DNJ
Brac University
BSRM School of Engineering
Department of Electrical and Electronic Engineering
Program: BSEEE
HW-1, Fall 2025
EEE 557; Advanced Optoelectronics
Marks: 23
Q1. An engineer wants to design a refractometer (an instrument for measuring the refractive
index) using the lateral displacement of light through a glass plate. His initial experiments
involve using a plate of thickness L and measuring the displacement of a laser beam when the
angle of incidence i is changed, for example, by rotating (tilting) the sample. For i = 40° he
measures a displacement of 0.60 mm, and when i = 80° he measures 1.69 mm. Find the
refractive index of the plate and its thickness. (Note: You need to solve a nonlinear equation
for n numerically.)
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Q2. A) A dielectric mirror is made up of a quarter wave layer of GaAs with nH = 3.38 and AlAs
with nL = 3.00 at around 1550 nm. The light is incident on the mirror from another
semiconductor of refractive index n0 = 3.40. Find out the number of pairs of layers N needed
to get 90% reflectance. Find out the band width of the reflected light.
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B) For a single-layer AR coating of index n2 on a mate rial with index n3 (>n2 > n1), as
shown in Figure 2.1 (a), the minimum reflectance at normal incidence is given by
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(d) What two materials would you choose to obtain a V-coating? Note: The choice of an AR coating
also depends on the technology involved in depositing the AR coating and its effects on the interface
states between the AR layer and the semiconductor. Si1-xNx is a common AR coating on devices in as
much as it is a good passive dielectric layer, its deposition technology is well established and changing
its composition (x) changes its index.
Q3. A) Spectroscopic ellipsometry measurements on a germanium crystal at a photon energy
of 1.5 eV show that the real and imaginary parts of the complex relative permittivity are 21.56
and 2.772, respectively. Find the complex refractive index. What is the reflectance and
absorption coefficient at this wavelength? How do your calculations match with the
experimental values of n = 4.653 and K = 0.298, R = 0.419 and a = 4.53 x106 m-1?
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Calculate the absorption coefficient and the reflectance of CdTe at 60 um and 80 um.
B) Consider a light wave of wavelength 870 nm traveling in a semiconductor medium (GaAs)
of refractive index 3.60. It is incident on a different semiconductor medium (AlGaAs) of
refractive index of 3.40, and the angle of incidence is 80°. Will this result in total internal
reflection? Calculate the phase change in the parallel and perpendicular components of the
reflected electric field.
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