Nonlinear effects in optical fibers - v1 Miguel A. Muriel UPM-ETSIT-MUIT-CFOP Miguel A. Muriel-015/10-1
Nonlinear effects in optical fibers 1) Introduction ) Causes 3) Parameters 4) Fundamental processes 5) Types 6) Envelope nonlinear equation Miguel A. Muriel-015/10-
1-Introduction -The propagation properties depend on the optical signal, traveling along the optical fiber -The presence of an optical field can modify optical properties of the medium I W PW A m m I E -High optical intensity it Nonlinear regime Interaction ti between light and a nonlinear medium. Miguel A. Muriel-015/10-3
-Causes - Increase of capacity through WDM technologies many channels in fiber - Optical transmitters are more powerful - Optical amplifiers -B T B high peak power - Low temporal dispersion pulses are widened very little they keep their peak power along transmission - Rd Reduced ddimension i of core fiber high h power density 1 mw Win SMF 1 MW/m. Miguel A. Muriel-015/10-4
Linear Media -Linear displacement of electrons with the incident field -The reemitted wave has the same frequency as the incident Nonlinear Media -Nonlinear displacement of electrons with the incident field -The reemitted wave has the same frequency as the incident, together with harmonics. www.wikipedia.org Miguel A. Muriel-015/10-5
Linear regime - Output power proportional to the input power - Phase change proportional to theeffective refractive index - New wavelengths aren t generated Nonlinear regime - Output power NOT proportional to input power extra attenuation - Phase change NOT proportional to effective refraction index generation of chirp pulse - New wavelengths are generated different carriers interacting between themselves crosstalk and distortion Miguel A. Muriel-015/10-6
3-Parameters 1- Effective core area - Effective length Miguel A. Muriel-015/10-7
3-1- Effective core area ( A eff ) - Non uniform density of field and power in the transversal section of the fiber - Effective area Equivalent area with uniform density A eff Cartesian IdA da dxdy I da Cylindrical da rdr A eff Miguel A. Muriel-015/10-8
- SMF, fundamental mode LP 01 Er () e r w Ir () Er () e r w w Mode field radius MFD w Mode field diameter A eff w MFD 4 Miguel A. Muriel-015/10-9
Effective core area of various fiber types (typical values) ITU-T fibre type A eff @ 1550 nm (µm²) G.65 (SMF) 80 G.653 (DSF) 50 G.654 (CSF) 90 G.655 (NZDSF) 55 (D>0), 60 (D<0) (DCF) 0 SMF: Single Mode Fiber DSF: Dispersion Shifted Fiber CSF: Cutoff Shifted Fiber NZDSF: Non-Zero DSF DCF: Dispersion Compensating Fiber Miguel A. Muriel-015/10-10
- A eff P th - The DSF fiber presents the smallest effective area among the line fibers. - Among special fibers, the effective area is particularly small in DCF Caution when fixing the DCM input power levels in dispersion compensated links. - In MM fibers A eff is estimated as core section. eff Miguel A. Muriel-015/10-11
3-- Effective length ( L eff ) - Signal power decreases exponentially with distance z P ( z ) P (0) e f z [ db / km )] 4,343 [1/ km] 0, 3 f f - Effective interaction length L eff is the length of a fiber with zero attenuation, which has the same nonlinear impact as a fiber with attenuation Miguel A. Muriel-015/10-1
P(0) P() z L eff z L P (0) L eff P ( z ) dz Leff z0 1 e f f L Miguel A. Muriel-015/10-13
L1 L L f L1 L f lim L L eff 1 f eff eff 1 f Example L00 Km, 0, [ db/ km )] f 0,05 [1/ km] f L f (0, 3)(0, )(00) 10,1 1 Leff 0 Km f Miguel A. Muriel-015/10-14
4) Fundamental processes In silica fibers there are two fundamental processes: 1) Stimulated Scattering Molecular vibration modes of Si O photon(out) photon(in) phonon ) Optical Kerr effect Variation of refraction index with optical intensity Miguel A. Muriel-015/10-15
4-1- Stimulated Scattering Rayleigh Brillouin Raman ( 0 ) ( 0 ± B ) ( ± R ) - Density fluctuations -Molecular vibrations - Particles -Acoustic waves -Molecular rotations - Local refractive index -Acoustic phonons -Electronic transitions variations - B ~ GHz -Optical phonons - R ~ THz www.vpiphotonics.com Miguel A. Muriel-015/10-16
Rayleigh Brillouin Raman phonon phonon h phonon www.wikipedia.org Miguel A. Muriel-015/10-17
http://www.intechopen.com/ Miguel A. Muriel-015/10-18
4-- Optical Kerr effect dn( E) 1 d n( E) ne ( ) n (0) E E de ( E 0) n de 0 ( E0) n n 1 ne ( ) n0 ne 1 Pockels Effect ne ( ) n0 ne 1 ne ne ( ) n 0 ne Kerr Effect (Fundamentals of Photonics, nd Ed., Saleh and Teich, 007) Miguel A. Muriel-015/10-19
The refractive index depends on the optical field power. ne ( ) n ne E 0 P I A eff n (,3,4) 10 0 ( m) W P nn0 ni n0 n A eff Miguel A. Muriel-015/10-0
Nonlinear coefficient kn 0 A eff In standard single mode fiber with: Aeff n 80 m,35 10 0 1, 55 m ( m) W 1 1, 76 ( Wkm ) Parameter/Fiber Type SSMF DSF DCF / W -1 km -1 1, 1,76 8,3 Miguel A. Muriel-015/10-1
5) Types 1- SBS Si Stimulated dbrillouin i Scattering - SRS Stimulated Raman Scattering 3- SPM Self-Phase Modulation 4- XPM Cross-Phase Modulation 5- FWM Four-Wave Mixing Miguel A. Muriel-015/10-
Stimulated Scattering Optical Kerr effect changes refractive index in the fiber Stimulated Raman Scattering (SRS) Stimulated Brillouin Scattering (SBS) Self Phase Modulation Four Wave Mixing (SPM) (FWM) Above threshold power Can be used for optical Cross Phase amplification Modulation (XPM) www.vpiphotonics.com Miguel A. Muriel-015/10-3
5-1-SBS (Stimulated Brillouin Scattering ) Brillouin scattering is a result of the interaction between the optical wave and the propagating density fluctuations in the fiber, due to thermo-elastic motions of the molecules, that can be regarded as acoustic waves, traveling through the fiber at the speed of sound. A strong pump wave generates a refractive index modulation (Bragg grating) in the material via the effect of electrostriction. A part of the pump wave is backscattered at the refractive index modulation (Bragg grating), this is the Stokes wave. Miguel A. Muriel-015/10-4
P S B Pump Doppler shifted Scattered Density (Acoustic) Brillouin P c P B S P B Frequency shift of the back scattered wave for: Pump wavelength, P = 1550 nm Refractive index, n = 1.45 Sound velocity, a = 5.96 km/s a n 11.15 GHz B P Miguel A. Muriel-015/10-5
- Full width half maximum (FWHM) of Brillouin Gain depends d on the pump power - ν B (Typical ) 50 MHz @ 1550 nm Lorentzian shape g B,max n llouin Gai f B Bri f P -f S =f B rel. Frequency www.vpiphotonics.com Miguel A. Muriel-015/10-6
Threshold Power P th KAeff 1 1 g L P B eff B -g B Brillouin-gain coefficient (~ 5 10-11 m/w) - K Constant determined by the polarization ( K ) - B, P Brillouin and pump spectral bandwidth www.vpiphotonics.com Miguel A. Muriel-015/10-7
5-- SRS Stimulated Raman Scattering - Raman scattering is a result of the interaction between the optical wave and the molecules of the material. Therefore, no phase matching condition is needed dd - The scattered wave could be shifted down (Stokes) or up (anti-stokes) in frequency. In optical fibers, the intensity of the downshifted wave is much higher - Scattering mainly in the propagation direction - The channels with a higher carrier frequency deliver a part of their power to the channels with a lower carrier frequency - In terms of wavelength, the channel with higher wavelength is amplified at the expense of the channel with the lower carrier wavelength Miguel A. Muriel-015/10-8
- The Raman gain in optical fibers is very broad (~40 THz) - The maximum of the frequency shift is at ~ 13 THz (105 nm) optical phonon ( R ) 13. THz R 6 Thz (Nonlinear Fiber Optics, 5 th Ed., Agrawal, 010) Miguel A. Muriel-015/10-9
Threshold Power P th 16 g L R eff A eff - g R Peak Raman Gain (~ 8 10-14 m/w) P th ~ 570 mw (@ 1.55 µm) con 16 Thz R Miguel A. Muriel-015/10-30
Input signals of equal power Relative output signals SRS Effect Miguel A. Muriel-015/10-31
SRS effect in WDM Input WDM input Channel 1 Channel Channel 1 1 0 1 0 1 0 The bits that overlap in time experience the Raman gain Most affected channel Acts as pumping signal 1 Channel 0 Output WDM output Miguel A. Muriel-015/10-3
5-3- SPM Self-Phase Modulation - SPM leads to a phase alteration of the wave due to its own intensity. - Phase alteration causes a spectral broadening of the pulses - Together with fiber dispersion, spectral broadening can be translated into an alteration of the temporal width of the pulse -In the case of normal dispersion ( D < 0 ) the pulse is additionally stretched, whereas it will be compressed for an anomalous dispersion ( D > 0 ) - Important in single-channel systems (Intra-SPM) Miguel A. Muriel-015/10-33
Pt () n () t n0 n I () t n0 n Aeff () t t k n() t L t k n L P() t L 0 0 0 0 0 Nonlinear www.wikipedia.org Miguel A. Muriel-015/10-34
d () t dp () t () t 0 L dt dt NL () t www.wikipedia.org Miguel A. Muriel-015/10-35
5-4- XPM, CPM Cross-Phase Modulation - Cross-phase modulation (XPM, or sometimes, CPM) is similar to SPM, but the origin of the spectral broadening of the pulses are the other pulses propagating at the same time in the waveguide; they will mutually influence each other, via the alteration of the intensity-dependent refractive index. - The refractive index that a wave experiences can be altered by the intensities of all other waves propagating in the fiber. - A pulse at one wavelength has an influence on a pulse at another wavelength. This effect can be exploited for optical switching and signal processing, but lead to a degradation of a communication system performance. - This is especially important for WDM systems where a huge number of pulses with different carrier wavelengths will be transmitted in one fiber (Inter-SPM) - The XPM is the fundamental effect that determines the capacity of optical transmission systems. Miguel A. Muriel-015/10-36
() t k n ( I () t c I ()) t L NL 0 a ab b NL dpa() t dpb() t () t L( cab ) dt dt - It is important that there in no coincidence of pulses Different velocities v g Different d1 0 D 0 d D XPM NZ-DSF fiber 1 Miguel A. Muriel-015/10-37
www.wikipedia.org Miguel A. Muriel-015/10-38
5-5- FWM Four-Wave Mixing - Four-wave-mixing (FWM), or sometimes four-photon-mixing (FPM), describes a nonlinear optical effect at which four waves or photons interact with each other due to the third order nonlinearity of the material -As a result, new waves with sum and difference frequencies are generated during the propagation p in the waveguide - It is comparable to intermodulation in electrical communication systems - For WDM systems in dispersion-shifted fibers, FWM is the most important nonlinear effect - FWM leads to a reduction of the SNR and, hence, an increase of the BER Miguel A. Muriel-015/10-39
-Inter-SPM Important in multichannel systems (N 3) th -With phase matching 3 tones interaction 4 tone 4 1 3 -They propagate in the same direction 13 31 13 31 11 33 1 3 113 1 3 331 3 13 1 31 Miguel A. Muriel-015/10-40
With two frequencies y ( ) 4 1 1 4 1 1 1 1 4 1 4 Miguel A. Muriel-015/10-41
19,8 19,9 193,0 193,1 193, 193,3 193,4 193,5 193,6 193,7 193,8 Optical lfrequencies (THz) M = N (N-1)/ N = nº of channels M = nº of new frequencies FWM Efficiency A eff n D P ( ) Miguel A. Muriel-015/10-4
5-6- Envelope nonlinear equation Nonlinear propagation constant β( ) ( ) Pt () kn 0 k0 n 0 n k0n0 A A A Linear eff eff Nonlinear Nonlinear coefficient (Kerr effect) Miguel A. Muriel-015/10-43
A A z t j j A A -This equation is referred as the Nonlinear Schrödinger (NLS) equation because it resembles the Schrödinger equation with a nonlinear potential term -The NLS equation is a fundamental equation of the nonlinear science SPM - In the general case of β 3 0 and α f 0, this equation is called the generalized (or extended) NLS equation 3 A A 3 A f j A j A A 3 z t 6 t SPM Miguel A. Muriel-015/10-44
In the more general case of three simultaneous signals, as in WDM: 3 A 1 A1 3 A 1 f * j A 3 1 j A1 A1 j A A3 A1 j A A3 z t 6 t st nd 1 order order GVD GVD Attenuation SPM XPM FWM Miguel A. Muriel-015/10-45