光纖光學(xué) - 導(dǎo)波光學(xué)

lesson8Guided-wave

Optics導(dǎo)波光學(xué)Planar-mirror

waveguidePropagation

constant

傳播常數(shù)Number

of

modes

模式數(shù)Group

velocities

群速度The

self-consistency

condition

自我復(fù)制條件Field

distribution

模式分布Dispersion

Relation

色散關(guān)系Multimode

Fields

多模傳輸

The

self-consistency

conditionThe

self-consistency

condition:

to

form

the

waveguide

mode.

=2

AC

/

2

2

AB/

2

qThe

self-consistency

condition自我復(fù)制條件Planar

dielectric

waveguidesPropagation

constant

傳播常數(shù)Number

of

modes

模式數(shù)Group

velocities

群速度The

self-consistency

condition

自我復(fù)制條件Field

distribution

模式分布Dispersion

Relation

色散關(guān)系Multimode

Fields

多模傳輸

Maxwell

equationBoundary

conditionWaveguide

modesThe

self-consistency

condition

自我復(fù)制條件sin

2

其中

ky

d

r

2

sin

m

兩次反射的相位差：

sin

C

n2

/

n1

因為根號下的量可以為負數(shù)，所以r，t都可以為復(fù)數(shù)

cos

2

1

sin2

1

/sin2

C經(jīng)過反射后的相位改變將由自復(fù)制條件求得的相位帶入上式

Self-consistency

Condition

(TE)作圖法左邊右邊Propagation

constantm由作圖法可求得容許傳播的入射角

m，且這些

是離散取值！Self-consistency

Condition

(TE)由投影法可以得到傳播常數(shù)：

m

kcos

m

n1k0

cos

m

臨界角入射角

<關(guān)鍵角：Number

of

modes自我復(fù)制條件波導(dǎo)中容許存在的模式數(shù)：單模運行條件：M=

1

2d

sin

cField

distribution

波在交界面不會消失（理想情況）！

波在交界面不一定發(fā)生半波損失！

波會部分滲透到包層里，形成倏逝波！

外部波內(nèi)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波在交界面不會消失！內(nèi)部波Field

distribution外部波倏逝波Ex(y,z)

amum(y)exp(

j

mz)2

2模場分布圖：Dispersion

Relation光錐下面表示容許存在！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