Fiber optics Fiber optics &&

Gradient-index opticsGradient-index optics

HistoryHistory

-It was suggested that the attenuation, energy absorption, scattering, and spreading was due to impurities in glass fibers

-It was speculated that if attenuation could be reduced to under 20 dB per kilometer, then fiber optics would become a practical communication medium

-In 1970 it was demonstrated that a fiber with 17 dB attenuation per kilometer could be made by doping pure silica with germanium

Guiding lightGuiding light

Bending light?Bending light?

John Tyndall (1820-1893)

Bending light!Bending light!

What is an Optical Fiber?What is an Optical Fiber?

An optical fiber is a waveguide for light

consists of :

core inner part where wave propagates

cladding outer part used to keep wave in core

buffer protective coating

jacket outer protective shield

can have a connector

too

Optical fiber cableOptical fiber cable

Fiber Optics Communication Technology-Mynbaev & Scheiner

Total Internal ReflectionTotal Internal Reflection

nntt

nnii

i

really weakreally weakevanescent waveevanescent wave

tii

tc n

n

nsin

i i c c for TIR for TIR

critical anglecritical angle

Types of FibersTypes of Fibersst

ep-i

ndex

mul

tim

ode nc

nc

nf

nc

nc

nf

nc

nc

nf

step

-ind

exsi

ngle

mod

eG

RIN

Step-index FiberStep-index Fiber

In

Out

Time

Inte

nsi

ty Disadvantage: Pulse broadening

Ray Trajectories in Step Index fiberRay Trajectories in Step Index fiber

Meridional Rays

Skew Rays

Double-clad fiber Double-clad fiber

Cross-section of circular double-clad fiber with offset core.

Cross-section of double-clad fiber with rectangular inner cladding

Graded-index fiberGraded-index fiber

In

Out

Time

Intensity remains almost constant

Pulse broadening is not so severe Refractive in

dex vary parabolically across the cross-section

Graded Index FiberGraded Index Fiber

nc

nc

nf

n va

ries

qua

dra

tica

lly

like a “restoring” force !

Graded-index Fiber, cont. Graded-index Fiber, cont.

In the graded-index fiber, light rays that In the graded-index fiber, light rays that traverse longer path lengths through the traverse longer path lengths through the outer periphery of the core travel faster outer periphery of the core travel faster in this lower index material in this lower index material all rays all rays arrive at the same time at the output arrive at the same time at the output almost no pulse broadening!almost no pulse broadening!

Photonics crystal fiberPhotonics crystal fiber

Scanning electron microscope image of a fused silica hollow core photonic crystal fiber (HC-PCF)

Special fibersSpecial fibers

Nano fibersNano fibers

Numerical Aperture (NA) of a FiberNumerical Aperture (NA) of a Fiber

max

maxsin outsidenNA

The NA defines a cone of acceptance for light that will be guided by the fiber

NA of a Step Index FiberNA of a Step Index Fiber

90-90-tt

tt

maxmax

nnff

nncc

must be > critical angle

maxsin outsidenNA

22cfstep nnNA

nnii

i

cf

step n

nnNA

22

NANA in air in air

NA of a GRIN FiberNA of a GRIN Fiber

2

DnNA f

Condition below assures a ray will Condition below assures a ray will have enough fiber to bend back towards have enough fiber to bend back towards the center axis:the center axis:

is a parameter describing how is a parameter describing how nn changes in the GRIN fiberchanges in the GRIN fiber

NA in airNA in air

)2

11()( 2

0 rnrn

NA and Light FluxNA and Light Flux

light gathering power ~ light gathering power ~ NANA22

max

Example:Example:Fiber with Fiber with NANA of 0.66 has 43% flux-carrying of 0.66 has 43% flux-carrying capacity of a fiber with an capacity of a fiber with an NANA of 1.0 of 1.0

NA and # of ModesNA and # of Modes

smallNA

largeNA

propagated ray

killed ray

Critical Bend radiusCritical Bend radius

source: RPI websiteCritical bend radius

Fiber TapersFiber Tapers

1

2

2211 sinsin dd

d1 d2

• Way to change the acceptance angles of a fiberWay to change the acceptance angles of a fiber

• Sometimes used to collimate light Sometimes used to collimate light

• Does not necessarily “get you more light” since NA changesDoes not necessarily “get you more light” since NA changes

PolarizationPolarization

If the ray rotates during propagation, then If the ray rotates during propagation, then the polarization state will changethe polarization state will change

linear polarized beam translates into elliptical beamlinear polarized beam translates into elliptical beam

S

S

E

E

B

B

PolarizationPolarization

•In some applications, polarization is not needed:In some applications, polarization is not needed:

example: diffusive spectroscopyexample: diffusive spectroscopy

•In others it is critical: In others it is critical:

example: PS OCTexample: PS OCT

•must remove the circular symmetry of the fibermust remove the circular symmetry of the fiber

change change nn profile profile so that polarizations are not coupled so that polarizations are not coupledsort of like birefringencesort of like birefringence

Cross section of polarization maintain fiberCross section of polarization maintain fiber

AttenuationAttenuation

in

out

P

PA log10

Fibers are made of “glass”

- commonly high-quality fused silica (SiO2)- some trace impurities (usually controlled)

Losses due to:

- Rayleigh scattering (~ -4)- absorption (“low-OH” in UV versus “high-OH” in IR)- mechanical stress- coatings

Attenuation ProfilesAttenuation Profiles

absorption and scattering in fiberin the IR: “low-OH”

page 297

Rayleigh Scattering

IR absorption

89% transmission

Dispersion: The BasicsDispersion: The Basics

Light propagates at a finite speed

fastest ray

slowest ray

slowest ray: one entering at highest angle (“high order” mode)

fastest ray: one traveling down middle (“axial mode”)

there will be a difference in time for these two rays

Modal DispersionModal Dispersion

1

c

f

n

n

c

Lt

modal dispersion increases with:

L

~ NA2

usually the biggest dispersion problem in step index multi-mode fibers

Effect of Modal DispersionEffect of Modal Dispersion

time time time

modal example: step index ~ 24 ns km -1 GRIN ~ 122 ps km-1

initial pulse farther down farther still

FabricationFabrication

1. Make preform glass cylinder (blank)

Glass made by modified chemical vapor deposition (MCVD)

Gas vapors from MCVD are conducted onto the lathe to yield the fiber.

howstuffworks.com

FabricationFabrication

Preform heated so a drop falls by Preform heated so a drop falls by gravity yielding a single fiber.gravity yielding a single fiber.

Drawing rate regulated by a laser Drawing rate regulated by a laser micrometer to yield a consistent micrometer to yield a consistent diameter.diameter.

Fibers typically drawn at a rate of Fibers typically drawn at a rate of 10–20 m/s.10–20 m/s.

2. Draw the fibers from the preform.

howstuffworks.com

HHow ow toto make make in labin lab??[ figs courtesy Y. Fink et al., MIT ]

find compatible materials(many new possibilities)

chalcogenide glass, n ~ 2.8+ polymer (or oxide), n ~ 1.5

1

Make pre-form(“scale model”)

2

fiber drawing

3

Gradient-index opticsGradient-index optics

海市蜃楼海市蜃楼

nn11

nn33

nn22

nn55

nn44

θ1

θ2

θ3

θ4

θ5

Two-dimensional caseTwo-dimensional case

A special case: the refractive A special case: the refractive index of the media is uniform index of the media is uniform refractive index in each layer.refractive index in each layer.

According to the refraction law, According to the refraction law, we have:we have:

....sinsinsin 332211 constnnn

Two-dimensional caseTwo-dimensional case

222 )()()( dydxds

00 sin)(sin)(sin

1

nyyndx

ds

θ

dx

x

y

dy

The continuous case:The continuous case:

ds

With the relations below:With the relations below:

We have:We have:

1)(sin

)()(

022

0

22

n

yn

dx

dy

Two-dimensional caseTwo-dimensional case

1)(sin

)(

022

0

2

n

yn

dx

dy

)()( rnds

rdn

ds

dy

i.e.i.e.

For three-dimensional gradient-index media, the For three-dimensional gradient-index media, the light propagation trace follows the ray equation:light propagation trace follows the ray equation:

dy

dn

ndx

yd 2

022

02

2

)(sin2

1

oror

ExampleExample

yyy

ydx

dy

2)(2

1)1(

2

2

x

y

hh

机场跑道上方，由于存在温度梯度，空气的折射率不均匀，机场跑道上方，由于存在温度梯度，空气的折射率不均匀，折射率可近似写为：折射率可近似写为： n(y)=nn(y)=n00(1+(1+ββy), y), ββ≈1≈1.5.5×10×10-6-6/m/m 。考虑跑。考虑跑道上某处发出的沿水平方向传播的光的轨迹，如果该点光刚好道上某处发出的沿水平方向传播的光的轨迹，如果该点光刚好进入人眼，说明远离该点处的目标无法被人看见。确定了该点进入人眼，说明远离该点处的目标无法被人看见。确定了该点即可确定最远的可见距离。即可确定最远的可见距离。

根据光线方程根据光线方程

即即 2

2xy

ExampleExample

kmh

x 5.1105.1

75.1226

对于人眼，对于人眼， y=h=1.75my=h=1.75m ，得出最远可见距离为，得出最远可见距离为

因此，即使说能见度可达到因此，即使说能见度可达到 10km10km 的天气下，机场明视的天气下，机场明视距离介于距离介于 1-2km1-2km

Example2Example2：： GRIN lensGRIN lens

rr

dd

)2

11()( 2

0 rnrn 求折射率分布为：求折射率分布为： ，厚度为，厚度为 dd 的平板的焦距的平板的焦距

aa

FF

LL

光通过后，光通过后， r=ar=a 处于处于中心光的光程差中心光的光程差 LL 为：为：

drn

dndrn

n

dndanL

20

020

0

0

2

1

)2

(

)(

负号表明 负号表明 a a 越大，波面越大，波面越超前，形成光的汇聚。越超前，形成光的汇聚。

ff

(f2-a2)1/2

Example2Example2：： GRIN lensGRIN lens

aff

aaffL 当,

2

1 222

a

dnn

f

a

f

DAN ao )(4

2..

rr

dd

aa

FF

LL

对于焦距为对于焦距为 ff 的负透镜，径向的负透镜，径向 aa 处的波面与平面波的差异为处的波面与平面波的差异为

令令 L=L=ΔΔLL ，有，有

ff

(f2-a2)1/2 数值孔径为：数值孔径为：

dnn

a

dnf

danf

a

ao )(2

1

2

1

2

1

2

0

20

2