光纖的色散與非線性效應(yīng)

1、隨著脈沖在光纖中傳輸隨著脈沖在光纖中傳輸，脈沖的寬度被展寬脈沖的寬度被展寬光纖的色散光纖的色散10000100010010600km600km1 23 45 6 7 8 9 10調(diào)制速率調(diào)制速率（GbpsGbps）小色散光纖理論上小色散光纖理論上小色散光纖實際上小色散光纖實際上傳統(tǒng)光纖理論上傳統(tǒng)光纖理論上傳統(tǒng)光纖實際上傳統(tǒng)光纖實際上 This is caused by the fact that the refractive index of the glass we are using varies (slightly) with the wavelength. Some wavelengt

2、hs therefore have higher group velocities and so travel faster than others. Since every pulse consists of a range of wavelengths it will spread out to some degree during its travel. Normal Dispersion Regime :the long wavelengths travel faster than the short ones! Thus after travelling on a fibre wav

3、elengths at the red end of the pulse spectrum will arrive first. This is called a positive chirp! Anomalous Dispersion Regime: the short wavelengths (blue end of the spectrum) travel faster than the long wavelengths (red end). After travel on a fibre the shorter wavelengths will arrive first. This i

4、s considered a negative chirp. There is usually a very slight difference in RI for each polarisation. It can be a source of dispersion, usually less than .5 ps/nm/km. The effect is to cause a circular or elliptical polarisation to form as the signal travels along the fibre. Dispersion resulting from

5、 the birefringent properties of fibre is called “Polarisation Mode Dispersion” (PMD). The shape (profile) of the fibre has a very significant effect on the group velocity. This is because the amount that the fields overlap between core and cladding depends strongly on the wavelength. The longer the

6、wavelength the further the the electromagnetic wave extends into the cladding. since a greater proportion of the wave at shorter wavelengths is confined within the core, the shorter wavelengths “see” a higher RI than do longer wavelengths. Therefore shorter wavelengths tend to travel more slowly tha

7、n longer ones.常規(guī)常規(guī)G.655G.655大有效面積大有效面積G.655G.655G.653G.653單模光纖（單模光纖（DSFDSF）1550nm1310nm色色散散p ps s/ /n nm m k km m普普通通光光纖纖( (S SM MF F) )非非色色散散位位移移光光纖纖（N ND DS SF F，G G. .6 65 52 2）已已有有光光纖纖的的 9 95 5% %波波長長 色色散散位位移移光光纖纖（D DS SF F, ,G G. .6 65 53 3）非非零零色色散散位位移移光光纖纖（N NZ ZD DS SF F, ,G G. .6 65 55 5）180

8、D DW WD DM M波波長長范范圍圍正常色散區(qū)正常色散區(qū)反常色散區(qū)反常色散區(qū) in a typical single-mode fibre using a laser with a spectral width of 6 nm over a distance of 10 km : Dispersion = 17ps/nm/km 6 nm 10 km = 1020 ps At 1 Gbps a pulse is 1 ns long. So the system would not work. (20% is a good guideline for the acceptable limit.

9、) But it would probably work quite well at a data rate of 155 Mbps (a pulse length of 6.5 ns). A narrow spectral width laser might produce only one line with a linewidth of 300 MHz. Modulating it at 1 Gbps will add 2 GHz. 2,300 MHz is just less than .02 nm (at 1500 nm). So now: Dispersion = 17ps/nm/

10、km .02 nm 10 km = 3.4 ps In this case, dispersion just ceased to be a problem. 控制光源線寬 色散位移光纖 色散補償光纖 中途譜反轉(zhuǎn) 啁啾光纖光柵 Simple FP laser: over 5 nm; External cavity DBR laser: .01 nm Modulation adds to the bandwidth of the signal, by twice the highest frequency present in the modulating signal (1 Gbps, .04

11、nm)! Using more complex signal coding rather than simple OOK. Using WDM(a 2.5 Gbps signal has 1/4 of the problem with dispersion as a 10 Gbps signal). dispersion shifted fibre is designed with a dispersion zero point at around 1550 nm. However, it is not always possible or indeed desirable： In many

12、cases we cant have DSF because the fibre we must use is already installed. four-wave mixing effectively prohibit the use of DSF.DCF存在的問題存在的問題 高損耗(0.5dB/km) 小截面積(DCF: 20mm2 G-652: 80mm2 ), 比標(biāo)準(zhǔn)光纖的非線性系數(shù)高 2-4個數(shù)量級 非線性閾值低3-6dB 較大的色散斜率(DCF:-15 -20 ps/nm2/km;G-652: 0.09ps/ nm2/km). 短波長過補償，長波長欠補償。 The concep

13、t here is to use a device in the middle of the link to invert the spectrum. This process changes the short wavelengths to long ones and the long wavelengths to short ones. When the pulse arrives it has been re-built exactly - compensated for by the second half of the fibre.Principle This spectral in

14、version is performed by a process called “optical phase conjugation”. Devices that change the wavelength using either 4-Wave Mixing or Difference requency Generation invert the spectrum as a biproduct of their wavelength conversion function. These can be used as spectral inverters if we can tolerate

15、 the wavelength shift involved.Chirped Bragg grating longshortTo compensate for 100 km of standard (17 ps/nm/km) fibre the chirped grating needs to be 17 cm long for every nm of signal bandwidth! In this instance a WDM system with channels spread over (say) 20 nm would need a chirped FBG (20 x 17) 3

16、40 cm long!啁啾光柵用作色散補償啁啾光柵用作色散補償 啁啾光柵的色散： (2neffL/c) (1/Dc) neff ：有效折射率； c ：光速 Dc 光柵兩邊緣反射波長之差. 5 cm 長的線性啁啾光柵可以補償300 km的10Gb/(光譜寬度0.1nm)傳輸線的色散( 5100ps/nm) 單信道單信道 多信道多信道 折射率效應(yīng)折射率效應(yīng) 自相位調(diào)制自相位調(diào)制 (SPM) 交叉相位調(diào)制交叉相位調(diào)制 (XPM) 四波混頻四波混頻 (FWM) 散射效應(yīng)散射效應(yīng) 受激布里淵散射受激布里淵散射 (SBS) 受激拉曼散射受激拉曼散射 (SRS) 光纖的非線性效應(yīng)光纖的非線性效應(yīng)What h

17、appen Increase in significance exponentially with the level of optical power in the fibre. “Elastic” effects: no energy exchange between the optical wave and the matter (four-wave mixing). “Inelastic Scattering”: there is an energy transfer between the matter involved and the optical wave.光纖非線性的形成光纖

18、非線性的形成 單信道系統(tǒng)，功率水平10mw,速率不超過2.5Gb/s時，光纖可以作為線性介質(zhì)處理，即：光纖的損耗和折射率都與信號功率無關(guān) WDM系統(tǒng)中，即使在中等功率水平和比特率下，非線性效應(yīng)也很顯著。 非線性效應(yīng)的產(chǎn)生的原因是：光纖傳輸損耗（增益）和折射率以及光功率相關(guān)。 非線性相互作用取決于傳輸距離和光纖的橫截面積。折射率非線性變化折射率非線性變化 光纖折射率隨光功率變化：n=n0 + n2P/Ae其中P 是光功率， Ae 是光纖有效截面積 折射率變化引起光波相位變化，導(dǎo)致光脈沖展寬 ，形成 SPM, XPM and FWM 在負色散區(qū)導(dǎo)致色散代價；在正色散區(qū)，導(dǎo)致色散補償 The pre

19、sence of light in a fibre causes a (tiny) change in the refractive index of the fibre. This is because the electromagnetic field that constitutes the light acts on the atoms and molecules that make up the glass. This is called the “Kerr Effect”. At low intensities the effect is linear; that is, the

20、amount of RI change varies linearly with the intensity of the light. At high intensities the effect is highly non-linear. This is called the “Nonlinear Kerr Effect”.How it works At very high powers Kerr nonlinearities can be used to balance the effects of chromatic dispersion in the fibre and a “sol

21、iton” is formed. At medium power levels (below the level needed to form solitons) Kerr effect has been used to construct devices that compress and re-form pulses and hence “undo” the effects of chromatic dispersion. At low power levels the results of Kerr effect are “self-phase modulation” and “cros

22、s-phase modulation”.自相位調(diào)制自相位調(diào)制(SPM) 自相位調(diào)制（SPM）的產(chǎn)生是由于本信道光功率引起的折射率非線性變化，這一非線性折射率引起與脈沖強度成正比的感生相移，因此脈沖的不同部分有不同的相移，并由此產(chǎn)生脈沖的啁啾 SPM效應(yīng)在高傳輸功率或高比特率的系統(tǒng)中更為突出。 SPM會增強色散的脈沖展寬效應(yīng)。從而大大增加系統(tǒng)的功率代價。SPM的特點的特點 E(Z,t)=Ecos(wot-Boz) 自相位調(diào)制（SPM）：電場E（z,t）的相位隨E2z變化，即：SPM引起的相位變化正比于電場強度E2與傳播距離z。2)3(0083ExnncwB交叉相位調(diào)制交叉相位調(diào)制(XPM) 交叉

23、相位調(diào)制（XPM）的產(chǎn)生是由于外信道光功率引起的折射率非線性變化，導(dǎo)致相位變化 相位正比于 ，其中第一項來源于SPM，第二項即交叉相位調(diào)制(XPM)。 若E1=E2 則XPM的效果將是SPM的兩倍。因此XPM將加劇WDM系統(tǒng)中SPM的啁啾及相應(yīng)的脈沖展寬效應(yīng)。 增加信道間隔可以抑制XPM DSF高速(10Gb/s)WDM系統(tǒng)中，XPM將成為一個顯著的問題。zEEE)2(1221四波混頻四波混頻(FWM) 折射率對于光強的相關(guān)性，不僅引起信道中的相移，而且產(chǎn)生新頻率分量的信號，這種現(xiàn)象稱為四波混頻（FWM） 三光子混頻： w4= w1+w2+w3 兩光子混頻： w4+w3= w1+w2 單光子混

24、頻： w4+w3= 2wp (wp=w1=w2) 兩束光產(chǎn)生混頻兩個邊帶：斯托克斯頻率： wS= 2w1- w2反斯托克斯頻率： wA= 2w2- w1四波混頻的特點四波混頻的特點 FWM的影響有賴于相互作用的信號之間的相位關(guān)系。如果相互作用的信號以同樣的群速度傳播（無色散時就是這種情況），則FWM的影響加強，另一方面，如果存在色散，不同的信號以不同的群速度傳播，因此不同光波之間的交替地同相疊加和反相疊加，其凈效果是減小了混頻的效率。在有色散的系統(tǒng)中，信道間隔越大，群速度的差異就越大。 色散位移光纖中的色散值很低，F(xiàn)WM效率要高得多。 在色散位移光纖中，信道數(shù)增加時，會產(chǎn)生更多的FWM項 信道

25、間隔減小時，相位失配減小，F(xiàn)WM效率增加 信號功率增加，F(xiàn)WM呈指數(shù)增加降低降低FWM的措施的措施 仔細選擇各信道的位置，使得那些拍頻項不與信道帶寬范圍重疊。這對于較少信道數(shù)的WDM系統(tǒng)是可能的，但必須仔細計算信道的確切位置。 增加信道間隔，增加信道之間的群速度不匹配。但缺點是增加了總的系統(tǒng)帶寬，從而要求放大器在較寬的帶寬范圍內(nèi)有平坦的增益譜，另外還增加了SRS引起的代價。 增加光纖的有效截面，降低光纖中光功率密度。 對于DSF使用大于1560nm的波長。這種方法的思路是：即使對于DSF，這一范圍內(nèi)也存在顯著的色散量，從而可以減小FWM的效率。這依賴于L-band的EDFA。 針對不同的波長信

26、道引入延時，從而擾亂不同波長信道的相位關(guān)系。受激布里淵散射受激布里淵散射(SBS) 受激布里淵散射（SBS）是由于光子受到聲學(xué)聲子的散射所產(chǎn)生的,形成斯托克斯波與反斯托克斯波。 SBS產(chǎn)生頻移，只發(fā)生在很窄的線寬內(nèi)，在1.55mm處，WB=11.1GHZ。 斯托克斯波和泵浦波沿反方向傳播。只要波長間隔比20MHZ大得多（這是典型的情況），SBS不引起不同波長之間的相互作用。 SBS在朝向光源的方向上產(chǎn)生增益，會引起光源不穩(wěn)定 SBS閾值功率低(單波長信道：9dBm). 增加光源線寬能夠提高SBS閾值功率 (100MHz光源:16 dBm ） SBS的增益系數(shù)gB約為410-11m/W，且與波長

27、無關(guān)。 In long distance systems where the span between amplifiers is great and the bit rate low (below about 2.5 Gbps). In WDM systems (up to about 10 Gbps) where the spectral width of the signal is very narrow. In remote pumping of an erbium doped fibre amplifier (EDFA) through a separate fibre. EDFA

28、pumps typically put out about four lines of around only 80 MHz wide. Each of these lines is limited by SBS in the amount of power that can be used.降低降低SBS的措施的措施 使單信道功率保持在SBS閾值以下。 增 加 光 源 的 線 寬 , 大 于 1 0 0 M H z（0.1nm)。 采用相位調(diào)制。受激喇曼散射受激喇曼散射(SRS) SRS是光子受到振動分子散射所產(chǎn)生的。SRS同時存在于在光傳輸方向或者與之相反的方向 閾值比SBS高3個數(shù)量級，具有100nm頻移間隔 SRS 引起 DWDM不同信道之間發(fā)生耦合，導(dǎo)致串?dāng)_。 長波長信號被短波長信號放大，引起信道功率不平衡 僅當(dāng)兩個波長信號都處于高電平狀態(tài)才會發(fā)生SRS. 色散可以減小SRS。因為這時不同信道的信號以不同的速度傳播，從而減小了不同波長的脈沖在光纖中任一點處都重合的概率 波長間隔大容易產(chǎn)生SRS降低降低SRS的措施的措施 使信道間隔減小 傳輸功率保持在SRS閾值以下。 引入一定的色散 The signal to be a