, and Optical multiplexer/demultiplexer 7/21 Summary
2. Textbook written in Japanese 米津 宏雄 著、光通信素子工学 - 発光・受光素子 - 、工学図書 霜田 光一 編著、量子エレクトロニクス、裳華房 山田 実著、電子・情報工学講座 15 光通信工学、培風館 伊藤弘昌 編著、フォトニクス基礎、朝倉書店 第 5 章
3. Questions E-mail: [email protected], or ECEI 2nd Bld. Room 203
4. Lecture note dounload URL: http://www5a.biglobe.ne.jp/~babe
http://www.jpix.ad.jp/en/technical/traffic.html
Data traffic explosion on the Internet
Trend of data traffic processed by a domestic network node
Double/3 years
Rapid increase of double per 2.5 years
Dat
a ra
te (
Gbi
t/s)
M/D/Y
double/year
Double/5 years
Double/2.5 years
year
2005 2006 2007 2008 2009 2010 20112004 20132012
Cited from: H26 年度版情報通信白書
Total download traffic in Japan
Total upload traffic in Japan
Daily average value
Growth of internet traffic in Japan
Total download traffic in Japan was about 2.6T bps at the end of 2013
Annual growth rate: 30%
Optical fiber submarine networks
Cited from http://www1.alcatel-lucent.com/submarine/refs/index.htm
Power consumption forecast of network equipments
Domestic internet traffic is increasing 40%/yearIf increasing trend continue, by 2024, power consumption of ICT equipments will exceed total power generation at 2007
http://www.aist-victories.org/jp/about/outline.html
Ann
ual p
ower
con
sum
ptio
n of
ne
twor
k eq
uipm
ents
(×
1011
Wh)
year
Tot
al in
tern
et tr
affic
(T
bps)
Network traffic
Total power generation at 2007
Power consumption
Expanding applied area of optical communication
Backplane of a server(Orange color cables are optical fibers)
Nowadays, application area of optical communications are spreading from rack-to-rack of server to universal-bass-interface of PCs
Universal Bass interface (Light Peak)installed in SONY VAIO Z
Photonic devices used for optical communications
1. Passive optical device, Passive photonic device
2. Active optical device, Active photonic device
- Light-emitting diode (LED)- Semiconductor laser, Laser diode (LD)- Optical amplifier
- Optical waveguide, optical fiber- Optical splitter- Optical directional coupler- Optical wavelength filter- Wavelength multiplexer/demultiplexer (MUX/DEMUX)- Light polarizer- Wave plate- Dispersion control device- Optical attenuator- Optical isolator- Optical circulator- Optical switch, Photonic switch- Photo detector, Photo diode (PD)
Various optical devices for use in optical networks
3. Other devices(Wavelength converter, Optical coherent receiver, etc.)
: Treated in our lecture
Photonic devices: supporting life of 21st century
- charge-coupled device (CCD) image sensor- CMOS image sensor- solar cell, photovoltaic cell- photo-multiplier- image pick-up tube- CRT: cathode-ray tube, Braun tube- liquid crystal display (LCD)- plasma display- organic light emitting display- various recording materials (CD, DVD, BLD, hologram, film, bar-code)- various lasers (gas laser, solid laser, liquid laser)- non-linear optical devices
Various photonic devices used for applications other than optical communication
These devices collectively means “Photonic devices”
Electronics
Photonics
SpintronicsGMR HDDMRAM
Opto-spinics
Electron Tube, Diode, Tr, FET, LSITunnel effect devices
Magnetics
HDDLaser
LD, LED
magnet-optical disk
What is Photonic Device ?
Optical diskMagnetic tape
Display
Optical fiber
solar cell
Photo-electronics(Opt-electronics)
Manipulating electron charge
Manipulating photon
Manipulating spin of materials
Energy and number
amplitude and phase
Electromagnetic wave
voltage and current
Photo detector, PD
CCD, CMOS sensor
?
Manipulating both spin and charge of electrons
Magnetic Recording
Manipulating photon and electron charge
Unexplored
Manipulating wavefunction of electron
Basis of semiconductor photonic devices
Properties required for semiconductor used as photonic devices
Optical absorption coefficient of major semiconductor materials
0.4 0.6 0.8 1.0 1.2 1.4 1.6
Wavelength: λ (μm)
Opt
ical
abs
orpt
ion
coef
ficie
nt: α
(cm
-1) T = 300K
105
104
103
102
Si
InP
GaAs
Ge
In0.53Ga0.47As
Passive devices(Non light-emitting devices)
・ Transparent at operating wavelength
Active devices(Light-emitting devices)
・ Moderately-opaque at operating wavelength
・ To be obtained pn-junction (To be realized current injection devices)
・ Small nonlinear optical effect (as distinct from nonlinear optical devices)
・ Better for small material dispersion
・ High radiant transition probability in case of light-emitting devices (Direct transition semiconductor )
・ Small birefringence (polarization independence)
Band structure of semiconductors
Semiconductor and band structure
According to Bloch theorem, wave function of an electrons in crystal is described as a quantum number called “wave number” This predicts existing dispersion relation between energy and wave number of electron. This relation is called energy band (structure)
Dispersion relation of electron energy in Si
In bulk Si, holes distribute at around the Γ point, on the other hand, electrons distribute at around the X point (Indirect transition semiconductors)
Band gap ~1.1eV
Hole
Electron
Band structure of semiconductors
Band structure of compound semiconductors
GaAs InP
Both electrons and holes distribute at around the Γ point (Direct transition semiconductors)
Hole
Electron
Hole
Electron
Band structure of semiconductors
Band structure of Ge
Band structure of Ge
Ge which is group semiconductor is also Ⅳindirect transition type semiconductor, but by adding tensile strain, it changes a direct transition-like band structure
Recent year, Ge laser diode(RT, Pulse) was realized by current injection
1.6%tensile strain
Conduction band
Valence band Valence band
Indirect transition Direct transition
Conduction band
Basis of semiconductor photonic devices
Material dispersion
W. Sellmeier equation
Values of dielectric constant (refractive index), magnetic permeability depend on frequency of electromagnetic wave interacting with the material
)(),(),( n
Dielectric constant (refractive index) significantly changes at the resonance frequency of materials.In linear response, between real part and imaginary part of frequency response function holds Kramers-Kronig relation.
Phenomenologically-derived equation of relation between wavelength and refractive index
22
22 1
i
iAn
Here, λi = c/νi, c: light speed, νi: resonance frequency of material, Ai: Constant Calculation of dielectric function ε of Si
Rea
l par
tIm
agi
nary
par
t
Photon energy (eV)
Photon energy (eV)
Calc.
Calc.
HBED )(,)( Material equation
Basis of semiconductor photonic devices
Birefringence
In anisotropic medium, dielectric constant (refractive index), magnetic permeability are tensor
z
y
x
zzzyzx
yzyyyx
xzxyxx
z
y
x
E
E
E
D
D
D
(Material equation)
Crystal is optically anisotropic medium
Birefringence of calcite
In birefringence crystals, an incident direction where light beam does not split is called optical axis (correspond to c-axis of the crystal)
When light beam enter a crystal, it splits two beams (ordinary ray and extraordinary ray)
Optical axis
Incident ray
ordinary ray
extraordinary ray
Outgoing ray
Basis of semiconductor photonic devices
Nonlinear optical effect
Values of dielectric constant (refractive index), magnetic permeability depend on amplitude of electromagnetic field interacting with the material
)(),(),( HEnE
When strong electric field (light) applied to a material, nonlinear optical effects emerge. Wavelength conversion devices use this effects.
When intensity of incident light is weak, linear polarization P which proportional to the electric field E is induced.
EP 0),(),(
),(),(),()1(
),(),(),(
0
000
0
tt
ttt
ttt
ee
r
xPxE
xExExE
xExExD
Linear polarization
When intensity of incident light become strong, electric susceptibility become depended on the electric field E
EP )(0 E
: Electric susceptibility
EEEEEEE )4()3()2()1(0)(
HBED )(,)( HE Material equation
Basis of semiconductor photonic devices
Band structure of (a) GaAs and (b) Si
In case of indirect transition, phonon intervenes light emission or absorption
Electron transition in direct transition type and indirect transition type semiconductors
Light emission from materials
Light absorption and emission in material
All light come from atoms !
Sun light Nuclear fusion of hydrogen‥‥
Fluorescence of fireflies Chemical reaction of ‥‥organic materials
Light from burning materials Chemical reaction of ‥‥organic materials
Electroluminescence from LED Electron transition ‥‥in semiconductors
You have to learn about interaction mechanism of matter with electromagnetic field if you want to understand these phenomena
In the field of Quantum electronics
Ground state
Excited state
Excited state
Ground state
Nucleus
Light
Light
ΔE = hν
ΔEν
Why materials emit light?
Light emission from materials
+e
−eElectron
Proton
Rutherford atom model
m
r
vω
According to classical electromagnetics, Rutherford atom model is unstable. It predicts lifetime of atoms are order of 10-11 sec. (See the final subject in my lecture note Electromagnetics )Ⅱ
In order to solve this antinomy, Quantum mechanics was proposed
+e
−eProton
Bohr hydrogen atom model
N. Bohr proposed an atom model which electrons exist as standing wave of matter-wave. The shape of the standing wave is defined by the quantum condition, and it is arrowed in several discreet states. When an electron transits from one steady state to other state, it emit / absorb photon which energy correspond to energy difference between the two states. (ΔE = hν)
Why electrons make transition between the states ?
Which process occur ? Light emission or absorption ?
Theory describing light absorption and emission
Energy of electrons in semiconductor is quantized (Band structure), Electromagnetic field is also quantized (Field quantization)
There are three methods describing interaction of matter with electromagnetic fields
1. Classical theory
2. Semi-classical theory
Energy of electrons in semiconductor is quantized (Band structure), On the other hand, energy of electromagnetic field is treated by classical electromagnetics
3. Quantum theory
Classical theory
Semi-classical theory
Quantum theory
Electromagnetic fieldMatterMethod
Optical absorption
Possible
Stimulated emission
Impossible
Spontaneous emission
Classical Classical
ClassicalQuantum
Quantum Quantum
Possible
Possible
Possible Possible Possible
Impossible
Impossible
Three methods and their applicable phenomena
Description of electromagnetic field
In order to understand interaction of matter with electromagnetic field, we need to describe electromagnetic field and to understand its fundamental characteristics
Maxwell equations
0),(
),(
),(1),(),(
),(),(
2
t
t
t
t
vt
tt
t
tt
e
ee
xB
xE
ixE
ixE
xB
xBxE
Electric field E and magnetic field B can be also described as follows with electromagnetic potential A(x, t) and ϕ(x, t)
ABA
E
,t
Therefore, Maxwell equations can be replaced to equations with A and ϕ as values of electromagnetic field, instead of E and B
Description of electromagnetic field
t
tttttt LL
),(),(),(),,(grad),(),(
xxxxxAxA
Electromagnetic potentials can be described as follows with arbitrary scalar function χ(x, t).
0),(
),(div
t
tt L
L
xxA
When χ(x, t) was selected as AL and ϕL satisfying the following relation,
the gauge is called “Lorenz gauge”. In this case, basic equations that describe electromagnetic phenomena is reduced to two simple equations regarding AL and ϕL as follows.
),(1
),(),,(),(2
2
2
2
ttt
ttt eLeL xxxixA
This function χ(x, t) is called a “gauge function”, and selecting these new electromagnetic potential AL and ϕL is called “gauge transformation”.
These equations indicate that electromagnetic potential AL and ϕL caused by ie or e propagate as wave with light speed.
Description of electromagnetic field
AB
AE
t
Therefore, E and B is derived from A with the following relations
the gauge is called “Coulomb gauge”.
0 A
iA
tt 2
2
Other than Lorenz gauge, when A was selected as satisfying condition,
In this case, basic equations that describe electromagnetic phenomena is as follows
In free space where both electric charge ρe and electric current ie do not exist,
0,Const.2
2
At
By selecting Coulomb gauge, electromagnetic fields can be described by only vector potential A, because scalar potential ϕ is constant in whole space when electric charge dose not exist in the thinking space.
Interaction of charged particles with electromagnetic fields
When single charged particle (electron) is in electromagnetic field, Hamiltonian of the particle is described as follows
eVem
H 2)(2
1Ap
Here, p is the momentum operator, m is electron mass, V is potential of electron, e is elementary charge, and A is vector potential. Hamiltonian H can be also written as,
The last term in Hint is proportional to A2, and it reveals higher order effects (nonlinear optical effect). Here, we ignore it because the contribution is small.
Here, H0 is an Unperturbed Hamiltonian which is for an electron in space without electromagnetic field, and Hint is an Interaction Hamiltonian which is originated by interaction between an electron and electromagnetic field.
22
int
20
int02
2)(
2
2
1
)(2
1
ApAAp
p
Ap
m
e
m
eH
eVm
H
HHeVem
H
Electrical-dipole approximation of the interaction
Position of a charged particle is described astiti ee *
00 rrr
Momentum of a charged particle is described as
)( *00
titi eieimm rrrp
Vector potential is described astiti ee *
00 AAA
Electric field is
titi eieit
*00 AA
AE
Therefore,
ER
Er
ArArpAAp
e
iimm
e
m
eH )()(
2 0*
0*00int
Here, R = er, and it called electric dipole moment
E
+e
−e
e−iωt
e+iωt
r
Electrical dipole
Terms “ei2ωt ” or “e−i2ωt ” disappear when integrating for time
Polarization of atom
EPolarization of electron cloud
r
Electrical-dipole approximation of the interaction
)(2int pAAp
m
eH
Interaction Hamiltonian
only include effect by electric field “RE” although the derived interaction equation for a charged particle include effects by both electric field (Coulomb force) and magnetic field (Lorentz force). The reason is that we assume the motion of a charged particle as which is vibration at a limited place. If we assume parallel motion for it, effect by magnetic field will be also included.
titi ee *00 rrr
In this way, when the interaction only depend on electric field, and the interaction can be described as RE, it is called electric dipole approximation.In some case, higher order polarization “multipolar” (such as electric quadrupole or electric octopole) occasionally emerge.
工学で扱う物理現象は非常に複雑なものが多い。従って、全ての物理現象を取り入れた完璧な理論を構築することは不可能である。良きエンジニアとは、それら複雑な物理現象の中で、何が本質的に重要かを見極め、近似をうまく使い、無視できる物理現象は思い切って無視し、シンプルな理論を構築できる人である。ただし、どんな近似を使ったのかは決して忘れてはいけない。
皆さんへのメッセージ
Electrical dipole in semiconductor
In semiconductor, an electron and hole pair forms a electrical dipole
+
Hole
Electron −e Electrical dipole
+e
Electrical dipole in semiconductor
Conduction band
Valence band
Hole
Electron
Electrical dipole
E
Quantum statistics and density matrix
Physical quantities involving many particles (electrons) such as electrical current are statistical average values for the particles. Furthermore, expected values for multiple measurements of a single event is needed statistical treatments. We discuss about statistical nature for many particles or multiple measurements. State for ν th particle or ν th measurement can be described as
n
n nC )()( .
Here, is an energy eigenstate for single particle. It is assumed to form complete space. Therefore, any can be formed by linear combination of . does not required the suffix (ν).
nn)(
n
mn
mn mAnCCA,
)()*()()(
If operator for a physical quantity is assumed as A, expected value for ν th particle is
.
Next, we develop an average of expected values for the group of particle (ensemble average). We assume the contribution from the ν the particle (probability for finding n th particle) as P(ν) , and normalize it.
1)(P
Quantum statistics and density matrix
Statistical average (ensemble average) of the expected value is described as
mn
mn mAnCCPAPA,,
)()*()()()()(
Here, we rewrite as below
mnmnmnnm CCCCPmAnAAA *)()*()(,,
Matrix ρ having ρmn as its elements is called density matrix
2221
1211
Using density matrix
mm n
mnmnnmmn
mAmmAnnm
mAnnmAA
,,
.
n
nnI is identity operator
m
mAm is summation of on-diagonal elements of ρA, that is Trace.
)(Tr AmAmAm
, and 1)(Tr
Motion equation of density matrix
密度行列 ρ の性質が分かれば、集団内の個々の粒子についての状態 や抽出確率 P(ν) を知らなくても、統計性を含めた期待値 を知ることがで
きる。そこで、密度行列 ρ を表現する方程式、つまり ρ が従うべき方程式を求めてみる。
)(A
nPmnPm
mnPCCP mnmn
)()()()()()(
)()()()()*()(
従って密度行列は、 と書くことができる。
まず、密度行列の行列要素の定義式を、以下のように書き直す。
)()()( P
この式の両辺を時間 t で微分すると、
dt
dPP
dt
d
dt
d)(
)()()()(
)(
となる。
ただし、抽出確率 P(ν) の時間依存性はないとしている。
Motion equation of density matrix
,11
)()()()()()(
Hi
HHi
i
HPP
i
H
dt
d
)()( Hdt
di Schroedinger equation and its Hermitian conjugate
Hdt
di )()( より、
となる。
これは、密度行列の時間発展を表す式であり、密度行列の運動方程式或いは、量子リウヴィル (Liouville) 方程式もしくはリウヴィル - フォン・ノイマン方程式とも呼ばれる。
双極子との相互作用がある場合の密度行列
電子系の主ハミルトニアンを H0 とし、電気双極子能率を R とする。前に述べたように、電場が存在するときの相互作用ハミルトニアン Hint は、− RE と
なり、電子系全体のハミルトニアン H は、REHHHH 0int0 となる。
これを、密度行列の運動方程式に代入すると、
ERRi
HHi
REREi
HHi
HHidt
d
11
111
00
00
となる。
ここで、最後の ≈ では、１個の電子が存在する領域が電磁波の波長に比べて十分に小さく、その範囲内で電場の分布は一定と見なせることを仮定している。実際、気体原子に束縛されている電子の存在範囲はせいぜい数 Å 程度であり、また半導体中の電子に至ってもせいぜい数十 Å 程度である。それに対して、相互作用する光の波長は数千 Å もあるので、この仮定は妥当である。
双極子との相互作用がある場合の密度行列
次に、密度行列の行列要素に対する方程式を導出する。エネルギー固有状態には時間依存性が無いので、
ndt
dmnm
dt
d
dt
d mn と表すことができ、従って、
ll
ll
ll
ll
mn
EnllRmi
EnRllmi
nHllmi
nllHmi
EnllRmi
EnRllmi
nHllmi
nllHmi
EnRmi
EnRmi
nHmi
nHmidt
d
11
11
11
11
1111
00
00
00
と書くことができる。なお。ここで用いている固有状態は、主ハミルトニアン H0 の固有状態である。
双極子との相互作用がある場合の密度行列
従って、状態 は、エネルギー固有値 Wn をとり、状態間には直交性があるので、n
llnmllnmlnmmn
llnml
llnmlnmmn
llnm
mn
ERRi
i
ERi
ERi
WWi
EnllRmi
EnRllmi
Wnmi
nmWidt
d
1
111
1111
となる。
ただし ωmn は、順位 m と順位 n とのエネルギー差に対応する角周波数であり、
nmmn WW で与えられる。