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(1)

第二章

介質波導與光纖

(2)

目錄

‡ 2-1 對稱平面介質板波導

‡ 2-2 平面波導內的模色散與波導色散

‡ 2-3 步級折射率光纖

‡ 2-4 數值孔徑

‡ 2-5 單模光纖內的色散

‡ 2-6 位元率、色散、電以及光的帶寬

‡ 2-7 斜射率 (GRIN) 光纖

‡ 2-8 光吸收與散射

‡ 2-9 光纖中的衰減

‡ 2-10 光纖製造

(3)

2-1 對稱平面介質板波導

(4)

Light

n

2

A planar dielectric waveguide has a central rectangular region of higher refractive index n

1

than the surrounding region which has a refractive index n

2

. It is assumed that the waveguide is

infinitely wide and the central region is of thickness 2a. It is illuminated at one end by a monochromatic light source.

n

2

n

1

> n

2

Light

Light Ligh

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.1 一平面介質波導其中央矩形區域的折射率比周圍區域的折射 率高。假設此波導為無限寬且中央區域的厚度為,並由單色光源照 射其一端。

(5)

n2

n2

d = 2a θ θ

k1

Light

A B

C λ

β κ

E

θ n

1

A light ray travelling in the guide must interfere constructively with itself to propagate successfully. Otherwise destructive interference will destroy the wave.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

z y

x

圖2.2 一個在波導中行進的光線必須跟它自己發生建設性的干涉 以便能繼續傳播,要不然破壞性的干涉將使波受到破壞

(6)

波導條件

‡ 假設 k 1 為在 n 1 中的波向量 (wave vector),

,其中 k 和 為真空中的波 向量和波長,則對建設性的干涉, A 和 C 間 的相位差一定為 的整數倍,

(1)

λ π / 2

1

1

1

kn n

k = = λ

π 2

) 2 ( 2

) (

)

(

1

φ π

φ AC = k AC + BC − = m

(7)

‡ 為使波能沿著波導傳播,我們需要

(8)

‡ 以2去除 (2) 式,我們得到波導條件 (waveguide condition)

π (3)

φ λ θ

π n a m

m

m

− =

⎥⎦ ⎤

⎢⎣ ⎡

) cos 2

(

2

1

(9)

n

2

n

2

z 2a

y A

1

2 1

B

θ θ

A

θ

B

C

π−2θ 2θ−π/2

k

1

E

x n

1

Two arbitrary waves 1 and 2 that are initially in phase must remain in phase after reflections. Otherwise the two will interfere destructively and cancel each other.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.3 兩個任意波1和2初始同相位,反射後仍須同相位;否則此二 波將產生破壞性干涉並彼此相互抵消。

(10)
(11)
(12)

n2

z a y

A

1

2

θ θ

A

C

k E

x y

a

y

Guide center

π−2θ

Interference of waves such as 1 and 2 leads to a standing wave pattern along the y- direction which propagates along z.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.4 波的干涉例如1和2將導入一個在方向固定不變且沿著傳播 的波形。

(13)

n

2

Light

n

2

n

1

y

E(y)

E(y,z,t) = E(y)cos(

ω

t ?

β

0z)

m = 0

Field of evanescent wave (exponential decay)

Field of guided w ave

The electric field pattern of the lowest mode traveling wave along the guide. This mode has m = 0 and the lowest θ . It is often referred to as the glazing incidence ray. It has the highest phase velocity along the guide.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.5 沿著波導之行進波的最低模的電場圖樣。該模具有以及最 低的,且經常述說為光滑的入射線,沿著波導具有最高的相速 度。

(14)
(15)

y

E(y)

m = 0 m = 1 m = 2

Cladding

Cladding

Core 2a

n 1 n 2 n 2

The electric field patterns of the first three modes (m = 0, 1, 2) traveling wave along the guide. Notice different extents of field penetration into the cladding.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.6 沿著波導之行進波的前三個模 的電場圖樣。留意包層內不同 的場穿透範圍。

(16)

單模及多模波導

‡ 由 (3) 式我們可得到 的一個表示式,然後 應用內部全反射條件, ,證明模數 m 必須滿足

式中稱為V-數目 (V-number),它的大小由下列 所定義

θ

m

sin

c

m

θ

θ sin

sin >

(17)

Low order mode High order mode

Cladding Core Light pulse

t

0 t

Spread, ∆τ Broadened

light pulse Intensity

Intensity Axial

Schematic illustration of light propagation in a slab dielectric waveguide. Light pulse entering the waveguide breaks up into various modes which then propagate at different group velocities down the guide. At the end of the guide, the modes combine to

constitute the output light pulse which is broader than the input light pulse.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.7 光在平板介質波導中的傳播圖例。光脈衝進到波導後分解成各 種模態,然後以不同的群速度沿波導傳播下去。在波導末端,這些模 合併並組成輸出的光脈衝,而且比輸入的光脈衝寬。

(18)

θ θ E

B

y

B

z

z

y

O

θ θ B

E

//

E

y

E

z

(b) TM mode (a) TE mode

B

//

x (into paper)

Possible modes can be classified in terms of (a) transelectric field (TE) and (b) transmagnetic field (TM). Plane of incidence is the paper.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.8 可能的模態可用 (a) 橫向電場 (TE) 及 (b) 橫向磁場(TM)來分 類。入射面為紙面。

(19)
(20)
(21)
(22)
(23)
(24)
(25)

2-2 平面波導內的模色散與波導

色散

(26)
(27)

β

m

ω

Slope = c/n

2

Slope = c/n

1

TE0

ω

cut-off

TE1 TE2

Schematic dispersion diagram, ω vs. β for the slab waveguide for various TE

m

. modes.

ω

cut  ff

corresponds to V = π /2. The group velocity v

g

at any ω is the slope of the ω vs. β curve at that frequency.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.10 圖示平板波導之各種TEm模的 對 的色散曲線圖。

對應於 ,而在任意 的群速度 為在該頻率時 對 的曲線的斜率。

ω β

2 π /

=

V ω v β

g

ω ω

cut-off

(28)
(29)

y

E(y)

Cladding

Cladding Core

λ

2 >

λ

1

λ

1 >

λ

c

ω

2 <

ω

1

ω

1 <

ω

cut-off

v

g1

y

v

g2 > vg1

The electric field of TE

0

mode extends more into the

cladding as the wavelength increases. As more of the field is carried by the cladding, the group velocity increases.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.11 當波長增加時,TE0模的電場伸展到包層越多。若越多的 場被載於包層中,則群速度越增加。

(30)

2-3 步級折射率光纖

(31)

n y

n

2

n

1

Cladding

Core z

y

r φ

Fiber axis

The step index optical fiber. The central region, the core, has greater refractive index than the outer region, the cladding. The fiber has cylindrical symmetry. We use the coordinates r, φ , z to represent any point in the fiber. Cladding is

normally much thicker than shown.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.12 步級折射率光纖 ( 示意圖 )。中央區,核心,具有比外圍區,

包層,大的折射率。由於光纖為圓柱對稱,故其內任何一點 P 皆以 r 、 及 z 等座標表示。包層通常比所顯示的為厚。

ϕ

(32)

‡ 本質上此為圓柱形的介質波導,其內部核心介 質的折射率為 n1 比外部包層介質的折射率 n2 大。歸一化折射率差(normalized index

difference) 定義為

(33)

‡ 一個沿著光纖的導引LP模可用一個沿 z 的電場 分佈 的傳播來表示,此電場分佈 ( 或圖 樣 ) 在垂直於纖軸的平面上,因此只和 r 和 相關而與 z 無關。此外,由於存在著兩個邊 界,所以它的特性是由 和 m 兩個整數決定;

因此在一個LP模中的傳播電場分佈是由 給出,並表示為 。故一個 模可用

(1)

) , ( r ϕ

E ϕ

l

) , ( r ϕ E

lm

LP

lm

LP

lm

) (

exp )

,

LP E ( r j t z

E = lm ϕ ω − β lm

(34)

Fiber axis 1

2

3

4

5

Skew ray 1

3 2

4 5 Fiber axis

1

2

3 Meridional ray

1, 3

2

(a) A meridiona ray always

crosses the fibe axis.

(b) A skew ray does not have to cross the fiber axis. It zigzags around the fiber axis.

Illustration of the difference between a meridional ray and a skew ray.

Numbers represent reflections of the ray.

Along the fiber

Ray path projected on to a plane normal to fiber axis

Ray path along the fiber

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.13 子午光線與斜光線之間的差異的說明。數字代表光線 的反射。

(35)

E

r E01

Core

Cladding

The electric field distribution of the fundamental mod in the transverse plane to the fiber axis z. The light intensity is greatest at the center of the fiber. Intensity patterns in LP

01

, LP

11

and LP

21

modes.

(a) The electric field of the fundamental mode

(b) The intensity in the fundamental mode LP

01

(c) The intensity in LP

11

(d) The intensity in LP

21

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.14 基模在垂直於光纖軸之橫向平面上的電場分佈。最大的 光強度位在光纖的中央。所示為LP01、LP11 及 LP21 模的強度圖 樣。

(36)
(37)

‡ 一般單模光纖具有遠小於較多模光纖的核心半 徑以及較小的 。如果光源波長 足夠小,使 得 V 超過2.405時,單模光纖將變成多模,即 較高的模也將貢獻傳播。讓波長超過而使光纖 變成單模的截止波長 可由下式給出

(4)

∆ λ

λ

c

405 .

2 )

2 (

2 1/2

2 2

1 off

-

cut

= a nn =

V

λ

c

π

(38)
(39)

0 1 2 3 4 5 6

V b

1

0 0.8

0.6

0.4

0.2

LP

01

LP

11

LP

21

LP

02

2.405

Normalized propagation constant b vs. V-number for a step index fiber for various LP modes.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.15 一步級折射率光纖之各種LP模的歸一化傳播常數 b 對 V 數目的曲線圖。

(40)

‡ 因LP模的傳播常數隨波導特性以及光源波長而定,所以方便上採

(41)
(42)
(43)
(44)
(45)
(46)

2-4 數值孔徑

(47)
(48)

Cladding

α < αmax Core

A B

θ < θc

A B

θ > θc

α > αmax

n

0

n

1

n

2

Lost

Propagates

Maximum acceptance angle α

max

is that which just gives total internal reflection at the core-cladding interface, i.e.

when α = α

max

then θ = θ

c

. Rays with α > α

max

(e.g. ray B) become refracted and

penetrate the cladding and are eventually lost.

Fiber axis

©1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.16 最大可接受角 為剛好在核心-包層的界面上發生內部 全反射,即當 時, 的光線 ( 即光線B) 則變成折射而穿透到包層,最後損失掉。

α

max

α

max

α =

, α α

max

θ

θ =

c

>

(49)
(50)
(51)
(52)

2-5 單模光纖內的色散

(53)

τ t Spread, τ

0 t λ

Spectrum, λ

λ1 λo λ2

Intensity Intensity Intensity

Cladding Emitter Core

Very short light pulse

vg(λ2) vg(λ1) Input

Output

All excitation sources are inherently non-monochromatic and emit within a spectrum, λ, of wavelengths. Waves in the guide with different free space

wavelengths travel at different group velocities due to the wavelength dependence of n1. The waves arrive at the end of the fiber at different times and hence result in a broadened output pulse.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.17 所有的激發光源本質上皆為非單色光並發射出一頻譜波 長 。由於折射率 n1 為波長的函數,故波導中不同自由波長的波 將以不同的群速度行進。波將以不同的時間到達光纖的末端,因而 導致一個加寬的光脈衝。

λ

(54)

‡ 色散通常以單位長度的擴展表示並由下列給出

(55)

‡ 在 (1) 式中,由於有限的輸入頻譜, 因而 成為群延遲時間上的擴展。若 為基模的傳播 常數,則由定義

(3)

L τ /

∆ β

01

ω τ β

d d

01

1 =

=

g

g

v

(56)

0

1.2 1.3 1.4 1.5 1.6

1.1 -30

20 30

10

-20 -10

λ (µm)

Dm

Dm + Dw

Dw λ0

Dispersion coefficient (ps km-1 nm-1)

Material dispersion coefficient (Dm) for the core material (taken as SiO2), waveguide dispersion coefficient (Dw) (a = 4.2 µm) and the total or chromatic dispersion coefficient Dch (= Dm + Dw) as a

function of free space wavelength, λ.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.18 核心材料 的材料色散係數 、波導色散係數 以及總或色彩色散係數 為自由空間波長的函 數。

)

(SiO2 (Dm) (Dm

+

= m

ch D

D ( Dw)

)

(57)

波導色散

‡ 如圖2.17,我們若使用一個具有頻譜 之很短 的光脈衝當作輸入,則因波導色散,輸出光脈 衝單位長度的加寬或色散, ,可由下列求 得

(4)

λ

L

τ /

τ = λ

∆ | D

w

|

L

(58)

‡ 它是隨波導特性 ( 不瑣碎的方式 ) 而定,且在 的範圍,可由下列近似給出

(5)

2.4 5

.

1 < V <

2 2 2

2

2 ) 2

(

984 .

1

cn a

D

w

N

π

g

(59)

色彩色散或總色散

‡ 在一階近似時,此兩個色散效應可簡單地相加 而使單位長度的總色散變成

λ (6)

τ = +

∆ | D

m

D

w

|

L

(60)

外形與偏振色散效應

‡ 如果 隨波長改變,則光源中不同的波長將有 不同的群速度並經不同的群延遲而導致脈衝的 加寬。外形色散是色彩色散的一部分,因其隨 輸入的頻譜 變化

(7)

λ

τ = λ

∆ | D p |

L

(61)

Core

z

n1 x // x

n1 y // y

Ey

Ex

Ex

Ey

E

τ = Pulse spread

Input light pulse

Output light pulse

t

t

τ Intensity

Suppose that the core refractive index has different values along two orthogonal directions corresponding to electric field oscillation direction (polarizations). We can take x and y axes along these directions. An input light will travel along the fiber with Ex and Ey polarizations having different group velocities and hence arrive at the output at different times

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.19 假設核心折射率在相應於電場振盪方向 ( 偏振 ) 的兩個正 交方向上的值不相同;我們讓 x 和 y 軸沿此二方向,則一沿著光纖 行進的輸入光其 Ex 和 Ey 偏振具有不同的群速度因而以不同的時 間到達輸出端。

(62)

20

-10 -20

-30 10

1.1 1.2 1.3 1.4 1.5 1.6 1.7 0

30

λ (µm)

Dm

Dw

Dch = Dm + Dw λ1

Dispersion coefficient (ps km -1 nm-1)

λ2

n

r

Thin layer of cladding with a depressed index

Dispersion flattened fiber example. The material dispersion coefficient (D

m

) for the core material and waveguide dispersion coefficient (D

w

) for the doubly clad fiber result in a flattened small chromatic dispersion between λ

1

and λ

2

.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.20 色散平坦化光纖的例子。核心材料的材料色散係數

以及雙包層光纖的波導色散係數 導致 和 之間小而平坦的 色彩色散。

) (Dm

λ

1

λ

2

)

( D

w

(63)
(64)
(65)
(66)

2-6 位元率、色散、電以及光的

帶寬

(67)

0 t

Emitter

Very short light pulses

Input Output

Fiber

Photodetector Digital signal

Information Information

0 t

~2 τ

1/2

T

t

Output Intensity Input Intensity

² τ

1/2

An optical fiber link for transmitting digital information and the effect of dispersion in the fiber on the output pulses.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.22 一光纖連接以傳送數位訊息以及光纖中的色散對輸出脈衝 的效應。

(68)

‡ 脈衝可傳送的最大位元率,或簡稱位元率 B , 大約為

(1) )

2 /(

1 ∆ τ 1 / 2

2 / 1

5 . 0

τ

≈ ∆

B

(69)

t Output optical power

∆ τ

1/2

T = 4 σ

1

0.5

0.61 2 σ

A Gaussian output light pulse and some tolerable intersymbol

interference between two consecutive output light pulses (y-axis in relative units). At time t = σ from the pulse center, the relative magnitude is e -1/2 = 0.607 and full width root mean square (rms) spread is ∆ τ rms = 2 σ .

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.23 高斯輸出脈衝及兩連續輸出脈衝 ( y 軸為相對單位 ) 間之可 容忍的碼間干擾。距脈衝中心為 處的相對大小

,而全寬度均方根(ms) 延展為

a

t = 607

.

2

0

/

1

=

e

∆ τ

rms

= 2 σ

(70)

‡ 位元率 B 若以來表示 則需兩連續輸出光脈 衝之波峰間的分隔為 4 ,如圖2.23所示。因 此,

(2)

σ σ

σ 25 .

≈ 0

B

(71)

‡ 如果 D ch 為色彩色散係數,則輸出光脈衝的均 方根色散為 ,而乘積 BL ,稱為乘積

值,並由下列給出

(3)

σ

λ

LD

ch

σ

λ

σ | |

25 . 0 25

. 0

D

ch

BLL =

(72)

‡ 體色散若以一個均方根色散 表示則可由各個 均方根色散求得

(4)

σ

2

intramodal 2

intermodal

2 σ σ

σ = +

(73)

0 t

Pi = Input light power

Emitter

Optical Input

Optical Output Fiber

Photodetector Sinusoidal signal

Sinusoidal electrical signal t

0 t f

1 kHz 1 MHz 1 GHz

Po / Pi

fop 0.1

0.05 f = Modulation frequency

An optical fiber link for transmitting analog signals and the effect of dispersion in the fiber on the bandwidth, f

op

.

Po = Output light power

Electrical signal (photocurrent)

fel 0.7071

1 kHz 1 MHz 1 GHz f

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.24 用來傳送類比訊號的光纖連接以及光纖中的色散對帶寬 的效應。

(74)

‡ 如果光纖的色散特性為高斯的,則 σ (5)

19 . 75 0

.

0 ≈

B

f

op

(75)
(76)
(77)

2-7 斜射率 (GRIN) 光纖

(78)

n

1

n

2

2 1 3 O

n

n

1

2 1 3

n

n

2

O O' O''

n

2

(a) Multimode step index fiber. Ray paths are different so that rays arrive at different times.

(b) Graded index fiber.

Ray paths are different but so are the velocities along the paths so that all the rays arrive at the same time.

2 3

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.25 (a) 多模步級折射率光纖,光線路徑不同故光線以不同 的時間到達;

(79)

nb

nc

O O'

Ray 1 A

B'

B

θA θB

θB' Ray 2

M θB' c/n

b

c/na 21

B'' na

a b

c We can visualize a graded index fiber by imagining a stratified

medium with the layers of refractive indices na > nb > nc ... Consider two close rays 1 and 2 launched from O at the same time but with slightly different launching angles. Ray 1 just suffers total internal reflection.

Ray 2 becomes refracted at B and reflected at B'.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.26 我們可藉由想像一個層狀的介質,其層折射率

為 ,而瞭解斜射率光纖。考慮兩個靠近的光線 1及2,以相同的時間但不同的發射角由O發射。光線1正好遭 到內部全反射,而光線2先在 B 折射而後在 反射。

c

b

a

n n

n > >

B′

(80)
(81)

n decreases step by step from one layer to next upper layer; very thin layers.

Continuous decrease in n gives a ray path changing continuously.

TIR TIR

(a) A ray in thinly stratifed medium becomes refracted as it passes from one layer to the next upper layer with lower n and eventually its angle satisfies TIR (b) In a medium where n decreases continuously the path of the ray bends

continuously.

(a) (b)

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.27 (a) 薄層狀介質中的光線當它由一層通過下一個折 射率 n 較低的上層時變成折射直至最後它的角度滿足TIR;

(b) 在 n 連續減少的介質中,光線的路徑為連續彎曲。

(82)
(83)
(84)
(85)

2-8 光吸收與散射

(86)

Medium

k Attenuation of light in the direction of propagation.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

z E

圖2-28 光在傳播方向的衰減。

(87)

z A solid with ions

Light direction k E

x

Lattice absorption through a crystal. The field in the wave oscillates the ions which consequently generate "mechanical"

waves in the crystal; energy is thereby transferred from the wave to lattice vibrations.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖-29 通過晶體的晶格吸收。波內的場使離子振盪,結果在晶體 中產生“機械的”波,於是能量由波傳到晶格振盪。

(88)

Scattered waves

Incident wave Through wave

A dielectric particle smaller than wavelength

Rayleigh scattering involves the polarization of a small dielectric particle or a region that is much smaller than the light wavelength.

The field forces dipole oscillations in the particle (by polarizing it) which leads to the emission of EM waves in "many" directions so that a portion of the light energy is directed away from the incident beam.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.30 瑞利散射涉及一個遠小於光波長的小介電粒子或小區域的 極化。場迫使介質中的電偶極振盪導致電磁波在“很多”方向發射,

以致於一部分的光能由入射光束偏離。

(89)

2-9 光纖中的衰減

(90)
(91)
(92)

0.05 0.1 0.5 1.0 5 10

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Lattice absorption Rayleigh

scattering

Wavelength (痠)

Illustration of a typical attenuation vs. wavelength characteristics of a silica based optical fiber. There are two communications channels at 1310 nm and 1550 nm.

OH-absorption peaks

1310 nm

1550 nm

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.31 典型矽玻璃光纖之對波長的衰減特性的例子。在 1315nm及1550nm處有兩個通訊通道。

(93)

‡ 在單組成玻璃中因瑞利散射形成的衰減 的表 示式可由下列近似給出

(5) α

R

f B T

R

n β k T

λ

α π

43

(

2

1 )

2

3

8 −

(94)

Escaping wave

θ θ

θ′ < θ θθ > θc θ′

Microbending

R Cladding

Core Field distribution

Sharp bends change the local waveguide geometry that can lead to waves escaping. The zigzagging ray suddenly finds itself with an incidence angle θ′

that gives rise to either a transmitted wave, or to a greater

cladding penetration; the field reaches the outside medium and some light energy is lost.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.32 由銳利彎曲而改變局部的波導形狀而導致波的逃脫。彎 曲的光線突然發現它自己以一個入射角入射而引起一個透射波或 是一個較大的包層穿透;場到達外側的介質並損失部分的光能。

(95)

0 2 4 6 8 10 12 14 16 18 Radius of curvature (mm)

10−3 10−2 10−1 1 10 102

αB (m-1) for 10 cm of bend

λ = 633 nm

λ = 790 nm V = 2.08

V = 1.67

Measured microbending loss for a 10 cm fiber bent by different amounts of radius of curvature R. Single mode fiber with a core diameter of 3.9 µm, cladding radius 48 µm,

∆ = 0.00275, NA = 0.10, V = 1.67 and 2.08 (Data extracted and replotted from A.J.

Harris and P.F. Castle, IEEE J. Light Wave Technology, Vol. LT14, pp. 34-40, 1986;

see original article for discussion of peaks in αB vs. R at 790 nm).

From S.O. Kasap, Optoelectronics and Photonics: Principles and Practices (Prentice Hall)

圖2.33 10cm長的光纖以不同的曲率半徑彎曲所測量到的微彎曲 損失。單模光纖的核心直徑為3.9um,包層半徑為48um, , NA=0.11, 及2.08。

004 .

= 0

67

.

≈ 1

V

(96)
(97)
(98)

2-10 光纖製造

(99)

Preform feed

Furnace 2000蚓

Thickness

monitoring gauge

Take-up drum Polymer coater Ultraviolet light or furnace for curing

Capstan

Schematic illustration of a fiber drawing tower.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.34 光纖抽絲塔之圖解說明。

(100)

Protective polymerinc coating Buffer tube: d = 1mm

Cladding: d = 125 - 150 µm Core: d = 8 - 10 µm

n

r

The cross section of a typical single-mode fiber with a tight buffer tube. (d = diameter)

n1 n2

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.35 具有一個堅固緩衝管的典型單模光纖的橫切面。

(d=直徑)。

(101)

Vapors: SiCl4 + GeCl4 + O2

Rotate mandrel

(a)

Deposited soot Burner

Fuel: H2

Target rod

Deposited Ge doped SiO 2

(b)

Furnace Porous soot preform with hole

Clear solid glass preform Drying gases

(c)

Furnace

Drawn fiber Preform

Schematic illustration of OVD and the preform preparation for fiber drawing. (a)

Reaction of gases in the burner flame produces glass soot that deposits on to the outside surface of the mandrel. (b) The mandrel is removed and the hollow porous soot preform is consolidated; the soot particles are sintered, fused, together to form a clear glass rod.

(c) The consolidated glass rod is used as a preform in fiber drawing.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

圖2.36 OVD以及光纖抽絲所需預形體準備的圖解說明。(a) 燃燒器 火焰中的氣體反應產生玻璃煙灰並沉積在心軸的外表面;(b) 心軸移 走且中空多孔的煙灰預形體被固化,即煙灰顆粒昇華、熔化在一起 而形成一個透明的玻璃棒;(c) 所固化的玻璃棒當作光纖抽絲的預形 體。

(102)
(103)

vg (m/s)

ω

(1/s)

TE0

TE1

2.08×108

2.07×108

2.06×108

2.05×108

0 1×101 5 2×1015 3×101 5

ωcut-off = 2.3×1014

TE4

c/n2

c/n1

Group velocity vs. angular frequency for three modes for a planar dielectric waveguide which has n

1

= 1.455, n

2

= 1.44, a = 10 µm (Results from Mathview, Waterloo Maple math-software application). TE

0

is for m = 0 etc.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

(104)

0 0.5 1 1.5

0 1 2 3

V - number V[d

2

(Vb)/dV

2

]

[d

2

(Vb)/dV

2

] vs. V-number for a step index fiber (after W.A. Gambling et al., The Radio and Electronics Engineer, 51, 313, 1981)

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

2.38

一步級折射率光纖之V[d2(Vb)/dV 2] 對 V 數目的關係曲線。

(105)

n

2

n

1

O O'

B'

B A

Ray A

Ray B θ

A

θ

A

θ

B'

θ

B'

θ

B

θ

B '

y = 0 y = δ /2 δ /2 Medium 1

Medium 2

n

3

Medium 3 δ

δ

y = 3 δ /2 y = 5 δ /2

θ

B'

θ

B

B''

Step-graded-index dielectric waveguide. Two rays are launched from the center of the waveguide at O at angles θ

A

and θ

B

such that ray A suffers TIR at A and ray B suffers TIR at B'. Both TIRs are at critical angles.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

2.39

步級

-

斜射率介質波導。兩條光線由波導中心的 O 點分別以 角度 及 發射,使光線 A 在 A 點歷經

TIR

而光線 B 在 點歷 經

TIR

。兩個A

TIR

均在臨界角。

θ θ

B

B′

(106)

0.5P

O O'

(a)

0.25P

O

(b)

0.23P

O

(c)

Graded index (GRIN) rod lenses of different pitches. (a) Point O is on the rod face center and the lens focuses the rays onto O' on to the center of the opposite face. (b) The rays from O on the rod face center are collimated out. (c) O is slightly away from the rod face and the rays are collimated out.

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

參考文獻

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