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Those Interfering Signals

Those Interfering Signals. Modes and Dispersion in Fibers. What have we learned?. Any traveling sinusoidal wave may be described by y = y m sin( kx  w t + f )

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Those Interfering Signals

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  1. Those Interfering Signals Modes and Dispersion in Fibers

  2. 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.

  3. Non-return-to-zero (NRZ) Return-to-zero (RZ) Manchester Coding Bipolar Coding 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

  4. 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 n2 n0 n1 qi q0

  5. 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) n2 n0 n1 qi q0

  6. 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

  7. Mode 2: Electric Field across the fiber Mode 3: Electric Field across the fiber Mode 1: Electric Field across the fiber Mode 3: Intensity across the fiber ~E2 Mode 1: Intensity across the fiber ~E2 Mode 2: Intensity across the fiber ~E2 Modes in a Fiber • (Figures adapted from Photonics – not to scale) • The field distributions of successive modes look like the harmonics of standing waves! – the phenomena are very similar

  8. 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 • (Figures adapted from Photonics – not to scale) 2 Mode 2 Mode 1 Intensity Pattern of Sum

  9. 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!

  10. 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. n2 n0 n1 qi q0

  11. 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.

  12. Do the Activity Work as far as you can before Dr. Persans arrives

  13. 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 • Optical waveguides • ISDN These are private transmissions, and sent over range of frequencies

  14. 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

  15. 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

  16. 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

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