Photon Netw Commun (2010) 20:10–16
Soliton-like dispersion-free optical transmission based on optical
time-domain fractional Fourier transform
Qingsheng Han · Wei Li · Benxiong Huang
Received: 13 December 2009 / Accepted: 12 January 2010 / Published online: 11 February 2010
© Springer Science+Business Media, LLC 2010
Abstract In the present article, implementation of the
optical time-domain fractional Fourier transform (FRFT)
is achieved and a new method for soliton-like dispersion-
free optical transmission is proposed. With this method, the
pulses’ envelope will keep unchanged and non-broadened
after transmission under the combined effects of chromatic
dispersion and self-phase modulation in the ﬁber link with-
out any dispersion compensation. Numerical analysis shows
how a pulse evolves for different orders of FRFT.
Keywords Fractional Fourier transform · Self-phase
modulation · Chromatic dispersion
Fractional Fourier transform (FRFT) was invented as a gen-
eralization of the classic Fourier transform in mathematical
literature but had attracted much attention in electronic signal
processing  and estimating target radial acceleration .
FRFT had also been used in beam shaping  and distortion
analysis in trans-multiplexers . Almeida showed a num-
ber of properties of FRFT . FRFT has been widely real-
ized in space domain using thin lenses and free space [6,7].
However, there is not any research focused on time-domain
FRFT. Time-domain integral-order Fourier transform has
Q. Han · W. Li (
) · B. Huang
Wuhan National Lab for Optoelectronics, Huazhong University of
Science and Technology, 430074 Wuhan, People’s Republic of China
e-mail: firstname.lastname@example.org; email@example.com;
been used to eliminate dispersion distortion based on the prin-
ciple that the spectral envelope of optical pulses will remain
unchanged, when nonlinearities are negligible [8,9]. Time-
domain Fourier transform swaps the spectral envelope with
a pulse’s time-domain waveform.
Thus, the question arises, why not to use the time-
domain FRFT to eliminate linear and nonlinear distortions?
In this paper, we achieve an implementation of optical time-
domain FRFT and demonstrate a new scheme to ﬁnd the
proper domain between time-domain and frequency-domain
to obtain the best propagation performance of optical pulses,
such that they will keep non-broadened in time-domain under
the combined effects of chromatic dispersion (CD) and self-
phase modulation (SPM) based on the understanding of
FRFT. This works very nicely just as soliton-like transmis-
sion but is much simpler than solitons.
Our new scheme and its analysis are given in Sect. 2 and
the implementation of an optical time-domain FRFT is given
in Sect. 3. The simulation results are shown in Sect. 4.
Section 5 contains the conclusions.
2 Analysis on the combined effects of chromatic
dispersion and SPM and our new scheme
In order to eliminate linear and nonlinear distortion of pulse
propagation in long-haul ﬁber transmission, many researches
had been proposed. The most famous was the soliton.
It was ﬁrst proposed as optical communication technique in
1973. When launched into optical ﬁbers without attenuation,
the pulses will have good performance with no distortion
. But soliton transmission has a strict restriction for the
input pulses whose waveforms should be a hyperbolic secant,
which is not suitable to a current optical ﬁber communication