Nonlinear effects in optical fibers - v1 Miguel A. Muriel ...oa.upm.es/38010/1/Nonlinear effects in...

Nonlinear effects in optical fibers - v1p

Miguel A. Muriel

UPM-ETSIT-MUIT-CFOP

Miguel A. Muriel-2015/10-1

Nonlinear effects in optical fibers

1) Introduction

2) Causes

3) P t3) Parameters

4) Fundamental processes

5) Types

6) Envelope nonlinear equation


1-Introduction

-The propagation properties depend on the optical signal traveling along theThe propagation properties depend on the optical signal, traveling along theoptical fiber

-The presence of an optical field can modify optical properties of the mediump p y p p p

2 2

P WWIA

2 2

2

m A m

I E

Hi h ti l i t it N li i I t ti b t li ht d

I E

-High optical intensity → Nonlinear regime→ Interaction between light and anonlinear medium.


2-Causes

- Increase of capacity through WDM technologies → many channels in fiber

- Optical transmitters are more powerful

- Optical amplifiers

- B↑→TB↓ → high peak power

- Low temporal dispersion → pulses are widened very little → they keep theirLow temporal dispersion → pulses are widened very little → they keep their peak power along transmission

R d d di i f fib hi h d it 1 W i SMF- Reduced dimension of core fiber→ high power density → 1 mW in SMF →12 MW/m2.


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 ith the incident field-Nonlinear displacement of electrons with the incident field-The reemitted wave has the same frequency as the incident, together with harmonics.

Miguel A. Muriel-2015/10-5www.wikipedia.org

Linear regime

- Output power proportional to the input power

Ph h i l h ff i f i i d- Phase change proportional to the effective refractive index

- New wavelengths aren´t generated

Nonlinear regimeg

- 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


3-Parameters

1- Effective core area

2 Effective length2- Effective length


3-1- Effective core area ( Aeff )

Non uniform density of field and power in the transversal section of the fiber- Non uniform density of field and power in the transversal section of the fiber

- Effective area → Equivalent area with uniform density

2

CartesianIdA dA dxdyA

2 Cylindrical 2eff

yA

dA rdrI dA

AA


AAeffeff

- SMF, fundamental mode LP01

2rw

2

2 2

( )

( ) ( )

w

rw

E r e

I r E r e

( ) ( )

Mode field radius

I r E r e

w

Mode field radius2 Mode field diameter

wMFD w

22

4effMFDA w

4eff


Effective core area of various fiber types (typical values)

ITU-T fibre type Aeff @ 1550 nm (µm²)G 652 (SMF) 80G.652 (SMF) 80G.653 (DSF) 50G.654 (CSF) 90( )G.655 (NZDSF) 55 (D>0), 60 (D<0)(DCF) 20

SMF: Single Mode Fiber

DSF: Dispersion Shifted Fiber

CSF: Cutoff Shifted Fiber

NZDSF: Non-Zero DSF

DCF: Dispersion C i Fib


Compensating Fiber

- Aeff↑ → Pth↑

The DSF fiber presents the smallest effective area among the line fibers- The DSF fiber presents the smallest effective area among the line fibers.

- Among special fibers, the effective area is particularly small in DCF →Cautionh fi i h DCM i l l i di i d li kwhen fixing the DCM input power levels in dispersion compensated links.

- In MM fibers Aeff is estimated as core section.eff


3-2- Effective length ( Leff )

Si l d ti ll ith di t- Signal power decreases exponentially with distance z

( ) (0) f zP P ( ) (0)

[ / )] 4 343 [1/ ] 0 23

fP z P e

dB km km

[ / )] 4,343 [1/ ] 0,23f fdB km km

- Effective interaction length Leff is the length of a fiber with zero attenuation, which has the same nonlinear impact as a fiber with attenuation


( )P z(0)P(0)P

Lz

effL

1(0) ( )f LL

ff ffeP L P z dz L

0

(0) ( )eff efffz

P L P z dz L


1f effL L L 11

f ff

f efff

L L

1lim

f

effLf

L

f

Example 200 , 0,22 [ / )]L Km dB km p , , [ )]

0,05 [1/ ]f km , [ ]

(0, 23)(0, 22)(200) 10,12

1

f

f L

1 20efff

L Km


4) Fundamental processes

In silica fibers there are two fundamental processes:p

1) Stimulated Scattering1) Stimulated Scattering

Molecular vibration modes of Si O2

photon(OUT) photon(IN) phonon

2) Optical Kerr effect

Variation of refraction index with optical intensity


4-1- Stimulated Scattering

Rayleigh Brillouin Raman(0) (0± B) (± R)

- Particles - Density fluctuations -Molecular vibrationsMolecular rotationsParticles

- Local refractive index variations

-Acoustic waves-Acoustic phonons- B ~ GHz

-Molecular rotations-Electronic transitions-Optical phonons

TH


- R ~ THz

www.vpiphotonics.com

Rayleigh

hphonon

Brillouin phonon

phononRaman


Miguel A. Muriel-2015/10-18http://www.intechopen.com/

4-2- Optical Kerr effect

0

22

2( 0) ( 0)

2

( ) 1 ( )( ) (0)2E En

n

dn E d n En E n E EdE dE

1 22

0 120 1 2 2

0 2

( ) Pockels Effect( )

( ) Kerr Effect

n n

n E n n En E n n E n E

n E n n E


0 2( )

(Fundamentals of Photonics, 2nd Ed., Saleh and Teich, 2007)

The refractive index depends on the optical field power The refractive index depends on the optical field power.

20 2( )n E n n E

2

202

( )(2,2 3,4)·10 mnW

2 PE IA

W

effA

0 2 0 2Pn n n I n n

A

effA


Nonlinear coefficient

0 2

eff

k nA

In standard single mode fiber with:

eff

In standard single mode fiber with:

280effA m1

2

202

( )2,35·10 mnW

11,76( · )W km

1,55 m

Parameter/Fiber Type SSMF DSF DCF / W-1 km-1 1,2 1,76 8,3


5) Types

1 SBS S i l d B ill i S i1- SBS Stimulated Brillouin Scattering2- SRS Stimulated Raman Scattering

3- SPM Self-Phase Modulation4- XPM Cross-Phase Modulation5- FWM Four-Wave Mixing


StimulatedScattering

OpticalKerr effect

changes refractive index

StimulatedRaman

StimulatedBrillouin

changes refractive indexin the fiber

RamanScattering

(SRS)

BrillouinScattering

(SBS) Self PhaseModulation

Four WaveMixingModulation

(SPM)

Cross PhaseModulation

Mixing(FWM)• Above threshold power

• Can be used for opticallifi ti Modulation

(XPM)amplification

Miguel A. Muriel-2015/10-23www.vpiphotonics.com

5-1-SBS (Stimulated Brillouin Scattering )

Brillouin scattering is a result of the interaction between the optical waveBrillouin scattering is a result of the interaction between the optical waveand 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 soundthrough the fiber at the speed of sound.

A t t f ti i d d l ti (BA 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.( gg g g)


P S B Pump Density (Acoustic)Doppler shifted

BrillouinScattered

cP

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

B2

11.15 GHzan

y, a


BP

- → Full width half maximum (FWHM) of Brillouin Gain d d hdepends on the pump power

- νB (Typical ) ≈ 50 MHz @ 1550 nm

Lorentzian shapen

gB,max

Lorentzian shapello

uin

Gai

fB

Bri

rel. FrequencyfP-fS=fB


Threshold Power

eff Pth

B eff B

KAP

g L

21 1

- gB → Brillouin-gain coefficient (~ 5·10-11 m/W) - K → Constant determined by the polarization (≤ K ≤ 2)K → Constant determined by the polarization (≤ K ≤ 2) - B , P → Brillouin and pump spectral bandwidth


5-2- SRS Stimulated Raman Scattering

- Raman scattering is a result of the interaction between the optical waveand the molecules of the material. Therefore, no phase matching condition is

d dneeded

- The scattered wave could be shifted down (Stokes) or up (anti-Stokes) infrequency. In optical fibers, the intensity of the downshifted wave is muchhigher

- Scattering mainly in the propagation direction

- The channels with a higher carrier frequency deliver a part of their powerThe channels with a higher carrier frequency deliver a part of their powerto the channels with a lower carrier frequency

- In terms of wavelength the channel with higher wavelength is amplified at the- In terms of wavelength, the channel with higher wavelength is amplified at the expense of the channel with the lower carrier wavelength


- 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( ) 13.2 THz

R 6 Thz

Miguel A. Muriel-2015/10-29(Nonlinear Fiber Optics, 5thEd., Agrawal, 2010)

Threshold Power

16th effP A

Lth eff

R effg L

Peak Raman Gain ( 8 10-14 m/W)- gR → Peak Raman Gain (~ 8·10-14 m/W)

~ 570 mW (@ 1.55 µm) con 16 Thzth RP


Input signals of equal power Relative output signals

SRS Effect


SRS effect in WDM

1

Input WDM input

1

0

1Channel 1

0

1

Most affected channel

The bits that overlap in time experience

Channel 2

0

1Acts as pumping signal

in time experience the Raman gain

Channel 1

0

1

0

Channel 2

0

Output

WDM output


5-3- SPM Self-Phase Modulation5-3- 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- Together with fiber dispersion, spectral broadening can be translated intoan alteration of the temporal width of the pulse

I h f l di i ( D 0 ) h l i ddi i ll h d-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)


( )( ) ( ) P tn t n n I t n n 0 2 0 2( ) ( )eff

n t n n I t n nA

0 0 0 0 0

Nonlinear

( ) ( ) ( )t t k n t L t k n L P t L


( ) ( )( ) d t dP tt L0

( )

( ) ( )( )

NL t

t Ldt dt


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 performanceto 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)with different carrier wavelengths will be transmitted in one fiber (Inter-SPM)

- The XPM is the fundamental effect that determines the capacity of opticali i


transmission systems.

0 2( ) ( ( ) ( ))NL a ab bt k n I t c I t L

( ) ( )( ) ( )a bNL ab

dP t dP tt L cdt dt

- It is important that there in no coincidence of pulses

1

12

Different velocities Different

0 0

gv

d D

2 0 0

XPM NZ-DSF fiber

DdD


5-5- FWM Four-Wave Mixing

F i i (FWM) i f h i i (FPM)- 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 in the waveguideg p p g g

- 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


Inter SPM Important in multichannel systems (N 3)

th

-Inter-SPM Important in multichannel systems (N 3)

-With phase matching 3 tones interaction 4 tone

4 1 2 3

With phase matching 3 tones interaction 4 tone

-They propagate in the same direction

213123112

231321332

1 2 3

1 2 3113 3311 2 3223 132 221

312


1 2 2 1

4 1 2 1

With two frequencies y ( )2

4 2 1 22

1 2 1 2 4’4


193,2193,1 193,3 193,4 193,5 193,6 193,7 193,8193,0192,9192,8

O i l f i (TH )Optical frequencies (THz)

M = N2 (N-1)/2N = nº of channelsM = nº of new frequencies

2 P

22

)(

DAPn

eff

FWM Efficiency


5-6- Envelope nonlinear equation

Nonlinear propagation constant β( )

p q

20 2

0 0 2 0 0( )( )eff effLi

k nP tk n n k n AA A

eff effLinear

Nonlinear

→Nonlinear coefficient (Kerr effect)


2222

2

SPM2

A Aj j A Az t

-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

- In the general case of β3≠0 and αf ≠ 0, this equation is called the generalized (or extended) NLS equation

2 3232 fA A Aj A j A A

(or extended) NLS equation

2 3

SPM2 6 2

j A j A Az t t


In the more general case of three simultaneous signals, as in WDM:

2 32 2 2 2 *31 2 1 1

1 1 1 2 3 1 2 32 3

SPM FWM

22 6 2

fA A Aj A j A A j A A A j A Az t t

st nd

SPM FWMXPMAttenuation1 order 2 orderGVD GVD


Nonlinear effects in optical fibers - v1 Miguel A. Muriel ...oa.upm.es/38010/1/Nonlinear effects in...

Documents

Transcript of Nonlinear effects in optical fibers - v1 Miguel A. Muriel ...oa.upm.es/38010/1/Nonlinear effects in...