OPTICAL COMMUNICATIONS S

OPTICAL COMMUNICATIONS S-108.3110 1

Course program 1. Introduction and Optical Fibers 2. Nonlinear Effects in Optical Fibers 3. Fiber-Optic Components I 4. Transmitters and Receivers 5. Fiber-Optic Measurements and Review 2

Introduction Optical communication systems are sensitive to linear phenomena Attenuation (less power received) Dispersion (signal spreads in time) Gain (signal is amplified) and to nonlinear phenomena Increase in traffic requires an increase in the network capacity Increase in capacity achieved through Higher bit rates Multiple channels at different wavelengths transmitted simultaneously (Wavelength Division Multiplexing systems) Increase in bit rate or channels number results in higher sensitivity to nonlinear ects 3

Propagation Effects in Optical Fibers Loss t t Attenuation t Gain t Amplification Linear ects t Dispersion t Distortion Nonlinear scattering/nonlinear refractive index New wavelengths λ λ Nonlinear ects 4

What is Nonlinear Optics? Nonlinear optics leads to change in the color of a light beam, changes its shape in space and time Example: sending infrared light into a crystal yields this display of green light Nonlinear ects are typically detrimental to communications systems, but they can also be used to perform various functionalities (conversion, switching ) 5

Linear vs. Nonlinear Optics Linear optics (loss/gain and dispersion) Optics of weak light (low intensity) Light is deflected or delayed but its FREQUENCY is unchanged Nonlinear optics (nonlinear gain and new frequencies) Optics of intense light Light induces ects on its own AMPLITUDE/PHASE as it propagates p through a medium, which affects its FREQUENCY 6

Linear Optics Input Wave Output Wave Input Photon Energy Output Photon Energy Molecule/Atom energy levels Molecule/Atom A light wave acts on a molecule/atom which vibrates and then emits its own light wave that interferes with the original light wave 7

Nonlinear Optics Input Wave Output Wave new wavelength! Input Photon Energy Output Photon Energy Molecule/Atom energy levels Molecule/Atom If the intensity of light wave is large enough, frequencies corresponding to energy differences between energy levels are produced 8

Pulse Propagation in Optical Fibers Signal in time 2π/ω 0 Signal in frequency/wavelength Δλ t ω 0 ω λ 0 λ E F( r) modal distribution iω t r, z, t) = F( r) A( z, t) e A( z,t) time variation (amplitude) 2πc ω0 = carrier frequency λ0 ( 0 iωt E( r, z, ω) = + E( r, z, t) e dt = F( r) A( ω ω0, z) 9

Pulse Propagation in Optical Fibers Signal in time Signal in frequency t ω 0 ω Δλ λ λ 0 A pulse is a wave-packet that contains several frequencies The pulse travels at the group velocity (~average speed) v g d β = dω 1 c c = = dn dn n + ω n λ dω dλ c = 3 10 8 m/s : n β = n light velocity : ective refractive id index ω : propagation constant c 10

Pulse Propagation in Optical Fibers A(z,t) t E F( r) modal distribution iω t r, z, t) = F( r) A( z, t) e A( z,t) time variation (amplitude) 2πc ω0 = carrier frequency λ0 ( 0 Here we consider only the fundamental mode LP 01 which can be approximated by a spatial Gaussian distribution of width w 0 : 2 F( r) Modal distribution does not vary with propagation: F(r)=constant e When the pulse propagates a distance z, the electric field acquires a phase φ =β β z where β is the propagation constant of the mode LP 01, and can experiences loss α or gain g α g z z iω0t iϕ 2 2 iω0t (,,) = () (,) = () (,) E rzt FrAzte e e e FrA zte r 2 / w 0 11

Effective Area Light travels partly outside the core of the fiber Power is not uniformly distributed ib t d within the cross-section of the fiber To simplify we assume that the SPATIAL intensity of the electric field is equivalent to a constant intensity over an ective diameter For a given pulse power P(z,t), F(r) A I( z, t) 2 E( z, t) P( z, t) P( z, t) = = 2 A w 2w A π 0 0 r r Typical value for single-mode fiber A 85 μm 2 12

Nonlinear Effects in Optical Fibers The only quantity that varies with propagation is A'(z,t) A'(z,t)=A(z,t)e -iϕ e -α/2z e g/2z If the pulse intensity (power) is high The phase ϕ acquired by the eletric field starts depending on the intensity An intensity-dependent gain g arises nonlinear ects g[i]: induced by nonlinear scattering (Brillouin and Raman) ϕ [I]: induced by the nonlinear refractive index 13

Losses and Effective length Nonlinear interaction depends on transmission length longer length more interaction and nonlinear ects grows Most nonlinear ects occur early in the fiber span and diminish due to fiber attenuation as the signal propagates ( z + dz) E1 = E1( z) e α dz 2 where α is the loss Power at distance z can be expressed as where P 0 is the power at the fiber input 2 = 0 P ( z ) E ( z ) = P e αz Idea: assuming that the power is constant over a certain ective length L, in this way the fiber attenuation is included in L 14

Effective length. P 0 P 0 Power P out P T Power Length L Length L L P ( z) = P e 0 αz Power is constant over a certain ective length L P L 0 L = L 0 P ( z) dz 1 e = α αl 15

Classification of Nonlinear Effects Result from interaction between light and the transmission medium Scattering Brillouin Scattering Raman Scattering Nonlinear Refractive Index Self-Phase Modulation Cross-Phase Modulation Four-Wave Mixing Intensity-dependent Gain g[i] Intensity-dependent Phase ϕ [I] 16

Nonlinear Scattering In Nonlinear Scattering an intense signal of amplitude E p amplifies the electric field of another weaker signal E s (at different wavelength) so that t after a distance dz: s ( + ) = ( ) E z dz E z e e where α is the loss g is gain (depends on λ) and s 2 Ep ( z) g dz α dz 2 A 2 E p E s ( ) A is the ective area P ( L) = P (0) e Nonlinear Scattering Pp (0) g L A where L is the ective length Nonlinear scattering: power of g is gain (depends on λ) weak signal P s is amplified and A is the ective area s s P p p( (0): power of input intense signal 17

Nonlinear Refractive Index In optical fiber the refractive index depends on the instantaneous INTENSITY (POWER) of the electric field that propagates: Nonlinear Refractive Index Nonlinear refractive index Phase ects ω ϕ = βz = n z c n = n + n I t), n NL ( : ective refractive index of ω ω [ n + nnli( t) ] z = n z + nnl ω ϕ = I( t) z c c c ϕ ϕ L Linear Phase (dispersion) NL mode Nonlinear Phase (new frequencies generated) 18

Scattering Effects in Optical Fibers Linear Rayleigh scattering (leads to signal attenuation as seen in first lecture) Nonlinear Brillouin scattering Raman scattering 19

Origin of Nonlinear Scattering Photon from signal scatters off molecules oscillations/vibrations present in the material (glass) Scattered photons have their frequency lowered by an amount equivalent to the frequency of the molecule l oscillation/vibration ib (some energy is absorbed) ω osc ω s ω sc = ω s - ω osc 20

Brillouin Scattering Brillouin i Scattering is caused by light interaction ti with acoustic waves (induced by electrostriction, i.e. light deforms the glass and generate an acoustic wave) The acoustic waves itself produce a periodic change in the glass refractive index which in turn scatters part of the signal (moving grating) A wave with high intensity traveling in one direction induce narrowband (in frequency) gain for a wave traveling in opposite direction Amplified wave can grow from noise: reflected wave 21

Brillouin Scattering Signal photons interact with acoustic wave and part of signal is absorbed by acoustic wave (inelastic scattering) Transfer of energy into acoustic wave results in backwards scattering in fiber at a frequency shifted from the signal: Brillouin shift Brillouin frequency shift is equal to 2 n v /λ, where n is the mode refractive index at wavelength λ and v is the speed of sound in the material (silica) In optical fibers, speed of sound is 5.96 km/s and scattered light is ~11 GHz lower in frequency than the signal wavelength 22

Brillouin Scattering Input signal power: P S Reflected Brillouin signal power: P B Output signal λ 1 λ 1 λ 1 +Δλ scattered pow wer [dbm] Back -10-20 -30-40 -50-60 input ~ 11GHz shifted Brillouin scattering Rayleigh scattering & reflections Δ ν = λ 1 Δλ = c n : ective refractive index of 2n v v :speed of sound in glass λ1 λ1 :signal wavelength c :speed of light 2 Δν mode 1549.8 1550.0 1550.2 wavelength [nm] 23

P B (0) P B g P (0) L B S = ( ) L A P ( L) e e (0) = B P ( L) S Brillouin Scattering g : Brillouin gain Back scattered power [mw] 150 α B 100 A :ective area Threshold launched power P th 21A P S = g L B originates from noise th s defined as : 50 P B 0 24 25 26 27 28 Input power [dbm] Backscattered power increases exponentially with signal power When input power exceeds the threshold power value, the ect is important! Example: α=0.2 db/km g R =5 10-11 m/w A =85 μm 2 L = 21.7 km P th =1.5 mw 24

Brillouin Scattering If launched power is increased above the Brillouin threshold (which is very low), there is dramatic increase of backscattered light The received power is decreased accordingly Degradation of system performance 25

Brillouin Scattering To decrease the ect of Brillouin scattering: Use fibers with larger ective area in order to increase the Brillouin threshold Keep the power per channel below the Brillouin threshold Increase the spectral width of the signal since Brillouin scattering is a narrow-band ect 26

Raman Scattering Raman scattering results from interaction between light and molecular vibrations Energy of scattered light is less than that of the incident light and therefore the scattered light has a longer wavelength A wave with high intensity traveling in one direction induce broadband gain for a wave traveling in same AND opposite direction Amplified wave can grow from noise Generation/amplification of wave with higher wavelengths: Raman shift 27

Raman Scattering Input signal Output signal Raman signal power: P S power: P R λ 1 λ 1 1 λ 1 +Δλ λ 1 +Δλ Power transferred to λ 1 +Δλ increases exponentially with signal power P ( L) = R αl ( P (0) e ) R e g RPS (0) L A g A R : Raman gain : ective area originates from noise or other signal Raman gain g R 10-13 [m/w W] 10 1.0 0.8 0.6 0.4 0.2 0.0 0 10 20 30 40 Frequency shift [THz] 28

Raman Scattering P R ( L) = αl ( P (0) e ) R e g P L (0 R S ) A g A R :Raman gain : ective area th S Threshold launched power P defined as : Example: PR ( L) = PS ( L) α=0.2 db/km th 16A g R =10-13 m/w PS = A =85 μm 2 g R L L = 21.7 km P th =600 mw 29

Raman Scattering Shorter wavelength channels amplifies longer wavelength channels (and therefore lose power) Noise is also amplified Received signals are distorted 30

Raman Scattering Raman Scattering is not a problem in systems with small number of channels as the threshold for Raman Scattering is high BUT it is a problem in systems with high number of channels as channels with longer wavelengths receive gain from many channels with lower wavelengths (Raman gain is broadband!) To reduce Raman Scattering Keep channels very close to each other Reduce power below the Raman threshold power 31

Raman vs. Brillouin Scattering Unlike Brillouin Scattering, Raman Scattering occurs in both directions Brillouin Scattering provides gain over a narrow band whereas the Raman gain is broadband Raman Scattering requires higher power to take place in optical fibers compared to Brillouin Scattering Brillouin Scattering is already a problem in low-power systems Raman scattering becomes a problem only in high-power/large number of channels systems 32

Nonlinear Refractive Index Remember, signal propagation in optical fiber obeys the Equation: 2 2 1 E( r, t) P( r, t) E ( r, t ) + = μ 2 2 0 2 c t t with P( r, t) = P ( r, t) P ( r, t) L + In general, the polarization induced in the medium by the signal can be represented as: (1) (2) 2 (3) 3 P( r, t) = ε χ E( r, t) + ε χ E ( r, t) + ε χ E ( r, t)... NL 0 0 0 + E: electric field, ε 0 : dielectric constant of vacuum, andχ (i) is the i th susceptibility (material property) p At sufficiently high values of E, the nonlinear part of the polarization starts affecting light propagation in the fiber 33

Nonlinear Refractive Index Light intensity changes the refractive index n = n + n NL nnl I( t) = n + P( t) A Coicient n NL / A plays an important role in evaluating the system performance In silica, n NL 3 10-20 m 2 /W NL 34

Nonlinear Refractive Index Self-Phase Modulation Refractive index n depends on the intensity: n=n +n NL I(t) Intensity variations of the signal modulates n which in turn modulates the phase of the signal Cross-Phase modulation Intensity variations of one signal modulates n which in turn modulates the phase of a co-propagating signal Four-Wave Mixing Beating between two signals generates harmonics at the beating frequency Harmonics can lead to interference if they fall on adjacent signal channels Efficiency depends on signal power and dispersion 35

Self-Phase Modulation Self-phase modulation occurs when a short and intense pulse of light travel in a nonlinear medium The high intensity induces a variation of the refractive index of the medium This variation in refractive index produces a time-dependent change in the pulse phase, leading to a change of the pulse spectrum Self-phase modulation is an important ect in optical systems that use short, intense pulses of light 36

Self-Phase Modulation Signal varies with time P(t) I(t) n=n +n NL I(t) After a propagation distance z, the phase is φ=βz φ=nω/cz=[n +n NL I(t)]ω/cz=n ω/cz+n NL I(t)ω/cz=φ L+ φ NL Nonlinear phase-shift: φ NL =n NL I(t)ω/cz E ( z, t ) = A ( z, t ) e 0 = A ( z, t ) e iω t iϕ ( t) i 0 ( ω t ϕ ) iϕ ( t) L e NL Nonlinear phase-shift Change in the instantaneous frequency of the signal: [ ω t ϕ ϕ ( t) ] d φ d 0 L NL ) ω ( t ) = = = ω0 + δω dt dt dϕ NL ( t) ω0z di( t) with δω = = nnl dt c dt 37

Light modulates its own phase Self-Phase Modulation ω t) = ω n ω z c 0 ( 0 NL di( t) dt Self-Phase Modulation The frequency of the pulse is time-dependent: chirp (like the birds!) The magnitude of the frequency chirp increases with distance: the spectrum broadens with propagation! 38

Self-Phase Modulation dp dt > 0 δω Signal power varies with time: P(t) dp dt < 0 2π/ω 0 dp < 0 dt δω > 0 t Nonlinear refractive index n = n + n NL P( t) A Near the leading Near the trailing edge, ω =ω 0 +δω edge, ω =ω 0 +δω decreases increases (Red shift) (Blue shift) Spectral broadening t λ 39

Input pulse: Gaussian I (0, t ) = P A 0 e t 2 / t 2 0 ) Self-Phase Modulation I(t) I(ω) ) P 0 /A t 0 Δω=1/t 0 t ω L I(t) I(ω) Δω ϕ Max NL SPM with γ n = = 0.86Δωϕ Max NL NLω 0 P0 L = γ 0 c A P 0/A, Δω :initial spectral bandwidth P L nnlω0 : nonlinear coicient ca ω : carrier frequency 0 Δω SPM t 0 = t ω Self-Phase Modulation alone affects ONLY the spectrum 40

Self-Phase Modulation Self-Phase Modulation ALONE does not degrade system performance BUT Self-Phase Modulation combined WITH dispersion distorts the signals Dispersion ps/nm km λ t Pulses with large spectral width are more distorted by dispersion! 41

Self-Phase Modulation Self-Phase Modulation is only significant for high power values and/or short signal pulses Typically, optical fiber communication systems require φ Max NL<1 yp ca y, opt ca be co u cat o syste s equ e φ NL to avoid detrimental ects This limits the maximum power and/or the fiber length of the system Larger bit rate systems more sensitive to self-phase modulation 42

Cross-Phase Modulation Refractive index seen by an optical signal depends not only on its own intensity (Self-Phase Modulation), but also on the intensity of other co-propagating signals In systems with multiple frequency/wavelength channels, phase of one signal pulse is therefore affected by the intensity of other signal pulses This ect is called Cross-Phase Modulation: the intensity of a second channel modulates the phase of the first channel Cross-Phase Modulation is always accompanied by Self-Phase Modulation 43

Cross-Phase Modulation Consider 2 signals at frequencies ω 1 and ω 2 with intensities I 1 and I 2 [ ] z t I n z t I n z n t z t I t I n n n NL L NL NL NL 1 2 1 1 1 1 2 1 ) ( 2 ) ( ), ( ) ( 2 ) ( ϕ ϕ ω ω ω ϕ + = + + = + + = z c t I n z c t I n c c c NL NL NL NL L NL NL 1 2 1 1 1 2 1 1 ) ( 2 ) ( ) ( ) ( ), ( ω ω ϕ ϕ ϕ ϕ + = Self-Phase Modulation Cross-Phase Modulation The magnitude of Cross-Phase Modulation is twice that of Self-Phase Modulation 44

Cross-Phase Modulation Cross-Phase Modulation is very similar to Self-Phase modulation Involves two pulses changing the refractive index seen by the other When the two pulses OVERLAP in time they distort each other Cross-phase modulation broadens the signal spectrum ω The presence of chromatic dispersion (speed of pulse depends on its wavelength) stops the interaction between the interfering signals increasing the wavelength spacing between channels reduce Cross-Phase Modulation ects 45

Four Wave Mixing Nonlinear beating between two signals at ω 1 and ω 2 generates signal at the frequency difference ω 1 ω 2 Input ω ω 1 ω 2 Output 2ω 1 ω 2 2ω 2 ω 1 ω 46

Four-Wave Mixing In a system with two channels having two different frequencies (ω 1,ω 2 ), beating between the two signals interfere with the signal located at the difference frequency signal distortion In a three channel-system, the number of mixing products increases to nine Number of Mixing Terms: M = ½(N 3 N 2 ) Example: 40 channels M= 31,200 terms 47

Four-Wave Mixing Four-Wave Mixing is independent of the bit rate BUT Four-Wave Mixing depends on the channel spacing and dispersion Therefore, the ects of Four-Wave Mixing can be important even in moderate-bit-rate systems if channel spacing is small or dispersion of the fiber is low 48

Four-Wave Mixing When the channel spacing is even, the new mixing products fall on other channels degradation Unequal channel spacing allows to reduce Four-Wave Mixing ects Power transfered to new frequencies is inversely proportional to dispersion: more dispersion less Four-Wave Mixing 49

Four-Wave Mixing Input After 25 km of propagation... 50

Summary 2 types of nonlinear ects Nonlinear Scattering (Brillouin & Raman) Nonlinear Refractive Index (Self/Cross-Phase Modulation, Four-Wave Mixing) Nonlinear scattering: total power per channel Nonlinear refractive index: instantaneous power All nonlinear ects are inversely proportional to the ective area of the fiber and increase with fiber length 51

Summary Fiber nonlinearities becomes a problem when optical power levels a few mill watts or higher High density wavelength multi-channels systems are used High bit rates over 2.5 Gb/s are used Can be harmful (or beneficial) Interference, distortion, attenuation of signals Optical components Nonlinear applications Can be reduced by Increasing the ective area Reducing the power and /or fiber length Carefully managing the dispersion 52