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