光纤光学 - 导波光学

lesson8Guided-wave

Optics导波光学Planar-mirror

waveguidePropagation

constant

传播常数Number

of

modes

模式数Group

velocities

群速度The

self-consistency

condition

自我复制条件Field

distribution

模式分布Dispersion

Relation

色散关系Multimode

Fields

多模传输

The

self-consistency

conditionThe

self-consistency

condition:

to

form

the

waveguide

mode.

=2

AC

/

2

2

AB/

2

qThe

self-consistency

condition自我复制条件Planar

dielectric

waveguidesPropagation

constant

传播常数Number

of

modes

模式数Group

velocities

群速度The

self-consistency

condition

自我复制条件Field

distribution

模式分布Dispersion

Relation

色散关系Multimode

Fields

多模传输

Maxwell

equationBoundary

conditionWaveguide

modesThe

self-consistency

condition

自我复制条件sin

2

其中

ky

d

r

2

sin

m

两次反射的相位差：

sin

C

n2

/

n1

因为根号下的量可以为负数，所以r，t都可以为复数

cos

2

1

sin2

1

/sin2

C经过反射后的相位改变将由自复制条件求得的相位带入上式

Self-consistency

Condition

(TE)作图法左边右边Propagation

constantm由作图法可求得容许传播的入射角

m，且这些

是离散取值！Self-consistency

Condition

(TE)由投影法可以得到传播常数：

m

kcos

m

n1k0

cos

m

临界角入射角

<关键角：Number

of

modes自我复制条件波导中容许存在的模式数：单模运行条件：M=

1

2d

sin

cField

distribution

波在交界面不会消失（理想情况）！

波在交界面不一定发生半波损失！

波会部分渗透到包层里，形成倏逝波！

外部波内部波

Upward

wave:Downward

wave:

Symmetric

mode

(even

mode

/

TE

mode):Ex

2iAmsin(kymy)exp(i

mz)

amum(y)exp(i

mz)Where:Am

exp(ikymy

i

m

z)Am

exp(ikymy

i

m

z)Field

distribution波在交界面不会消失！内部波Field

distribution外部波倏逝波Ex(y,z)

amum(y)exp(

j

mz)2

2模场分布图：Dispersion

Relation光锥下面表示容许存在！Two

dimensional

WaveguidesIf

the

plane

wave

and

its

multiple

reflections

are

to

exist

self-consistent,

it

must

satisfy

the

conditions:The

number

of

the

modes

can

be

decided

by:The

number

of

the

modes

can

be

decided

by:Bragg-Grating

waveguidesPhotonic

crystal

waveguidesOptical

Coupling

In

Waveguides(3)Coupled

Waveguides1

When

the

interval

distance

between

adjacent

waveguides

wIincreases

to

a

certain

value

that

is

comparable

with

the

wavelength,e.

g.

around

wI=1000nm,

the

odd

mode

(the

1st

order)

appears

(asthe

blue

circle

line

in

Fig.

4a),

then

leading

to

a

beating

mechanismbetween

the

symmetric

(even)

and

anti-symmetric

(odd)

super-modes.

Given

the

complex

propagation

constants

S

i

S

a

i

a

for

the

symmetric

and

anti-symmetric

modesThe

Coupling

Length:The

Propagation

Length:LC

S

aLP

2

S

Sexp(

2

arctan(1/

))

2P

max

,

2LC

/(

LP)

Due

to

the

existence

of

propagation

losses,

a

total

(100%)

transfer

of

the

electromagnetic

energy

from

onewaveguide

to

the

other

is

not

possible.

The

maximum

power

obtainable

from

one

waveguide

to

the

other

due

tocoupling

is

then

defined

as:Periodic

Waveguides

Plasmonic

Waveguides

Sub-wavelength

metallic

waveguideIt

is

difficult

to

confine

an

optical

wave

to

dimensions

much

smaller

than

a

wavelength.

Bulk

metals