National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Homework #4 for ET4302701
Due on Tuesday 6/2/2015
1.
When the electric permittivity of a crystal is measured at =1 m with respect to an
arbitrary Cartesian coordinate system defined by x1 , x2 , and x3 , it is found to be given
by the following tensor:
National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Homework #4 for ET4302701
1. Solution:
Like my derivation in class, the eigenvalues for the diagonalized matrix is as follows:
4.786
0
0.168
0
5.01
0
0.168
0
4.884
0; 5.01,5.01,4.66
In the old coordinate system,
1
1
0
0.00719
4.786 0 0.168 4.786
National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Homework #2 for ET4302701
1.(a)
0
2n
m d df
2n 0
c
md
m d
f f
2n c
m 1
f f 0 f
2 c
c 2d
c
c
2dn 2d
f
c
2
n 1
2
2d
(b)
Resonance condition
2f
2kd m2 2
d m2
c
f
c
f d
d
d
d
For d 3 and FSR 260nm
You can utilize FSR in wavelength domain to get .
National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Homework #1 for ET4302701
1.(a)
Without the film
T12
4 n1 n2
(n1 n2 ) 2
With the film, the transmittance is
T1 f 2 T1 f T f 2
4 n1 n f
4 n f n2
16n1n2 n 2
f
2
2
2
(n1 n2 ) (n f n2 )
(n1 n f ) (n f n2 )2
We can maximize
n2
f
ln
2 ln( n f ) 2 ln( n1 n f
National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Homework #1 for ET4302701
Due on Monday 3/25/2013
1. A film with thickness index nf is placed between two media with
indices n1 and n2. (a) For light incident normally, passing from 1 to 2,
find the value of nf that maximizes the net transmittance, T1f2,
National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Homework #2 for ET4302701
Due on Monday 4/8/2013
1. (a) In a FabryPerot cavity, the free spectral range (FSR) is defined as the frequency
separation between adjacent modes. If the cavity length is d and the air is the medium of the
cavity, derive FSR in
National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Homework #5 for ET4302701 jjféF
Figure 6Q51 shows the equivalent circuit with the series resistance removed. The currents owing
into node A sum to zero (Kircho 5 current law). Currents into a node are positive and those leaving a
node are negative. Thu
National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Solutions for Optoelectronics and Photonics: Principles and Practices
1.4
Chapter 1/2/3/7
Antireflection coating
g
For light traveling in medium 1 incident on the 12 interface at normal incidence,
r12 =
n1 n2 n1 n1n3
=
=
n1 + n2 n1 + n1n3
1
1+
n3
n1
n3
n
National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Homework #1 for ET4302701
Due on Tuesday 3/31/2015
1. A film with thickness index nf is placed between two media with indices n1 and n2. (a) For
light incident normally, passing from 1 to 2, find the value of n f that maximizes the net
transmittance, T1f
National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Homework #3 for ET4302701
Due on Tuesday 4/21/2015
1.
Consider a symmetric planar dielectric waveguide. Allowed upward and downward traveling
waves inside the core of the planar waveguide setup a standing wave along y. The standing
wave can only exist i
National Taiwan University of Science and Technology
Optoelectronic Devices
ECE 4302701

Spring 2015
Homework #2 for ET4302701
Due on Tuesday 4/21/2015
1.
(a) In a FabryPerot cavity, the free spectral range (FSR) is defined as the frequency separation
between adjacent modes. If the cavity length is d and the air is the medium of the cavity, derive
FSR