3. (30P) The Figure 2 shows a light excitation. According to...

3. (30P) The Figure 2 shows a light excitation. According to this not scaled drawn figure; a. When the incident wave uniformly fills the cylindrical lens, what percentage of the power can be captured and guided by the fiber? (Hint: Assume a slab fiber and use geometric optics) b. What is the V number for this fiber? c. What is the highest frequency (shortest wavelength) that can be used if only a single TE or TM mode is to be guided by the slab fiber? d. What must the thickness of the cladding be in order for the field at the outside radius to be 10e-6 of that at the edge of the core? e. Find the phase constant $\beta$ in $cm^{-1}$ for the $TE_0$ mode.

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3. (30P) The Figure 2 shows a light excitation. According to this not-to-scale drawn figure: a. When the incident wave uniformly fills the cylindrical lens, what percentage of the power can be captured and guided by the fiber? (Hint: Assume a slab fiber and use geometric optics) b. What is the V number for this fiber? c. What is the highest frequency (shortest wavelength) that can be used if only a single TE or TM mode is to be guided by the slab fiber? d. What must the thickness of the cladding be in order for the field at the outside radius to be 10e-6 of that at the edge of the core? e. Find the phase constant β in cm⁻¹ for the TE mode. 5 cm Fig. 2 Cladding: n = 2.214 Core: n = 2.234 Cladding: n = 2.214 D = 2 μm 3. (30P) The Figure 2 shows a light excitation. According to this not-to-scale drawn figure, when the incident wave uniformly fills the cylindrical lens, what percentage of the power can be captured and guided by the fiber? (Hint: Assume a slab fiber and use geometric optics) b. What is the V number for this fiber? c. What is the highest frequency (shortest wavelength) that can be used if only a single TE or TM mode is to be guided by the slab fiber? d. What must the thickness of the cladding be in order for the field at the outside radius to be 10e-6 of that at the edge of the core? e. Find the phase constant β in cm⁻¹ for the TE mode. Cladding: n = 2.214 Core: n = 2.234 D = 2 μm Cladding: n = 2.214 Fig. 2

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