1、H64OCN, H64OCA, H64OCP Optical Communications (+)Lecture Notes 2010-11 Dr A J Phillips69In todays long distance fibre communication systems determining whether there will be enough signal power at the receiver is typically very complicated.A major reason for this is the presence of optical amplifier
2、s, which produce ASE noise. Because the process of photodetection can be described as square law detection the signal beats with ASE noise upon detection, causing signal-spontaneous beat noise. Also ASE beats with itself, causing spontaneous-spontaneous beat noise. This beating is a direct consequen
3、ce of the difference term obtained when squaring the sum of two input waves at different frequencies and then using )cos()cs(21osc BABAThe obtained photocurrent is: 222 )()()()()()()( tEttEtERtEtRti spspsigsigspsig (Esig(t) and Esp(t) are the signal and ASE optical fields in units W1/2 (so can direc
4、tly relate to signal and noise power) and the bar above the equation means time averaging over optical frequencies.The importance of this noise means that, to know what the ASE power is at the receiver, we need to track the OSNR through a chain of amplifiers to the receiver, where we need to know si
5、gnal power and ASE noise power spectral density (see signal-spontaneous beat noisespontaneous-spontaneous beat noiseplus ASE dc contrib.H64OCN, H64OCA, H64OCP Optical Communications (+)Lecture Notes 2010-11 Dr A J Phillips70p29-30). Typically these beat noises, and particularly signal-spontaneous, m
6、ean that the receiver is no longer dominated by thermal (or, sometimes in APD, shot) noise.When we recognize that effects like crosstalk, dispersion, PMD and nonlinear distortions of pulses have different power penalty effects depending on the OSNR being high or low we see that modelling system perf
7、ormance is hard (but very interesting)!Crosstalk may be:i) from an entirely different wavelength on ITU-T grid (generally the powers of the signals then just add on photodetection)ii) from a different laser using the same wavelength iii) from the same laser, travelling multiple paths due to loops or
8、 reflections. This has two subcategories depending on whether path length differences are large or small.The maths of crosstalk also follows from square law detection via: 222 )()()()()()()( tEttEtERtEtRti XTXTsigsigXTsig and a key consideration is whether the signal-crosstalk beat term falls within
9、 the receiver bandwidth. Clearly the signal to crosstalk ratio (Psig/PXT), also often stated in dB, needs to be tracked to enable this evaluation.H64OCN, H64OCA, H64OCP Optical Communications (+)Lecture Notes 2010-11 Dr A J Phillips713. Theory of Light Propagation in Optical Fibre3.1 Fibre ModesFibr
10、e modes are spatial distributions of optical energy across the fibre cross-section that (if they are guided modes or propagation modes, which are our main interest) are supported by the fibres waveguiding properties. Each is characterized by a propagation constant. Different modes have different pro
11、pagation constants and travel at different speeds (for the same frequency). This provides the origin of intermodal dispersion We start from Maxwells equations 0 BDtJHtBE E = electric field vectorH = magnetic field vectorD = electric flux densityB = magnetic flux densityJ = current density = charge d
12、ensityThe flux densities respond to the fields propagating in the medium as followsEPDr00HMB0 , 0 are permittivity, permeability of free space r , r are relative permittivity, permeability of the mediumP is the induced electric polarizationM is the induced magnetic polarizationH64OCN, H64OCA, H64OCP
13、 Optical Communications (+)Lecture Notes 2010-11 Dr A J Phillips72Now take into account the physical nature of the optical fibre: No free charge so =0 and no current flows so J=0 Non-magnetic so M=0, or equivalently r=1, leading to HB0NOTE: In writing we have also EPDr0assumed that the fibre materia
14、l is isotropic (same experience for E field in all directions) and linear with and =r-1 is the linear P0susceptibility.o In an anisotropic medium is no longer a scalar but a tensoro In a non-linear medium there are contributions from higher order susceptibilities. In semiconductors there is a 2nd or
15、der contribution from (2) but optical fibres have no 2nd order contribution and instead the highest nonlinearity is from (3)The non-linearity being only (3) in fibre has led to fibre being regarded as a very linear medium, and until power gets quite high it can generally be treated as linear. We wil
16、l do so for the moment.The net result of all the physical information is that Maxwells equations become: 0000 BEtHtEr (1) (2) (3) (4)H64OCN, H64OCA, H64OCP Optical Communications (+)Lecture Notes 2010-11 Dr A J Phillips73Take the curl of (1) and use (2) to write: - 20000 tEtEtHE rr A mathematical id
17、entity exists for :2)(This, with (3) , leads to the wave equation0E22tcnE for light propagation in the bulk material (silica, SiO2) from which a (linear) optical fibre is madeNote (n the refractive index of silica) and 2ris the vacuum speed of light.01cSimilarly, using (1), (2) and (4) for the H fie
18、ld:22tHcnUse cylindrical polar coordinates (r,z) to be in keeping with the fibre geometry so222 11zArArAwe can write 011 222 tcnzrrwhere A is any one of Ex, Ey, Ez, Hx, Hy, Hz.So far these results hold for the bulk material. Now we have to take account of the waveguide structure of the optical fibre
19、.H64OCN, H64OCA, H64OCP Optical Communications (+)Lecture Notes 2010-11 Dr A J Phillips74Assume a simple step index optical fibre.Consider specifically Ez:(*)011 222 tcnrEr zzzNow Ez (& other components) is a function of r,z and t. So separate the spatial distribution across fibre cross-section (dep
20、endent on r and ) from the wave behaviour (dependent on t and z): )(exp),(,1 tzjrEtzrEzz is the propagation constant of the optical fibre mode is the angular frequency of the light.Substitute this into (*) to see satisfies:,1rEz(*)011 121221 zzzz cnErEr Rotational symmetry of forces the choice ,1rzo
21、f where p is an integerprErEzz cos,21 so in 2 radians the modal pattern repeats p timesSubstituting this into (*) gives a DE for Ez2(r):01 2222 zz Erpcndrr This can be re-written as 02222 zz rpcnrdEr where the bulk material propagation constant k=n/c can now be used to write(*)022222 zzz EprkdrEdrk=
22、k1=n1/c in the core and k=k2=n2/c in the claddingH64OCN, H64OCA, H64OCP Optical Communications (+)Lecture Notes 2010-11 Dr A J Phillips75Modal propagation constant satisfies k20 we have normal dispersion.If 20 (which was then seen as normal!), and ultimately moved through operation around the disper
23、sion zero to longer wavelengths 20 C0) C is mainly negative for directly modulated semiconductor lasers, typically say -5 (Agrawal) Some externally modulated lasers (MZI based) can be virtually chirp free. The carrier period has been drawn massively increased relative to the pulse width to make the
24、effect obvious. H64OCN, H64OCA, H64OCP Optical Communications (+)Lecture Notes 2010-11 Dr A J Phillips84When transmitted in SMF with anomalous dispersion (20 initial pulse firstly becomes less positive and then becomes negatively chirped If we define T1 to be the pulse half width at the 1/e power po
25、int we can find an expression for T1/T0 in terms of z, chirp parameter C and dispersion length 20TLDi.e. solve ezAT1)0,(21(important exercise!) which gives 22201)sgn(DDLzLCzTIt is then straightforward to plot T1/T0 against z/LD for different values of C.We focus on the anomalous dispersion region (2
26、1310 nm). If we were interested in behaviour 1310 nm (dispersion zero in standard SMF) we would typically need to consider higher order dispersion, characterized by 3.H64OCN, H64OCA, H64OCP Optical Communications (+)Lecture Notes 2010-11 Dr A J Phillips85Pulse_spread z n 1Pulse_spread z n 5Pulse_spr
27、ead z n 0Pulse_spread z n 1Pulse_spread z n 5z n0 0.5 1 1.5 2 2.5 3024FIGURE: Pulse broadening T1/T0 as a function of normalized transmission distance zn=z/LD, for initial Gaussian pulse with different values of chirp parameter C (-5,-1,0,1,5)PA0.20.40.60.81PB0.51PC0.20.40.60.81FIGURE: Evolution of
28、pulse profile for initial Gaussian pulses with chirp parameters C=0 (left), C=1 (centre), C=-1 (right) over length of 4LD. Note in the case C=1 the pulse narrows, and peaks, initially. The pulse energy is unchanged (lossless case).-1-5150H64OCN, H64OCA, H64OCP Optical Communications (+)Lecture Notes
29、 2009-10 Dr A J Phillips86So now we have seen what happens when we just have dispersion. If we have dispersion and loss (but no nonlinearity) then the pulse shape will change in exactly the same way but its size will scale according to the amount of energy lost.e.g. a pulse traveling 15 km at 0.2 dB
30、/km will lose 3 dB of its energy, i.e. a half.So at 15 km a plot of power against T have the same 2),(TzAshape as the lossless case but the area under the curve of the plot (i.e. pulse energy=power x time) will be reduced by half.In principle the understanding of pulse broadening just developed may
31、be used to work out the dispersion penalty as function of distance for light from a specific transmitter in a specific fibre. However:1. The transmitter chirp needs to be known2. The transmitter output pulse shape needs to be known (it is not likely to be precisely Gaussian)though the dispersive fib
32、re channel is often modelled as producing Gaussian pulses when the output pulse is sufficiently dispersed to make the input pulse approximate a delta function in comparison3. Impact of receiver filters on patterning effects need to be understoodAnalysis enables the performance of different (linear) optical communication systems to be characterized by their bit ratelength product limit. This limit is much greater for transmitters with narrow spectral widths, since they suffer less from chromatic dispersion, leading to the popularity of DFB lasers and external modulators.
