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1、Chapter 5Optic Fiber Waveguides,Review,1.Nature of Light,Light,Review,1.Nature of Light,2.Advantages of Fibers,3.Applications of fiber optic communication,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 thei
2、r own fibers,you should have some idea of how it is accomplished.Proper choice and proper utilization require 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 pa
3、y particular attention to attenuation,modes,and information capacity.Construction and design of fiber cables are also discussed.,Chapter 5Optic Fiber Waveguides,attenuation,modes,dispersion,nonlinear,Index,Birefringence(双折射),polarization,cut-off wavelength,Fiber Structure,typical dimensionsCore:2a=5
4、0 m(for MMF)=10 m(for SMF)Cladding:2b=125 mcoating:2c=250 m,Optical cable,refractive index profile,Types of fiber,Step-index fiber,graded-index fiber,coating,cladding,core,5.1 step-index fiber,The step-index(SI)fiber consists of a central core whose refractive index is n1,surrounded by a cladding wh
5、ose refractive index is n2.Figure 5.1 illustrates the 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.,n1,n2,n0,5.1 step-index fiber,If any power cro
6、sses the boundary,the transmitted ray direction is given by Snells law.,n1,n2,n0,1,5.1 step-index fiber,2,If any power crosses the boundary,the transmitted ray direction is given by Snells law.,critical angle,n1,n2,n0,C,5.1 step-index fiber,Critical angle c sinc=n2/n1,Total reflection requires that
7、the angle is equal to or greater than the critical 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)the case.Actually,some
8、 of the light travels in the cladding in the form of an evanescent wave（消逝波）,as discussed in Chapter 4 for the slab waveguide.If the cladding is nonabsorbent(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
9、cladding if it is 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)problems arise when attempting to handle or support this type of structure
10、.Any lossy material attached to the core for support will cause losses in the propagating wave.The freely suspended(悬挂)core could bend or be easily scratched(刮伤),causing additional losses.The cladding protects the core from contamination(污染物)and helps preserve its physical integrity（完整性）.,5.1 step-i
11、ndex fiber,n1,n2,n0,n0sin=n1sinz1=900-z 1 c,5.1 step-index fiber,Coupling efficiency,lost,c,i,n1,n2,n0,Numerical-Aperture(NA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 cor
12、e and eventually leave the fiber.,c,i,n1,n2,n0,Numerical-Aperture(NA),fractional refractive index change,Numerical-Aperture(NA),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 t
13、he cladding has a lower refractive index than the cladding itself.Figure 5.3 illustrates the possible ray paths.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
14、 cladding beyond the critical angle for that boundary and totally reflects back toward the fiber axis.The light 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 r
15、ays traveling along paths that cross the fiber axis at angles greater than those of the modes guided by the 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 de
16、flected（偏离）beyond the core-mode angles.The light traveling in a cladding mode attenuates more rapidly 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 r
17、eflection,causing radiation losses.We can often observe power in cladding modes at points close 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,trade-off,5.2 graded-index fiber,The gra
18、ded-index(GRIN)fiber has a core material whose refractive index decreases continuously with distance from the fiber axis.,refractive index variation,n2=cladding indexn1=core indexa=core radius=parameter describing the refractive-index profile variation=parameter determining the scale of the profile
19、change,Light rays travel through the fiber in the oscillatory(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 particular variations in Eqs.(5.3.a)and Eqs.(5.3.b)cause them to be periodically refocused.We can illustrate t
20、his 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 the number of steps.Many GRIN fibers resemble(类似)this step model because their cores are fabricated in layers.The be
21、nding 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)when traveling from a high to a lower refractive index.With this in mind,the ray trace in Fig.5.6 becomes reasonable.A ray crossing the fiber axis strikes a series of bounda
22、ries,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 angle exceeds the critical angle and is totally reflected back toward the fiber axis.Now the ray goes from low-to higher-index medi
23、a,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 oscillate back and forth as it propagates down the fiber.,parabolic profile,The parabolic（抛物线的）profile results in continual refocusing of the ra
24、ys in the core,and compensates for multimode distortion.,=2,Rays crossing the axis nearly horizontally（水平地）in Fig.5.5 are turned back after traveling only a short distance away from the axis.Steeper(陡峭的)rays travel farther from the axis.Some rays start out so steeply that they will not be turned bac
25、k 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 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 a
26、cceptance angle.The expression for the NA depends on the parameters and.,In the preceding（前述的）discussion,we considered only rays that excite(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 b
27、ecause they travel only a short distance through the core in the transverse（横向的）direction.If one of these rays enters 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 in
28、sufficient to create a critical-angle reflection,and the ray will pass into the cladding.,We conclude that 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 f
29、rom the axis.Coupling from a planar light source butted against a GRIN fiber is pictured in Fig.5.7.The 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,r
30、egardless of the entry point.For this reason,the coupling efficiency is generally higher for an SI fiber than it is for a GRIN fiber that has the same core size and the same fractional refractive index change.,5.3 attenuation,Signal attenuation is a major factor in the design of any communications s
31、ystem.,insertion loss,Connectors generally consist of a ferrule(金属环)for each fiber and a precision sleeve into which the ferrules fit.,loss in a fiber-to-fiber connection,Lateral misalignment,Angular misalignment,Gap between ends,Non-flat ends,splice loss,attenuation,Receiver need a minimum amount o
32、f power for signal recovery.Loss reduce the signal power reaching the receiver.The transmission distance is limited by the loss.,attenuation coefficient,Pin:input powerL:length of fiberPout:output power,:attenuation coefficient,in unit of dB/km,0 dB/km:,attenuation coefficient,no loss,We need concer
33、n ourselves only with which fiber communications is most practical about 0.5 to 0.6 m.This is the range within which fiber communications 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
34、 so outside this region.,Improvements in Fiber Attenuation,As was mentioned earlier,fibers are made of plastics or glasses.Requirements for the material include low loss and the ability to be formed into long hair-like fibers.Additionally,the material must be capable of slight variations,so that two
35、 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-index fibers can be made from plastic or glass.Graded-index fibers are normally glass,although graded-index plastic fibers have been developed.
36、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 interest is that formed by fusing(熔化)molecules of silica(硅石).The resulting glass is not a compound but a mixture of SiO2 molecules that have variatio
37、ns in molecular locations throughout the material.This is quite unlike the structure of a crystal,in which the locations of the component atoms form fixed and repetitive patterns.To obtain different refractive indices,other materials are added to the mixture.This doping is done with titanium(钛),thal
38、lium(铊)germanium(锗)，boron(硼)and other materials.Because germanium increases the refractive index of silica,it is often used to dope the 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,absor
39、ption,geometric effects,scattering,5.3.2 Absorption,Even the purest glass will absorb heavily within specific wavelength regions.This is intrinsic absorption,a natural property of the glass itself.,Glass absorption in ultraviolet Glass absorption in infrared hydroxylion(OH 氢氧基)absorption peak,0.5 0.
40、6 0.7 1 1.2 1.5 2 3 5 10,1001010.10.01,Attenuation(dB/km),Wavelength(m),5.3.2 Absorption,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 l
41、oss in the ultraviolet and diminishing(逐渐缩小)loss as the visible region is approached.,0.5 0.6 0.7 1 1.2 1.5 2 3 5 10,1001010.10.01,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
42、 such as the silicon-oxygen(SiO)bond.,0.5 0.6 0.7 1 1.2 1.5 2 3 5 10,1001010.10.01,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 toward the ultraviolet as well as tow
43、ard longer wavelength.,5.3.2 Absorption,0.5 0.6 0.7 1 1.2 1.5 2 3 5 10,1001010.10.01,Glass absorption in ultraviolet,Glass absorption in infrared,Attenuation(dB/km),Wavelength(m),5.3.2 Absorption,Impurities are a major source of loss in any practical fiber.The most important impurity to minimize is
44、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)for the OH ion is the stretching vibration(张驰振动),just as for the absorption by the SiO bond(结合).
45、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)and combination bands of this resonance lie within the range of interest.,The most significant OH losses occur at 1.37,1.2
46、3,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 must be kept to less than a few parts per million.Special precautions(预防)are taken during the glass manufacture to ensur
47、e a low OH levels,and wet fibers just a bit more.Within the low-intrinsic-loss region,OH absorption dictates(规定)which wavelengths must be avoided for most efficient propagation.,Atomic defects also contribute to fiber absorption.As an example,titanium,used to dope glass,does not absorb.During fiberi
48、zation(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 absorbs heavily.This reduction process can be minimized by proper manufacturing techniques.,5.3.3 Rayleigh Scattering（瑞利散射）,Molecules move randoml
49、y through the glass in the molten(熔融)state during manufacture.The heat applied provides the energy for the motion.As the liquid cools,the motion ceases.Upon reaching the solid state,the random molecule locations are frozen within the glass.This results in localized variations in density and,thus,loc
50、al variations in the refractive index can be modeled as small scattering objects.The size of these objects is much smaller than optic wavelengths.,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 10,1001010.10.01
