Optical fiber 第二章光导纤维的传输原理 communication 112021/2/19 Lenses- Wave Picture Collimated The lens is thinner on the periphery, so the (parallel)incident the center part, resulting in curved phase front g peripheral parts of the beam are delay less tha optical beam The curvature of the wavefronts focus the beam to a point 1. we can also consider the wavefronts of the light passing through the lens to understand its operation 2. The lens is delaying the center part of the beam with respect to the sides such that all parts of the beam arrive at the focus in phase 3.In other words, all parts of the beam are interfering constructively at the focus, which leads to high intensity at this point
1-11 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 Lenses – Wave Picture Collimated (parallel) incident optical beam The lens is thinner on the periphery, so the peripheral parts of the beam are delay less than the center part, resulting in curved phase fronts The curvature of the wavefronts focus the beam to a point 1.we can also consider the wavefronts of the light passing through the lens to understand its operation 2.The lens is delaying the center part of the beam with respect to the sides such that all parts of the beam arrive at the focus in phase 3.In other words, all parts of the beam are interfering constructively at the focus, which leads to high intensity at this point
Optical fiber 第二章光导纤维的传输原理 communication 122021/2/19 Diffraction limits resolution In the ray-optics(geometrical- In reality, diffraction limits optics)approximation, the focus is the focusing ability of the lens a pon 1. Ray optics is a useful approximation for many considerations but the fact that it does not consider diffraction 2.The main one is that it predicts that a gives it some major lens focuses light to a mathematical point flaws 3.This is not possible(even for a perfect lens) with wave phenomena of finite wavelength 4.The central spot of the focus of a perfect, uniformly illuminated lens is d=2.44.f/D, where n is the wavelength, f is the focal length, and d the lens diameter
1-12 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 Diffraction limits resolution In the ray-optics (geometricaloptics) approximation, the focus is a point In reality, diffraction limits the focusing ability of the lens 1.Ray optics is a useful approximation for many considerations, but the fact that it does not consider diffraction gives it some major flaws 2.The main one is that it predicts that a lens focuses light to a mathematical point 3.This is not possible (even for a perfect lens) with wave phenomena of finite wavelength 4.The central spot of the focus of a perfect, uniformly illuminated lens is d=2.44•λ•f/D, where λ is the wavelength, f is the focal length, and D the lens diameter
Optical fiber 第二章光导纤维的传输原理 communication 132021/2/19 i Ray Tracing in Ideal Lenses Focal plane Central rays(rays that pass through the center of the let ns To trace rays through ideal lenses we need only two simple facts: 1. Each ray goes through the focal plane at the same point as its parallel central ray 2. Central rays are not deflected This is very useful for first order analysis of lens systems
1-13 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 Ray Tracing in Ideal Lenses •To trace rays through ideal lenses we need only two simple facts: 1.Each ray goes through the focal plane at the same point as its parallel central ray 2.Central rays are not deflected •This is very useful for first order analysis of lens systems
Optical fiber communication 第二章光导纤维的传输原理 142021/2/19 Imaging Focal plane Image Object Thin lens equation: 1/a+1/b=1/f Magnification: b/a .a<f=> diverging beams, no imaging a=f=> collimation f<a<2f=> Imaging according to the lens equation with M>l a=2f=> Imaging according to the lens equation with M=l ea>2f=> Imaging according to the lens equation with M<l
1-14 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 Imaging •Thin lens equation: 1/a +1/b = 1/f •Magnification: b/a •a<f => diverging beams, no imaging •a=f => collimation •f<a<2f => Imaging according to the lens equation with M>1 •a=2f => Imaging according to the lens equation with M=1 •a>2f => Imaging according to the lens equation with M<1
第二章光导纤维的传输原理 Optical fiber com Fresnel law A:E= Eoi exp i(风,)B:反射系数RE=9(24) jk (k,) 传递系数TT==7exp(2) 模表示强度,幅角表示相位 E,E0,E是入射光,反射光和透射光的矢量复数振幅 C:水平偏振浪TE横电浪 n, cos0-n cos 0 RT n,cos0,+n, cos 2n, Cos B, cos0,+n2 cos 0, x+H.%
1-15 Copyright Wang Yan 2021/2/19 Optical fiber communications 第二章 光导纤维的传输原理 Fresnel Law ( ) ( ) E E ( jk r) E E jk r E E jk r t t t r r r i i i = − = − = − exp ~ ~ exp ~ ~ exp ~ ~ 0 0 0 E0i E0r E0t ~ , ~ , ~ A: 是入射光，反射光和透射光的矢量复数振幅 反射系数R 传递系数T ( ) ( ) 2 0 0 1 0 0 ~ exp 2 ~ ~ exp 2 ~ T j E E T R j E E R i t i r = = B: = = 模表示强度，幅角表示相位 C:水平偏振波 TE横电波 Hi Hr Ht Ei Er Et i t r n1 n2 x z i k r k t k i t i t i t n n n T n n n n R cos cos 2 cos cos cos cos cos 1 2 1 1 1 2 1 2 + = + − =