(b) 在 n 連續減少的介質中，光線的路徑為連續彎曲。

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；

2-8 光吸收與散射

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。

z A solid with ions

Light direction k E

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。

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。

2-9 光纖中的衰減

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。

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

f B T

n β k T

λ

α π

₄³

(

1 )

3 8 −

≈

Escaping wave

θ θ

θ′ < θ θθ > θ_c 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。

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

10⁻³ 10⁻² 10⁻¹ 1 10 10²

α_B (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 α_B 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

2-10 光纖製造

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。

Protective polymerinc coating Buffer tube: d = 1mm

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

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)。

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.

?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。

v_g(m/s)

ω

(1/s)

TE₀

TE₁

2.08×10⁸

2.07×10⁸

2.06×10⁸

2.05×10⁸

0 1×10^{1 5} 2×10¹⁵ 3×10^{1 5}

ω_cut-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)

0 0.5 1 1.5

0 1 2 3

V - number V[d

(Vb)/dV

]

[d

(Vb)/dV

] 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)

圖

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。

n

₁

O O'

B'

B A

Ray A

Ray B θ

θ

_B'

θ

_B'

θ

_{B '}

y = 0 y = δ /2 δ /2 Medium 1

Medium 2

n

Medium 3 δ

δ

y = 3 δ /2 y = 5 δ /2

θ

_B'

θ

B''

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

and θ

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)

圖

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′

在文檔中介質波導與光纖 (頁 81-106)

(b) 在 n 連續減少的介質中，光線的路徑為連續彎曲。

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)

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；

2-8 光吸收與散射

Medium

k Attenuation of light in the direction of propagation.

z E

z A solid with ions

Light direction k E

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.

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.

2-9 光纖中的衰減

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

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.

 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

n β k T

λ

α π

(

1 )

3

8 −

≈

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

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

67

.

≈ 1

V

2-10 光纖製造

Schematic illustration of a fiber drawing tower.

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

ω

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

= 1.455, n

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

is for m = 0 etc.

0 0.5 1 1.5

0 1 2 3

V - number V[d

(Vb)/dV

]

[d

(Vb)/dV

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

2.38

n

n

O O'

B'

B A

Ray A

Ray B θ

θ

θ

θ

θ

θ

y = 0 y = δ /2 δ /2 Medium 1

Medium 2

n

Medium 3 δ

δ

y = 3 δ /2 y = 5 δ /2

θ

θ

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

_B′