planar waveguide circular waveguide optical fibertera.yonsei.ac.kr/class/2016_2_1/lecture/Lect 15 Optical Fiber.pdf · planar waveguide circular waveguide optical fiber. Lect. 15:

Lect. 15: Optical Fiber

Optoelectronics (16/2) W.-Y. Choi

3-dimentioanl dielectric waveguide?

planar waveguide circular waveguide

optical fiber



n

y

n2 n1

Cladding

Core z

y

r

Fiber axis

The step index optical fiber. The central region, the core, has greater refractiveindex than the outer region, the cladding. The fiber has cylindrical symmetry. Weuse the coordinates r, , z to represent any point in the fiber. Cladding isnormally much thicker than shown.

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

Optical Fiber: Circular dielectric waveguide made of silica (SiO2)

SiO2:Ge

What is special about fiber?

Loss in rectangular metal waveguide

- Extremely low loss: 0.2dB/km

- Can be very long: 100’s of km



Optical Communication Networks

Total undersea fiber length: 0.4 billion km ( 628 round trips between earth and moon)



Protective polymerinc coating

Buffer tube: d = 1mm

Cladding: d = 125 - 150 m

Core: d = 8 - 10 mn

r

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

n1

n2


for single-mode fiber

(For multi-mode fiber, d: several tens of m)



SiCl4 + O2 ->SiO2 + 2Cl2

GeCl4 + O2 ->GeO2 + 2Cl2

(b)

Furnace

Porous sootpreform with hole

Clear solidglass preform

Drying gases

Sintering at 1400-1600 deg C

Vapors: SiCl 4 + GeCl4 + O2

Rotate mandrel

(a)

Deposited sootBurner

Fuel: H 2

Target rod

Deposited Ge doped SiO 2



Preform feed

Furnace 2000°C

Thicknessmonitoring gauge

Take-up drum

Polymer coater

Ultraviolet light or furnacefor curing

Capstan



Solving for guided modes for circular dielectric waveguide problem in (r, , z) coordinate is very complicated.

0 2 4 61 3 5V

b

1

0

0.8

0.6

0.4

0.2

LP01

LP11

LP21

LP02

2.405( , ) e lmj z

LP lmE E r 12 2 20 1 2( )

( : fiber core radius)V k a n na

22

202 2

1 2

nkb

n n

n1n2

a

It can be shown that with a little approximation, LP (linearly polarized) mode solutions are obtained.



E

r

E01

Core

Cladding

The electric field distribution of the fundamental modin the transverse plane to the fiber axis z. The lightintensity is greatest at the center of the fiber. Intensitypatterns in LP01, LP11 and LP21 modes.

(a) The electric fieldof the fundamentalmode

(b) The intensity inthe fundamentalmode LP01

(c) The intensityin LP11

(d) The intensityin LP21


For LPlm mode,m represents the number of peaks along r, 2l represents the number of peaks along



Loss in fiber

0.05

0.1

0.51.0

5

10

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Latticeabsorption

Rayleighscattering

Wavelength ()

OH- absorption peaks

1310 nm

1550 nm

Loss(dB/km)



z

Si and O ions

Light directionk

Ex

Lattice Absorption: EM waves cause vibration of ions inside fiber. Peak absorption occurs at around = 9 m in Silica fiber.



Scattered waves

Incident wave Through wave

A dielectric particle smaller than wavelength

Rayleigh scatteringA small portion of EM waves get directed away from small dielectric particles that are due local fluctuation of fiber refractive index.More scattering with smaller wavelength (inversely proportional to 3).



Dispersion in Fiber

- Multi-Mode Fiber: Modal Dispersion

n1

n2

21

3

nO

n1

21

3

n

n2

OO' O''

n2

(a) Multimode stepindex fiber. Ray pathsare different so thatrays arrive at differenttimes.

(b) Graded index fiber.Ray paths are differentbut so are the velocitiesalong the paths so thatall the rays arrive at thesame time.

23


Each mode has its own group velocity

If a light pulse is decomposed into many modes, the pulse gets dispersed (broadened) after propagation

Prevention: Use single mode fiber!



- Material (or chromatic) dispersion:Refractive index of any material depends on wavelength (frequency)

But single mode fiber also has small but non-zero dispersion

vg for SMF depends on wavelength(frequency)

- Waveguide dispersionWaveguide solution depends on wavelength

t

Intensity

t

Spread

Intensity

Dispersive SMF



Mathematically,

0 0

22

0 0 2

1( ) ( )2

Dispersion exists because is not not linear with

20 1 0 2 0

1( ) ( ) ( ) 2

22In Silica fiber, ~ 20 ps /km at =1.5 m

0

20

0

1 1 1 = ( )( ) 2g gv v

2With 0, increases as increasesgv



Often, dispersion parameter D is used.

1D

t

Intensity

t

Spread (

Intensity

Dispersive medium (L,D)Spectrum (

Intensity

~ D L

1

2

2 c

2

22

2D c

2( )kc c

psD~16 at 1.5km nm m



Homework

Documents

planar waveguide circular waveguide optical fibertera.yonsei.ac.kr/class/2016_2_1/lecture/Lect 15 Optical Fiber.pdf · planar waveguide circular waveguide optical fiber. Lect. 15: