EE 230: Optical Fiber Communication Lecture 2

From the movieWarriors of the Net

Fibers from the view of Geometrical Optics

Total Internal Reflection

1 1 2 2

1 3

1 2 1 2

21 2

1

1

:sin sin

Re

90 deg

sin sin

c c

c

c

Snells Lawn n

flection Condition

When n n and as increases eventually

goes to rees andn

n n orn

is called the Critical angleFor there is no pro pagating refracted ray

Reflection as a function of angle

Fiber Optics Communication Technology-Mynbaev & Scheiner

This additional Phase Shift is not accounted for

in geometrical wave approach

The reflectivities of waves polarizedparallel and perpendicular to the plane of incidence as given by the Fresnel equations

Principal Types of Optical Fiber

Understanding Fiber Optics-Hecht

Types of Fibers

•Single mode/Multi-mode

•Step Index/Graded Index

•Dispersion Shifted/Non-dispersion shifted

•Silica/fluoride/Other materials

•Major Performance Concerns for Fibers

•Wavelength range

•Maximum Propagation Distance

•Maximum bitrate

•Crosstalk

Fabrication of Optical Fiber

• Fabrication of fiber preform: macroscopic version with correct index profile

• Drawing of preform down into thin fiber

• Jacketing and cabling

Step-Index Fiber

• Cladding typically pure silica

• Core doped with germanium to increase index

• Index difference referred to as “delta” in units of percent (typically 0.3-1.0%)

• Tradeoff between coupling and bending losses

• Index discontinuity at core-clad boundary

Basic Step index Fiber Structure

Fiber Optics Communication Technology-Mynbaev & Scheiner

Ray Trajectories in Step Index fiber

Meridional Rays

Skew Rays

Coupling Light into an Optical Fiber

Fiber Optics Communication Technology-Mynbaev & Scheiner

Acceptance Angle

Optics-Hecht & Zajac

The acceptance angle (i) is the largest incident angle ray that can be coupled into a guided ray within the fiber

The Numerical Aperature (NA) is the sin(i) this is defined analagously to that for a lens

#

tan

1

2

f ff

D FullAccep ceAngle

NA

º =

=×

1 1 12 2 22 2 2

1 2

1 2 1 2

( ) (2 ) (2 )

and 2

NA n n n n

n n n nWhere n

n

= - = D = D

- +D º º

φ1

φ2

θ1

θ2

nCO

nCL

n0

From Snell’s Law, 21 sinsin CLCO nn

For total internal reflection, θ2=90º

CO

CLc n

n11 sin

What value of φ1 corresponds to θc?

That is the maximum acceptance angle for the fiber. φ2 = 90º-θc sinφ2 = cos θc

CO

CLc n

nsin , so

CO

CLCOc n

nn 22

cos

NAnnn

nnnn CLCO

CO

CLCOCOCO

22

22

2sin

Again from Snell’s Law,

21 sinsin COo nn

(= NA), so

0

11 sin

n

NAc

Numerical Aperture

210 sinsin COnn

For Corning SMF-28 optical fiber

nco=1.4504, nCL=1.4447 at 1550 nm

NA = 0.13

Acceptance angle = 7.35 degrees

Geometrical View of Modes

Fiber Optics Communication Technology-Mynbaev & Scheiner

•Ray approximation valid in the limit that goes to zero

•Geometrical Optics does not predict the existance of discrete modes

•Maxwells Equations and dielectric boundary conditions give rise to the requirement that the fields and phase reproduce themselves each “cycle”

Rays and Their E-field Distribution

Origin of Modal Dispersion• Straight path along fiber axis has distance L and velocity c/nCO for

transit time of LnCO/c

• Path at maximum acceptance angle φc has distance L/cosφ2 where φ2=90º-θc and thus a longer transit time.

• Transit time difference equal to

• Dispersion limits rate of signals that fiber can handle

• If spread can be up to 70% of bit period, then maximum bit rate is 1.4cnCO/L(NA)2

2

22

2 1sin1cos

COn

NA

112

CL

COCO

n

n

c

Lntt

Intermodal Dispersion

Fiber Optics Communication Technology-Mynbaev & Scheiner

1SI

2

1 2SI2

SI

Lt c

Lt for c( )Lt c 2

nnn

n n n

NAn

D = D

D @ D @

D @

Bandwidth for Various Fiber Types

Fiber Optics Communication Technology-Mynbaev & Scheiner

21

21 8

4

1Bit Rate BR<4

14 4

2

2

SI

SISI

GI

GIcBRLn

t

cBRt Ln

cBRn L

cBR n L

= =D

D

D

= =D D

=D

D

No intermodal time shift for single Mode Fiber

Graded Index Fiber

Fiber Optic Communication Systems-Agarwal

1

1 2

21

21

21

( ) 1 for <a

( ) 1 =n for >a

for 2 a "parabolic profile"

NA=n 2 1 which varies with

8GI

n na

n n

a

Lnt

c

Fiber Optic Communications-Palais

Ray Propagation in Graded-Index Fiber

Graded Index Slab Uniform in X and Z

Fundamentals of Photonics - Saleh and Teich

Ray spreading comparison

3

4

8 COGI cn

NALt

CO

SI cn

NALt

2

2

Comparison, continued

If NA=0.13 and nCO=1.45,

∆tSI/L=19 ps/m

∆tGI/L=0.039 ps/m

Graded-index fiber has substantially less modal dispersion