1. The bandwidth of a single telephone channel is 4 kHz. In a
particular telephone system, the transmission rate is 44.7 Mbps. In an
actual system, some channels are devoted to housekeeping functions such
as synchronization. In this system, 26 channels are so devoted. How many
independent telephone channels can the system accommodate? Get solution
2. Determine the limit to the number of TV station channels that could transmit on a single optical beam of 1.55 μm wavelength ifa. The entire bandwidth (Δν = ν) of the signal was used.b. A bandwidth of 4 × 1012 Hz is used. (This corresponds to a typical DWDM system.) Get solution
3. a. Referring to Figure 10-3, show that, for a guided ray traveling at the steepest angle relative to the fiber axis, the skip distance Ls can be expressed by ...b. How many reflections occur per meter for such a ray in a step-index fiber with n1 = 1.460, n2= 1.457, and d = 50 μm? Get solution
4. Refractive indices for a step-index fiber are 1.52 for the core and 1.41 for the cladding. Determine (a) the critical angle; (b) the numerical aperture; (c) the maximum incidence angle θm for light that is totally internally reflected. Get solution
5. A step-index fiber 0.0025 in. in diameter has a core of index 1.53 and a cladding of index 1.39. Determine (a) the numerical aperture of the fiber; (b) the acceptance angle (or maximum entrance cone angle); (c) the number of reflections in 3 ft of fiber for a ray at the maximum entrance angle, and for one at half this angle. Get solution
6. a. Show that the actual distance xs a ray travels during one skip distance is given by ...where θ is the entrance angle and the fiber is used in air.b. Show that the actual total distance xt a ray with entrance angle θ travels over a total length L of fiber is given by ...c. Determine xs,Ls, and xt for a m-long fiber of diameter 50 μm, core index of 1.50, and a ray entrance angle of θ = 10°. Get solution
7. How many modes can propagate in a step-index fiber with n1 = 1.461 and n2= 1.456 at 850 nm? The core radius is 20 μm. Get solution
8. Determine the maximum core radius of a glass fiber so that it supports only one mode at 1.25 μm wavelength, for which n1= 1.460 and n2 = 1.457. Get solution
9. Consider a slab waveguide of AlGaAs for which n1 = 3.60 and n2 = 3.55. How many independent modes can propagate in this waveguide if d = 5λ and d = 50λ? (See Figure 10-4.) Get solution
10. A signal of power 5 μW exists just inside the entrance of a fiber 100 m long. The power just inside the fiber exit is only 1 μW. What is the absorption coefficient of the fiber in db/km? Get solution
11. An optic-fiber cable 3 km long is made up of three 1-km lengths, spliced together. Each length has a 5-db loss and each splice contributes a 1-db loss. If the input power is 4 mW, what is the output power? Get solution
12. The attenuation of a 1-km length of RG-19/U coaxial cable is about 12 db at 50 MHz. Suppose the input power to the cable is 10 mW and the receiver sensitivity is 1 μW. How long can the coaxial cable be under these conditions? If optical fiber is used instead, with a loss rated at 4 db/km, how long can the transmission line be? Get solution
13. A Ge-doped silica fiber has an attenuation loss of 1.2 db/km due to Rayleigh scattering alone when light of wavelength 0.90 μm is used. Determine the attenuation loss at 1.55 μm. Get solution
14. a. Show that the attenuation db/km is given by αdb= (10 db/km) log10(l − f)where f is the overall fractional power loss from input to output over a 1-km-long fiber.b. Determine the attenuation in db/km for fibers having an overall fractional power loss of 25%, 75%, 90%, and 99%. Get solution
15. Determine (a) the length and (b) transit time for the longest and shortest trajectories in a step-index fiber of length 1 km having a core index of 1.46 and a cladding index of 1.45. (See Figure 10-9.) Get solution
16. Evaluate modal distortion in a fiber by calculating the difference in transit time through a 1-km fiber required by an axial ray and a ray entering at the maximum entrance angle of 35°. Assume a fused silica core index of 1.446. What is the maximum frequency of input pulses that produce nonoverlapping pulses on output due to this case of modal dispersion? Get solution
18. Calculate the group delay between the fastest and slowest modes in a 1-km-long step-index fiber with n1 = 1.46 and a relative index difference Δ = (n1 − n2)/n2 = 0.003, using a light source at wavelength 0.9 μm. Get solution
19. Plot the refractive index profile for a GRIN fiber of radius 50 μm and with n1 = 1.5 and Δ = 0.01. Do this for the profile parameter αp = 2 and repeat for αp = 10. Get solution
20. Calculate the delay due to modal dispersion in a 1-km GRIN fiber with αp = 2. The maximum core index is 1.46 and the cladding index is 1.44. By what factor is this fiber an improvement over a step-index fiber with n1 = 1.46 and n2 = 1.44? Get solution
21. Equation (10-19) allows calculation of bandwidth for distances less than the equilibrium length of fiber (see footnote 10). Assume an equilibrium length of 1 km and determine for this fiber length the 3-db bandwidth of a step-index multimode fiber whose pulse broadening is given by 20 ns/km. Get solution
22. Determine the material dispersion in a 1-km length of fused silica fiber when the light source is (a) a LED centered at 820 nm with a spectral width of 40 nm and (b) a LD centered at 820 nm with a spectral width of 4 nm. Get solution
23. The total delay time δτ due to both modal distortion and material dispersion is given by (δτ)2= (δτmod)2 + (δτmat)2Determine the total delay time in a 1-km fiber for which n1 = 1.46, Δ = 1%, λ = 820 nm, and Δλ = 40 nm. Get solution
24. Waveguide dispersion is measured in a silica fiber at various wavelengths using laser diode sources with a spectral width of 2 nm. The results are λ(μm)δ(τ/L)(ps/km)0.701.880.905.021.107.081.408.401.708.80a. Plot the waveguide parameter M′ versus λ in the range 0.70 to 1.70 μm.b. Determine the waveguide dispersion in ps/km at λ = 1.27 and 1.55 μm for a source with a spectral width of 1 nm. Get solution
25. Compare pulse broadening for a silica fiber due to the three principal causes—modal distortion, material dispersion, and waveguide dispersion—in a step-index fiber. The core index is 1.470 and the cladding index is 1.455 at λ = 1 μm. Assume a LED source with a spectral width of 25 nm. The values of the parameters M and M′ are 43 ps/nm-km and 3 ps/nm-km, respectively.a. Determine each separately by calculating δτ for a 1-km length of fiber.b. Determine an overall broadening δτ for a 1-km length of fiber, using (δτ)2= (δτmod)2 + (δτmat)2 + (δτwg)2 Get solution
26. Consider the Mach-Zehnder interferometer depicted in Figure 10-16a. Take the transmission coefficients of the beam splitters to be real. Find the irradiance of the light exiting each of the output ports of the interferometer and show that the sum of these output irradiances is equal to the input irradiance. Get solution
27. a. Find the difference in frequency between two wavelength channels near 1550 nm that differ in wavelength by 0.8 nm.b. Find the frequency bandwidth Δν of a DWDM system utilizing 40 wavelength channels near 1550 nm if the channels are separated by 0.8 nm. Get solution
28. Consider a Mach-Zehnder fiber demultiplexer depicted in Figure 10-16b. Assume that n = 1.5000.a. Find a difference in path length between the two arms of the fiber interferometer ΔL that will efficiently demultiplex a signal containing wavelength components λ1 = 1550.8 nm and λ2= 1550.0 nm. Assume that the λ1 component exits through Output 1. (Take care to ensure that your solution nearly satisfies both Eqs. (21) and (22) with integer m.)b. If the path length difference is as found from part (a), through which output port would light of wavelength λ3 = 1551.6 nm exit the interferometer?c. If the path length difference is as found from part (a), find the ratio of the irradiances exiting through the two output ports if the input signal has a wavelength of 1550.4 nm. Get solution
2. Determine the limit to the number of TV station channels that could transmit on a single optical beam of 1.55 μm wavelength ifa. The entire bandwidth (Δν = ν) of the signal was used.b. A bandwidth of 4 × 1012 Hz is used. (This corresponds to a typical DWDM system.) Get solution
3. a. Referring to Figure 10-3, show that, for a guided ray traveling at the steepest angle relative to the fiber axis, the skip distance Ls can be expressed by ...b. How many reflections occur per meter for such a ray in a step-index fiber with n1 = 1.460, n2= 1.457, and d = 50 μm? Get solution
4. Refractive indices for a step-index fiber are 1.52 for the core and 1.41 for the cladding. Determine (a) the critical angle; (b) the numerical aperture; (c) the maximum incidence angle θm for light that is totally internally reflected. Get solution
5. A step-index fiber 0.0025 in. in diameter has a core of index 1.53 and a cladding of index 1.39. Determine (a) the numerical aperture of the fiber; (b) the acceptance angle (or maximum entrance cone angle); (c) the number of reflections in 3 ft of fiber for a ray at the maximum entrance angle, and for one at half this angle. Get solution
6. a. Show that the actual distance xs a ray travels during one skip distance is given by ...where θ is the entrance angle and the fiber is used in air.b. Show that the actual total distance xt a ray with entrance angle θ travels over a total length L of fiber is given by ...c. Determine xs,Ls, and xt for a m-long fiber of diameter 50 μm, core index of 1.50, and a ray entrance angle of θ = 10°. Get solution
7. How many modes can propagate in a step-index fiber with n1 = 1.461 and n2= 1.456 at 850 nm? The core radius is 20 μm. Get solution
8. Determine the maximum core radius of a glass fiber so that it supports only one mode at 1.25 μm wavelength, for which n1= 1.460 and n2 = 1.457. Get solution
9. Consider a slab waveguide of AlGaAs for which n1 = 3.60 and n2 = 3.55. How many independent modes can propagate in this waveguide if d = 5λ and d = 50λ? (See Figure 10-4.) Get solution
10. A signal of power 5 μW exists just inside the entrance of a fiber 100 m long. The power just inside the fiber exit is only 1 μW. What is the absorption coefficient of the fiber in db/km? Get solution
11. An optic-fiber cable 3 km long is made up of three 1-km lengths, spliced together. Each length has a 5-db loss and each splice contributes a 1-db loss. If the input power is 4 mW, what is the output power? Get solution
12. The attenuation of a 1-km length of RG-19/U coaxial cable is about 12 db at 50 MHz. Suppose the input power to the cable is 10 mW and the receiver sensitivity is 1 μW. How long can the coaxial cable be under these conditions? If optical fiber is used instead, with a loss rated at 4 db/km, how long can the transmission line be? Get solution
13. A Ge-doped silica fiber has an attenuation loss of 1.2 db/km due to Rayleigh scattering alone when light of wavelength 0.90 μm is used. Determine the attenuation loss at 1.55 μm. Get solution
14. a. Show that the attenuation db/km is given by αdb= (10 db/km) log10(l − f)where f is the overall fractional power loss from input to output over a 1-km-long fiber.b. Determine the attenuation in db/km for fibers having an overall fractional power loss of 25%, 75%, 90%, and 99%. Get solution
15. Determine (a) the length and (b) transit time for the longest and shortest trajectories in a step-index fiber of length 1 km having a core index of 1.46 and a cladding index of 1.45. (See Figure 10-9.) Get solution
16. Evaluate modal distortion in a fiber by calculating the difference in transit time through a 1-km fiber required by an axial ray and a ray entering at the maximum entrance angle of 35°. Assume a fused silica core index of 1.446. What is the maximum frequency of input pulses that produce nonoverlapping pulses on output due to this case of modal dispersion? Get solution
18. Calculate the group delay between the fastest and slowest modes in a 1-km-long step-index fiber with n1 = 1.46 and a relative index difference Δ = (n1 − n2)/n2 = 0.003, using a light source at wavelength 0.9 μm. Get solution
19. Plot the refractive index profile for a GRIN fiber of radius 50 μm and with n1 = 1.5 and Δ = 0.01. Do this for the profile parameter αp = 2 and repeat for αp = 10. Get solution
20. Calculate the delay due to modal dispersion in a 1-km GRIN fiber with αp = 2. The maximum core index is 1.46 and the cladding index is 1.44. By what factor is this fiber an improvement over a step-index fiber with n1 = 1.46 and n2 = 1.44? Get solution
21. Equation (10-19) allows calculation of bandwidth for distances less than the equilibrium length of fiber (see footnote 10). Assume an equilibrium length of 1 km and determine for this fiber length the 3-db bandwidth of a step-index multimode fiber whose pulse broadening is given by 20 ns/km. Get solution
22. Determine the material dispersion in a 1-km length of fused silica fiber when the light source is (a) a LED centered at 820 nm with a spectral width of 40 nm and (b) a LD centered at 820 nm with a spectral width of 4 nm. Get solution
23. The total delay time δτ due to both modal distortion and material dispersion is given by (δτ)2= (δτmod)2 + (δτmat)2Determine the total delay time in a 1-km fiber for which n1 = 1.46, Δ = 1%, λ = 820 nm, and Δλ = 40 nm. Get solution
24. Waveguide dispersion is measured in a silica fiber at various wavelengths using laser diode sources with a spectral width of 2 nm. The results are λ(μm)δ(τ/L)(ps/km)0.701.880.905.021.107.081.408.401.708.80a. Plot the waveguide parameter M′ versus λ in the range 0.70 to 1.70 μm.b. Determine the waveguide dispersion in ps/km at λ = 1.27 and 1.55 μm for a source with a spectral width of 1 nm. Get solution
25. Compare pulse broadening for a silica fiber due to the three principal causes—modal distortion, material dispersion, and waveguide dispersion—in a step-index fiber. The core index is 1.470 and the cladding index is 1.455 at λ = 1 μm. Assume a LED source with a spectral width of 25 nm. The values of the parameters M and M′ are 43 ps/nm-km and 3 ps/nm-km, respectively.a. Determine each separately by calculating δτ for a 1-km length of fiber.b. Determine an overall broadening δτ for a 1-km length of fiber, using (δτ)2= (δτmod)2 + (δτmat)2 + (δτwg)2 Get solution
26. Consider the Mach-Zehnder interferometer depicted in Figure 10-16a. Take the transmission coefficients of the beam splitters to be real. Find the irradiance of the light exiting each of the output ports of the interferometer and show that the sum of these output irradiances is equal to the input irradiance. Get solution
27. a. Find the difference in frequency between two wavelength channels near 1550 nm that differ in wavelength by 0.8 nm.b. Find the frequency bandwidth Δν of a DWDM system utilizing 40 wavelength channels near 1550 nm if the channels are separated by 0.8 nm. Get solution
28. Consider a Mach-Zehnder fiber demultiplexer depicted in Figure 10-16b. Assume that n = 1.5000.a. Find a difference in path length between the two arms of the fiber interferometer ΔL that will efficiently demultiplex a signal containing wavelength components λ1 = 1550.8 nm and λ2= 1550.0 nm. Assume that the λ1 component exits through Output 1. (Take care to ensure that your solution nearly satisfies both Eqs. (21) and (22) with integer m.)b. If the path length difference is as found from part (a), through which output port would light of wavelength λ3 = 1551.6 nm exit the interferometer?c. If the path length difference is as found from part (a), find the ratio of the irradiances exiting through the two output ports if the input signal has a wavelength of 1550.4 nm. Get solution
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