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Ch3: Lightwave Fundamentals

Ch3: Lightwave Fundamentals. E = E o sin( wt-kz ). k: propagation factor = w/v. k = w/v = wn/c, k o =w/c, k=k o n , l = v/f, k =2 p / l. wt-kz : phase. kz : phase shift owing to travel z length. Plane wave: phase is same over a plane. Lossy medium: E = E o e - a z sin( wt-kz ).

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Ch3: Lightwave Fundamentals

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  1. Ch3: Lightwave Fundamentals • E = Eo sin(wt-kz) • k: propagation factor = w/v • k = w/v = wn/c, ko=w/c, k=kon, l=v/f, k=2p/l • wt-kz: phase • kz: phase shift owing to travel z length • Plane wave: phase is same over a plane • Lossy medium: E = Eo e-azsin(wt-kz)

  2. Dispersion & pulse distortion • Source emit @ range of wavelengths: line width or spectral width • Smaller linewidth►more coherent • Zero linewidth► monochromatic • Df/f = Dl/l • Spectrum: wavelength or frequency content

  3. Material Dispersion & pulse distortion • v=c/n, n varies with wavelength • Dispersion: velocity variation with wavelength • Material dispersion • Waveguide dispersion • Modal dispersion

  4. Material Dispersion & pulse distortion Qualitative description

  5. Dispersion: Prism

  6. Dispersion Treatment • Can be controlled by either: • Source: smaller BW • Fiber: shift lo • Pulse: dispersion compensation • Wavelength: operate ~ lo • Combination: Solitons

  7. Broadend Pulse Optical Circulator Chirped FBG Input Pulse Recompressed Pulse Dispersion Compensation:FBG

  8. Short  Long  Dispersion Compensation:FBG

  9. Solitons • Soliton: Pulse travel along fiber without changing shape • Fiber non-linearity: pulse shape & power • Solitons attenuate ► should be amplified • ps soliton pulses are realizable

  10. Dispersion: quantitative • Let t be pulse travel time / length L • Consider a pulse of shortest and longest wavelengths being: l1 & l2 • Dl = l2 – l1 , source spectral width • D t: FWHM pulse duration

  11. Dispersion & pulse distortion • D (t/L) = -M Dl • Units: ps/(nm.km) • -ve sign explanation • In practice, no operation on 0 dispersion • Dispersion curve approximation

  12. Information rate • Let modulation limit wavelengths be l1, l2 • Max allowable delay Dt ≤ T/2 • Modulation frequency f=1/T ≤ 1/2Dt • Approximates 3dB BW • Deep analysis: f=1/2.27Dt • 3 dB optic BW: f3dB=1/2Dt • f3dBxL =1/2D(t/L)

  13. Information rate: Analog • Attenuation La + Lf • From equation, Lf =1.5dB @ 0.71 f3dB • f1.5dB(opt)= f3dB (elect) =0.71 f3dB(opt) • f3dB (elect) =0.35/Dt • f3dB (elect)xL =0.35/D(t/L)

  14. Information rate: RZ Digital Signal • Compare to analog, using 3dB electrical BW to be conservative: • RRZ=1/T, by comparison T=1/f, RRZ=f3dB (elect) =0.35/Dt • by considering power spectrum of pulse: f ≤ 1/T, and we can substitute as above to end with result

  15. Information rate: NRZ Digital Signal • Compare to analog, using 3dB electrical BW to be conservative: • RNRZ=1/T, by comparison f=1/2T, RNRZ=2f3dB (elect) =0.7/Dt • by considering power spectrum of pulse: f ≤ 1/2T, and we can substitute as above to end with result

  16. Resonant Cavities • RF oscillator, feed back, steady state • Laser – optic oscillator • Mirrors: Feed back • Both mirrors might transmit for output and monitoring • Fluctuations are determined and corrected

  17. Resonant Cavity: SWP

  18. Resonant Cavity • To produce standing wave, L=ml/2 • Resonant frequencies, l=2L/m, f=mc/2nL • Multiple modes: Longitudinal modes • Frequency spacing: Dfc=c/2nL • Laser spectrum

  19. Reflection at a plane boundary • Reflections with fibers • Reflection coefficient • Reflectance • Reflection between glass/air, Loss of 0.2 dB • Plane of incidence • Polarizations referring to plane of incidence

  20. Reflection

  21. Reflection Fresnel’s laws of reflection rP & rS , R=|r|2

  22. Reflection • Note: • 4% glass/air loss for small angles • R=0, Full transmission • R=1, full reflection • Consider R=0, qi=Brewster’s angle • Tanqi=n2/n1

  23. Reflection • To minimize reflection at a plane boundary, coat with l/4 thin material (n2) • Antireflection coating • Specular and diffuse reflection

  24. Critical Angle reflection • R=1, independent of polarization • r=1 • Complex reflection coefficients • Phase shifts • Typical critical angle values

  25. Critical Angle reflection • Reflections create a standing wave • Although all power is reflected, a field still exists in 2nd medium carrying no power called evanescent field • It decays exponentially • qi close to qc, field penetrates deeper inside 2nd medium and decays slower

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