Principal Types of Optical Fiber

Principal Types of Optical Fiber

• Cladding typically pure silica

C d d ith i t i i d

• Core doped with germanium to increase index

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

( yp y )

• Tradeoff between coupling and bending losses

• Index discontinuity at core clad boundary

• Index discontinuity at core-clad boundary

Meridional Rays

Skew Rays

For Corning SMF-28 optical fiber, n

=1.4504, n

=1.4447 at 1550 nm

NA = 0.13, Acceptance angle = 7.35 degrees

2 2

2 2

1 1

U U U 0

n k U

∂ ∂ ∂

+ + + =

Helmholtz equation :

2 2 2

n k U

0

r ⁺ r r ⁺ r φ ^{+ =}

∂ ∂ ∂

With a propagation constant β { ^{n k > > β n k} }

With a propagation constant β { n k

> > β n k

}

n

n

a

z

0

E ≈

k

: transverse propagation constant

γ : decay constant

Spatial (radial) distribution function

l 0 l = 0

l = 0

l = 3

l = 1

l = 2

V parameter of fibers (Normalized frequency of fibers)

V parameter or Normalized frequency

2 2

V k

k NA V-parameter or Normalized frequency

0 1 2 0

V = k a n − n = k a NA

: Characteristic Equation

: Characteristic Equation

2 2

V k

X

X

2 2

0 1 2

V = k a n − n

01

X

X

Fiber modes Æ Linearly polarized modes Æ LP

modes

Linearly polarized modes in fibers Æ LP _lm modes

( )

u r ( ) u r

LP 01

( )

u r

LP 34

modes

LP lm

(for low V)

If V >> 1;;

8.2 Graded-index fibers

If 2 ( b li i d fil )

If p = 2 (parabolic index-profile)

d

0

2 d M = λ

1-d Mirror Guide For the mirror guide

the number of modes is just the number of ½ wavelengths that can fit.

0

2 d

M NA

≈ λ

1-d Dielectric Guide For dielectric guides

it is the number that can fit but now limited by the angular

2

4 M π d

λ

⎛ ⎞⎟

⎜ ⎟

≈ ⎜ ⎜ ⎜ ⎟ ⎟ 2-d Mirror Guide

cutoff characterized by the NA of the guide

The V parameter

4 λ ⎟ ⎜⎝ ⎠

2d

π ⎛ ⎜ ⎞⎟

characterizes the number of wavelengths that can fit across the core guiding region in a fiber.

0

2 4

M π d NA λ ⎟

⎜ ⎟

≈ ⎜ ⎜ ⎜⎝ ⎟ ⎟ ⎠ 2-d Dielectric Guide

2 2

2

0

4 16 a

M V NA

π λ

⎛ ⎞⎟

⎜ ⎟

≈ = ⎜ ⎜ ⎜⎝ ⎟ ⎟⎟ ⎠

2-d Dielectric fiber (step-index) ^{( a = d / 2)}

2-d dielectric fiber (graded-index) ¹

for p = 2

M ≈ 4 V

8.3 Attenuation and dispersion

Definitions Definitions

Group velocity

− 1

⎟ ⎠

⎜ ⎞

⎝

⎛

∂

= ∂

ω β

v g

Group delay

⎠

⎝ ∂ ω

∂

∂ β β

τ ¹

Group delay

k c ∂

∂ =

= ω τ

Dispersion

λ τ

∂

= ∂

D

Types of dispersion Types of dispersion

∂

λ τ

∂

= ∂ D

• Modal dispersion: different modes propagate at different

λ

∂

• Modal dispersion: different modes propagate at different group velocities

• Material dispersion: the index of refraction of the medium Material dispersion: the index of refraction of the medium changes with wavelength

• Waveguide dispersion: different wavelengths in a mode Waveguide dispersion: different wavelengths in a mode have different delays

• Polarization mode dispersion: if waveguide is birefringent p g g