Q1)
Q2)
derivative fof this one:
Newton: xn+1=xn+f(xn)/f (xn), start x0=2.5:
X1=2.67
X2=2.83
X3=2.93
X4=3.04
X5=3.05
So optimum number is 3 spacing is 500/3 = 167 km.

Q1)
x2 y2 z2
+
+
+ 2 xyr63 E z = 1;
no2 no2 ne2
x cos
=
y sin
sin x
x = x cos 45 + y sin 45, y = x sin 45 + y cos 45
cos y
x2 y2 z2
+
+
+ 2 xyr63 E z
no2 no2 ne2
x 2 cos 2 45 + 2 x y cos 45 sin 45 + y 2 sin 2 45 + x 2 sin 2 45 2 x y cos 45 sin 45

HW 2 Solutions
1)
E3
E2
E1
13: B13 N1
32: A32 N 3
31: A31 N 3
21: A21 N 2
b)
dN 3
= B13 N 1 A32 N 3 A31 N 3
dt
dN 2
= A32 N 3 A21 N 2
dt
2)
(a)
E3 ( kB 300 K )
N 3 N ge
E E
k 300 K )
hc ( kB 300 K )
=
= e ( 3 2) ( B
=e
N 2 N ge E2 ( kB 300 K )
where is

Q1)
Using the matrices from the lecture slides, the retarder has to be rotated by 135
degrees in order to be in the same position like the retarder in the drawing. With the
polarizers the matrices are:
1 0 cos 135o sin 135o 1 0 cos( 135o ) sin( 135o ) 0 0

Photonics
Homework
Sheet 2
1.
Assume a system with three energy levels E1, E2 and E3. E1 is the
ground state with a very high population.
a) Write down the rates for all the transitions possible under the
assumption that only radiation with energy E3 - E1

Photonics
Homework
Sheet 7
1.
Show that for the KDP crystal with an electric field in z-direction, the same
formula is obtained for the dependence of the refractive indices on the electric
field as in the lecture if the new principle axes are the old ones

Photonics
Sheet 6
1.
Assume the following set up for a Pockels Cell:
Use Jones Matrices to find the transmission formula T=sin2(/2), with
being the phase angle introduced by the retarder. Hint: T is proportional
to E2, and use the following identity:
x

Photonics
Homework
Sheet 4
1.
What is the maximum gain G of a 1.48-m pumped erbium-doped fiber amplifier
when the pump power Pp = 80 mW? What is the gain when the output light
power P is 1 mW? The relevant parameters are:
Note: You have to use the contain

Photonics
Homework
Sheet 3
1.
What is the signals stimulated emission cross section s of Er3+ if you
have the following information: =1550 nm, transition width =50 nm,
refractive index n=1.46, level life time =10 ms?
2.
Consider an EDFA with a fiber lengt

Optoelectronics
Homework
Sheet 2
1.
Prove (using the corresponding matrices) that the focal length of two lenses with focal
length f1 and f2 combined (no space in between them) is given by the formula
1
1
1
=
+
f
f1 f 2
2.
Tiny glass balls are often used

Photonics
Homework
Sheet 5
1.
Calculate the formula for the point at which a Raman amplifier reaches its
maximum amplification.
2.
Derive the formula for the maximum gain (= Ps,max/Ps,0) using the result
from question 1.
3.
Assume a single mode silica fib