光纤通信基础_第二章 光导纤维的传输原理（光纤）

Optical fiber 第二章光导纤维的传输原理 communication 12021/2/19 Optical Fibers 1光纤的结构 Cladding Core SMF: 2a=4 10 μ 2b=125 理论分析中,可以认为包 层是无限大的 MMF:(阶跃多模光纤) 2a=50m2b=125 2阶跃光纤和渐变光纤 Step-Index Fiber& Graded- Index Fiber Step Graded Index index 3光纤制作 reading:P15P19

1-1 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 一. Optical Fibers 1.光纤的结构 b SMF:2a=4- 10m,2b=125 理论分析中，可以认为包 层是无限大的 MMF:(阶跃多模光纤) 2a=50m,2b=125 2.阶跃光纤和渐变光纤 Step-Index Fiber & Graded-Index Fiber 3.光纤制作 reading:P15-P19

Optical fiber 第二章光导纤维的传输原理 communication 22021/2/19 二几何光学 Geometrical Optics 1. Speed of light in a medium of refractive index n m v=c/n n 2. Law of eflection: e:= 0 k 3 Snell's lawn●sine= oy: normal line. o-Xz: boundary n sin 0i 4. When all apertures are much larger than a wavelength, we can model the light as ray traveling in straight lines perpendicular to the wavefront

1-2 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 二.几何光学 Geometrical Optics 4.When all apertures are much larger than a wavelength, we can model the light as ray traveling in straight lines perpendicular to the wavefront 1.Speed of light in a medium of refractive index n: v=c/n 2.Law of reflection:i= r 3.Snell’s law:nt•sin t= ni•sin i oy:normal line.o-xz:boundary

Optical fiber 第二章光导纤维的传输原理 communication 32021/2/19 Uniform plane wave均匀平面波 A: Maxwell Equations B在稳态简谐条件下,线性 ( undamental equations)各项同性非色散,不导电媒 质中 Maxwel! Equations aB V×E at V×E=-jopH V×H D V×H=jEE V·D=P V·E=0 D= Ck V·H=0 B=uH

1-3 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 三.Uniform plane wave 均匀平面波 A:Maxwell Equations (fundamental equations) t J D J t D H t B E     = −   = +     = −     = −          B:在稳态简谐条件下，线性 各项同性非色散，不导电媒 质中Maxwell Equations 0 0   =   =   =   = − H E H j E E j H         B H D E       = =

Optical fiber 第二章光导纤维的传输原理 communication 42021/2/19 C. Helmholtz方程 VE+kE=O E C VH+kH=0 where k2=0E B E,(,t)=Eo exp[j(ot-k2lI H(, t)=Ho exp[jlot-k-) 1时间参量角频率o,周期T,频率60=712 2丌 2空间参量:纵向相移常数或角波数k2,浪长λx,波数1/zk

1-4 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 C. Helmholtz方程 0 0 2 2 2 2  + =  + = H k H E k E     ( ) ( ) ( , ) exp[ ( )] , exp[ ] 0 0 H z t H j t k z E z t E j t k z y x = − = −   x y z   2 2 k = 1.时间参量:角频率，周期T，频率f。      1 2 . 2 = 2 = = = f T T f 2.空间参量:纵向相移常数或角波数kz，波长z，波数1/ z . where z z k  2 =

Optical fiber 第二章光导纤维的传输原理 communication 52021/2/19 3空间与时间的联系相速度 phase velosity v==A,f 均匀平面波的纵向相移常数等于空间相移常数k.=k=a√E 其相速度等于光速vn=E 4电磁联系;阻抗对均匀平面液n=/E E+ E 77 H+ H 真空中n=A/0≈120n2≈3702 均匀平面波是电磁浪的最基本的形式,它是沿固定方向传播的等 幅行浪,垂直于传播方向的平面是等相面或称浪阵面。其等相位 面同时是等振幅面,其电场和磁场都垂直于传播方向且互相垂直 故称为横电磁波(TEM: Transverse Electromagnetic wave)波。 同时是等幅浪,即振幅不随传播距离而增加或衰减,等幅均匀平 面波中电场与磁场同相,波阻抗为实数

1-5 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 3.空间与时间的联系:相速度 phase velosity f k v z z p   = = •均匀平面波的纵向相移常数等于空间相移常数 k = k =  z 其相速度等于光速 = 1  p v 4.电磁联系:波阻抗 − − = − + + = H E H E  对于均匀平面波  =   真空中  = 0  0 120  370 均匀平面波是电磁波的最基本的形式，它是沿固定方向传播的等 幅行波，垂直于传播方向的平面是等相面或称波阵面。其等相位 面同时是等振幅面，其电场和磁场都垂直于传播方向且互相垂直， 故称为横电磁波(TEM:Transverse Electromagnetic wave)波。 同时是等幅波，即振幅不随传播距离而增加或衰减，等幅均匀平 面波中电场与磁场同相，波阻抗为实数

Optical fiber communication -62021/2/19 若在空间垂直于电场的面放置两块平行的导体平板,则因在导体 表面切向电场为0,两导体板不影响平面波的传播。这就形成双平 板传输线中的TEM模式的行浪,它是双平板传输线中的主模,或 称最低模。 TE: transverse electric wave. TM: transverse magnetic Wave

1-6 Copyright Wang Yan 2021/2/19 Optical fiber communications 若在空间垂直于电场的面放置两块平行的导体平板，则因在导体 表面切向电场为0，两导体板不影响平面波的传播。这就形成双平 板传输线中的TEM模式的行波，它是双平板传输线中的主模，或 称最低模。 TE:transverse electric wave.TM:transverse magnetic wave

Optical fiber 第二章光导纤维的传输原理 communication -7 2021/2/ Plane Waves at a Dielectric Interface y 1. Consider a monochromatic plane wave k incident on a dielectric interface n described by the surface normal s 2.The plane wave takes the form E=Eo cos(o, t-k p)

1-7 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 Plane Waves at a Dielectric Interface 1.Consider a monochromatic plane wave incident on a dielectric interface described by the surface normal S 2.The plane wave takes the form: E E ( t k r) i i i i     = 0 cos  −

cm第二章光导纤维的传输原理 82021/2/19 Plane Waves at a Dielectric Interface i 3. The corresponding reflected and transmitted. coso, t -k, r+a fields are: E,=Eo cos(, t-K, r+a where ar and at are phase constants Non-zero values of the phase constants can be interpreted as a spatial shift. 4. Maxwells Equations tell us that the tangential component of the electric field must be continuous at the interface, so we have: S×E.+S×E.=S×E.→ §×E0cos(-k)+5×E0cos(01-kr+a,) S×E0cos{(o,t-k,+a

1-8 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 4.Maxwell’s Equations tell us that the tangential component of the electric field must be continuous at the interface, so we have: Plane Waves at a Dielectric Interface ( ) ( ) ( ) t t t t i i i r r r r i r t S E t k r S E t k r S E t k r S E S E S E      =  − +  − +  − +  +  =                  cos cos cos 0 0 0 3.The corresponding reflected and transmitted fields are: ( ) ( ) t t t t t r r r r r E E t k r E E t k r     = − + = − +         cos cos 0 0 where r and t are phase constants.Non-zero values of the phase constants can be interpreted as a spatial shift

Optical fiber 第二章光导纤维的传输原理 communication 92021/2/19 nn■ Laws of Refraction Similarly we find from the second of the two equations: kF=,-a,→k-kF=-a It follows that k is also in the incident plane, and k. sin 0=k.sin. sin 0=n. sin e k=0√A=0/vn,n ue/yAo This is snell's law of refraction 1.The laws of reflection and refraction forms the basis for Geometrical optics 2 Geometrical optics also assumes collimated optical beams(rays), which are unphysical 3. Geometrical optics is nevertheless very useful for modeling a large number of optical devices and phenomena

1-9 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 Laws of Refraction Similarly we find from the second of the two equations: ( ) i t t i t t k r = k r −  k − k r = −        It follows that kt is also in the incident plane, and i i t t ni i nt t k sin  = k sin   sin  = sin  0 0 =   =  , = =    p p k v n c v This is Snell’s law of refraction. 1.The laws of reflection and refraction forms the basis for Geometrical optics 2.Geometrical optics also assumes collimated optical beams (rays), which are unphysical 3.Geometrical optics is nevertheless very useful for modeling a large number of optical devices and phenomena

Optical fiber 第二章光导纤维的传输原理 communication 02021/2/19 Lenses- Ray picture The rays are deflected at the air-lens interface The effect of due to the higher index the ray of the lens Collimated deflectio (parallel n is that optical all the beam rays pass If the lens is thin, we through consider both the focus deflections to take Center plane place at the center plane of the lens. 1. The operation of lenses can be understood by tracing individual rays through the lens 2. The rays all bend in different ways at the air-lens interface 3. The shape of the lens surfaces is chosen such that each ray passes through the focus

1-10 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 Lenses – Ray Picture The rays are deflected at the air-lens interface due to the higher index of the lens. The effect of the ray deflectio n is that all the rays pass through the focus Collimated (parallel) optical beam If the lens is thin, we consider both deflections to take place at the center plane of the lens. 1.The operation of lenses can be understood by tracing individual rays through the lens 2.The rays all bend in different ways at the air-lens interface 3.The shape of the lens surfaces is chosen such that each ray passes through the focus