Non-linear polarization orthogonality loss in a
semiconductor optical amplifier
Wei Zhang (章 威)
1,2
, Zhengyong Li (李政勇)
1,2,
*, Haiyang Wang (王海洋)
1,2
,
Xiangkong Zhan (詹翔空)
1,2
, Zhongbo Song (宋中波)
1,2
,and
Chongqing Wu (吴重庆)
1,2
1
Key Laboratory of Education Ministry on Luminescence and Optical Information Technology,
Beijing Jiaotong University, Beijing 100044, China
2
Institute of Optical Information, School of Science, Beijing Jiaotong University, Beijing 100044, China
*Corresponding author: zhyli@bjtu.edu.cn
Received March 10, 2016; accepted June 24, 2016; posted online July 25, 2016
Polarization-based optical communications are attracting more attention recently, where the crucial points are
polarization features and their measurements. Based on the Müller matrix method, we obtain measurable ex-
pressions for the polarization-dependent gain (PDG) and the loss of polarization orthogonality (LPO), while give
the boundary of the LPO for any PDG devices. We experimentally demonstrate that non-linear LPO can be
created in a semiconductor optical amplifier and find that the LPO will slightly skim over the boundary near the
threshold of the injected current. Furthermore, an empirical formula is achieved to gauge the LPO-induced
power penalty, which is proven to be valid in differential polarization shift-keying transmission by executing
a bit error rate measurement. Our conclusions are applicable to non-orthogonal polarization cases and valuable
to polarization-related communications, even orbital angular momentum multiplexing.
OCIS codes: 060.2330, 260.5430, 060.2340.
doi: 10.3788/COL201614.090601.
Optical communication based on states of polarization
(SOPs) has prominent advantages, such as power equali-
zation, better polarization characteristics, and less power
penalty (PP), which further suppress the polarization
mode dispersion (PMD) and improve the spectrum
efficiency
[1,2]
. For example, increasing the polarization
alternation of optical signals can efficiently prevent non-
linear degradation
[3]
. At present, to enhance the capacity
expansion of existing optical communication systems,
there has been increasing interest in polarization division
multiplexing (PolDM) and polarization shift keying
(PolSK)
[4–9]
. Generally, orthogonal SOPs are utilized to
multiply or modulate the optical signals. To perform
SOP-based communications, there is the key point that
the polarization correlations such as the orthogonality
should be preserved well in the transmission. In a linear
optical system with polarization-dependent loss (PDL),
the SOPs will keep their orthogonality for a long distance,
for example, orthogonal SOPs preserve well after trans-
mitting in a fiber with a length longer than 50 km
[10]
.
However, we have found, for the first time to our knowl-
edge, that the orthogonality will be lost or trimmed down
in a non-linear semiconductor optical amplifier (SOA),
whose refractive nonlinearity is 10
8
times larger than an
equivalent length of optical fiber
[11]
. Further analysis
shows that the loss of polarization orthogonality (LPO)
is non-linearly related to the polarization-dependent
gain (PDG) of the SOA. Based on Müller matrix (MM)
method, we derive the measurable expressions for the
PDG and the LPO while obtaining the LPO bounda ry
for any devices with PDG, and we experimentally
demonstrate it by MM-based measurements. Moreover,
we investigate the impact of LPO on the bit error rate
(BER) of the PolSK signals while indicating how much
PP the LPO creates and how the BER varies when they
pass through the SOA.
In Stokes space, any optical system such as an SOA can
be described by a 4 × 4 MM M ¼fm
ij
g
4×4
. Therefore, the
SOPs for input and output optical fields described by
Stokes vectors
S
i
and
S
o
are related by
S
o
¼ M
S
i
. Similar
to the PDL, the PDG can be completely determined by
the first row of matrix M as follows
[12]
:
PDG ¼ 10 log
m
11
þ
m
2
12
þ m
2
13
þ m
2
14
p
m
11
−
m
2
12
þ m
2
13
þ m
2
14
p
: (1)
Accordingly, to gauge the PDG of an SOA, one
needs to obtain the MM M in the first step. In general,
by inputting into an SOA four kinds of linear-independent
SOPs producing an invertible matrix S
in
¼½
S
i1
;
S
i2
;
S
i3
;
S
i4
and by simultaneously measuring the corresponding
output SOPs, we can get another matrix, S
out
¼
½
S
o1
;
S
o2
;
S
o3
;
S
o4
. Since S
out
¼ MS
in
, the MM M can
be achieved by
M ¼ S
out
S
−1
in
: (2)
Due to the noticeable PDG, when two optical waves
with orthogonal SOPs are launched into an SOA, they
cannot remain orthogonal anymore, which means an evi-
dent LPO caused by the SOA. According to Ref. [
10], the
COL 14(9), 090601(2016) CHINESE OPTICS LETTERS September 10, 2016
1671-7694/2016/090601(4) 090601-1 © 2016 Chinese Optics Letters