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 )

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

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

Material Dispersion & pulse distortion Qualitative description

Dispersion: Prism

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

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

Dispersion Compensation:FBG Short Long

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

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

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

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 

Information rate: Analog Attenuation L a + L f Attenuation L a + L f From equation, L f 0.71 f 3dB From equation, L f 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 

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

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

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

Resonant Cavity: SWP

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

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

Reflection

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

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

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

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

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