光纤通信07 Optic Fiber Waveguides

1、chapter 5 optic fiber waveguides review review we are now ready to address the major item in our communications systems, the optic fibers. although only a few will ever design and fabricate their own fibers, you should have some idea of how it is accomplished. proper choice and proper utilization re

2、quire a deep understanding of fiber construction and fiber characteristics. with this in mind, we will study the major types of fibers and the properties of waves propagating through them. we will pay particular attention to attenuation, modes, and information capacity. construction and design of fi

3、ber cables are also discussed. chapter 5 optic fiber waveguides fiber structure 2a 2b optical cable types of fiber 5.1 step-index fiber the step-index (si) fiber consists of a central core whose refractive index is n1, surrounded by a cladding whose refractive index is n2. figure 5.1 illustrates the

4、 structure, sometimes referred to as the step-index matched-clad fiber. as with the dielectric slab, complete guidance requires that the reflection angle be equal to or greater than the critical angle c. 5.1 step-index fiber n2 n1 sin sin if any power crosses the boundary, the transmitted ray direct

5、ion is given by snells law. 1 2 5.1 step-index fiber n2 n1 sin sin 1 2 if any power crosses the boundary, the transmitted ray direction is given by snells law. critical angle 5.1 step-index fiber critical angle c sinc = n2/n1 total reflection requires that the angle is equal to or greater than the c

6、ritical angle c . 5.1 step-index fiber efficient transmission requires that the core and cladding be as free of loss as possible. although the ray diagram implies that the light travels entirely within the core, this is not precisely (精确地精确地) the case. actually, some of the light travels in the clad

7、ding in the form of an evanescent wave （消逝波）（消逝波）, as discussed in chapter 4 for the slab waveguide. if the cladding is nonabsorbent (无吸收的无吸收的) , then this light is not lost but travels along the fiber. the evanescent fields decay rapidly, so that no light will reach the edge of the cladding if it i

8、s a few tens of microns thick. the question arises as to the need for the cladding at all. a core of glass surrounded by air satisfies the requirement n1n2, and would indeed guide a light wave. however, severe(严重的严重的) problems arise when attempting to handle or support this type of structure. any lo

9、ssy material attached to the core for support will cause losses in the propagating wave. the freely suspended(悬挂悬挂) core could bend or be easily scratched(刮伤刮伤), causing additional losses. the cladding protects the core from contamination (污染物污染物)and helps preserve its physical integrity（完整性）（完整性）.

10、5.1 step-index fiber n0sin=n1sinz 1 = 900-z 1 c 5.1 step-index fiber los t numerical-aperture (na数值孔径数值孔径) if a ray enters the fiber at an angle within the corn then it will be captured and propagate in the fiber. if a ray at an angle outside the cone then it will leave the core and eventually leave

11、 the fiber. numerical aperture is the sine of the largest angle contained within the cone of acceptance. numerical-aperture (na) i nsinna 0 ci nncossin 10 2 1212 1cossinnnnn cc 2 2 2 110 cossinnannnn ci 2 1 1 2 nna 1 21 2 1 2 2 2 1 2n nn n nn fractional refractive index change numerical-aperture (na

12、) 2 2 2 1 nann review of the step-index structure indicates that light can also be trapped by total internal reflection at the outer boundary of the cladding if the material surrounding the cladding has a lower refractive index than the cladding itself. figure 5.3 illustrates the possible ray paths.

13、 in the example shown, the ray angle at the core cladding interface is less than the critical angle, so some light is transmitted into the cladding. this light strikes the outer surface of the cladding beyond the critical angle for that boundary and totally reflects back toward the fiber axis. the l

14、ight represented by this ray never leaves the fiber and is thus guided by it. 5.1 step-index fiber this example illustrates the existence of cladding modes. cladding modes are characterized by rays traveling along paths that cross the fiber axis at angles greater than those of the modes guided by th

15、e core. they are excited by light introduced into the fiber end at angles beyond the acceptance angle. they might also begin at discontinuities, such as splices and connectors, where light can be deflected （偏离）（偏离） beyond the core-mode angles. the light traveling in a cladding mode attenuates more r

16、apidly than the light in a core mode because the outer boundary of the cladding normally is in contact with a lossy material. in addition, small bends in the fiber reduce the ray angle below that for total reflection, causing radiation losses. we can often observe power in cladding modes at points c

17、lose to the light source. this power attenuates so rapidly that the cladding modes are insignificant at the end of a long fiber. typical step-index fiber characteristics constructi on corecladdin g n1n2na all glass glass glass1.48 1.46 0.0135 0.24 pcsglass plastic1.46 1.40.041 0.41 all plastic plast

18、i c plastic1.49 1.41 0.054 0.48 5.2 graded-index fiber the graded-index (grin) fiber has a core material whose refractive index decreases continuously with distance from the fiber axis. refractive index variation n2= cladding index n1= core index a=core radius =parameter describing the refractive-in

19、dex profile variation =parameter determining the scale of the profile change arnnrn ararnrn , 21 1 21)( ,21)( light rays travel through the fiber in the oscillatory (摆动的摆动的) fashion of fig.5.5. the changing refractive index continually causes the rays to be redirected toward the fiber axis, and the

20、particular variations in eqs.(5.3.a) and eqs.(5.3.b) cause them to be periodically refocused. we can illustrate this redirection by modeling the continuous change in refractive index by a series of small step changes, as shown in fig.5.6. this model can be made as accurate as desired by increasing t

21、he number of steps. many grin fibers resemble (类似类似) this step model because their cores are fabricated in layers. the bending of the rays at each small step follows snells law. as was described in section 2.1, rays are bent away from the normal (法线法线)when traveling from a high to a lower refractive

22、 index. with this in mind, the ray trace in fig.5.6 becomes reasonable. a ray crossing the fiber axis strikes a series of boundaries, each time traveling into a region of lower refractive index, and thus bending farther toward the horizontal axis. at one of the boundaries away from the axis, the ray

23、 angle exceeds the critical angle and is totally reflected back toward the fiber axis. now the ray goes from low- to higher-index media, thus bending toward the normal until it crosses the fiber axis. at this point the procedure will repeat. in this manner, the fiber traps a ray, causing it to oscil

24、late back and forth as it propagates down the fiber. parabolic profile the parabolic （抛物线的）（抛物线的）profile results in continual refocusing of the rays in the core, and compensates for multimode distortion. =2 rays crossing the axis nearly horizontally （水平（水平 地）地）in fig.5.5 are turned back after travel

25、ing only a short distance away from the axis. steeper (陡峭的陡峭的) rays travel farther from the axis. some rays start out so steeply that they will not be turned back at all. they are never bend enough to suffer critical-angle reflections. these rays will not be trapped. we now see that only rays within

26、 a limited angular range will propagate along a grin fiber. the si and grin fibers have this property in common. a grin fiber has a numerical aperture and a related acceptance angle. the expression for the na depends on the parameters and. in the preceding（前述的）（前述的） discussion, we considered only ra

27、ys that excite (激励激励) the fiber at its center point. suppose that a ray enters a point away from the axis, as do the upper rays shown in fig.5.7. these rays are not bent very much because they travel only a short distance through the core in the transverse （横向的）（横向的）direction. if one of these rays e

28、nters nearly horizontally, then it could be bend enough to be redirected toward the axis and continue through the waveguide. at some relatively small entrance angle, however, the bending is insufficient to create a critical-angle reflection, and the ray will pass into the cladding. we conclude that

29、the entry angle yielding trapped rays decreases as the excitation point moves away from the fiber axis. in other words, the acceptance angle and numerical aperture decrease with radial distance from the axis. coupling from a planar light source butted against a grin fiber is pictured in fig.5.7. the

30、 relative sizes of the acceptance-cone angles are indicated. coupling is more efficient near the axis than farther out. this is unlike the behavior of the si fiber, for which the na remains the same, regardless of the entry point. for this reason, the coupling efficiency is generally higher for an s

31、i fiber than it is for a grin fiber that has the same core size and the same fractional refractive index change. splice loss insertion loss signal attenuation is a major factor in the design of any communications system. modulator light source transmitter fiber connectorconnector amplifier circuit r

32、eceiver light sensor fiber loss connectors generally consist of a ferrule (金属环金属环) for each fiber and a precision sleeve into which the ferrules fit. loss in a fiber-to-fiber connection splice loss splice loss insertion loss modulator light source transmitter fiber connectorconnector amplifier detec

33、tor receiver light sensor fiber loss receiver need a minimum amount of power for signal recovery. loss reduce the signal power reaching the receiver. the transmission distance is limited by the loss. attenuation coefficient lpp inout exp pin : input power l : length of fiber pout : output power : at

34、tenuation coefficient in unit of db/km 343. 4log 10 10 in out p p l kmdb in out p p l kmdb 10 log 10 )/( 0 db/km : attenuation coefficient no loss we need concern ourselves only with which fiber communications is most practical about 0.5 to 0.6 m. this is the range within which fiber communications

35、is most practical. reasons for this include the ability to construct low-loss fibers and efficient sources and detectors in this region and the difficulty of doing so outside this region. as was mentioned earlier, fibers are made of plastics or glasses. requirements for the material include low loss

36、 and the ability to be formed into long hair-like fibers. additionally, the material must be capable of slight variations, so that two refractive indices, one for the core and one for the cladding, can be obtained. for a graded-index fiber, a continuous variation in index must be possible. step-inde

37、x fibers can be made from plastic or glass. graded-index fibers are normally glass, although graded-index plastic fibers have been developed. glass fibers generally have lower absorption than plastic fibers, so they are preferred for long- distance communications. 5.3.1 glass the glass of most inter

38、est is that formed by fusing (熔化熔化) molecules of silica(硅石硅石) . the resulting glass is not a compound but a mixture of sio2 molecules that have variations in molecular locations throughout the material. this is quite unlike the structure of a crystal, in which the locations of the component atoms fo

39、rm fixed and repetitive patterns. to obtain different refractive indices, other materials are added to the mixture. this doping is done with titanium(钛钛), thallium (铊铊)germanium(锗锗)，boron(硼硼) and other materials. because germanium increases the refractive index of silica, it is often used to dope th

40、e core . the result is a high-silica-content glass, which can be formed into a low-loss fiber if high chemical purity is achieved. fiber loss fiber loss total loss absorption geometric effects scattering 5.3.2 absorption even the purest glass will absorb heavily within specific wavelength regions. t

41、his is intrinsic absorption, a natural property of the glass itself. glass absorption in ultraviolet glass absorption in infrared hydroxylion (oh 氢氧基氢氧基) absorption peak 0.5 0.6 0.7 1 1.2 1.5 2 3 5 10 100 10 1 0.1 0.01 glass absorption in ultraviolet attenuation (db/km) wavelength (m) 5.3.2 absorpti

42、on intrinsic absorption is very strong in the short-wavelength ultraviolet portion of the electromagnetic spectrum. the absorption, owing to strong electronic and molecular transition bands, is characterized by peak loss in the ultraviolet and diminishing (逐逐 渐缩小渐缩小) loss as the visible region is ap

43、proached. 0.5 0.6 0.7 1 1.2 1.5 2 3 5 10 100 10 1 0.1 0.01 glass absorption in ultraviolet attenuation (db/km) wavelength (m) 5.3.2 absorption intrinsic absorption peaks also occur in the infrared. the infrared loss is associated with vibrations of chemical bonds such as the silicon-oxygen (sio) bon

44、d. glass absorption in infrared 0.5 0.6 0.7 1 1.2 1.5 2 3 5 10 100 10 1 0.1 0.01 glass absorption in ultraviolet attenuation (db/km) wavelength (m) intrinsic losses are mostly insignificant in a wide region where fiber systems can operate. but these losses inhibit the extension of fiber systems towa

45、rd the ultraviolet as well as toward longer wavelength. glass absorption in infrared 5.3.2 absorption 0.5 0.6 0.7 1 1.2 1.5 2 3 5 10 100 10 1 0.1 0.01 glass absorption in ultraviolet glass absorption in infrared attenuation (db/km) wavelength (m) 5.3.2 absorption oh absorption peak impurities are a

46、major source of loss in any practical fiber. the most important impurity to minimize is the hydroxylion (oh) arising from excess water content. from a practical point of view, the most important impurity to minimize is the hydroxyl ion (oh) arising from excess water content. the loss mechanism (机制机制

47、) for the oh ion is the stretching vibration (张驰振动张驰振动), just as for the absorption by the sio bond (结合结合). the oxygen and hydrogen atoms are vibrating in thermal motion. the resonant frequency occurs at the wavelength 2.73 m. although the peak absorption lies at 2.73 m , the overtones (谐波谐波) and co

48、mbination bands of this resonance lie within the range of interest. the most significant oh losses occur at 1.37, 1.23,and 0,95 m when oh ions are embedded in a silica fiber. oh absorption peaks can be observed on the fiber-loss curve in fig.5.9. to achieve results like those shown, the oh impurity

49、must be kept to less than a few parts per million. special precautions (预防预防) are taken during the glass manufacture to ensure a low oh levels, and wet fibers just a bit more. within the low-intrinsic-loss region, oh absorption dictates (规定规定) which wavelengths must be avoided for most efficient pro

50、pagation. atomic defects also contribute to fiber absorption. as an example, titanium, used to dope glass, does not absorb. during fiberization (the forming of the hairlike fiber from the preformed glass ), reduction of some ti4+ atoms to the ti3+ atoms state occurs. in the latter state, titanium ab

51、sorbs heavily. this reduction process can be minimized by proper manufacturing techniques. 5.3.3 rayleigh scattering （瑞利散射）（瑞利散射） molecules move randomly through the glass in the molten( 熔融熔融) state during manufacture. the heat applied provides the energy for the motion. as the liquid cools, the mot

52、ion ceases. upon reaching the solid state, the random molecule locations are frozen within the glass. this results in localized variations in density and, thus, local variations in the refractive index can be modeled as small scattering objects. the size of these objects is much smaller than optic w

53、avelengths. so a beam of light passing through such a structure will have some of its energy scattered by these objects. 0.5 0.6 0.7 1 1.2 1.5 2 3 5 10 100 10 1 0.1 0.01 glass absorption in ultraviolet glass absorption in infrared attenuation (db/km) wavelength (m) oh absorption peak scattering loss

54、 5.3.3 rayleigh scattering r a y l e i g h s c a t t e r i n g i s proportional to -4 . so it becomes increasingly important as the wavelength diminishes. there is another cause of scattering loss. when a fiber material consists of more than one oxide, concentration fluctuations (浓度起伏浓度起伏) of the co

55、nstituent oxides may occur. this is a problem of imperfect chemical bonding of the various components. in this case, the actual glass composition varies from place within the glass. again, we have a localized refractive-index variation resulting in a rayleigh loss following the -4 dependence. the de

56、nsity and compositional losses just described are intrinsic losses. they can not be removed by any processing techniques. they can be removed only by actually changing the composition. the scattering losses introduced by these two phenomena are considered to be a minimum; a fiber with less loss cann

57、ot be manufactured for a given glass. material inhomogeneities unintentionally introduced into the glass during manufacture also cause scattering losses. imperfect mixing and dissolution of chemicals can cause in homogeneities within the core. imperfect processing can produce a rough core-cladding i

58、nterface. the scattering objects in these instances are larger than the optic wavelength. unlike rayleigh scattering the losses introduced by large objects are independent of wavelength. in addition, these losses can be controlled by proper manufacturing techniques. 5.3.4 inhomogeneities 5.3.5 geome

59、tric effects bending a fiber causes attenuation macroscopicmicroscopic large-scale of bending 125m diameter fibers can be bent with radii of curvature as small as 25mm with negligible loss. loss is not the only adverse affect of bending. in addition, bending reduces the fibers tensile strength. a fi

60、bers strength depends on the microscopic flaws located on its surface. these flaws will grow over time if the fiber is subjected to stress (or moisture), weakening the fiber. thus, the stress produced by bending might cause the early failure of a fiber. for commercial 125 m fibers, the given minimum