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光纤的色散与非线性效应

光纤的色散与非线性效应. 光纤的色散. 劣化的程度随数据速率的平方增大 决定了电中继器之间的距离. 随着脉冲在光纤中传输 ， 脉冲的宽度被展宽. 模间色散 (Mode Dispersion) 色度色散 (Cromatic Dispersion) 偏振色散 (Polarization Mode Dispersion). 色散对传输的限制. Material (Chromatic) Dispersion.

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光纤的色散与非线性效应

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  1. 光纤的色散与非线性效应

  2. 光纤的色散 劣化的程度随数据速率的平方增大 • 决定了电中继器之间的距离 随着脉冲在光纤中传输，脉冲的宽度被展宽 模间色散(Mode Dispersion) • 色度色散(Cromatic Dispersion) • 偏振色散(Polarization Mode Dispersion)

  3. 色散对传输的限制

  4. Material (Chromatic) Dispersion • This is caused by the fact that the refractive index of the glass we are using varies (slightly) with the wavelength. Some wavelengths 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.

  5. Group Velocity Dispersion” (GVD) • Normal Dispersion Regime :the long wavelengths travel faster than the short ones! Thus after travelling on a fibre wavelengths 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 is considered a negative chirp.

  6. Polarisation Mode Dispersion (PMD) • 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 the birefringent properties of fibre is called “Polarisation Mode Dispersion” (PMD).

  7. Waveguide Dispersion • 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 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 than longer ones.

  8. 传输使用的三种不同类型的单模光纤 G.652单模光纤（NDSF） G.653单模光纤（DSF） G.655单模光纤（NZ-DSF） 常规G.655 大有效面积G.655

  9. G.652单模光纤（NDSF） • 大多数已安装的光纤 • 低损耗 大色散分布 大有效面积 • 色散受限距离短 • 2.5Gb/s系统色度色散受限距离约600km • 10Gb/s系统色度色散受限距离约34km • G.652+DCF方案升级扩容成本高 • 结论: • 不适用于10Gb/s以上速率传输，但可应用于 2.5Gb/s以下速率的DWDM。

  10. G.653单模光纤（DSF） 低损耗 零色散 小有效面积 长距离、单信道超高速EDFA系统 四波混频（FWM）是主要的问题，不利于DWDM技术 结论: 适用于10Gb/s以上速率单信道传输，但不适用于 DWDM应用，处于被市场淘汰的现状。

  11. G.655单模光纤（NZ-DSF） • 在1530－1565nm窗口有较低的损耗 • 工作窗口较低的色散，一定的色散抑制了非线性效应（四波混频）的发生。 • 可以有正的或负的色散——海底传输系统 • 正色散SPM效应压缩脉冲，负色散SPM效应展宽脉冲。 • 为DWDM系统的应用而设计的 结论: 适用于10Gb/s以上速率DWDM传输， 是未来大容量传输，DWDM系统用光纤的理想选择。

  12. 三种光纤色散情况比较 正常色散区 反常色散区

  13. Calculating Dispersion • 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.) 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/km × .02 nm × 10 km = 3.4 ps • In this case, dispersion just ceased to be a problem.

  14. 色散补偿技术 • 控制光源线宽 • 色散位移光纤 • 色散补偿光纤 • 中途谱反转 • 啁啾光纤光栅

  15. Control of Spectral Width • 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 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).

  16. Dispersion Shifted Fibre • 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 cases we can't have DSF because the fibre we must use is already installed. • four-wave mixing effectively prohibit the use of DSF.

  17. Dispersion Compensating Fibre

  18. Balancing Dispersion on a Link

  19. DCF存在的问题 • 高损耗(0.5dB/km) • 小截面积(DCF: 20mm2 G-652: 80mm2 ), 比标准光纤的非线性系数高 2-4个数量级 • 非线性阈值低3-6dB • 较大的色散斜率(DCF:-15 ~ -20 ps/nm2/km;G-652: 0.09ps/ nm2/km). • 短波长过补偿，长波长欠补偿。

  20. Mid-Span Spectral Inversion • The concept 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.

  21. Principle • This spectral inversion 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 the wavelength shift involved.

  22. l l long short ChirpedBragg grating • • •  Chirped Fibre Bragg Gratings To 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) 340 cm long!

  23. 啁啾光栅用作色散补偿 • 啁啾光栅的色散： (2neffL/c) (1/Dlc) neff：有效折射率； c ：光速 Dlc光栅两边缘反射波长之差. • 5 cm 长的线性啁啾光栅可以补偿300 km的10Gb/(光谱宽度0.1nm)传输线的色散(~ 5100ps/nm)

  24. 单信道 多信道 折射率效应 光强度波动引 起的折射率的 调制 自相位调制 交叉相位调制 (SPM) (XPM) 四波混频 (FWM) 散射效应 受激布里渊散射 受激拉曼散射 (SBS) (SRS) 光纤的非线性效应

  25. What happen • 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.

  26. 光纤非线性的形成 • 单信道系统，功率水平<10mw,速率不超过2.5Gb/s时，光纤可以作为线性介质处理，即：光纤的损耗和折射率都与信号功率无关 • WDM系统中，即使在中等功率水平和比特率下，非线性效应也很显著。 • 非线性效应的产生的原因是：光纤传输损耗（增益）和折射率以及光功率相关。 • 非线性相互作用取决于传输距离和光纤的横截面积。

  27. 折射率非线性变化 • 光纤折射率随光功率变化： n=n0 + n2P/Ae 其中P 是光功率， Ae是光纤有效截面积 • 折射率变化引起光波相位变化，导致光脉冲展宽 ，形成 SPM, XPM and FWM • 在负色散区导致色散代价；在正色散区，导致色散补偿

  28. Carrier-Induced Phase Modulation • The presence 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 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”.

  29. How it works • At very high powers Kerr nonlinearities can be used to balance the effects of chromatic dispersion in the fibre and a “soliton” 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 “cross-phase modulation”.

  30. 自相位调制(SPM) • 自相位调制（SPM）的产生是由于本信道光功率引起的折射率非线性变化，这一非线性折射率引起与脉冲强度成正比的感生相移，因此脉冲的不同部分有不同的相移，并由此产生脉冲的啁啾 • SPM效应在高传输功率或高比特率的系统中更为突出。 • SPM会增强色散的脉冲展宽效应。从而大大增加系统的功率代价。

  31. SPM的特点 • E(Z,t)=Ecos(wot-Boz) • 自相位调制（SPM）：电场E（z,t）的相位随E2z变化，即：SPM引起的相位变化正比于电场强度E2与传播距离z。

  32. 交叉相位调制(XPM) • 交叉相位调制（XPM）的产生是由于外信道光功率引起的折射率非线性变化，导致相位变化 • 相位正比于 ，其中第一项来源于SPM，第二项即交叉相位调制(XPM)。 • 若E1=E2则XPM的效果将是SPM的两倍。因此XPM将加剧WDM系统中SPM的啁啾及相应的脉冲展宽效应。 • 增加信道间隔可以抑制XPM • DSF高速(≥10Gb/s)WDM系统中，XPM将成为一个显著的问题。

  33. 四波混频(FWM) • 折射率对于光强的相关性，不仅引起信道中的相移，而且产生新频率分量的信号，这种现象称为四波混频（FWM） • 三光子混频： w4= w1+w2+w3 • 两光子混频： w4+w3= w1+w2 • 单光子混频： w4+w3= 2wp(wp=w1=w2) • 两束光产生混频两个边带： 斯托克斯频率： wS= 2w1- w2 反斯托克斯频率： wA= 2w2- w1

  34. Four Wave Mixing Effects

  35. 四波混频的特点 • FWM的影响有赖于相互作用的信号之间的相位关系。如果相互作用的信号以同样的群速度传播（无色散时就是这种情况），则FWM的影响加强，另一方面，如果存在色散，不同的信号以不同的群速度传播，因此不同光波之间的交替地同相叠加和反相叠加，其净效果是减小了混频的效率。在有色散的系统中，信道间隔越大，群速度的差异就越大。 • 色散位移光纤中的色散值很低，FWM效率要高得多。 • 在色散位移光纤中，信道数增加时，会产生更多的FWM项 • 信道间隔减小时，相位失配减小，FWM效率增加 • 信号功率增加，FWM呈指数增加

  36. 降低FWM的措施 • 仔细选择各信道的位置，使得那些拍频项不与信道带宽范围重叠。这对于较少信道数的WDM系统是可能的，但必须仔细计算信道的确切位置。 • 增加信道间隔，增加信道之间的群速度不匹配。但缺点是增加了总的系统带宽，从而要求放大器在较宽的带宽范围内有平坦的增益谱，另外还增加了SRS引起的代价。 • 增加光纤的有效截面，降低光纤中光功率密度。 • 对于DSF使用大于1560nm的波长。这种方法的思路是：即使对于DSF，这一范围内也存在显著的色散量，从而可以减小FWM的效率。这依赖于L-band的EDFA。 • 针对不同的波长信道引入延时，从而扰乱不同波长信道的相位关系。

  37. 受激布里渊散射(SBS) • 受激布里渊散射（SBS）是由于光子受到声学声子的散射所产生的,形成斯托克斯波与反斯托克斯波。 • SBS产生频移，只发生在很窄的线宽内，在1.55mm处，WB=11.1GHZ。 • 斯托克斯波和泵浦波沿反方向传播。只要波长间隔比20MHZ大得多（这是典型的情况），SBS不引起不同波长之间的相互作用。 • SBS在朝向光源的方向上产生增益，会引起光源不稳定 • SBS阈值功率低(单波长信道：9dBm). 增加光源线宽能够提高SBS阈值功率 (100MHz光源:16 dBm ） • SBS的增益系数gB约为4×10-11m/W，且与波长无关。

  38. SBS Threshold Variation with Wavelength

  39. Major problem with SBS • 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 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.

  40. 降低SBS的措施 • 使单信道功率保持在SBS阈值以下。 • 增加光源的线宽,大于100MHz（0.1nm)。 • 采用相位调制。

  41. 受激喇曼散射(SRS) • SRS是光子受到振动分子散射所产生的。SRS同时存在于在光传输方向或者与之相反的方向 • 阈值比SBS高3个数量级，具有100nm频移间隔 • SRS 引起 DWDM不同信道之间发生耦合，导致串扰。 • 长波长信号被短波长信号放大，引起信道功率不平衡 • 仅当两个波长信号都处于高电平状态才会发生SRS. • 色散可以减小SRS。因为这时不同信道的信号以不同的速度传播，从而减小了不同波长的脉冲在光纤中任一点处都重合的概率 • 波长间隔大容易产生SRS

  42. Stimulated Raman Scattering

  43. 降低SRS的措施 • 使信道间隔减小 • 传输功率保持在SRS阈值以下。 • 引入一定的色散

  44. Raman Effect Amplifiers • The signal to be amplified must be longer in wavelength than the pump. • Optimal amplification occurs when the difference in wavelengths is around 13.2 THz. • At very high power it is possible for all of the signal power to be transferred to the Stokes Wave. • In regular Ge-doped fibre the effect is very small and it takes a relatively long length of (about 1 km).

  45. Wavelength Changing with SRS

  46. A 1310 nm Band SRA • Signal light and pump light enter the device together through a wavelength selective coupler. • The pump light at 1064 nm is shifted to 1117 nm and then in stages to 1240 nm. • The 1240 nm light then pumps the 1310 band signal and amplification is obtained. • A high level of Ge dopant is used (around 20%) to increase the SRS effect.

  47. Pump Source PUMP SIGNAL Output WDM Gain Flattening Filter SRFA

  48. Comparison of the OAs

  49. 宽带光放大 • (C+L)波段EDFA • C波段EDFA+SRFA • TDFA（Thulium-doped fluoride fiber amplifier）+SRFA • 多波长SRFA • SOA

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