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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?