Transcript Waveguide Optics

Waveguide Optics
Teacher : Lilin Yi
Email : [email protected]
Office : SEIEE buildings 5-517
Tel ：34204596
http://front.sjtu.edu.cn/~llyi/waveguid
e
State Key Lab of Advanced Optical
Communication System and Networks
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Self-introduction
简
历
荣
誉
及
奖
励
代
表
性
研
究
成
果
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2012.6-现在
2010.12-现在
2010.4-现在
2008.5-2010.3
2006.10-2008.3
2004.9-2008.4
2002.9-2005.3
1998.9-2002.7
上海交通大学电子工程系
上海交通大学电子工程系
上海交通大学电子工程系
Oclaro(原Avanex) Corporation
法国国立高等电信学校（ENST）
上海交通大学电子工程系
上海交通大学物理系光学专业
上海交通大学物理系
博士生导师
副教授
讲师/硕士生导师
产品开发经理/高级工程师/光学工程师
博士
博士
硕士
学士
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上海市教委“晨光”学者
全国优秀博士论文，2010
上海市优秀博士论文，2009
Oclaro/Avanex杰出员工奖，2009/2008
SPIE Asia Pacific Optical Communications Conference，Best Student Paper Awards (亚太
光通信国际会议SPIE最佳学生论文奖), 2007
• 上海市优秀硕士论文, 2006
• 国家优秀奖学金、3M创新奖学奖、中科院奖学金，2005
• 上海市三好学生, 2004
• 共发表学术论文68篇(SCI论文35篇)，其中第一作者论文24篇(包括SCI论文15篇、国际会议
论文16篇),发表论文被SCI他引250次，以下列出部分代表性论文：
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Lilin Yi, Weisheng Hu, Yi Dong, Yaohui Jin, Wei Guo, and Weiqiang Sun, “A polarization-independent subnanosecond 22 multicast-capable optical switch using a
sagnac interferometer,” IEEE Photon. Technol. Lett. vol. 20, pp. 539-541, 2008.
• Lilin Yi, Yves Jaouen, Weisheng Hu, Yikai Su and Sébastien Bigo, “Improved slow-light performance of 10 Gb/s NRZ, PSBT and DPSK signals in fiber broadband SBS,”
Optics Express，vol. 15, no. 25, pp. 16972-16979, 2007.
• Lilin Yi, Yves Jaouen, Weisheng Hu, Junhe Zhou, Yikai Su and Erwan Pincemin, “Simultaneous demodulation and tunable-delay of DPSK signals using SBS-based
optical filtering in fiber,” Optics Letters, vol. 32, no. 21, pp. 3182-3184, 2007.
• Lilin Yi, Li Zhan, Weisheng Hu, Yuxing Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering with phase-modulated pump,” IEEE Photon.
Technol. Lett. vol. 19, no. 8, pp. 619-621, 2007.
• Lilin Yi, Weisheng Hu, Yikai Su, Mingyi Gao, and Lufeng Leng, “Design and system demonstration of a tunable slow-light delay line based on fiber parametric process,”
IEEE Photon. Technol. Lett. vol. 18, no. 24, pp. 2575-2577, 2006.
Research Fields
optical signal processing
PON
Microwave Photonics
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Syllabus(flexible)
Chapter 1 Introduction
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§ 1-1 History and Present State
§ 1-2 Essential Questions in Waveguide Optics
§ 1-3 Basic Research Method of Waveguide Optics
Chapter 2 Analytical method
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§ 2-1 Geometrical Optics Method
§ 2-2 Electrodynamics Fundamentals
§ 2-3 Wave Optics Method
Chapter 3 Fiber Mode Theory
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§ 3-1 Modes in The Step Refractive Index Fiber
§ 3-2 Linearly Polarized Modes in The Weak-guidance Optical Fiber
§ 3-3 Universal Properties of Modes in Waveguide
§ 3-4 Perturbation Method in Transversely Non-uniform Waveguide
§ 3-5 Vertically Non-uniform Waveguide and The Coupled Mode Equations
Chapter 4 Single Mode Fiber Theory
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§ 4-1 The Step-index Monomode Fiber
§ 4-2 Gaussian Fitting Method for SMF and Mode Field Diameter
§ 4-3 Approximate Solution of SMF
§ 4-4 Main Types of SMF
§ 4-5 Polarization Character of SMF
§ 4-6 Production of SMF and Fiber Optic Cable
Chapter 5 Signal Degrade in Fiber
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§ 5-1 Attenuation
§ 5-2 Chromatic Dispersion
§ 5-3 Nonlinearity
Chapter 6 Semiconductor Laser
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§ 6-1 Physical Basis of Semiconductor Laser
§ 6-2 Structure of Semiconductor Laser
§ 6-3 Performance Characteristic of Semiconductor Laser
Chapter 7 Photodetectors and Optical Receivers
• § 7-1 Photodetectors
• § 7-2 Characteristic Index of Photodetectors
• § 7-3 Optical Receivers
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Chapter 8 Modulation Formats
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§ 8-1 General Concepts of Optical Modulation
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§ 8-2 electro-optic effect
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§ 8-3 Electro-optical Modulator
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§ 8-4 Modulation Format
Chapter 9 High bit rate transponder
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§9-1 Standard evolution
§9-2 100G commercial transponder
§9-3 Technical trend for 400G and 1T
Chapter 10 Fiber Amplifier Design
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§10-1 EDFA Design
§10-2 Raman Amplifier Design
Chapter 11 EDFA design process
Chapter 12 Semiconductor Optical Amplifier
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§12-1 SOA in Transmission
§12-2 SOA in Signal Processing
Chapter 13 PON
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§13-1 EPON/GPON (TDMA)
§13-2 WDM-PON
§13-3 CDMA
§13-4 OFDM-PON
Chapter 14 Optical Switching
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§14-1 Forms of Optical Switching
§14-2 Key Technology of OPS
§14-3 Optical Buffer
Seminar
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References
 《光波导理论与技术》李玉权等 人民邮电出版社
 《导波光学》 范崇澄 北京理工大学出版社
 《非线性光纤光学》，G. P. Agrawal,天津大学出
版社，
 《光纤通信》， Joseph C. Palais, 电子工业出版社
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Chapter 1
Introduction
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1 History and Present State
Wavelength range： 0.1μm～10μm(300THz~30THz)
Frequency(Hz)
102
103
104
105
106
107
ELF
VF
VLF
LF
MF
HF
101
electricity
wireless
phone
TV
108
109
VHF
UHF
1010 1011
SHF
1012 1013 1014 1015
EHF
microwave
infrared visible
light
FM
AM
Fiber
satellite
/microwave
coaxial cable
Fiber
twisted pair
107
106
105
104
103
102
101
100
10-1
10-2
free space wavelength(m)
10-3
10-4
10-5
10-6
An ancient optical system: smoke signals on the beacon tower
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Modern communication demonstration for the first time :
telephone
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In 1880 Bell invented the “photophone” after the telephone.
The voice signals propagate for 200m.
The beam varies with the vibrations of the speaking trumpet.
This process is called modulation.
Bell treated the photophone as the most important invention in
his lifetime, but it has not been used due to the light source and
transmission medium problems.
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Underground optical communication
Research focus on underground: underground communication
experiments emerged such as reflection waveguide and lens
waveguide, but the prices are high. Besides, adjustment and
maintenance are difficult.
Difficulties in optical communication：
1. No suitable light sources
• General light sources has bad directivity and
coherency, similar to the noise and cannot be
modulated.
2. No suitable transmission medium
• Optical frequency is extremely high and cannot go
through obstacles easily. (low loss materials are
required.)
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The invention of laser
In 1960 Maiman invented the ruby laser
The laser has good mono-chromaticity, directivity,
coherency, high brightness, high power
The invention and application
communication into a new stage
make
optical
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The prototype of the optical fiber
In 1870, British physicist Tyndall
sunlight bends with the water flow
nwater > nair light occurs total reflection
In 1953, Dr. Kapany of the London Institute invented glass
optical fiber: core + cladding (ncore>ncladding) – fibers
In 1960, the lowest fiber loss was 1000 dB/km, and it can
only be used in medical treatment, such as endoscope
The principle of total reflection in the glass has
been used at short distance (m) transmission.
Circular
cross-section
dielectric
optical
waveguide is researched theoretically and
experimentally by E.Snitzer in 1961.
Until the mid-60s, the best transmission loss of
optical glass is still as high as 1000 dB/km.
Without reliable and low-loss transmission
medium, optical communication research was
into a low ebb at that point.
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The birth of optical fiber
In seemingly hopeless situations, Charles Kao
in 1966 published an paper which was
subsequently proven to be epoch-making. In
this paper, Kao foresaw the transmission loss
may be less than 20 dB/km by using optical
fibers made of high-purity quartz glass with
cladding material. (95.5% after 10m，1% after
1km)
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Charles Kao (left)
awarded a medal
by the IEE in the
UK(1998).
In 1966, Kao and C.A.Hockham published the paper on the new
concept of transmission media “Dielectric-fiber surface waveguides
for optical frequency”. They pointed out that raw material purification
is the right approach to producing suitable low-loss optical fiber for
long distance communication.
It lay the foundation for modern optical communication--fiber-optic
communication.
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In 1970, come into being!!!
1970 Corning Glass Company first developed
fibers with attenuation of 20 dB/km.
Optical fiber communication begun!
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Basic idea : low loss
• (1) Dope oxides into pure quartz to form the required
refractive index distribution.
• (2) Using vapor deposition technique (still in use
today).
The former ensures excellent physical and
chemical properties.
The latter make the process flexible and help
materials “purification” ensuring low loss.
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Optical fibers: new generation of transmission medium
The loss of current production (silica single mode fiber) can be
reduced to 0.20 dB/km (wavelength of 1.55 μm). The lab records is as
low as 0.151dB/km. （95.5% after 1km, 1% after 100km)
The silica optical fiber became the new generation of transmission
medium due to its wide band, low dispersion, high tensile strength,
strong anti-jamming, resource-rich etc.
Novel optical fibers: Erbium-doped optical
compensation fiber, Photonic crystal fiber…
fiber,
Dispersion
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Fiber-optical communication
Another important event in the early 70 is the
implementation of continuous operation of semiconductor
lasers at room temperature.
Optical fiber communication received unprecedented
attention. Laboratory research quickly transformed to
industrial products which brought about huge social and
economic benefits.
Fiber optics, integrated Photonics and integrated
optoelectronics are the basis of modern optical fiber
communication.
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Developing trends
multimode fiber  single mode fiber
short wavelength 0.8μm  long wavelength 1.31 μm,
1.55 μm
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Era of optical fiber communications
• 96ch*100Gb/s*10,608km= 108 Gb/s•km
• OFC2010-Tyco
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Transmission trend
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Switching
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Optical interconnects
IBM, Intel
rack-to-rack, server-to-server, service room to
service room
CPU interconnect, Multi-core CPU
Silicon Photonics
PIC
Hybrid Integration
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Photonic integration circuit -PIC
100Gb/s (10*10Gb/s) capacity line card
10 discrete transceivers vs. WDM system on a chip
InP based PIC can integrate active functions (laser, modulator, detector) and
passive functions (DWDM, VOA and switch) on a single chip, which benefits the
system size, power consumption, reliability and cost.
400Gb/s (10*40Gb/s) PIC – more than 100 devices on a single chip (OFC2008)
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PIC – optical router
Hybrid integration
Fiber-optic sensing
Changes in environmental factors have an impact on the
propagation characteristics of light in waveguides (intensity, phase,
and polarization).
Optical waveguide (mainly fiber) sensing devices on：pressure,
stress, strain, displacement, velocity, acceleration, turning, liquid
level, flow rate, flow, temperature, voltage, electric current, electric
field, magnetic field, gamma-ray chemical composition.
Some of them have been transferred to the production since the
70s.
One of the hot spots in waveguide optics because of the
importance of information-access in modern societies.
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References since the 80 's
Optical waveguide theory and calculations：
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1. A. J. Adams, An Introduction to Optical Waveguides, John Wiley and Sons, New York, 1981.
2. A. W. Snyder and J. D. Love, Optical Waveguide Theory, Chapman and Hall, London, 1983.
3. H. A. Haus, Waves and Fields in Optoelectronics, Prentice Hall, 1984.
4. T. Tamir, Guided-Wave Optoelectronics, 2nd Ed., Springer-Verlag, 1990.
6. K. Okamoto, Fundamentals of Optical Waveguides, Academic Press, San Diego,2000.
7. K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis, John Wiley & Sons, New
York, 2001.
Fiber nonlinearity:
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1. G. P. Agrawal, Nonlinear Fiber Optics (3rd Ed.), Academic Press, San Diego,2001.
2. G. P. Agrawal, Applications of Nonlinear Fiber Optics, Academic Press, San Diego, 2001.
Optical fiber communication system:
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1. T. Li(Ed.),Topics in Lightwave Transmission Systems,Academic Press, San Diego,1992.
2. L. Kazovsky, S. Bennedetto and A. Willner, Optical Fiber Communication Systems, Artech
House, 1996.
3. I. P. Kaminow and T. L. Koch(Ed.), Optical Fiber Telecommunications (III A,B), Academic
Press, San Diego,1997.
4. I. P. Kaminow and T. Y.Li(Ed.), Optical Fiber Telecommunications (IV A,B), Academic Press,
San Diego,2002.
5. 杨祥林，光纤通信系统，国防工业出版社，北京，2000.
EDFA:
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1. E. Desurvire, Erbium-doped Fiber Amplifiers-Princples and Applications, John Wiley and Sons,
New York, 1994.
2. P. C. Becker, N. A. Olsson and J. R. Simpson, Erbium-doped Fiber Amplifiers-Fundamantals
and Technology, Academic Press, San Diego,1999.
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Main academic publications
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1. Nature Photonics
2. Optics Letters
3. Optics Express
4. IEEE/OSA Journal of Lightwave Technology
5. IEEE Photonics Technology Letters
6. IEEE Journal of Quantum Electronics
7. IEEE JSTQE
8. Optics Communications
9. Electrons Letters
10. Chinese Optics Letters
11. 电子学报
12. 中国激光
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2 Optical Waveguide
Basic structures and modes
The waveguide is infinite in the vertical direction to the section.
The refractive index is only the function of the horizontal coordinates.
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If light is confined in waveguides, it
is possible to achieve long-distance
transmission. This situation is
called guided wave mode.
conversely, if light is radiated in the
horizontal direction, it is called
radiation mode.
Refraction rule: in cylindrical
waveguide structure, light in the
transverse direction is always tends
to be concentrated in the larger
refractive index along the vertical
transmission.
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Types
one-dimensional: planar optical waveguide/ thin film optical waveguide
two-dimensional: strip optical waveguide/fiber
step index optical waveguide/ graded index optical waveguide
Refractive index difference of optical waveguide is generally small, at
the 10-2~10-3 level which is favorable for simplifying analysis.
Protective coating to improve the mechanical properties
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3 Essential Questions
The distribution of light fields on the cross section of waveguides
The propagation of light fields along the waveguides
The coupling between modes when waveguide disturbed
Attenuation of signal when travelling along the optical waveguide
Distortion of signal when travelling along the optical waveguide
Nonlinear effects in optical fiber
The polarization of light fields along the waveguide
Active optical fiber
Optical waveguide excitation
"comprehensive" issue: how to design optical waveguide or
related devices to meet a given performance.
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4 Geometrical Optics Method
Geometrical (Ray) Optics Method
Ray can represent propagation direction of light
and intensity but can not describe field phase and
vibration direction (λ→0 and ignoring wave
character )
main features:
• Waveguide can confine light when the incoming light
satisfies the total reflection condition i.e. the angle of
incoming light is changeable continuously.
• Light field outside the core was completely ignored
when satisfying the total reflection condition .
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5 Waveguide Optics Method
Strictly speaking, optical waveguide problem
should be solved by electromagnetic method.
Solve electromagnetic wave equation and
lateral boundary conditions to yield
horizontal distribution (eigenfunctions) and
longitudinal propagation constant (intrinsic
value)
Each solution corresponds to a mode, also
known as the mode-field method.
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Application Fields
Geometry optics method is a special case of wave optics
when λ → 0.
The above two features correspond to two unique areas
in wave optics method:
• To solve single-mode (or few-mode) optical waveguide
where separation characteristics of propagation
constants behave very obvious.
• To solve the loss caused by cladding, energy coupling
between optical waveguide, building process of steadystate distribution in optical fiber.
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Solving methods
Analytical solution of wave equations are often unable to
be found. The following two methods are adopted instead:
• Numerical solution:
Applicable to many kinds of refractive index distribution.
Existing problems: solution accuracy, convergence.
• Approximate analytical solution:
Weak-guidance approximation: The refractive index of the
core and cladding has little distinction.
A particular mode field distribution can be equivalent to a
known analytic function.
A practical waveguide which has multiple modes can be
equivalent to a waveguide which has a known analytical
solution.
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Chapter 2
Analytical method
Geometrical Optics Method
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In the geometrical optics method, the intensity and
propagation direction of the light are taken into account,
but ignoring the wave (phase, polarization) effects.
The ray represents light propagation path.
Main contents:
• Starting from The Ray Equation, discuss one-dimensional and
two-dimensional non-destructive optical waveguide, yield the
basic rules of light propagation directions, as well as the
classification of light (constraints).
• In one-dimensional and two-dimensional optical waveguide,
there is one and two ray invariants describing light propagation
directions respectively, which correspond to "traditional" and
"General" law of refraction (Snell's law).
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The Ray Equation
In geometrical optics, the trajectory is determined by the
ray equation:
S is the distance along the light trails, n(r) is the spatial
distribution of refractive index, r is radius vector
The ray equation is yielded from：
• Maxwell equation when λ → 0.
• Fermat's principle
ds
r r+dr
• Snell's law(treat n(r) as n slices and use
Snell's law at every boundary)
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Light propagation
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One-dimensional planar optical waveguide and
Geometrical optics description
basic structure
•
n1
Consisting of multi-layer planar
n2
n3
n4
dielectric waveguide structures
• Refractive index changes on the
perpendicular direction
Three layer uniform：
n1 ,0  x  h

nx   n2 , x  0 n1  n2  n3 
n , x  h
 3
symmetrical structure： n2 = n3
y
x
h
z
confinement layer
n3
waveguide layer
n1
confinement layer
n2
asymmetric structure： n2  n3
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Total reflection at the interface
Snell’s law
H
1  1 , n1 sin 1  n2 sin  2
• Goos- Haenchen displacement 
• penetration depth h
• displacement of Incident point
E
k
E H
n2 TE 2
n1
1 1’
k
TM
and reflection point
• reflection phase loss 
sin 2 1  sin 2  c
  arctan
cos1
1 ：incidence angle
c ：critical angle
h

amplitude
R  R exp  j 
reflection coefficient
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Total reflection condition
>c12>c13 sin   n2 n1 h kx
transmission constant
  k z  k0 n1 sin 
k = k0n1
k
kz
A

n3
n1
C
B
D
3
n2
wavefront
k0 n2    k0 n1
coherence emphasis condition
AD  BC 
2n1

  2   3  2m , m  0,1,2,...
characteristic equation
2k0 n1h cos   2  3  2m
AD  BC  2h cos
specific incident angles make
several modes
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Transverse resonance condition = characteristic
kx
k
equation
2k x h   2  3  2m
k x  k0 n1 cos
kz
TE mode and TM mode have the different reflection phase
loss（ 2+3 ）and different characteristic equation
cut-off wavelength：cm
4h n1  n2

2m   2   3
2
cm
2
number of modes
4h
2
2
n1  n2   2   3
mM  
2
one m，
two modes：
TEm、TMm
fundamental mode ：
TE0 mode has the
longest cut-off
wavelength
Polarization degeneracy：
total number of modes：2M
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Wave Optics Method
Ray
Equation
raytrace
refractive
index
distribution
Maxwell's
equations
Wave
equation
Helmholtz
equation
transmission
characteristic
boundary
conditions
eigensolution
eigenvalue
waveguide
field
equation
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Electromagnetic theory
Maxwell equation
2.1   E  
B
t
2.2   H  J f 
D
t
2.3   D  ρ f
2.4   B  0
2.5 D   0 E  P  E
2.6 B  H
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Harmonic electromagnetic field
Er, t   Er  cost   Re Er  exp  jt 
H r, t   H r  cost   Re Hr  exp  jt 
Maxwell equation Helmholtz equation

2
 j , 2   2
t
t
  E   j0 H
 2E  k 2E  0
  H  jE
D  0
B  0
2H  k 2H  0
2
n
 2E  2
c
2
n
2H  2
c
 2E
0
2
t
 2H
0
2
t
k  k0 n, k0 

c

2f 2

c

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Longitudinal field and transverse field
E=exEx+ eyEy+ezEz, H=exHx+eyHy+ezHz  e x
E=Et+ ezEz
 t  Et   j0 H z
 t  H t  jE z
E
 t  E z  e z  t   j0 H t
z
H t
t  H z  e z 
 jEt
z

  t  e z
z
H=Ht+ezHz
Hz 
1
j0
Ez  
1
j



 ey
 ez
x
y
z
 t  Et 
1
j0
t  H t  
t  e z  Et 
1
j
t  e z  H t 
Et
1
1

ez 
  j0 H t 
e z   t   t  e z  H t 
z
j


H t
1
ez 
 j 0 Et 
e z   t  t  e z  Et 
z
j0
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One-dimensional planar optical waveguide and
Wave optics description
Field division and classification of modes
uniformity and symmetry
x
   ( x) exp(  jz )
 y  0,  z   j
h
principle of superposition
TE
Mode
TM
Mode
Ex  0
Hx  
Hx  0
Ex  
Ez  0
z
y
confinement layer
n3
waveguide layer
n1
confinement layer
n2

j dE y
Ey , H z 
, Ez  H y  0
0
0 dx
Hz  0

j dH y
H y , Ez 
, H z  Ey  0

 dx
56
Maxwell Equation
E  
B
D
, H 
t
t
In rectangular coordinate system
 H z H y 
 H y H x 
 H x H z 
  e y 
  j e x E x  e y E y  e z E z 
e x 



  e z 
z 
x 
y 
 z
 y
 x
 E z E y 
 E y E x 
 E x E z 


   j0 e x H x  e y H y  e z H z 
ex 

 ey


  e z 

z 
x 
y 
 z
 y
 x
Ez  0 E y  0 H x
dE y
dx
  j0 H z
dH z
jH x 
  jE y
dx
TE
H y  E x
dH y
dx
Hz  0
 jE z
jE x 
dE z
 j0 H y
dx
TM
57
Field equation
TE :  E y
d 2
2
2
2
 k0 n j     0, j  1,2,3
2
TM :  H y
dx


Mode solution
0 xh
 A cosx   B sin x 

 x    A exp  2 x 
,
x0
A cos h  B sin h exp   x  h 
xh
3

 2  k12   2 ,  2 2   2  k2 2 ,  32   2  k32 , k j  k0 n j ,  j  1,2,3
：衰减系数
58
Thank You！
59