ENE 429Antenna and Transmission lines Theory

Lecture 9 Optical fiber

DATE: 04/09/06 08/09/06

Review (1) TE wave in rectangular waveguides (Hz = 0) For lossless TE rectangular waveguides,

A dominant mode for TE mode is TE01

A dominant mode for TM mode is TM11

Rectangular cavity resonator To minimize the field radiation due to comparable size of

component to the wavelength. To confine field inside the enclosed cavity.

0 cos cos /j zz

m x n yH H e A m

a b

Review (2) Magnetic field representation for TEmnp mode is

Electric field representation for TMmnp mode is

Resonant frequency is

0( , , ) sin sin cos / .z

m x n y p zE x y z E V m

a b d

0( , , ) cos cos sin / .z

m x n y p zH x y z H A m

a b d

2 2 2

2p

mnp

u m n pf resonant frequency Hz

a b d

Optical fiber

operates at optical frequency (1014 Hz) Three primary transmission windows are

centered around 850, 1300, 1550 nm. telephone system cable TV interconnects in computer

How does it work?

wave travels using total internal reflection at the core-cladding boundary.

core and cladding are typically made of silica. jacket is typically made of polyethelene interconnects in computer

Dimension

50/125 fiber means 50 m diameter core and 125 m diameter cladding.

Pros and Cons advantage: carry much more info than coaxial cable, smaller,

lighter, more flexible, and less attenuation than coax. disadvantage: hard to repair when it breaks

Types of the optical fiber

1. step-index fiber – abrupt change in n-refractive index

2. single-mode fiber – supports only one propagating mode

3. multi-mode fiber – supports several modes.

step-index fiberGraded-index fiber (for multi-mode)

Propagating mode (1)

There will be a propagating mode if the wavelength

where k01 = first root of the zeroth-order Bessel function = 2.405

a = radius of the core.

If we can control to be small, we can support more modes.

2 2

01

2 f ca n nm

k

2 2f cn n

Propagating mode (2)

For a step-index multimode fiber, the total number of propagating modes is approximately

22 22 ( ).f c

aN n n

Typical Characteristics of Glass optical fiber

See table 7.2

Numerical aperture (1) To initiate mode propagation, use Snell’s law.

0 sin sina f bn n

Note that

that gives

( )c i cri

sin( ) .ci crif

nn

Define the maximum acceptance angle a = a cone of Acceptance over which light will propagate along the fiber.

Numerical aperture (2)

sin cosc b

Let

and by geometry,

then from

we have

Therefore at , or Numerical

Aperture (given by the manufacturer)

( )c i cri

2 20 sin 1 cos 1 sin .a f b f cn n n

2 2sin cos 1b b

2 2

0

sinf c

a

n nNA

n

( )c i cri

Ex1 Which optic fiber would be better to use for wave guiding?

1) Fiber 1, core index = 1.465, cladding index = 1.463

2) Fiber 2, core index = 1.465, cladding index = 1.450

Signal degradation

Intermodal dispersion Chromatic dispersion

Waveguide dispersion Material dispersion

Attenuation due to interaction inside fiber material

Graded-indexed fiber (GRIN)

Single-mode step-index fiber has a small cone of acceptance.

Multimode fiber suffers from intermodal dispersion. GRIN is one approach to minimize dispersion in a

multimode fiber. Common size: 50/125 and 85/125

Fiber optic communication systems Basic components of a fiber optic

communication system:

To boost up the signal due to the limited cover-age of the fiber

Optical sources: LED

Light emitting diodes (LEDs) Photon (light) is emitted when excited electrons are

relax and fall back to lower energy state. Gallium Arsenide (GaAs) is popular. The wavelength of light emitted can be adjusted by

adding some compounds.

LED configurations (1)

Surface-emitting configuration Mount the fiber on the surface close to p-n junction A beamwidth is approximate 120.

Edge-emitting configuration Photon propagate out the side of the device. A beamwidth is approximate 30.

LED configurations (2)

Optical sources: Laser diode (1)

Semiconductor laser diode Heavily doped layers (p+ and n+) Diode layers (p-AlGaAs and n-AlGaAs) Lasing region is where photon production occurs.

Optical sources: Laser diode (2) narrow beamwidth can be modulated at an order of frequency higher than

LEDs higher drive currents than LEDs wear out faster than LEDs

Property comparison for LEDs and Laser diodes

See table 7.3

Optical detectors: PIN photodiode

PIN photodiode An intrinsic layer of semicon-ductor is sandwiched by p-typeand n-type regions. When a photon is captured,it generates an electron-holepair thereby producing a weakcurrent proportional to the lightintensity. an avalanche photodiode (APD)is a heavily doped structure with a large reverse-bias voltage.

Comparison of Optical detectors

See table 7.4

Repeater The optical system is limited by the operating distance.

Repeaters or optical amplifiers are needed to boost a signal.

Repeaters are costly and need their own source of power.

Optical amplifier Erbium-doped fiber amplifier (EDFA) enable direct

amplification of an optical signal. The EDFA features high gains and high output power

capability with low noise.

Connections Made from the optical source to fiber, fiber to the optical detector,

and between lengths of fiber. 12 dB loss is produced between an LED and a mulitmode fiber, > 32

dB loss if connected to a single mode fiber while it only produces about 2 dB loss with laser diodes.

Efficient coupling between a fiber and a detector produces only 1.5 dB loss.

Attenuation arisen from joining a pair of fiber produce less than 1 dB loss, with 0.7 dB being typical.

Splices are considered a permanent connection, generally no more than 1 dB, with 0.05 dB being typical loss.

A matching refractive index epoxy is usually applied to attach the source-to-fiber and fiber-to-detector connections.

Typical losses associated with connections

See table 7.5

Optical link design (1)

Power budget to ensure enough power at the receiver end. The optical source must supply enough power to

overcome source-to-fiber loss, connector and splice loss, and fiber-to-detector loss.

Optical link design (2)

Rise-time budget: to verify the received signal has not been distorted For high information rates and long operating

distance, digital transmission is more reliable than the analog one.

Return-to-zero format is a popular digital signals

Rise-time budget The rise time of the source and the detector as well as

the effects of dispersion in the fiber cause the spreading of the pulse.

The accepted bit error rate (BER) is 1 error in 109 bits.

Rise-time budget calculation (1) A time period T is related to the data rate (bit per second

or bps) such that

The total system response time ts is typically require such that

The total system response time can be determined.

where tt = transmitter response time (s)

tf = fiber response time (intermodal + chromatic) (s)

tr = receiver response time (s)

1T

bps S.

12st T S.

2 2 2s t f rt t t t S.

Rise-time budget calculation (2) The pulse width of the output signal (Tpw)out can be

expressed as

Total rise time of the fiber can be expressed as

S.

S.

2 2( ) ( )pw out pw in st t t

2 2f int ermod al chromatict t t

Ex2 What is the proper optical detector to detect the receiving power from an optical link that transmits data over a 1 km distance, given an 850nm LED source with 1 mW (0 dBm) power that launches a signal into 850 nm step-index multimode fiber and a system margin for unexpected losses of 8 dB?

Ex3 Calculate the system rise time from Ex2 , is this rise-time budget satisfied?