Lightwave Fundamentals Electromagnetic Waves

Lightwave Fundamentals 

Savera Tanwir 

Electromagnetic Waves 

‣ Light consists of an electric field and a magnetic 

field that oscillate at very high rates 

‣ These fields travel in a wave-like fashion at very 

high speeds 

t 1 

t 2 

t 3 

z 

Electric 

Field 

λ 

Fiber Optic Communication Systems 2


‣Wave Number 

– Reciprocal of wavelength (1/λ) 

‣Electric Field 

– E = E 0 sin(ωt – kz) 

• E 0 = Field Amplitude 

• ω = Radian Frequency = 2πf radians/sec 

• k = Propagation Factor 

• z = distance traveled 

‣Propagation Factor 

– k = ω/v 

• v = velocity of the wave 

Fiber Optic Communication Systems 3 

‣Phase 


– ωt – kz is the phase of the wave 

– kz is the phase shift owing to travel over 

length z 

– A plane wave is the one that has same phase 

over a planar surface 



‣If t is constant 

– Sinusoidal spatial variation of the field 

– At t=0, E = -E 0 sin kz 

‣If position is fixed 

– Sinusoidal time variation of the field 

– At z=0, E=E 0 sin ωt 



‣Propagation Constant 

– k = ω/v 

– k = ωn/c (as v =c/n) 

– In free space n=1 

k 0 = ω/c 

– Thus 

k = k 0 n 

– Also k in terms of λ 

k = 2π/λ 



‣Wavelength 

– λ = v/f 

– λ 0 = c/f 

– λ/ λ 0 = c/v = n 

– Thus, λ in a medium is shorter that in free 

space, because n > 1 


Irradiance 

‣Power density is called irradiance. The 

units are watts/square meter 

‣Power in an optic beam is proportional to 

Intensity 

‣Intensity is defined as the square of 

electric field 

‣Intensity is proportional to irradiance 


Attenuation 

‣ Modification to the Electric field definition 

is required in case of attenuation 

‣ Correct Equation 

– E = E 0 e -αz sin(ωt – kz) 

• α = attenuation coefficient (losses in the fiber) 

• The value of α determines the rate at which the electric 

field diminishes as it travels through a lossy medium 

– Although the decay is exponential, the 

attenuation coefficient for quality fibers is so 

small that there is little attenuation, even over 

long paths 


Attenuation 

Electric 

Field 

z 

Dashed Line Represents exp -αz 


‣Power 

Attenuation 

– As power is proportional to intensity, for a 

path of length L, the ratio of output power to 

input power in case of attenuation is 

exp(-2αL) 

– Power Reduction in dB 

dB = 10log 10 exp(-2αL) 

This will be negative in case of lossy medium 


Attenuation 

‣Relation b/w α and power change 

dB/km = -8.685 α 

‣Beer’s Law 

–P out /P in = 10 γL/10 

L = path length 

γ = power change in dB/km 


Terminology 

‣ Line Width 

– Real sources produce radiation over a range of 

wavelengths. This range is called line width or 

spectral width. 

‣ Coherence 

– The smaller the line width the more coherent the 

source 

‣ Monochromatic source 

– A perfectly coherent source emits light at a single 

wavelength. Thus it has zero line width and it is 

perfectly monochromatic source. 


Typical source spectral widths 

Source 

LED 

Laser Diode 

Nd:YAG laser 

HeNe Laser 

Line width (∆λ) (nm) 

20-100 

1 – 5 

0.1 

0.002 

‣ Laser diodes are more coherent than LEDs 

‣ The solid state neodymium yttrium-aluminum garnet laser and the 

helium-neon laser are even better 

‣ The small size and lower power requirements of LDs and LEDs 

make them more practicable for fiber systems, even though they 

have greater line-widths. 


‣The conversion between spectral width in 

wavelengths ∆λ and bandwidth in 

frequency ∆f is 

»∆f/f = ∆λ/λ 

» Where f is the center frequency and 

» λ is the center wavelength 

‣Spectrum 

– The wavelength or frequency content of a 

signal is called its spectrum 

The line width is normally taken to 

be the width to the half power 

points so here ∆λ = 30nm (805 – 835) 


Dispersion 

‣ Dispersion is the "spreading" of a light pulse as it travels 

down a fiber 

‣ ν=c/n, where n is refractive index then 

‣ Dispersion is the property of velocity variation with 

wavelength 

Time 


Material Dispersion 

‣ When velocity variation is caused by some 

property of material. 

‣ For fibers and other waveguides, dispersion can 

also be caused by the structure themselves. 

This is called waveguide dispersion 



Pulse spreading caused by propagation through a dispersive material. 



Dispersion causes loss in amplitude of an analog signal 


Reducing Dispersion 

‣ Dispersion can be reduced by using sources 

with smaller bandwidths – that is by using more 

coherent emitters 

‣ LDs are better than LEDs 

‣ Filtering the light beam at the transmitter or 

receiver allowing only a narrow beam of 

wavelengths to reach the photodetector 

– Filters cant be constructed with passband narrow 

enough to be effective 

– A narrow band filter will greatly reduce the optic 

power by eliminating light at the unwanted 

wavelengths 



Zero-Dispersive medium 

Dispersive medium 

τ is the time for a pulse to travel a path having length L. 

τ/L is the travel time/unit Length 




Material Dispersion of pure Silica 


Example 

‣Find the amount of pulse spreading in 

pure silica for an LED operating at 0.82 

µm and having a 20 nm spectral width. 

‣The path is 10 Km long if λ =1.5 µm and 

λ∆=50nm. 


‣ Given 

Wavelength = 0.82 µm 

Spectral width ∆λ = 20 nm 

∆(τ/L) = ? 

∆(τ /L) = -M ∆λ 

Solution 

‣ M=110ps/(nm x km) ) at 0.82 µm. 

‣ ∆(τ/L)=110(20) 

‣ =2200ps/Km 

‣ =2.2ns/km 

‣ Spread of wavelength after 10 km = 10 * 2.2= 22 

ns. 

‣ Wavelength= 1.5 µm & ∆λ = 50 nm 

‣ M=15 ps/(nm x km) 

‣ ∆(τ /L)= 15 * 50 = 750 ps/km. = 0.75 ns/km 

‣ After 10 km the spread is 7.5 ns. 


Example 2 

‣Repeat example 1 if the source is a laser 

diode with 1-nm width. 

∆(/T/L= -M*λ∆). 

The 10 km pulse spreads are then 

22/20 =1.1 ns at 0.82 µm 

the 7.5/50=015 ns at 1.5 µm 


Minimizing Pulse Spreading 

‣Pulse spreading reduces bandwidth and 

data capacity 

‣Solutions: 

– Operating at zero-dispersion 

– Coherent light source 

– Solitons 


Solitons 

‣A soliton is a pulse that travels along a 

fiber without changing shape 

‣How? 

– Fiber Non-Linearity: Index of refraction depends on 

intensity of the light beam 

– Pulse velocity depends on index of refraction 

– So intensity of the beam can influence the speed of 

various wavelengths propagating along the fiber 


Solitons 

‣ The product of pulse energy and pulse width is 

constant. 

– The value of this constant depends on magnitude of 

dispersion and non-linearity 

‣ Therefore, solitons have shape, spectral content and 

power level designed to take advantage of nonlinear 

effects in an optical fiber waveguide 


Information Rate 

‣ Pulse Spreading limits information rate 

‣ Consider a sinusoidal beam. Here modulation frequency 

is f and period is T=1/f. 

‣ Two optic wavelengths λ 1 and λ 2 are radiated 

‣ We know that modulated power carried at wavelengths 

between λ 1 and λ 2 will have delayed 

Canceling the modulation 

when two carrier wavelengths 

have a delay of half the 

modulation period 



‣ When two carrier wavelengths have a delay of half the 

modulation period, they cancel 

‣ Delay has to be smaller than T/2 

‣ Max allowable pulse spread 

∆τ≤T/2 

2∆τ≤T 

Modulation frequency 

f=1/T=1/(2∆τ)=(2∆τ) -1 



‣ 3-dB bandwidth 

– Modulation frequency at which the signal power 

diminishes by half 

f 3-dB =(2∆τ) -1 

Frequency-length product 

f3-dB x L=1/2∆(τ/L) 



‣ Total loss = L a + L f 

‣ Two Types 

–L a : fixed losses occur due to absorption and 

scattering 

–L f : due to modulation frequency 

Gaussian response 

– L f =-10 log {exp[-0.693 (f / f 3-dB ) 2 ]} 

– The loss is 1.5 dB at a frequency equal to 

0.71f 3-dB 



‣ f 1.5-dB = 0.71f 3-dB 

‣ f 1.5-dB (optic) = f 3-dB (electrical) 

= 0.71 f 3-dB (optic) 

– It corresponds to the frequency at which the 

electrical power in the receiver diminishes by half. 

‣f 3-dB (electrical)= 0.35/ ∆(τ) 

f 3-dB (electrical) x L= 0.35 / ∆(τ/L) 


Rate-length in digital signals 

In Return-to-Zero (RZ) 

R RZ =1/T= f 3-dB (electrical)= 0.35 / ∆(τ) 

or 

f 3-dB (electrical) x L= 0.35 / ∆(τ/L) 

In Non-Return-to-Zero (NRZ) 

R=1/T=2f 

R NRZ = 2 f 3-dB (electrical) = 0.71 / ∆(τ) 

R NRZ x L=0.71 / ∆(τ/L) 


Example 

‣For conditions stated in example 1 & 2 

compute the rate-length and frequencylength 

product? 


Polarization 

‣ Polarization is the direction of electric field 

‣ An electric field that points in just one point is said to be 

linearly polarized 

‣ The direction of polarization is determined by the 

polarization of the light source 

‣ Mode refers to the different ways a wave can travel in a 

given direction 

‣ A wave is un polarized if electric vector varies randomly 

in direction 

E 

v 


Resonant Cavities 

‣ Laser is light amplification through stimulated emission 

of radiation 

‣ To achieve laser action, it is necessary to contain 

photons in a laser medium and maintain condition for 

coherence 

‣ A laser consists of gain medium inside an optical cavity 

which supplies energy to gain medium 



‣ Gain medium (material e.g gas, liquid) transfers external 

energy into optical beam 

‣ A cavity consists of 2 mirrors that bounce light back and 

forth 

‣ Mirrors make sure that most light makes many passes 

through the gain medium 

‣ One of the mirrors is partially transparent to output laser 

beam 



‣ Oscillation occur over a small range of frequencies 

where the cavity gain is sufficient to overcome the losses 

‣ Radiation in the cavity builds up like standing waves 

between the mirrors. 

‣ The standing waves exist at specific frequencies called 

resonant frequencies 


‣ L = λm/2 

Resonant Frequencies 

‣ λ = 2L/m 

‣ f = mc/2nL 

‣ ∆f c = c/2Ln 

‣ ∆λ c = λ o2 ∆f c / c 


Example 3-7 


Reflection 

A B C D 

‣Reflection coefficient 

ρ = n1 – n2 / n1 + n2 

‣ Reflectance 

R = (n1 – n2 / n1 + n2) 2 


Critical Angle 

‣ When light travels from denser medium to rarer 

the refracted beam bends away from the normal 

‣ The incidence angle at which transmitted angle 

is 90 o is critical angle 

‣ At angles greater than critical angle total internal 

reflection takes place 


Critical Angles 

Boundary 

n1 

n2 

θ c 

Glass- air 

1.5 

1.0 

41.8 

Plastic - plastic 

1.49 

1.39 

68.9 

Glass - plastic 

1.46 

1.4 

73.5 

Glass – glass 

1.48 

1.46 

80.6

Lightwave Fundamentals Electromagnetic Waves

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