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