Week 8 (March 4 to March 8)

  1. A Fabry-Perot optical cavity has identical mirrors with reflectance 0.9 spaced 100 mm apart in air. Calculate the cavity mode nearest to 900 mm. Calculate the mode separation, the finesse, and the spectral width of each mode in terms of frequency and wavelength.
  2. A silicon pn-junction diode has Nd=Na=1018 cm-3 and ni=1.45x1010 cm-3 and area 1 mm2. For silicon er =11.9. When Nd=1018 cm-3, mp=130 cm2V-1s-1 and when Na=1018 cm-3, mn=250 cm2V-1s-1. Also the recombination times tn=tp=25 ns. Given that a forward bias 0.6V is applied, calculate the diffusion and recombination contributions to the diode current. What is your conclusion?
  3. GaAs has an effective density of states NC=4.7x1017 cm-3 and NV=7x1018 cm-3. Given a bandgap Eg=1.42 eV, calculate the intrinsic carrier concentration and location of the Fermi level at 27oC. Assuming that NC and NV scale with temperature as T3/2, what is the intrinsic carrier concentration at 127oC?

Week 9 (March 11 to March 14)

  1. Derive an expression for the temperature sensitivity of the peak wavelength of an LED spectrum. For GaAs at 300K, Eg=1.42 eV, dEg/dT= -5x10-4 eV/oC , what is the shift in wavelength for 10oC temperature increase?
  2. An infrared LED is made using In1-xGa xAsyP 1-y alloy. What is the alloy composition for peak emission at 1300nm at 27oC? What is the expected linewidth?
  3. An AlGaAs LED emitter for use in a local optical fiber network is designed for peak emission at 820 nm at 25oC. The linewidth at 25oC is 40 nm.
    1. What is the bandgap of AlGaAs in this LED at 25oC?
    2. Given that the bandgap changes with temperature as û4.5x10-4 eV/oC, what is the peak emission wavelength at temperatures û40oC and at 85 oC?
    3. What is the linewidth at temperatures û40oC and at 85 oC?
    4. What is the composition of the AlGaAs in this LED?

Week 10 (March 18 to March 22)

  1. The LED in problem 29 has responsivity 30mW/mA. When the forward current is 50 mA at 25oC, the voltage across the LED is 1.5V.
    1. What is the LED output power?
    2. What is the external efficiency?
    3. If the radiative lifetime is 50ns and the non-radiative lifetime is 100ns, what is the internal efficiency?
    4. What is the internal optical power generated?
    5. If the optical power coupled into a multimode fiber through a small spherical glass lens is 500 mW, what is the overall efficiency?
    6. What is the modulation bandwidth?
  1. What wavelengths will silicon (Eg=1.12eV) absorb? What wavelengths will GaAs (Eg=1.42eV) absorb? Design a AR coating for a silicon (n=3.6) photodetector at 635 nm.

Week 11 (March 25 to March 29)

  1. A semiconductor Fabry-Perot optical cavity has cavity length 200 mm with end mirrors that have reflectance 0.8 each. The refractive index is 3.7 .
    1. What is the cavity mode nearest to the free space wavelength of 1300 nm?
    2. Calculate the separation of the modes and the spectral width.
  1. Consider an InGaAsP-InP laser diode which has an optical cavity of length 250 mm. The peak radiation is at 1550 nm and the refractive index is 3.4. The optical gain bandwidth (FWHM) is 8 nm at the operating DC diode current.
    1. What is the mode integer m of the peak radiation?
    2. What is the mode spacing in wavelength?
    3. How many modes are there in the cavity?
    4. What is the reflectance at the cleaved mirror surfaces?
    5. What would the cavity length need to be to operate single mode?
  1. A Bragg grating is added to the laser diode in problem 33 to make a DFB laser. What is the required period for a first-order grating?
  2. Consider a double heterostructure InGaAsP laser diode operating at 1310 nm. The cavity has length 60 mm , active layer width 10 mm and active layer thickness 0.25 mm. The refractive index is n=3.5 . The loss coefficient for the cavity is 10 cm-1.
    1. Find the total loss and gain at threshold and the photon lifetime.
    2. If the threshold current density is 500 A/cm2 and tsp=10 ps, what is the threshold electron concentration?
    3. What is the lasing optical power and intensity when the diode current is 5 mA?

Week 12 (April 2 to April 9)

  1. Consider an ideal photodiode with 100% quantum efficiency and no dark current. What is the expression for the NEP for the quantum noise limit? If the device operates at 1300nm with a bandwidth of 500MHz, calculate the NEP and the corresponding photocurrent.
  2. A silicon photodiode has an intrinsic layer which is 20 mm wide. The P+ layer on the illumination side is very thin (0.1mm). The diode is reverse biased at 100V. A very short pulse of light at wavelength 900nm illuminates the active area. What is the duration of the photocurrent if absorption occurs over the entire I-layer? (use absorption coefficient 3x104 m-1 at 900nm, ve~vesat, vh=7x104 m/s)
  3. Consider a Ge pn junction photodiode that has responsivity 0.25A/W, 0.55A/W, and 0.72A/W at 850nm, 1300nm, and 1550nm, respectively. Its photosensitive area is .01 mm2. It is used at reverse bias 10V when the dark current is 0.3 mA and the junction capacitance is 4 pF. The rise time of the diode is 0.5ns.
    1. Calculate its quantum efficiency at 850nm, 1300nm, and 1550nm.
    2. What is the intensity of light at 1550nm that gives a photocurrent equal to the dark current?
    3. What would be the effect of lowering the temperature on the responsivity?
    4. Given that the dark current is in the range of microamperes, what would be the advantage in reducing the temperature?
    5. Suppose that the diode is used with a 100W resistance to sample the photocurrent, what limits the speed of the response?
  1. Consider an InGaAs APD with x~0.7 which is biased to operate at M=10 at 27oC. At small bias the responsivity is 0.8 A/W and the dark current is 10nA. The bandwidth is 700MHz when used with a load resistor of 50W.
    1. What is the APD noise current per square root of bandwidth?
    2. What is the APD noise current for the operating bandwidth?
    3. What is the thermal noise power?
    4. What is the minimum optical power for a SNR of 10dB?
    5. What is the approximate capacitance of the device?
  1. A fiber optic link is constructed at 1300 nm using an AlGaAs laser diode, single mode fiber, and a InGaAs pin photodiode. The photodiode has responsivity 0.8A/W at 1300nm.The laser diode can launch 2mW of power into the fiber which has attenuation 0.35dB/km. For an acceptable SNR in the receiver, the photodiode must have at least 5nA photocurrent. What is the maximum length of the link without using repeaters or optical amplifiers?