Optics and Photonics Journal, 2013, 3, 187-191
doi:10.4236/opj.2013.32B045 Published Online June 2013 (http://www.scirp.org/journal/opj)
Nonlinear Polarization Rotation Characteristic
Phenomenon in a Bulk Semiconductor Optical Amplifier
Xanghua Feng1, Jiarong Ji2, Guomin Zhang1
1College of Science,Informa t ion E ng ineeri ng Univer si ty, Zhengzhou, China
2College of Opto electronic Science and Engineering National University of Defense Technology, Changsha, China
Received 2013
ABSTRACT
The phenomena of polarization rotation induced by self-modulation in se miconducto r optical amplifier (SOA) are ana-
lyzed theoretically. The relationship between polarization parameters and gain as well as phase is obtained by the cor-
relation parameter of ellipse polarization and SOA nonlinearity polarization rotation theory. The experiment employs
polarizer drive by walking electromotor and power meter, the light power of 360 degree is measured. The transforma-
tion law of output polarization power components is found for obvious polarization rotation in the selected coordinate
axes based on connection of polarization state in difference axes. U sing this law make the manipulation easily on get-
ting ideal polarization state. It can offer a fine method to realize all-optical switch and other logic elements in experi-
ment. This work is of great significance for the applications of SOA nonlinear polarization rotation at high-speed
all-optical signal processing and all-optical logic gate.
Keywords: Strai ned Bulk S OA; Nonlinear Polariz a tion Rotation; Phase Difference; Polar izatio n Azimuth
1. Introduction
H.Soto and D.Erasme [1] first raised a concept of cross-
polariza tio n-modulatio n (X PolM) in 1999. They investi-
gate the transformation law of SOA birefraction with
Jone–matrix. The nonlinear polarization rotation induced
by SOA birefraction was used on all-optical wavelength
conve rsion, switch, l ogic gate in the paper [2,3].
From 2003, Dorren [4,5] et al. researched all-logic ele-
ments and all-optical switch base on XP o lM in theory
and experiment, and raised a theory model for polariza-
tion depende nt gai n saturation in te nsile strai n bulk SO A.
L.Q.Guo et al. set a 2.5 Gbit/s all-optical AND gate base
on XPolM [6-8]. They proved extinction ratio increased
8dB contrast all-optical AND gate base on cross-gain-
modulation. Due to the polarization rotation can induce
the variety of output power, the polarization rota tion co m-
bining other non-linearity effect can use in all-optical
nonlinear regeneration [9] and all-optical sampling [10]
and optical buffer [11] and optical data comparator [12].
Recently, with investigate deeply, the applications of SOA
nonlinear polarization rotation at high-speed all-optical
signal processing and all-optical logic are more and more
widespread along with research deeply [13,14].
2. Theory Model and Simulations
The tensile strain bulk SOA is used for experime nt. Based
on Dorren’s theory, The polarized optical field are de-
composed into a transverse electric (TE) and trans- verse
magnetic (TM) component. TE and TM mode propagate
“independently” through the SOA, although they have
indirect interaction with each other via the gain satura-
tion. Because of different confinement factor and effec-
tive refractive indexes experienced by TE and TM modes,
it results in a phase shift TE and TM modes of the light
upon leaving the SOA. When a light transit SOA, the out
powers for each polarization can be expressed as:
int
( )( )exp()
TE TETE
TE TE
out in
g
gL
PP v ττ α
Γ
= −
(1)
int
( )( )exp()
TM TMTM
TM TM
out in
g
gL
PP v ττ α
Γ
= −
(2)
where Pin is input power, Pout is output power, Γ is the
confinement factor, g is the gain, L is the length of the
SOA.
By relation of gain and phase, output phase through L
can be expressed as
0
2
TE TE TE
TE TE
g
g L
v
α
φφ
Γ
= −
(3)
0
2
TM TMTM
TM TM
g
g L
v
α
φφ
Γ
= −
(4)
where α is phase modulation coefficients, it express the

X. H. FENG ET AL.
188
coupling rel atio n of gain and refractive index in SOA.
Through L, the phase difference between TE and TM
modes can be computed from (3) and (4)
TMTE
φφφ −=∆
(5)
In the most simple approach, one would choose
TM TE
αα =
. By(1)-(5), we can get:
0
(lnln )
2
TM TM
out in TE TE TE
out in
PP
PP
α
φφ ∆ =−+∆
(6)
(6) express the relation of phase difference and input/
output power. Due to the change of TE and TM output
powers, the phase difference between TE and TM modes
change.
ln
TM
out
TE
out
P
P
is more and the phase difference is mo r e,
as Figure 1. Three curves represent the phase difference
range of 800(curve1), 1000 (curve3) and 1200 (curve2).
The calculation parameters of this paper use parameters
of literature [4 ] .
It is get different rotation degree by same input phase
difference and different TE/TM input powers. It is also
get different rotation degree by differe nt input phase dif-
ference and same TE/TM input powers. As Figure 2, the
rotation degree of curve1 is more. More rotation degree
can be obtained by chose right input phase difference.
Definition extinction ratio
10log( )
P
cP =
long axis
short axis
.
The output extinction ratio change with input polariza-
tion state. The linear output can be obtained by adjusting
input phase difference at arbitrarily input powers, as Fig-
ure 3. Curve 1 express when input power is -1dBm,
Curve 2 express when input power is -5.9dBm, output
light is linearly polarized light.
The experiment employs polarizer driving by walking
electromotor and power meter. If the polarizer axis(x, y
axis) is different to SOA perpendicular axis (TE, TM
-10-8 -6 -4-20 2 46
0
20
40
60
80
100
120
140
160
180
In put Power(dBm)
Phase Difference(deg)
curve 1
curve 2
curve 3
Figure 1. P hase dif fere nce va riations d epen d on diff erent TE
mode and the TM mode output po wer.
-10 -8 -6 -4 -2 0246
-30
-20
-10
0
10
20
30
40
In put P ower (dB m )
Pol arizat ion A zim uth
curve1
curve2
curve3
Figure 2. Polarization Azimuth variations depend on different
phase difference of TE mode and the TM mode.
-10 -8 -6 -4 -2 0246
0
5
10
15
20
25
30
35
In put Power (dB m )
Ext inction Ratio(dB )
curve1
curve2
Figure 3. Extinction ratio variations depend on different phase
difference of TE mode and the TM mode
axis), the power satisfy:
22
cossinsin 2cos
xTETMTE TM
P PPPP ϕ ϕϕφ =+− ∆
(7)
22
sincossin 2cos
yTETMTE TM
P PPPP ϕ ϕϕφ =++ ∆
(8)
where
ϕ
is angle between x axis and T E axi s. Px and Py
are affected by
φ ∆
obviously. The phase difference
cosine law appear on x y axis from Figure 4. We can
speculate cosine changing is more obvious, polarization
state changing is more. The biggest difference between
Px and Py is more, output light is more close to linearly
polarized light. It means SOA output polarization state
variety with input power is known by polarizer. So expe-
riment operation become easily. So long as adjusting
suitable input polarization state, we can get expect pola-
rization state at ar bitrarily input power.

X. H. FENG ET AL.
189
3. Experimental Results
Experimental setup is used to measure SOA nonlinear
polarization rotation as Figure 5. A commercial polari-
zation-independent SOA is employed. Its saturation power
is 10dBm. A walking electromotor controlled by com-
puter drive a polarizer, so the light power of every orient-
tation is measured. The walking electromotor rotate cir-
cuit, sampling point is 400. The distribution of power is
displayed on computer.
In this paper, two input pump polarization states(A and
B) are selected as contra st. Figure 6 is an input and output
polarization light power of A polarization state corre-
sponding with 360 degree.
-10 -8-6-4-20 2 4 6
-2
0
2
4
6
8
10
12
14
In put Power (dB m )
Output P ower(dBm)
x axes
y axes
Figure 4. SOA output power o n xy perpendic ular a xes.
Laser
EDFA
SOA
ATT
PM
PC
PL
Figure 5. Experimental setup is used to measure SOA polariza-
tion power. EDFA: erbium-doped fiber amplifier, ATT:
Attenuat or, PC: Polarizati on co ntroller, PL: Polarizer, PM :
Power meter.
0.5
1
1.5
30
210
60
240
90
270
120
300
150
330
180 0
1
2
3
4
5
30
210
60
240
90
270
120
300
150
330
180 0
(a) (b)
Figure 6. Input and output polarization light power of A
polarizatio n state co rres pond w it h 36 0 degree. (a) Input; (b)
output.
Figure 7 is an input and output polarization light power
of A polarization state corresponding with 360 degree.
In Figures 6 or 7, long axis power
P
ξ
, short axis
power
P
η
, angle
θ
of x axis and long axis, x axis
power
x
P
, y axis power
y
P
, 450 power
45
P
are easy to
find out. According to transform relation of different
axis,
22
45
cossinsin 2cos
44 2
x yxy
P PPPP
ππ π
φ = +−∆
(9)
get:
45
( )/2
cos
xy
xy
PP P
PP
φ
+−
∆=
(10)
For arbitrary orthogonal axis, phase difference betwee n
perpendicular components can be getting at this coordi-
nate.
Figure 8 is output probe power
x
P
,
y
P
correspond-
ing A and B.
Figure 9 is polarization Azimuth variatio n curves cor-
respond to A and B. Because polarization state drift and
systemic vibration make power measurement error, po-
larization azimuth extinction ratio will produce error.
Figure 10 is extinction ratio variation curves correspond
to A and B. Figure 11 is phase difference of x and y var-
iation curves correspond to A and B.
4. Conclusions
From ahead experimental resul t, we can get the conclusion.
Polarization state rotation always occurs through SOA,
rotation degree is different follow different input power
and input po lariza tion sta te. Two d iffere nt i nput polar iza-
tion states lead to output power and gain obvious differ-
ence of x and y axis. Their phase difference, polarization
Azimuth and extinction ratio are difference obviously.
Due to x and y axis do not coincide TE and TM axis,
obvious cosine variation curve is observed at Figure 8(a).
It implies input polarization state of Figure 6(a) arise
phase difference of TE and TM modes bigger change,
and it arise rotation bigger degree and extinction ratio
0.5
1
1.5
30
210
60
240
90
270
120
300
150
330
180 0
1
2
3
4
5
30
210
60
240
90
270
120
300
150
330
180 0
(a) (b)
Figure 7. Input and output polarization light power of B
polarizati o n state corres p ond w ith 36 0 degree. (a) Input; ( b)
output

X. H. FENG ET AL.
190
-10 -8-6-4-20 2 46
3
4
5
6
7
8
9
Input P ower(dB m )
Out put Power(dBm)
x axes
y axes
(a)
-10 -8 -6 -4 -2 0246
1
2
3
4
5
6
7
8
9
Input P ower(dB m )
Out put Power(dBm)
x axes
y axes
(b)
Figure 8. Output polarization light power. (a) Correspond
to A polarization state; (b) correspond to B polarization state.
-10 -8-6-4-20 2 46
-40
-30
-20
-10
0
10
20
30
40
Input Power(dBm )
Polarizat ion Azi m uth(deg)
(a)
-10 -8 -6 -4 -202 4 6
80
85
90
95
100
105
110
115
Input P ower(dB m )
Polarizat ion Azi m uth(deg)
(b)
Figure 9. Polarization azimuth variation curve. (a) Correspond
to A polarization state; (b) correspond to B polari zati on state.
-10 -8 -6 -4 -2 0246
2
4
6
8
10
12
14
16
Input P ower(dBm )
Extincti on Ratio( dB )
(a)
-10 -8-6-4 -20 2 46
3
4
5
6
7
8
9
Input P ower( dBm )
Extincti on Ratio( dB )
(b)
Figure 10. Extinction ratio variation curve. (a) Correspond to
A polarization state; (b) correspond to B polarization state.
-10-8 -6 -4 -20 2 4 6
70
80
90
100
110
120
130
140
150
160
Input P ower(dB m )
Phase Di fference( de g)
(a)
-10 -8-6-4-20 2 4 6
80
85
90
95
100
105
110
115
120
125
Input Power(dBm )
Phase Di ff erece(dBm)
(b)
Figure 11. Phase difference variation curve. (a) Correspond
to A polarization state; (b) correspond to B polarization s tate .

X. H. FENG ET AL.
191
bigger change. Cosine variation curve is not observed at
Figure 8 (b). It implies input p olarization state of Figure
7(a) do not arise phase difference of TE and TM modes
bigger change, and it not arise rotation and extinction
ratio bigger change. Thus it can be seen, if input polari-
zation state arise phase difference of TE and TM modes
bigger change, output powers at x axis or y axis appear
cosine variation. It proves in theory and experiment, ar-
bitrary output probe polarization states can be obtained
through adjusting input pump polarization states. In ex-
periment, the adjusting of polarization states can mani-
pulate easily base on transform relation of different coor-
dinate syste m.
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