1. An engineer has two Ga(1-x)Al(x)As LEDs: one has band gap energy of 1.540 eV and the other has x = 0.015.
a. Find the aluminium mole fraction x and the emission wavelength for the first LED
answer :

Eg = 1,424 + 1.266X + 0.266X^2
1.540 = 1.424 + 1.266X+0.266X^2
X = 0.09
b. Find the band gap energy and the emission wavelength of the other LED
answer :
Eg = 1.424 + 1.266x + 0.266×2
Eg = 1.424 + 1.266(0.015) + 0.266(0.015)2
Eg = 1.443 eV

2. A double heterojunction InGaAsP LED emitting at a peak wavelength of 1310 nm has radiative and nonradiative recombination time sof 25 and 90 ns, respectively. The drive current is 35 mA.
answer :
a. Find the internal quantum efficiency and the internal power level.
Internal quantum efficiency :

Internal power level :

b. If the refractive index of the light source material is n = 3,5, find the power emitted from the device.
answer :
Power emitted from device :
Po = n2 = 3.52 = 12.25 Watt

3. a GaAl As laser diode has a 500cavity length which has an effective absorption coeffient of 10 cm-1. For the uncoated facets the reflectives are 0.32
a. What is the optional gain at the lasing threshold?
answer :

b. If one end of the laser is coated with a dielectric reflector so that its reflectivityis now 90%, what is the optical gain at the lasing threshold?
answer :
R = 0.9 x 0.32 = 0.288

c. If the internal quantum efficiency is 0,65, what is the external quantum effiency is cases (a) and (b)?
answer :

4. A GaAs laser emitting at 800 nm has a 400 cavity length with a refractive index n = 3.6. If the gain exceeds the total loss throughout the range 750 nm < < 850 nm, how many modes will exist in the laser?
answer :

5. A distributed feedback laser has aBragg wavelength of 1570 nm, a second-order grating with = 460 nm, and a 300 cavity length. Assuming perfecttly symmetrical DFB laser, find the zeroth-, first-, and the second-order lasing wavelength to a tenth of a nanometer. Draw a relative amplitude-versus wavelength plot.
answer :

2.8 A point source of light is 12 cm below the surface of a large body of water (n = 1.33 for water). What is the radius of the largest circle on the water surface through which the light can emerge?
Answers :

2.10 Show that the critical angle at an interafce between doped silica with n1 = 1.460 and pure silica with n2 = 1.450 is 83.3 degree.
Answers :

2.13 Consider a dielectric slab having a thickness d = 10 mm and index of refraction n1 = 1.50. Let the medium above and below the slab be air, in which n2 = 1. Let the wavelength be λ = 10 mm (equal to the thickness of the waveguide).
(a) What is the critical angle for the slab waveguide?
(b) Solve Eq. (2.26b) graphically to show that there are three angles of incidence which satisfy this equation.
(c) What happens to the number of angles as the wavelength is decreased?
Answers :
(a) critical angle for the slab waveguide

(b) The Equation :

2.18 A step-index multimode fiber with a numerical aperture of 0.20 supports approximately 1000 modes at an 850-nm wavelength.
(a) What is the diameter of its core?
(b) How many modes does the fiber support at 1320 nm?
(c) How any modes does the fiber support at 1550 nm?
Answers :
(a) Number of modes is given by,

(b)

(c)

Fiber a = 25 μm, n1 = 1,48; Δ = 0,01; λ = 0,84 μm;
calculate V; M; Pclad/P;
if Δ = 0,003, calculate M and Pclad/P;
V= (2πan_1)/λ √2Δ
V= (2π.25.〖10〗^(-6))/(0,84.〖10〗^(-6) ) √2.0,01
V= 26.445 m/s
M = V2 / 2 = (26,445)2 / 2 = 349,67
Pclad/P = 4/3 (M)-0.5
= 4/3 (349.67)-0.5
= 0.07
if Δ = 0,003 then,
V= (2πan_1)/λ √2Δ
V= (2π.25.〖10〗^(-6))/(0,84.〖10〗^(-6) ) √2.0,003
V= 14,48 m/s
M = V2 / 2 = (14,48)2 / 2 = 104,8352
Pclad/P = 4/3 (M)-0.5
= 4/3 (104,8352)-0.5
= 0,13

d = 10 μm
λ1 = 850 nm
λ2 = 1300 nm
λ3 = 1550 nm
If given Numerical Aperture 1 %,2 %, and 3 %, Calculate the V-parameter and define the optical fiber mode!
(Note : d = diameter, λ = wavelength)
Answers :
V = k . a . NA

NA1 = 1 %

NA2 = 2 %

NA3 = 3 %

The Requirement of Multimode is : V > 2,405
So, Even Though NA 1%, 2 %, and 3 %, The Value of V are still under 2,405 so the value tha we got is Single mode Fiber Optic.

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