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Transcript
Those Interfering Signals
Modes and Dispersion in Fibers
What have we learned?
• Any traveling sinusoidal wave may be described by
y = ym sin(kx  wt + f)
• f is the phase constant that determines where the wave
starts; w = 2pf = 2p/T; k = 2p/l; v = l/T = lf = w/k
• Light always reflects with an angle of reflection equal to
the angle of incidence (angles are measured to the normal).
• When light travels into a denser medium from a rarer
medium, it slows down and bends toward the normal.
• The Fourier spectrum of a wider pulse will be narrower
than that of a narrow pulse, so it has a smaller bandwidth.
• Your bandwidth B must be as large as the rate N at which
you transfer different amplitudes.
What Else Have We Learned?
• Can represent binary data with pulses in a variety of ways
• 10110 could look like . . .
Notice that the NRZ
takes half the time of
the others for the
same pulse widths
Non-return-to-zero
(NRZ)
Manchester
Coding
Return-to-zero
(RZ)
Bipolar Coding
Phase differences and interference
• Light rays taking different paths will travel different
distances and be reflected a different number of times
• Both distance and reflection affect the how rays combine
• Rays will combine in different ways, sometimes adding
and sometimes canceling
n0
q0
n2
qi
n1
Modes
• Certain combinations of rays produce a field that is
uniform in amplitude throughout the length of the fiber
• These combinations are called modes and are similar to
standing wave on a string
• Every path can be expressed as a sum of modes (like
Fourier series)
n0
q0
n2
qi
n1
Creating a Mode
• (Figures adapted from Photonics – not to scale)
• The resulting pattern is uniform throughout the length of
the fiber – this is a mode of the fiber
Modes in a Fiber
Mode 1: Electric
Field across the fiber
Mode 1: Intensity
across the fiber ~E2
Mode 2: Electric
Field across the fiber
Mode 2: Intensity
across the fiber ~E2
Mode 3: Electric
Field across the fiber
Mode 3: Intensity
across the fiber ~E2
• The field distributions of successive modes look like the harmonics
of standing waves! – the phenomena are very similar
• (Figures adapted from Photonics – not to scale)
Modes Combine to Give Path of Light
• To add Mode 1 and Mode 2, must add fields.
• BUT, modes travel at different speeds, so sum of fields changes as
go down the fiber
• Result is one of the paths light will take
Mode 1
Mode 2
2
Intensity Pattern of Sum
• (Figures adapted from Photonics – not to scale)
Modal Dispersion
• Since different modes travel different distances in
the fiber, they will arrive at the end at different
times.
• For graded-index fibers, not only do different
modes travel different distances, they travel
through different media!
Reducing the number of Modes
• Different modes interact differently with the fiber, so
modes will spread out, or disperse
• If the fiber is narrow, only a small range of q0 will be able
to enter, so the number of modes produced will decrease
• A small enough fiber can have only a single mode
• BUT, you will lose efficiency because not all the light
from the source enters the fiber.
n0
q0
n2
qi
n1
Chromatic Dispersion
• Index of refraction is dependent on wavelength.
• Typical materials exhibit higher indices of
refraction for lower wavelengths (higher energies)
• Thus violet light bends the most through a prism
or water and appears on the outside of a rainbow.
Do the Activity
Work as far as you can before Dr.
Persans arrives
What Are Some Ways That We Can Send Signals?
• Radio antenna (AM frequencies around 1000 kHz,
FM frequencies around 100 MHz)
• TV antenna (VHF frequencies are around 100 MHz,
on either side of FM frequencies, UHF frequencies
around 500 MHz)
These are public transmissions, and so the carrier
frequencies are set and regulated
• Coaxial cable
These are private
• Optical waveguides
transmissions, and sent
over range of frequencies
• ISDN
Optical waveguides pros and cons
• Message remains private
• Flexibility
• Low Loss
• Insensitive to EM interference
BUT
• Expensive to connect to every house
• Require electricity-to-light converters
• Either multi-modal, or less efficient
What exactly is a decibel?
• A ratio, often of power
• BUT, in logarithmic form:
• dB = 10 log (P2/P1)
• e.g., if my received signal is 1/10 as big as my transmitted
signal, my “gain” would be
gain dB = 10 log (1/10) = -10
• The minus sign denotes loss, or a second power less than the
initial power
Why do I care about decibels?
• Signal-to-noise ratios are often given in decibels
• You want the signal to be larger than the noise, so the ratio
(in dB) should be positive
• For digital data, we use bit error rate, not signal-to-noise
• Bit error rate is ratio of wrong bits to total bits - it should be
small, whereas SNR should be large
• Bit error rate can be expressed as a plain number, or in
decibels