Waveguide OpticsTeacher : Lilin Yi

Email : lilinyi@sjtu.edu.cn

Office : SEIEE buildings 5-517

Tel ： 34204596

http://front.sjtu.edu.cn/~llyi/waveguide

1

State Key Lab of Advanced Optical Communication System and Networks

Self-introduction

• 2012.6- 现在 上海交通大学电子工程系 博士生导师• 2010.12- 现在 上海交通大学电子工程系 副教授• 2010.4- 现在 上海交通大学电子工程系 讲师 / 硕士生导师• 2008.5-2010.3 Oclaro( 原 Avanex) Corporation 产品开发经理 / 高级工程师 / 光学工程

师• 2006.10-2008.3 法国国立高等电信学校（ ENST ） 博士• 2004.9-2008.4 上海交通大学电子工程系 博士• 2002.9-2005.3 上海交通大学物理系光学专业 硕士• 1998.9-2002.7 上海交通大学物理系 学士

简历

• 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

荣誉及奖励

• 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：

• Lilin Yi, Weisheng Hu, Yi Dong, Yaohui Jin, Wei Guo, and Weiqiang Sun, “A polarization-independent subnanosecond 22 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.

代表性研究成果

Research Fields

optical signal processing

PON

Microwave Photonics

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Syllabus(flexible)

Chapter 1 Introduction• § 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• § 2-1 Geometrical Optics Method• § 2-2 Electrodynamics Fundamentals • § 2-3 Wave Optics Method

Chapter 3 Fiber Mode Theory• § 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• § 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

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Chapter 5 Signal Degrade in Fiber• § 5-1 Attenuation• § 5-2 Chromatic Dispersion• § 5-3 Nonlinearity

Chapter 6 Semiconductor Laser • § 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

Chapter 8 Modulation Formats• § 8-1 General Concepts of Optical Modulation

• § 8-2 electro-optic effect

• § 8-3 Electro-optical Modulator

• § 8-4 Modulation Format

Chapter 9 High bit rate transponder• §9-1 Standard evolution• §9-2 100G commercial transponder• §9-3 Technical trend for 400G and 1T

Chapter 10 Fiber Amplifier Design• §10-1 EDFA Design• §10-2 Raman Amplifier Design

Chapter 11 EDFA design process

Chapter 12 Semiconductor Optical Amplifier• §12-1 SOA in Transmission• §12-2 SOA in Signal Processing

Chapter 13 PON• §13-1 EPON/GPON (TDMA)• §13-2 WDM-PON• §13-3 CDMA• §13-4 OFDM-PON

Chapter 14 Optical Switching• §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

9

101

107

102

106

103

105

104

104

105

103

106

102

107

101

108

100

109

10-1

1010

10-2

1011

10-3

1012

10-4

1013

10-5

1014

10-6

1015

ELF VF VLF LF MF HF VHF UHF SHF EHF

free space wavelength(m)

Frequency(Hz)

electricity

phone

wireless

TV

microwave infrared visible light

twisted pair

coaxial cable

Fibersatellite

/microwave

AM FM

Fiber

Wavelength range ： 0.1μm ～ 10μm(300THz~30THz)

1 History and Present State

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.

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.

Underground optical communication

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

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The laser has good mono-chromaticity, directivity, coherency, high brightness, high power

The invention and application make optical communication into a new stage

In 1870, British physicist Tyndall

sunlight bends with the water flow

nwater > nair light occurs total reflection

The prototype of the optical fiber

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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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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Charles Kao (left) awarded a medal by the IEE in the UK(1998).

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 mediumThe 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 fiber, Dispersion compensation fiber, Photonic crystal fiber…

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Fiber-optical communicationAnother 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 trendsmultimode 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 interconnectsIBM, 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

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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)

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 'sOptical waveguide theory and calculations ：

• 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: • 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: • 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: • 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

• 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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Typesone-dimensional: planar optical waveguide/ thin film optical wave-

guide

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 properties38

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 FieldsGeometry 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 steady-state distribution in optical fiber.

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Solving methodsAnalytical 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).

45

The Ray EquationIn 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

• Snell's law(treat n(r) as n slices and use

Snell's law at every boundary)

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r+dr

ds

r

Light propagation

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One-dimensional planar optical waveguide and Geometrical optics description

basic structure• Consisting of multi-layer planar

dielectric waveguide structures

• Refractive index changes on the

perpendicular direction

Three layer uniform ：

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321

3

2

1

,

0,

0,

nnn

hxn

xn

hxn

xn

confinement layer

waveguide layer

confinement layer n3

n1

n2

x

y

zh

symmetrical structure ： n2 = n3

asymmetric structure ： n2 n3

n4

n1

n2

n3

Total reflection at the interface

Snell’s law

• Goos- Haenchen displacement • penetration depth h

• displacement of Incident point

and reflection point

• reflection phase loss

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221111 sinsin, nn TE

kH E

TM

kHE

n1

n2

1’1

2

h

jRR expamplitude reflection coefficient

1

21

2

cos

sinsinarctan

c

1 ： incidence anglec ： critical angle

Total reflection condition

>c12>c13

transmission constant

coherence emphasis condition

characteristic equation

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12sin nn kkxkz

h

A

B

C

D

wavefront

n1

n2

n3

3

sin10nkkz 1020 nknk k = k0n1

,...2,1,0,22

321 mmn

BCAD

cos2hBCAD mhnk 2cos2 3210 specific incident angles make

several modes

Transverse resonance condition = characteristic equation

TE mode and TM mode have the different reflection phase

loss （ 2+3 ） and different characteristic equation

cut-off wavelength ： cm

number of modes

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mhkx 22 32 cos10nkkx

kkx

kz

one m ，two modes ：TEm 、 TMm

fundamental mode ：TE0 mode has the longest cut-off wavelength

32

22

21

2

4

m

nnhcm

2

432

22

21

nn

h

Mm

Polarization degeneracy ：total number of modes ： 2M

Wave Optics Method

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Maxwell's equations

Wave equation

Helmholtz equation

refractive index

distribution

RayEquation

waveguide field

equation

boundary conditions

raytrace

eigensolution eigenvalue

transmission characteristic

Electromagnetic theory

Maxwell equation

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0

B

D

DJH

BE

f

f

ρt

t

HB

EPED

0

2.3

2.1

2.2

2.4

2.5

2.6

Harmonic electromagnetic field

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tjtt

tjtt

expRecos,

expRecos,

rHrHrH

rErErE

0

0

0

B

D

EH

HE

j

j

22

2

,

tj

t

22

,

0

0

00

22

22

c

f

cknkk

k

k

HH

EEHelmholtz equationMaxwell equation

02

2

2

22

tc

n EE

02

2

2

22

tc

n HH

Longitudinal field and transverse field

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E=exEx+ eyEy+ezEz, H=exHx+eyHy+ezHz

E=Et+ ezEz H=Ht+ezHz

zyx zyx

eee

zzt

e

tt

zzt

tt

zzt

ztt

ztt

jz

jz

j

j

EH

eH

HE

eE

EH

HE

0

0

tztttz

tztttz

jjE

jjH

HeH

EeE

11

11

00

tzttztt

z

tzttztt

z

jj

z

jj

z

EeeEH

e

HeeHE

e

00

0

1

11

One-dimensional planar optical waveguide and Wave optics descriptionField division and classification of modes

uniformity and symmetry

principle of superposition

56

)exp()( zjx

jzy ,0

0xE

0xH

0,,00

yzy

zyx HEdx

dEjHEH

0,, yzy

zyx EHdx

dHjEHE

0zE

0zH

TE Mode

TM Mode

confinement layer

waveguide layer

confinement layer n3

n1

n2

x

y

zh

57

zzyyxxxy

zzx

yyz

x

zzyyxxxy

zzx

yyz

x

HHHjy

E

x

E

x

E

z

E

z

E

y

E

EEEjy

H

x

H

x

H

z

H

z

H

y

H

eeeeee

eeeeee

0

tt

D

HB

E ,Maxwell Equation

In rectangular coordinate system

yz

x

zy

xy

Ejdx

dHHj

Hjdx

dE

HE

0

0

TE

0zE

yz

x

zy

xy

Hjdx

dEEj

Ejdx

dH

EH

0

TM

0zH

58

hx

x

hx

hxhBhA

xA

xBxA

x

0

0

,

expsincos

exp

sincos

3

2

3,2,1,022202

2

jnkdx

dj

y

y

HTM

ETE

:

:

Field equation

Mode solution

3,2,1,,,, 02

322

32

222

222

12 jnkkkkk jj

guided mode

condition

：衰减系数

Thank You ！

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