Introduzione alle fibre ottiche Edoardo Milotti Corso di Fondamenti Fisici di Tecnologia Moderna A. A. 2019-20
1.2 Bit rate basso 1.0 Larghezza di banda piccola 0.8 0.6 0.4 0.2 0.0 0 2 4 6 8 10 1.2 Bit rate alto 1.0 Larghezza di banda grande 0.8 0.6 0.4 0.2 0.0 0 2 4 6 8 10
µ Figure 7-3 A typical fiber optic communication system: T, transmitter; C, connector; S, splice; R, repeater; D, detector Le fibre ottiche permettono di stabilire canali di telecomunicazione a larga banda
Problema: un anello misterioso …
n 1 > 1 Riflessione totale: se non tutti gli angoli di rifrazione n 2 sono possibili, infatti sin θ 2 = n 1 sin θ 1 n 2 allora esiste un angolo limite tale che (lim) = 1 (lim) = arcsin n 2 n 1 sin θ 1 θ 1 n 2 n 1
(lim) = arcsin n 2 θ 1 n 1 nel caso dell � interfaccia aria-acqua n 1 ≈ 1.33, n 2 ≈ 1, allora (lim) ≈ 48 ° .75 θ 1
Figure 7-2 Schematic of the photophone invented by Bell. In this system, sunlight was modulated by a vibrating diaphragm and transmitted through a distance of about 200 meters in air to a receiver containing a selenium cell connected to the earphone. vedi: Ghatak and Thyagarajan, "Optical Waveguides and Fibers", Fundamentals of Photonics, Module 1.7 https://spie.org/publications/fundamentals-of-photonics-modules
= < = > < ∆ ∆ ≡ ∆ = < + = > ∆ = ≈ ≈ <latexit sha1_base64="gETK9S7yHouSkdweMNEtN+Jq7YQ=">A CKHicbVDLTgIxFG3xhfgAdOm kZi4kcygRpdENy4xkUcCk0mnU6Ch0 7ajgkhfIlb3fg17gxbv8TOMAsBT3KTk3PuKyeIOdPGcRawsLW9s7tX3C8dHB4dlyvVk46WiSK0TS XqhdgT kTtG2Y4bQXK4qjgN uMHlM/e4rVZpJ8WKmMfUiPBJsyAg2VvIrZeG76AoJv4EGnCPXr9ScupMBbRI3JzWQo+VXIRyEkiQRFYZwrHXfdWLjzbAyjHA6Lw0STWNMJnhE+5YKHFHtzbLP5+jCKiEaSmVLGJSpfydmONJ6GgW2M8JmrNe9VPzP6ydmeO/NmIgTQwVZHhomHBmJ0h QyBQlhk8twUQx+ysiY6w MTaslSvpbiMl13YJDkOW5oY5SmWU6aWSDc1dj2iTdBp197p+ 3xTaz7k8RXBGTgHl8AFd6AJnkALtAEBCXgD7+ADfsIv+A0Xy9YCzGdOwQrgzy8H/aN </latexit> <latexit sha1_base64="7zKRgrbI0v BZwZbIbeWkvBl/dk=">A CPHicbZDLbhMxFIbtUmgJhSZ0ycZqhMSm0cxAVTZIVcuCZ DIRcpNZzye1KrH tlnkKJRHoCn6b d9D3Yd4e67RpPkgVJOJKl3/+52V+cK+kwCH7TnWe7z1/s7b+svTp4/eaw3njbda wXHS4Ucb2Y3BCS 06KFGJfm4FZLESvfj6s r3fgr pNE/cJaLUQZTLVPJAb01qTeHX4VCYF/YMLXASz0Jx E7YXoSjaN5Gfn73FcFrWARbFuEK9Ekq2hPGpQOE8OLTGjkCpwbhEGOoxIsSq7EvDYsnMiBX8NUDLzUkAk3Khe/mbP3 klYaqw/GtnC/bejhMy5WRb7ygzwym3mKvN/uUGB6edRKXVeoNB8uSgtFEPDKjQskVZwVDMvgFvp38r4FXgq6AGubalmozHK+SGQJLJiCYpVNlv4tZqHFm4i2hbdqBV+bJ1+/9Q8v1jh2yfvyDH5QEJyRs7JN9ImHcLJL3JDbskdvacP9A9 XJbu0FXPEVkL+vQXGLyraw= </latexit> < = < n n for r a ∆ 1 = > n n for r a 2 ∆ ≡ < ∆ (a) ∆ 2 + ∆ ≡ ( n n )( n – n ) ( n – n ) ( n – n ) ∆ = n 2 1 − n 2 ∆ = 1 2 1 2 ≈ 1 2 ≈ 1 2 2 n 1 � n 2 ⌧ 1 2 2 n n n 2 n 1 1 1 2 ∆ (questo è un parametro importante per caratterizzare la fibra ) + ∆ = ≈ ≈
= < = > < ∆ ∆ ≡ ∆ + ∆ = ≈ ≈ For a typical (multimode) fiber, a ≈ 25 µ m, n 2 ≈ 1.45 (pure silica), and ∆ ≈ 0.01, giving a core index of n 1 ≈ 1.465. The cladding is usually pure silica while the core is usually silica doped with germanium. Doping by germanium results in a typical increase of refractive index from n 2 to n 1 . Now, for a ray entering the fiber core at its end, if the angle of incidence φ at the internal core- φ
= < µ = > < ∆ µ ∆ ≡ ∆ + µ ∆ = ≈ ≈ θ θ θ = θ <latexit sha1_base64="zSZegf vqR6R5KxMxP+u37vtY3g=">A <latexit sha1_base64="7ZNthg/FkbsE8khO+yqONEA4Qdo=">A CGnicbVA5T8MwGLXLVcLVwshiUSExVQmHYKxgYSyCHlIbVY7jtFYdO7IdpKrqT2CFhV/DhlhZ+Dc4aQba8iRLT+9 l1+QcKaN6/7A0tr6xuZWedvZ2d3bP6hUD9taporQFpFcqm6ANeVM0JZh tNuoi OA047wfgu8zvPVGkmxZOZJNSP8VCwiBFsrPQoBu6gUnPrbg60SryC1ECB5qAKYT+UJI2pMIRjrXuemxh/ipVh NOZ0 81T AZ4yHtWSpwTLU/zW+doVOrhCiSyj5hUK7+7ZjiWOtJHNjKGJuRXvYy8T+vl5roxp8ykaSGCjJfFKUcGYmyj6OQKUoMn1iCiWL2VkRGWGFibDwLW7LZRkqu7RAchixLCnOUySjXHceG5i1HtEra53Xvon71cFlr3BbxlcExOAFnwAPXoAHuQRO0A FD8AJewRt8hx/wE37NS0uw6DkC 4Dfv3YJn5I=</latexit> <latexit sha1_base64="X6mfwa7wbHMFBz8 B7axbuI/omU=">A CGHicbVA5T8MwGLXLVcrVwshiUSExVQmHYKxgYWwlekhtVDmO01p17Mh2kKqov4AVFn4NG2Jl49/gpBloy5MsPb3 X 5+zJk2jvMDSxubW9s75d3K3v7B4VG1dtzVMlGEdojkUvV9rClngnYM 5z2Y0Vx5HPa86cPmd97pkozKZ7MLKZehMeChYxgY6U2G1XrTsPJgdaJW5A6KNAa1SAcBpIkERWGcKz1wHVi46VYGUY4nVeGiaYxJlM8pgNLBY6o9tL80jk6t0qAQqnsEwbl6t+OFEdazyLfVkbYTPSql4n/eYPEhHdeykScGCrIYlGYcGQkyr6NAqYoMXxmCSaK2VsRmWCFibHhLG3JZhspubZDcBCwLCfMUSajXK9UbGjuakTrpHvZcK8aN+3revO+iK8MTsEZuA u AVN8AhaoAMIoOAFvI 3+A4/4Cf8WpSWYNFzApYAv38BLoWe6g= </latexit> CmnicbVFNb9QwEHXCV1kobE qBziMWCGVQ7dJAJUDlarCAcSlSN2 0ia7chxn16pjB3tSsYpy4GfyC/gbOMki0ZaRbD29 2bGek5LKSwGwS/Pv3X7zt17G/cHDx5uPno83HpyanVlGJ8wLbU5T6nlUig+QYGSn5eG0yKV/Cy9+NjqZ5fcWKHVCa5KnhR0oUQuGEVHzYc/YysUCPgAcW4oq9U8bNwVNB LnuMUQtjt4c5fQ9R0rtiIxRJfzyLoUTKrw73I9dGyNPoHxPa7wdbpHLvg2mZOPHAg7JUo/sQl0mY+HAXjoCu4CcI1GJF1Hc+3PC/ONKsKrpBJau0 DEpMampQM mbQVxZXlJ2QRd86qCiBbdJ3WXVwCvHZJBr4 5C6Nh/O2paWLsqUucsKC7tda0l/6dNK8zfJ7VQZYVcsX5RXklADW3wkAnDGcqVA5QZ4d4KbEldpOi+58qWdjZqLa0bQrNMtD9FJbQ0dPxg4EILr0d0E5xG4/DN+N23t6PDo3V8G+Q5eUl2SEj2ySH5TI7JhD y29v0tr1n/gv/yP/if+2tvrfueUqulH/yB2t3yJ0=</latexit> θ = L' apertura numerica φ sin i n θ = 1 i φ = θ > φ sin n 0 > n φ = θ 2 sin ( cos ) (riflessione totale interna) θ = θ φ n n 0 1 L O G I F 12 θ = θ 2 φ = θ > M P n J θ < 2 sin 1 – H K M P N Q n 1 θ = θ θ < ◆ 2 # 1 / 2 " ✓ n 2 √ sin i < n 1 q n 2 1 − n 2 2 ∆ 1 − 2 = n 1 θ < ≈ n 0 n 1
CVnicbZDLSgMxFIYz473eqi7dBIugmzLjBd0I3hauRMGq0CnlTCbV0EwyJmfEMvRpfBq3utGXETO14PVA4Oc7t5w/zqSwGARvnj8yOjY+MTlVmZ6ZnZuvLixeWp0bxhtMS2 uY7BcCsUbKFDy68xwSGPJr+LuUZm/u fGCq0usJfxVgo3SnQEA3SoXd2LUsBbkxanB326RyMwzAq15uhD5AQV61+UqnY 2TuDxUZ0zCVCv12tBfVgEPSvCIeiRoZx1l7wvCjRLE+5QibB2mY ZNgqwKBgkvcrUW5 BqwLN7zp IKU21YxuLNPVx1JaEcb9xTSAf3eU BqbS+NXWV5lf2dK+F/uWaOnd1WIVSWI1fsc1EnlxQ1LU2jiTCcoew5AcwI91fKbsEAQ2ftjy3lbNRaWjcEk SULoOkJaYDXqk408LfFv0Vlxv1cLO+fb5V2z8c2jdJlskKWSMh2SH75ISckQZh5JE8kWfy4r167/6YP/FZ6nvDniXyI/zqB2 dtAE=</latexit> <latexit sha1_base64="9AI53p8x5fI7VjPspLEjybTka+Q=">A CmnicbVFNb9QwEHXCV1kobE qBziMWCGVQ7dJAJUDlarCAcSlSN2 0ia7chxn16pjB3tSsYpy4GfyC/gbOMki0ZaRbD29 2bGek5LKSwGwS/Pv3X7zt17G/cHDx5uPno83HpyanVlGJ8wLbU5T6nlUig+QYGSn5eG0yKV/Cy9+NjqZ5fcWKHVCa5KnhR0oUQuGEVHzYc/YysUCPgAcW4oq9U8bNwVNB LnuMUQtjt4c5fQ9R0rtiIxRJfzyLoUTKrw73I9dGyNPoHxPa7wdbpHLvg2mZOPHAg7JUo/sQl0mY+HAXjoCu4CcI1GJF1Hc+3PC/ONKsKrpBJau0 DEpMampQM mbQVxZXlJ2QRd86qCiBbdJ3WXVwCvHZJBr4 5C6Nh/O2paWLsqUucsKC7tda0l/6dNK8zfJ7VQZYVcsX5RXklADW3wkAnDGcqVA5QZ4d4KbEldpOi+58qWdjZqLa0bQrNMtD9FJbQ0dPxg4EILr0d0E5xG4/DN+N23t6PDo3V8G+Q5eUl2SEj2ySH5TI7JhD y29v0tr1n/gv/yP/if+2tvrfueUqulH/yB2t3yJ0=</latexit> <latexit sha1_base64="7ZNthg/FkbsE8khO+yqONEA4Qdo=">A = = ∆ ◆ 2 # 1 / 2 " ✓ n 2 √ sin i < n 1 q n 2 1 − n 2 2 ∆ 1 − 2 = n 1 ≈ n 0 n 1 = = = ∆ √ NA = arcsin(max sin i ) = arcsin n 1 2 ∆ For a typical step-index (multimode) fiber with n 1 ≈ 1.45 and ∆ ≈ 0.01, we get m = ∆ = × = sin i n 1 2 1 45 2 . ( . 0 01 ) 0 205 . so that i m ≈ 12 ° . Thus, all light entering the fiber must be within a cone of half-angle 12°. α α ≈
λ λ λ Attenuazione nelle fibre ottiche Figure 7-10 Typical wavelength dependence of attenuation for a silica fiber. Notice that the lowest attenuation occurs at 1550 nm [adapted from Miya, Hasaka, and Miyashita].
Example 7-3 Calculation of losses using the dB scale become easy. For example, if we have a 40-km fiber link (with a loss of 0.4 dB/km) having 3 connectors in its path and if each connector has a loss of 1.8 dB, the total loss will be the sum of all the losses in dB; or 0.4 dB/km × 40 km + 3 × 1.8 dB = 21.4 dB. Example 7-4 Let us assume that the input power of a 5-mW laser decreases to 30 µ W after traversing through 40 km of an optical fiber. Using Equation 7-12, attenuation of the fiber in dB/km is therefore [10 log (166.7)]/40 ≈ 0.56 dB/km.
µ ≈ Dispersione degli impulsi nelle fibre ottiche 1. Different rays take different times to propagate through a given length of the fiber. We will discuss this for a step-index multimode fiber and for a parabolic-index fiber in this and the following sections. In the language of wave optics, this is known as intermodal dispersion because it arises due to different modes traveling with different speeds. 4 2. Any given light source emits over a range of wavelengths, and, because of the intrinsic property of the material of the fiber, different wavelengths take different amounts of time to propagate along the same path. This is known as material dispersion and will be discussed in Section IX. 3. Apart from intermodal and material dispersions, there is yet another mechanism—referred to as waveguide dispersion and important only in single-mode fibers. We will briefly discuss this in Section XI. In the fiber shown in Figure 7-7, the rays making larger angles with the axis (those shown as
Figure 7-11 Pulses separated by 100 ns at the input end would be resolvable at the output end of 1 km of the fiber. The same pulses would not be resolvable at the output end of 2 km of the same fiber. θ + θ = = = θ = θ θ θ θ θ θ =
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