Fiber Optics and Ray Propagation

• Outline

–Silica fiber optics

–Optical guiding

–Optical rays

–Total internal reflection

–Single mode and multimode fibre

Silica fiber optics

SNELL’S LAW

• Two methods to explain:– Ray theory

(geometric)– Wave theory

(Maxwell’s equation)

• Reflection of a ray of light at boundry of two media obeys Snell’s Law– n1 sin f1 = n2 sin f2

– f1 and f2 are incident and refraction angle respectively

Total internal reflection

• Snell’s law: n1 sinf1 = n2 sinf2

• When f2 = p/2 (i.e.q2=0) , f1 = fc, critical angle.

– n1 sinfc = n2

– sin fc = n2/n1

– Critical angle of incidence fc is minimal f that supports

– qc total internal reflection.

Critical angle at interface between 2 media:

fc = sin-1( n2/n1), n1>n2

Optical Guiding

• Total internal reflection occurs when

– f > fcr (i.e. q < qc)

n0=1; ncore> nclad> n0

Numerical Aperture (NA) of a fiber optic

NA = sqrt (n2core – n2

clad) ~ ncore * sqrt (2D)

Fractional refractive index changeD = (ncore – nclad)/ncore

ACCEPTANCE ANGLE

• The angle that determines the cone of external ray that are guided by fiber optic

• Acceptance angle

qa

NAnnnn cladcoreccoreao 22sinsin qq

o

an

NA1sin q

Types of fiber optics

• Multimode fiber (MMF)

– Core diameter : 50, 60.25 mm

• Single mode fiber (SMF)

– Core diameter : 5 – 10 mm

• Graded index fiber (GRIN)

– Core index varies to equation

MMF vs SMF

• Differences

– Core size

– Travelling mode inside the core

• Problem

– Modal dispersion

– Coupling

Differential mode delay

• Fiber length, L

• Fundemental ray, q = p/2

• Transmission delay

• Extreme zigzag, q = qc

c

Ln

nc

Lt core

core

1

core

cladc

n

n

p

z qsin

zn

np

clad

core

Lcn

n

n

n

c

Lnt

clad

core

clad

corecore

2

2

Differential mode delay

• Therefore, differential mode delay

• Question

– MMF ncore = 1.45 nclad = 1.445. Find differential mode delay for 5km long MMF.

D 112

clad

core

clad

core

n

n

n

Lnttt

Data transmission rate

•Differential modal delay = time delay between the two rays taking the shortest and the longest paths.

•It measures the broadening of an impulse launched into the fiber.

•Time delay is related to the bit rate B.

•The time delay should be at least four times shorter than the allocated bit slot T = 1/B.

• transmission capacity limit due to differential mode delayt

BD

4

1

L

c

nnn

nB

cladcorecore

clad

4)(

Normalized frequency

• Also called V-number (for step index fiber)

OR

• It is a measure of guidance of light inside the core at certain wavelength

• V-number also determines number of modes propagating inside fiber.

• For step index fiber, V = 2.405 cutting-off all modes except HE11

222cladcore nn

aV

pNA

aV

p2

Number of modes in MMF

• Fiber with large V-number (due to large D and/or a) supports many modes

• It can be calculated by

• True for V > 42

2VN