Question

plz solve Exercise 13.1 and you might need Example 13.1 that is provided.

Exercise 13.1 In Example 13.1, assume the propagation is from material (2) into material (1) and calculate: (a) The reflection and transmission coefficients at the interface. (b) The amplitude of the electric and magnetic field intensities at a distance 1 km from the interface in material (1) assuming the amplitude of the incident electric field intensity in material (2) at the interface equals E2. Use the same properties and assumptions as in Example 13.1. where (0) indicates that this is at the interface. At d - 10 km, the amplitude is -1.15x10-3x10 The electric field intensity has been reduced by about a factor of 10 in 10 km. The magnetic field intensity at the same location is 2 x 1.115 x 10-5 2E2 E2 En 5.915 x 10-8E 377 The time-averaged power across the interface may be written from the Poynting theorem (see Example 12.9) EEE(TE) 2712n1 272 or Using the reflection and transmission coefficients and the intrinsic impedances in (b) we get 188.5-188.5 × 0.1012-153.91 × 1.1012 186.57-186.57 → The equality shows that power is conserved across the interface. ωμ2 The transmission and reflection coefficients are calculated in terms of the intrinsic impedances. Using μι-μ2 = 0, we get from Eqs. (13.23) and (13.24) x10s 0.101 43.972 × 106 2P 1.101 꺼 + ½ P2 +pi 21.986 × 10° + 17.952 × 10° Note that since the reflection coefficient is positive, the transmission coefficient must be larger than 1, as can be seen from Eq. (13.21) The incident electric field intensity in fiber (1) is known. We will take this as Eii. First, we calculate the electric field intensity across the interface and then, using the attenuation in material (2), calculate the amplitude of the electric field intensity at a distance of 10 km. The amplitude of the electric field intensity in material (2) is Example 13.1 Application: Optical Fiber Connectors Two optical fibers are connected through a connector to form an interface as shown in Figure 13.3. In optical fibers, the attenuation is indicated in dB/km. Fiber (1) is rated as 1 dB/km (a good fiber) and the second as 10 dB/km. The source of light is in free space (not shown), at a wavelength of 700 nm (a red laser or light emitting diode). Assume both fibers are low-loss dielectrics (which in practice they are; conductivity of glass is about 101 S/m) and that propagation is from fiber (1) into fiber (2). Calculate: (a) The reflection and transmission coefficients at the interface. (b) The amplitude of the electric and magnetic field intensities at d- 10 km from the interface, in material (2), assuming the amplitude of the incident electric field intensity in material (1) is known at the interface as Eii- (c) Show that power is conserved across the interface, that is, that the transmitted time-averaged power density must equal the incident time-averaged power density minus the reflected time-averaged power density.

Answer 1

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