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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

Key Laboratory of Education Ministry on Luminescence and Optical Information Technology,

Beijing Jiaotong University, Beijing 100044, China

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

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

4×4

. Therefore, the

SOPs for input and output optical fields described by

Stokes vectors



and



are related by



¼ M



. Similar

to the PDL, the PDG can be completely determined by

the first row of matrix M as follows

[12]

PDG ¼ 10 log



þ m

−



þ m

: (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

¼½



;



;



;





and by simultaneously measuring the corresponding

output SOPs, we can get another matrix, S

out



;



;



;



. Since S

out

¼ MS

, the MM M can

be achieved by

M ¼ S

out

−1

: (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

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