Homework Chapter 1: Introduction
1.1.
Calculate the carrier frequency for optical communication systems operating at
0.88, 1.3, and 1.55 μm. What is the photon energy (in eV) in each case? 1.2.
A continuous 12 km-long optical fiber link has a loss of 1.5 dB/km.
a.
What is the minimum optical power level that must be launched into the fiber to
maintain an optical power level of 0.3 μW at the receiving end? b.
What is the required input power if the fiber f iber has a loss of 2.5 dB/km?
1.3.
A 1.55 m digital communication system operating at 1 Gb/s receives an average
power of −40 dBm at the detector. Assuming Assu ming that 1 and 0 bits are equally likely to occur, calculate the number of photons received within each 1 bit. 1.4.
Sketch the variation of optical power with time for a digital NRZ bit stream
010111101110 by assuming a bit rate of 2.5 Gb/s. What is the duration of the shortest and widest optical pulse? Homework Chapter 2 Fiber o
2.1. Light traveling in air strikes a glass plate at an angle θ 1 =33 , where θ1 measured between the incoming ray and the glass surface. Upon striking the glass, part of the beam is reflected and part is refracted. If the refracted and reflected beams make an angle of 0
90 with each other, what is the refractive index of the glass? What is the critical angle for this glass? 2.2. Find the core radius necessary for single-mode operation at 820 nm of a step-index fiber with n 1=1.48 and n 2=1.478. What is the numerical aperture and maximum acceptance angle of this fiber? 2.3. A manufacturer wishes to make a silica-core, step-index fiber with V=75 and a numerical aperture NA=0.3 to be used at 820 nm. If n 1=1.458, what should the core size and cladding index be? 2.4. Determine the normalized frequency at 0.82 μm for a step -index fiber having a 25μm core radius, n1=1.48, and n 2=1.46. How many modes propagate in i n this fiber at 0.82μm?
How many modes propagate at a wavelength of 1.3μm? What percentage of the optical power flows in the cladding in each case? Homework Chapter 3: Sources
3.1 A laser diode has a maximum average output of 1mW (0dBm). The laser is to be amplitude-modulated with a signal x(t) that has a dc component of 0.2 and a periodic component of +2.56 and -2.56. If the current-input to optical-output relationship is P(t)=i(t)/10, find the values of I 0 and m if the modulating current is i(t)=I o[1+mx(t)]. 3.2. A GaAs laser emitting at 800 nm has a 400- μm-long cavity with a refractive index n=3.6. If the gain dg exceeds the total loss α, throughout the range 750nm<λ<850nm, how many modes will exist in the laser? 3.3.
The derivation of this quation
assumes that the refractive index n is
independent of wavelength.
a.
Show that when n dpends on λ, we have
b.
If the group refractive index (n- λdn/dλ) is 4.5 for GaAs at 850 nm, what is the
mode spacing for a 400-μm-long laser? 3.4. An optical source is selected from a batch characterized as having lifetimes which follow a slow internal degradation mode. The -3dB mean time to failure of these devices at room temperature is specified as 5.10 4 h. If the device emits 1 mW at room temperature, what is the expected optical output power after 1 month of operation? After 1 year? after 5years? Homework Chapter 4: Receiver
4.1. Draw a block diagram of a digital optical receiver showing its various components. Explain the function of each component. How is the signal used by the decision circuit related to the incident optical power?
4.2. An InGaAs pin photodiode has the following parameters at a wavelength of 1300 nm, ID=4nm, η=0.65, R L=1000Ω, and the surface leakage current is negligible. The incident optical power is 300 nW(-35dBm), and the receiver bandwidth is 20 MHz. Find the various noise trems of the receiver. 4.3. A digital fiber optic link operating at 850 nm requires a maximum BER of 10 -9 a.
Find the quantum limit in terms of the quantum efficiency of the detector and
energy of the incident photon. b.
Find the minimum incident optical fiber P 0 that must fall on the photodetector to -9
achieve a 10 BER at a data rate of 10Mb/s for a simple binary-level signaling scheme( the detector quantum efficiency η=1) 4.4.
Suppose an avalanche photodiode has the following parameters: I L=1nA, ID=1nA,
η=0.85, F =M 1/2, R L=103Ω, and B=1kHz. Consider a sinusoidal varying 850 -nm signal, which has a modulation index m=0.85 and an average power level P 0=-50dBm, to fall on the detector at room temperature. At what value of M does the maximum signal-to-noise ratio occur?