chapter 4

chapter 4 - THE FIBER FORUM Fiber Optic Communications...

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Click to edit Master subtitle style 5/13/10 THE FIBER FORUM Fiber Optic Communications JOSEPH C. PALAIS PRESENTED BY
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5/13/10 Joseph C. Palais 4.1 22 Chapter 4 INTEGRATED OPTIC WAVEGUIDES
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5/13/10 Joseph C. Palais 4.1 33 Section 4.1 Dielectric Slab Waveguide n3 n2 n1 d z x y Trapping of light ray in a waveguide n2 < n1 n3 < n1 θ
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5/13/10 Joseph C. Palais 4.1 44 Integrated Optics The wave is guided by total internal reflection. Why study this structure? 1. It is the basis of integrated optics. Various components can be constructed on a single substrate. 2. The waveguide shares many properties with the fiber waveguide. It is easier to analyze.
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5/13/10 Joseph C. Palais 4.1 55 Integrated Optics For complete guidance, we need > ¾ c, where 1 3 1 2 sin sin n n n n c c = = θ lower boundary upper boundary whichever yields the largest value of c is used. We also need smooth boundary surfaces.
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5/13/10 Joseph C. Palais 4.1 66 Integrated Optics MATERIALS USED Lithium niobate (LiNbO3) (1) strong electro-optic effect (2) loss â 1 dB/cm (3) used for modulator and switches
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5/13/10 Joseph C. Palais 4.1 77 INTEGRATED OPTICS Gallium Arsenide (GaAs) (1) semiconductor (2) light sources and photodetectors (3) loss + 2 dB/cm For integrated waveguides, the wave is mainly in the central thin film (n1), but evanescent tails reach into the two substrate regions (n2 and n3).
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5/13/10 Joseph C. Palais 4.1 88 INTEGRATED OPTICS Unsymmetrical Waveguide n3 = 1 (air) and n2 not 1. Symmetrical Waveguide n2 = n3 The symmetrical waveguide is analogous to the fiber optic waveguide.
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Click to edit Master subtitle style 5/13/10 THE FIBER FORUM Fiber Optic JOSEPH C. PALAIS PRESENTED BY
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5/13/10 Joseph C. Palais 4.2 1010 Section 4.2 MODES IN THE SYMMETRIC-SLAB WAVEGUIDE n2 n2 n1 n1 > n2 Range of Z for bound waves: ° 90 θ c
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5/13/10 Joseph C. Palais 4.2 1111 Mode in The Symmetric-Slab Waveguide For an axial ray, 7 = 90 ° and neff = n1 For a critical angle ray [ = &c and 2 1 2 1 1 sin n n n n n n c eff = = θ The range of neff is now (4.9) 1 2 n n n eff Define the effective index of refraction: sin 1 n n eff
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5/13/10 Joseph C. Palais 4.2 1212 4.2.1 M ode Condition The tw o boundaries (upper and low er) form a cavit y. A cavity is resonant w hen t he round trip phase shift is 2 m (w here m = 1,2,3 …). Expressing this m at hem atically, w e get = m 2ª (4.10)
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5/13/10 Joseph C. Palais 4.2 1313 Mode Condition n& is the phase shift for one complete cycle of the zigzag path. It includes the phase shift at the two totally reflected surfaces. Equation (4.10) can be satisfied (for a given &) for several distinct ray angles (between a c and 90º). The waves traveling at these allowed angles are the modes of the waveguide. Waves traveling at other angles will interfere destructively and will not propagate.
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5/13/10 Joseph C. Palais 4.2 1414 4.2.2 and 4.2.3 TE and TM Polarization and TE Mode Chart Derivation of fields in the symmetric waveguide: n n E d n 2 n 2 n 1 z y 1 2 0 2 0 2 1 0 1 k k n k k n μ = = = = TE polarization (Transverse Electric) This is the same as perpendicular polarization (s).
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chapter 4 - THE FIBER FORUM Fiber Optic Communications...

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