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

2. Dispersion & pulse distortion Source emit @ range of wavelengths: line width or spectral width Source emit @ range of wavelengths: line width or spectral width Smaller linewidth ►more coherent Smaller linewidth ►more coherent Zero linewidth ► monochromatic Zero linewidth ► monochromaticSource Linewidth (nm) LED20-100 LD1-5 Nd:YAG0.1 HeNe0.002  f/f =  /  f/f =  / Spectrum: wavelength or frequency content Spectrum: wavelength or frequency content

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

4. Material Dispersion & pulse distortion Qualitative description

5. Dispersion: Prism

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

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

8. Dispersion Compensation:FBG Short Long

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

10. Dispersion: quantitative Let  be pulse travel time / length L Let  be pulse travel time / length L Consider a pulse of shortest and longest wavelengths being: 1 & 2 Consider a pulse of shortest and longest wavelengths being: 1 & 2  = 2 – 1, source spectral width  = 2 – 1, source spectral width  : FWHM pulse duration  : FWHM pulse duration

11. Dispersion & pulse distortion  L   L  Units: ps/(nm.km) Units: ps/(nm.km) -ve sign explanation -ve sign explanation In practice, no operation on 0 dispersion In practice, no operation on 0 dispersion Dispersion curve approximation Dispersion curve approximation

12. Information rate Let modulation limit wavelengths be 1, 2 Let modulation limit wavelengths be 1, 2 Max allowable delay  ≤ T/2 Max allowable delay  ≤ T/2 Modulation frequency f=1/T ≤ 1/2  Modulation frequency f=1/T ≤ 1/2  Approximates 3dB BW Approximates 3dB BW Deep analysis: f=1/2.27  Deep analysis: f=1/2.27  3 dB optic BW: f 3dB =1/2  3 dB optic BW: f 3dB =1/2  f 3dB xL =1/2  L  f 3dB xL =1/2  L 

13. Information rate: Analog Attenuation L a + L f Attenuation L a + L f From equation, L f =1.5dB @ 0.71 f 3dB From equation, L f =1.5dB @ 0.71 f 3dB f 1.5dB (opt)= f 3dB (elect) f 1.5dB (opt)= f 3dB (elect) =0.71 f 3dB (opt) f 3dB (elect) =0.35/  f 3dB (elect) =0.35/  f 3dB (elect)xL =0.35/  L  f 3dB (elect)xL =0.35/  L 

14. Information rate: RZ Digital Signal Compare to analog, using 3dB electrical BW to be conservative: Compare to analog, using 3dB electrical BW to be conservative: R RZ =1/T, by comparison T=1/f, R RZ =f 3dB (elect) =0.35/  R RZ =1/T, by comparison T=1/f, R RZ =f 3dB (elect) =0.35/  by considering power spectrum of pulse: f ≤ 1/T, and we can substitute as above to end with result 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: Compare to analog, using 3dB electrical BW to be conservative: R NRZ =1/T, by comparison f=1/2T, R NRZ =2f 3dB (elect) =0.7/  R NRZ =1/T, by comparison f=1/2T, R NRZ =2f 3dB (elect) =0.7/  by considering power spectrum of pulse: f ≤ 1/2T, and we can substitute as above to end with result 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 RF oscillator, feed back, steady state Laser – optic oscillator Laser – optic oscillator Mirrors: Feed back Mirrors: Feed back Both mirrors might transmit for output and monitoring Both mirrors might transmit for output and monitoring Fluctuations are determined and corrected Fluctuations are determined and corrected

17. Resonant Cavity: SWP

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

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

20. Reflection

21. Reflection Fresnel’s laws of reflection  P &  S, R=|  | 2

22. Reflection Note: Note: 4% glass/air loss for small angles 4% glass/air loss for small angles R=0, Full transmission R=0, Full transmission R=1, full reflection R=1, full reflection Consider R=0,  i =Brewster’s angle Consider R=0,  i =Brewster’s angle Tan  i =n 2 /n 1 Tan  i =n 2 /n 1

23. Reflection To minimize reflection at a plane boundary, coat with /4 thin material (n 2 ) To minimize reflection at a plane boundary, coat with /4 thin material (n 2 ) Antireflection coating Antireflection coating Specular and diffuse reflection Specular and diffuse reflection

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

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