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Ch3: Lightwave Ch3: Lightwave FundamentalsFundamentals
E = EE = Eoo sin( sin(wt-kzwt-kz))k: propagation factor = w/vk: propagation factor = w/v
wt-kzwt-kz: phase: phasekzkz: phase shift owing to travel : phase shift owing to travel zz length length
Plane wave: phase is same over a planePlane wave: phase is same over a plane
k = w/v = wn/c, kk = w/v = wn/c, koo=w/c, k=k=w/c, k=koonn, , ==v/f, kv/f, k=2=2//
Lossy medium: E = ELossy medium: E = Eoo e e--zzsin(sin(wt-kzwt-kz))
Dispersion & pulse distortionDispersion & pulse distortion
Source emit @ range Source emit @ range of wavelengths: line of wavelengths: line width or spectral width or spectral widthwidth
Smaller linewidthSmaller linewidth►more ►more coherentcoherent
Zero linewidthZero linewidth► ► monochromaticmonochromatic
SourceSource LinewidthLinewidth(n(nm)m)
LEDLED 20-10020-100
LDLD 1-51-5
Nd:YAGNd:YAG 0.10.1
HeNeHeNe 0.0020.002
f/f = f/f = // Spectrum: wavelength or frequency Spectrum: wavelength or frequency
contentcontent
Material Dispersion & pulse Material Dispersion & pulse distortiondistortion
v=c/n, nv=c/n, n varies with varies with wavelengthwavelength
Dispersion: velocity Dispersion: velocity variation with variation with wavelengthwavelength
Material dispersionMaterial dispersion Waveguide dispersionWaveguide dispersion
Modal dispersionModal dispersion
Material Dispersion & pulse Material Dispersion & pulse distortion Qualitative descriptiondistortion Qualitative description
Dispersion: PrismDispersion: Prism
Dispersion TreatmentDispersion Treatment
Can be controlled by either:Can be controlled by either:Source: smaller BWSource: smaller BWFiber: shift Fiber: shift oo
Pulse: dispersion compensationPulse: dispersion compensationWavelength: operate ~ Wavelength: operate ~ oo
Combination: SolitonsCombination: Solitons
Dispersion Dispersion Compensation:FBGCompensation:FBG
Chirped FBG
Recompressed Pulse
Input Pulse
Broadend Pulse Optical
Circulator
Dispersion Dispersion Compensation:FBGCompensation:FBG
Short
Long
SolitonsSolitons
Soliton: Pulse travel Soliton: Pulse travel along fiber without along fiber without changing shapechanging shape
Fiber non-linearity: Fiber non-linearity: pulse shape & power pulse shape & power
Solitons attenuate Solitons attenuate ► should be amplified► should be amplified
ps soliton pulses ps soliton pulses are realizableare realizable
Dispersion: quantitativeDispersion: quantitative
Let Let be pulse travel be pulse travel time / length Ltime / length L
Consider a pulse of Consider a pulse of shortest and longest shortest and longest wavelengths being: wavelengths being: 11 & & 22
= = 22 – – 11 , source , source spectral widthspectral width
: FWHM pulse : FWHM pulse durationduration
Dispersion & pulse distortionDispersion & pulse distortion
LL Units: ps/(nm.km)Units: ps/(nm.km) -ve sign explanation -ve sign explanation In practice, no In practice, no
operation on 0 operation on 0 dispersiondispersion
Dispersion curve Dispersion curve approximationapproximation
Information rateInformation rate Let modulation limit Let modulation limit
wavelengths be wavelengths be 11, , 22
Max allowable Max allowable delay delay ≤ T/2 ≤ T/2
Modulation frequency Modulation frequency f=1/T ≤ 1/2f=1/T ≤ 1/2
Approximates 3dB BWApproximates 3dB BW Deep analysis: Deep analysis:
f=1/2.27f=1/2.27 3 dB optic BW: 3 dB optic BW:
ff3dB3dB=1/2=1/2 ff3dB3dBxL =1/2xL =1/2LL
Information rate: AnalogInformation rate: Analog Attenuation LAttenuation Laa + L + Lff
From equation, LFrom equation, Lff =1.5dB @ 0.71 f=1.5dB @ 0.71 f3dB3dB
ff1.5dB1.5dB(opt)= f(opt)= f3dB3dB (elect) (elect)
=0.71 f=0.71 f3dB3dB(opt) (opt)
ff3dB3dB (elect) =0.35/ (elect) =0.35/
ff3dB3dB (elect)xL (elect)xL =0.35/=0.35/LL
Information rate: RZ Digital Information rate: RZ Digital SignalSignal
Compare to analog, using 3dB electrical BW to be Compare to analog, using 3dB electrical BW to be conservative: conservative:
RRRZRZ=1/T, by comparison T=1/f, =1/T, by comparison T=1/f, RRRZRZ=f=f3dB3dB (elect) =0.35/ (elect) =0.35/
by considering power spectrum of pulse: f ≤ 1/T, by considering power spectrum of pulse: f ≤ 1/T, and we can substitute as above to end with resultand we can substitute as above to end with result
Information rate: NRZ Digital Information rate: NRZ Digital SignalSignal Compare to analog, using 3dB electrical BW to be Compare to analog, using 3dB electrical BW to be
conservative: conservative:
RRNRZNRZ=1/T, by comparison f=1/2T, =1/T, by comparison f=1/2T, RRNRZNRZ=2f=2f3dB3dB (elect) =0.7/ (elect) =0.7/
by considering power spectrum of pulse: f by considering power spectrum of pulse: f ≤ 1/2T, and we can substitute as above to ≤ 1/2T, and we can substitute as above to end with resultend with result
Resonant CavitiesResonant Cavities
RF oscillator, feed RF oscillator, feed back, steady stateback, steady state
Laser – optic oscillatorLaser – optic oscillator
Mirrors: Feed backMirrors: Feed back Both mirrors might Both mirrors might
transmit for output transmit for output and monitoringand monitoring
Fluctuations are Fluctuations are determined and determined and corrected corrected
Resonant Cavity: SWPResonant Cavity: SWP
Resonant CavityResonant Cavity
To produce standing To produce standing wave, L=mwave, L=m/2/2
Resonant frequencies, Resonant frequencies, =2L/m, f=mc/2nL =2L/m, f=mc/2nL
Multiple modes: Multiple modes: Longitudinal modesLongitudinal modes
Frequency spacing: Frequency spacing: ffcc=c/2nL=c/2nL
Laser spectrumLaser spectrum
Reflection at a plane Reflection at a plane boundaryboundary
Reflections with Reflections with fibersfibers
Reflection coefficientReflection coefficient
ReflectanceReflectance
Plane of incidencePlane of incidence
Reflection between Reflection between glass/air, Loss of 0.2 dBglass/air, Loss of 0.2 dB
Polarizations referring to plane of incidencePolarizations referring to plane of incidence
ReflectionReflection
ReflectionReflectionFresnel’s laws of reflectionP & S , R=||2
ReflectionReflection Note:Note: 4% glass/air loss for small 4% glass/air loss for small
anglesangles
R=0, Full transmissionR=0, Full transmission
R=1, full reflectionR=1, full reflection Consider R=0, Consider R=0,
ii=Brewster’s angle=Brewster’s angle
TanTanii=n=n22/n/n11
ReflectionReflection
To minimize reflection To minimize reflection at a plane boundary, at a plane boundary, coat with coat with /4 thin /4 thin material (nmaterial (n22))
Antireflection coatingAntireflection coating
Specular and diffuse reflectionSpecular and diffuse reflection
Critical Angle reflectionCritical Angle reflection R=1, independent R=1, independent
of polarizationof polarization =1=1 Complex reflection coefficientsComplex reflection coefficients
Phase shiftsPhase shifts
Typical critical Typical critical angle valuesangle values
Critical Angle reflectionCritical Angle reflection Reflections create Reflections create
a standing wavea standing wave Although all power is Although all power is
reflected, a field still reflected, a field still exists in 2exists in 2ndnd medium medium carrying no power carrying no power called evanescent fieldcalled evanescent field
It decays exponentiallyIt decays exponentially
ii close to close to cc, field penetrates deeper , field penetrates deeper inside 2inside 2ndnd medium and decays slower medium and decays slower
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