Photon Netw Commun (2010) 20:216–223
DOI 10.1007/s11107-010-0262-2
A minimum distortion transmission scheme under combined
effects of chromatic dispersion and SPM based on optical
time-domain fractional Fourier transformation
Qingsheng Han · Wei Li · Qiyu He
Received: 14 January 2010 / Accepted: 20 July 2010 / Published online: 15 August 2010
© Springer Science+Business Media, LLC 2010
Abstract In this paper, an optical time-domain fractional
Fourier transformation (FRFT) system is proposed to achieve
the minimum distortion transmission under combined effects
of chromatic dispersion and self-phase modulation (SPM). In
the new method, the pulses operated as FRFT will propagate
in a new domain, in which the waveform in time domain will
keep nearly unchanged through the transmission. The novel
method achieves a 400 km optical transmission for an opti-
cal pulse with the full width at the 1/e point of peak power
of 80 ps without any dispersion compensation and the pulse
offers a nice performance with negligible nonlinear distor-
tion. Compared with the soliton communication, this scheme
shows more advantages on linear and nonlinear distortions
without strict restriction to input pulses.
Keywords Fractional Fourier transformation ·
Chromatic dispersion · Self-phase modulation ·
Nonlinear distortion
1 Introduction
Recently, 100 Gbit/s per channel is becoming a trendy optical
transmission system. In t his region the optical pulse shape in
time domain is severely degraded during propagating in the
Q. Han · W. Li (
B
)
Wuhan National Laboratory for Optoelectronics,
Huazhong University of Science and Technology,
Wuhan 430074, People’s Republic of China
e-mail: weilee@mail.hust.edu.cn; weilee020116@yahoo.com.cn
Q. Han
e-mail: hanqingsheng1001@163.com
Q. He
Yunnan University of Nationalities, Kunming 650031, China
fibre due to both linear distortions such as the chromatic dis-
persion, polarization mode dispersion (PMD), timing jitter
and nonlinear effects which could severely restrict transmis-
sion speed and distance.
Nonlinear effects and dispersions are two main restric-
tions to the development of optical communication for high
speed, long haul transmission under the current optical fiber
systems [1–4].
Chromatic dispersion leads to a pulse broadening that lim-
its the maximum pulse transmission distance. And the higher
bit rate requires shorter pulses, which results in greater broad-
ening of pulses. The higher transmitted power gives arise to
larger nonlinear effects induced by self-phase modulation
(SPM). They are combined effects shown in the nonlinear
Schrödinger equation, which are very complex. Then, in the
current circumstance, the nonlinear effects and linear disper-
sion are compensated separately. A lot of papers pay great
attentions on the combined effects of chromatic dispersion
and self-phase modulation [1–6]. Second we had presented
a new perturbation method for the nonlinear Schrödinger
equation to study signal-noise interactions in amplified
multi-span fiber-optic systems [1]. References [5–7]also
studied the effects of the SPM on optical communication
systems.
For linear distortions compensations, the first order and
second order dispersion-compensation methods need care-
ful control and management of the transmission fibre’s dis-
persion, which make the system complicated and expensive.
The nonlinear effects can only be solved by reducing the
input power, increasing the span of wavelength, or reducing
the number of channels, etc.
A famous theory to remove the combined distortion is sol-
iton communication which has the great superiority over any
long distance transmission with no distortion [8–10]. How-
ever, soliton communication has a strict restriction to input
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