3.1.1 Introduction
The concept o f transparent optical networks has in the last few years become a rapidly developing research area. Many different network architectures suitable for various types o f communication have been proposed. Common to many, in particular the large scale networks, is that they rely on Wavelength Division Multiplexing (WDM) and optical amplifiers, typically Erbium Doped Fibre Amplifiers (EDFAs). Both o f these techniques, however, give rise to increased distortion of transmitted signals. EDFAs do not naturally exhibit uniform gain throughout their ~35nm transmission window. Hence, cascading a number o f amplifiers together requires either gain flattening o f the amplifier or some method o f gain equalisation in order to ensure that the shorter wavelength carriers may be
80
recovered. In addition, a amplifier chain means that Amplified Spontaneous Emission (ASE) noise will build up and eventually also make the carrier message unrecoverable. Finally, densely multiplexing optical carriers within the frequency domain generally means a high spectral power density, which may stimulate non-linear effects within the optical fibre. We assume there is no crosstalk induced by the EDFAs.
In this section, we develop a method for optimising the number o f amplifiers as a function of the total transmission distance, the number of multiplexed carriers, the separation between carriers and the parameters of the fibre. We present results which test the assumptions made relating to our own [1-3] and other previously published network architectures.
Fig. 3.1 depicts the spectrum used in the transmission model. It is a Sparsely Filled Densely Wavelength Division Multiplexed (SF-DWDM) spectrum as it has fV wavelength slots, each o f which accommodate one of /f V carriers with probability / . In networks where a number of optical channels, distinct in the frequency domain, are used to make transparent optical connections between sets o f nodes, the case /< ! permits greater flexibility when allocating channels. In general this makes it easier to avoid contention between optical channels holding identical wavelength slots. In terms o f architecture and control, this permits a much simplified network. In fact, using this technique we have shown it is possible to design a high performance national transparent optical network without the use o f wavelength or time shifting [1-3], refer also Part II. In terms of optical transmission, however, using this technique means that for a given number of optical carriers, some will be spaced closer together. In turn this causes a locally higher spectral power density and an increased susceptibility to optical nonlinearities. The case /= ! is equivalent to system which make use o f a fully filled transmission spectrum with equally spaced carriers.
1 2 fW-1 fW
,n , ,n , ■■■ ,n ,n, ,
1
2
3
W- 2
W- 1
W
81 Optical fibre can, in the context of telecommunications, normally be treated as a linear medium. However, it does in reality exhibit a number of different nonlinear effects. Therefore, a high power density, caused by a large number of frequency multiplexed optical carriers, within a single fibre, might cause degradation of the carried signals due to one or more of these effects. Consequently, we would like to minimise the optical power per carrier so as not to invoke any of these nonlinearities. On the other hand, in order to avoid a fatal build-up in ASE noise, we should maximise the input power of the optical carriers to each segment of amplified fibre and thereby reduce the number of amplifiers required for a given transmission distance. Thus, we have an optimisation problem which is dependent on the number of amplifiers, the number of frequency multiplexed carriers and the length of fibre, as well as all the individual parameters describing each o f the nonlinearities for any given system. The succeeding sections each present a short review of the nonlinear effects Stimulated Brillouin Scattering (SBS), Stimulated Raman Scattering (SRS), Self Phase Modulation (SPM), Cross Phase Modulation (CPM), Four Photon Mixing (FPM) and the noise implications o f cascading amplifiers; followed by analysis and results.
3.1.2 Stimulated Raman Scattering
SRS is induced by the vibrations o f silica molecules in optical fibre modulating the effective dielectric constant. In a WDM system it causes the optical power contained in the channels transmitted on the shorter wavelengths to be transferred to the channels transmitted on the longer wavelengths [4-8]. That is, the higher fi-equency channels will experience excess attenuation due to SRS. This attenuation will be the greatest for the carrier occupying the shortest wavelength channel slot. The worst case attenuation for this channel in a WDM spectrum, D, is approximated in eqn. (3.1), where yi is the Raman gain coefficient. Pi is the input power and Xi is the wavelength o f the i*^.
A sketch o f the Raman gain curve versus channel spacing is shown as the dashed line in Fig. 3.2. By approximating it by a sawtooth curve, eqn. (3.2) (shown as the solid line in Fig. 3.2), we can derive the maximum attenuation condition due to SRS, eqn. (3.3), assuming the transmission window is less than 15thz.
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c3 D<8.4 -
7.0 - %
I5.6 1
4 . 7 - 1 2 . 8 - 1 ! / i /1.4 -! /
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/6
12 IS 24 30 36 42
Channel separation (THz)
Fig. 3.2 - Raman gain profile
r.=]
iAu 5 1 0 ' / y P , for iA f< 1.5x10'^ , for iAf > 1 .5 x 1 0 " (3.2) 6 10" / ) (3 3)3.1.3 Stimulated Brillouin Scattering
SBS is caused by interaction between light and acoustic waves in the fibre and results in backwards scattering of the light. However, unlike SRS it is independent of the number of multiplexed channels regardless of the separation between them. In order to ensure that a systems performance is not reduced due to SBS, the relationship described in eqn. (3.4)
83 must be upheld for each channel independently, where Avl is the laser linewidth, Avg is the optical bandwidth for SBS and y is the SBS gain coefficient [4,5,8,9]
The exact values for Avg and y naturally vary depending on the properties of the silica fibres used. However, for the purpose of this report we assume y = 4xlO'^^mAV and Avg = 20 MHz [4]. Eqn. (3.4) assumes a CW source. For a signal with bandwidth B the threshold is increased by approximately B/Avg. Hence, dithering the transmitter laser frequency or employing modulation schemes which produce broad spectra has the effect o f increasing the SBS threshold. For example, a 5dB improvement is possible using PSK [10]
3.1.4 Optical fibre nonlinearities
In addition to SRS and SBS a signal propagating through a fibre will be subject to fijrther deterioration due to the Kerr non-linearities. Although these may be expressed in terms o f intensity dependence o f the refractive index and analysed collectively through numerical manipulation of Schrodinger’s non-linear wave equation, we shall for the purposes o f our discussion in this chapter analyse & discuss them & their effects separately. Namely as Self Phase Modulation (SPM) — how the intensity variations of one channel affects its own phase, Cross Phase Modulation (CPM) — how the intensity variations of all other channels affects the phase in one channel and Four Photon Mixing (FPM) — how combinations of channels produce spurious power at new frequencies.
Carrier Induced Phase noise
The refractive index o f silica fibres, n, is given as « = wo + U2l, where / is the optical
intensity. Consequently a signal propagating through a fibre will experience a change in refractive index in relation to the intensity o f its pulses. This in turn, will cause the phase o f the signal to vary. SPM and CPM are the effects whereby the intensity modulation of a signal modulates the phase o f the signal in its own or another channel. Collectively we refer to SPM and CPM as Carrier Induced Phase (CIP) noise. The phase modulation caused by CLP broadens the signal spectrum, which in turn stimulates further pulse broadening due to dispersion (assuming we are operating in the normal dispersion region).
The variation in phase in radians, o*, due to SPM is given in eqn. (3 .5), where Op is the fluctuation in injected power in militates and %e is the electronic nonlinear susceptibility [11].
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cr^ =_ 4 0 X ~ ^ tT û) z j J.7” ^
trc~ A e^P (3 5)
The phase variation due to CPM, can likewise be expressed as a function of the fluctuation in input power and effective transmission length eqn. (3 .6), where %' is the sum of the electronic and Raman nonlinear susceptibilities [11].
80 X10 7 f (Û ,
G J, — ; ; ~r
rrc" (3 6)
The electronic nonlinear susceptibility, Xe' = 3.5x10"^^ esu, is assumed to be independent of wavelength. The Raman nonlinear susceptibility, Xr, Hes in the range [-0.5x10"^^, 0.5x10"^^] esu dependent on the channel spacing. Hence, the total phase fluctuation in radians is at, eqn. (3.7), where bi = [1.37x10"^^, 1.82x10"^^].
f r