Communication and Network, 2010, 2, 44-49
doi:10.4236/cn.2010.21006 Published Online February 2010 (http://www.scirp.org/journal/cn)
A Historical Narrative of Study of Fiber Grating
Solitons
Xiaolu Li1, Yuesong Jiang2, Lijun Xu1
1School of Instrumentation Science and Opto-electronics Engineering, Beihang University, Beijing, China
2School of Electronic and Information Engineering, Beihang University, Beijing, China
Received September 18, 2009; accepted November 10, 2009
Abstract: A brief historical narrative of the study of grating solitons in fiber Bragg grating is presen ted from
the late 1970’s up to now. The formation o f photogenera tion grating s in optical fiber by sustained ex posure of
the core to the interference pattern produced by oppositely propagating modes of argon-ion laser radiation
was first reported in 1978. One important nonlinear application of fiber Bragg grating is grating solitons, in-
cluding gap soliton an d Bragg soliton. This paper summarily introduces the numerous theoretical and experi-
mental results on this field, each indicating the potential these solitons have in all-optical switching, pulse
compression, limiting, and logic operations, and especially important for the optical communication systems.
Keywords: nonlinear optics, periodic structure, fiber Bragg grating, kerr nonlinearity, dispersion, grating
solitons, Bragg soliton, gap soliton
1. Introduction
After the invention of the laser, there has been much in-
terest in propagating nonlinear pulses through the peri-
odic medium such as a fiber Bragg grating (FBG), which
is a periodic variation of the refractive index of the fiber
core along the length of the fiber. Since the tirst demon-
stration of photo-induced optical fiber Bragg gratings by
Hill and coworkers in 1978 [1], significant progress was
made in the fabrication technology of fiber Bragg reflec-
tors [2–5]. The concept of “photonic band structure” is
introduced by Yablonovitch in the late 1980’s [6]. A no-
table feature of this linear periodic structure is the pres-
ence of stop gap in the d ispersio n cu rve popularly k nown
as photonic band gap (PBG) [7,8]. This PBG exists at
frequencies for wh ich the medium turns highly reflective
and hence the light pulse will not be able to propagate
through the periodic structure. Light interaction with
nonlinear periodic media yields a diversity of fascinating
phenomena, among which two solitonic phenomena have
been studied most inten sively, namely, discrete (or lattice)
solitons [9–11] and gap (or Bragg) solitons [12–17].
While discrete solitons are spatial phenomena in two-
dimensional or three-dimensional arrays of coupled
waveguides, gap solitons are usually considered as a
temporal phenomenon in one-dimensional (1D) periodic
media [18–20]. Perhaps the most fascinating feature of
solitons is their particle like behavior. Survival of two
such colliding solitons is even more remarkable if one
notes that solitons interact strongly with each other dur-
ing the collision. But for copropagating solitons, the in-
teraction is either attractive or repulsive, depending on
the relative phase between two soliton s. In both cases the
evolution of the soliton pair is well understood [21–24].
As first pointed out by Winful [25], because the dis-
persion is many orders of magnitude larger than the total
dispersion due to the combined effects of material and
waveguide dispersions that arise in the conventional fi-
bers, the interactions lengths are reduced accordingly.
Hence, the grating induced dispersion dominates over the
total dispersion in the conventional fibers. When the en-
tire spectral components of the input pulse lie within the
PBG structure, the grating induced dispersion counter-
balanced by the Kerr nonlinearity through the self-phase
modulation (SPM) and cross-phase modulation (XPM)
effects, forming solitons are referred to as gap solitons
since their spectral components are within the PBG
structure. Many research groups [3–10] theoretically
predicted th e existence of gap solitons and Bragg gr ating
solitons in FBG and the investigations on these exciting
entities are going on. However, it can be noticed that, in
literatures, nowadays the distinction between gap soli-
tons and Bragg solitons is hardly maintained and, in
general, they are simply called grating solitons [26]. Ul
[25], because the dispersion is many orders of magnitude
larger than the total dispersion due to the combined ef-
fects of material and waveguide dispersions that arise in
the conventional fibers, the interactions lengths are re-
duced accordingly. Hence, the grating induced dispersion
dominates over the total dispersion in the conventional

X. L. LI ET AL.
45
fibers. When the entire spectral components of the input
pulse lie within the PBG structure, the grating induced
dispersion counterbalanced by the Kerr nonlinearity
through the self-phase modulation (SPM) and cross-
phase modulation (XPM) effects, forming solitons are
referred to as gap solitons since their spectral compo-
nents are within the PBG structure. Many research
groups [3–10] theoretically predicted the existence of
gap solitons and Bragg grating solitons in FBG and the
investigations on these exciting entities are going on.
However, it can be noticed that, in literatures, nowadays
the distinction between gap so liton s and Bragg so lito n s is
hardly maintained and, in general, th ey are simply called
grating solitons [26].
2. Theory
The usual quantitative description of grating solitons
employs coupled-mode theory, leading to the nonlinear
coupled-mode equations. In addition, in the appropriate
limit, the envelope of the electric field satisfies the
nonlinear Schrödinger (NLS) equation. The pulse propa-
gation through the FBG is described by the nonlin-
ear-coupled mode (NLCM) equations which are nonin-
tegrable in g eneral. Ther efore, the an alytical solutions of
the NLCM equations are not solitons but solitary waves
that can propagate through FBG without changing their
shape. These are obtained from the approximated non-
linear Schrödinger (NLS) equation that results from re-
ducing the NLCM equations using the multiple scale
analysis. The relation between the NLSE and the more
general CME description, which was discussed earlier
[28], is important. Gap solitons are obtained from the
NLCM equations and their spectra lie within the pho-
tonic bandgap structure. There is another class of solitons
called Bragg solitons obtained from the NLS equations
whose frequencies fall close to, but outside, the band
edge of the photonic bandgap. Generally speaking, the
gap solitons are the special class of Bragg solitons.
For the first time, Chen and Mills [12] have analyzed
the properties of these gap solitons in nonlinear periodic
structure. Thereafter, Sipe and Winful published analyses
showing that these “gap-solitons” are not only funda-
mental solutions in the weak-field regime but could be
detected as propagating solutions in structures of finite
length [14]. The general gap soliton so lutions to the cou-
pled mode equations were first obtained in a limiting
case by Christodoulides and Joseph [16]. The solutions
were first reported in their most general form by Aceves
and Wabnitz [17]. Aceves and Wabnitz appoint parame-
ters to form gap solitons in fiber Bragg grating, and the
unique dispersion relation of the fiber grating, and the
corresponding solitons, allows in theory all velocities
from zero to the speed of light in the bare fiber. Their
starting point is the massive Thirring model(MTM), and
quantitative description of gap solitons employs cou-
pled-mode theory, leading to the nonlinear coupled-mode
equations [16,17]. At same time, Sipe and de Sterke ex-
amined, in further publications [27–29], the pulse trans-
mission behavior as a function of both pulse energy and
detuning from the Bragg resonance. Among the contribu-
tions of de Sterke, Sipe and others was a rigorous devel-
opment of coupled-wave and multiple-scales approxima-
tions as well as the description of numerical methods [30]
suitable for examining the regimes of instability of these
structures. In a word, Sipe and Winful [14], Christo-
doulides and Joseph [16], Aceves and Wabnitz [17], and
Winful et al. [31] have obtained the analytical solutions
for the grating solitons. These solitons in FBGs have
been extensively reviewed in [19,32]. Comprehensive
analyses of Bragg solitons stability have also been re-
ported [33,34]. Still other generalizations have been dis-
cussed by Feng and Kneubuhl [35] and by Feng [36]. In
order to better simulate experimental conditions, Brod-
erick, de Sterke and Jackson presented a method of nu-
merically modeling periodic structures having optical
nonlinearities [37]. Other important extensions and gen-
eralizations include a series of papers by Aceves and
coworkers extending many of these principles to wave-
guide arrays [38].
Inverse scattering transform (IST) is currently the
standard analytical technique for obtaining the soliton
solution for the homogenous NLSE [39,40]. IST has
been used to solve the two-dimensional space-time
NLSE with initial-boundary conditions and coupled
NLSE in the form of fundamental and higher-order soli-
tons [39]. To our knowledge, no other analytical method
has been published besides the IST for solving the NLSE
systems. Another method can be described as effective
particle pictures EPP’s, since they represent the continu-
ous field distribution as a point particle with a limited
number of degrees of freedom. The key difference be-
tween the NLSE and NLCME’s is that the NLSE is inte-
grable, whereas NLCME’s are not [37], hence that an
EPP would be more accurate in that case [42–46]. How-
ever, previously, gap soliton propagation in the presence
of uniform gain and loss was succesfully treated using an
EPP [43,47] method, which was also used by Capobi-
anco et al. to treat propagation between two quadratically
nonlinear materials [48]. One method to analyze deep
gratings is using Bloch wave solutions as the fundamen-
tal waves. Actually the modulation of a single Bloch
wave is known to obey the nonlinear Schrödinger equa-
tion in Kerr optical media [13,49,50], and its fundamen-
tal soliton corresponds to gap solitons in this geometry.
Note that the Bloch function formalism has the feature
that the linear system needs to be solved first, and the
nonlinearity is then considered as a perturbation which
can be treated in a variety of approximations. A different
formalism developed for linear gratings only to treat
deep gratings was reported by Sipe et al. [51]. The linear

X. L. LI ET AL.
46
properties are therefore not obtained exactly, but in terms
of an asymptotic series, only a few terms of which are
retained. Nonetheless, the method leads naturally to
low-order corrections to the coupled mode equations for
shallow gratings. Then, one may expect that the model
may give rise to two qualitatively different families of
gap solitons: low-frequency ones, in which the
self-focusing (cubic) nonlinearity is balanced by the dis-
persion branch with a sign corresponding to anomalous
dispersion, and high-power solitons, supported by the
balance between self- defocusing (quintic) nonlinearity
and the normal branch of the dispersion. The simplest
model of this type may be based on the cubic-quintic
(CQ) nonlinearity that has recen tly attracted considerable
attention, as the combination of the SF cubic and SDF
quintic terms prevents collapse and makes it possible to
anticipate the existence of stable solitons [52–60]. Atai
and Malomed introdu ced the qu intic nonlinearity in to the
NLCM equations and investigated two different families
of zero-velocity solitons. One family was the usual
Bragg grating solitons supported by the cubic nonlinear-
ity. The other family was named as twotier solitons sup-
ported by the quintic nonlinearity [26]. In fact, in the
cubic model, the final soliton retains only 11.6% of the
initial energy, while the energy-retention share in the
cubic-quintic model is 92.4% [59].
3. Experimentation and Applications
Recently conducted experiments have provided strong
evidence for the existence of the grating solitons in FBGs
[61–66]. To our knowledge, it was Larochelle, Hihino,
Mizrahi and Stegeman [67] who were the first to report
(in 1990) an experimental investigation of the optical
response of nonlinear periodic structures. They employed
an optical Kerr-effect cross-phase modulation in fiber
gratings to achieve switching of a probe beam by a con-
trol beam.The first detailed experimental observation of
all-optical switching dynamics in a nonlinear periodic
structure was reported by Sankey, Prelewitz and Brown
in 1992 [68]. Experimental observations of nonlinear
grating behaviour are limited, principally by the diffi-
culty in getting sufficiently high power densities within
the core of a FBG in a suitable spectral and temporal
range. In order to reduce the nonlinear threshold for gap
soliton formation one can use the somewhat weaker dis-
persive properties of FBGs outside of the band gap. An
investigation of nonlinear pulse propagation in uniform
fiber gratings was published by Eggleton et al. in 1996
[61].In this report, the Bragg solitons are most easily
generated in the laboratory travel at 60–80% of veocity
of light in fiber absence of grating [61,64]. This was fol-
lowed by further reports from the same group, which
both refined the experimental technique and broadened
the experimental understanding of the dynamics of pulse
propagation in periodic structures [65]. In their initial
experimental observations of Bragg solitons [61,62,64],
the agreement between the experiments and the numeri-
cal calculations was qualitative. However, stationary (or
nearly stationary) gap solitons have not been observed
yet. Subsequently, the Southhampton group [69] first
demonstrated switching at the important optical commu-
nication wavelength of 1550 nm, and in doing so have
confirmed certain key aspects of the physics of pulse
propagation in nonlinear periodic structures. We now
understand that a Bragg soliton need not be centered near
the Bragg resonance--indeed, some very interesting
propagation effects occur rather far from the band edge.
Experimental studies of BG solitons were further devel-
oped including, in particular, formation of multiple BG
solitons inRefs [42]. Broderick et al. also report the first
experimental demonstration of a novel type of all-optical
pulse compression [71]. It is significant experimentation
that Taverner et al. [42,70] reported the first observation
of gap soliton generation in a Bragg grating at frequen-
cies within the photonic bandgap. Furthermore the sets of
experiments were performed in relatively short gratings.
Thus, in these experiments, pure soliton propagation ef-
fects are difficult to distinguish from effects due to soli-
ton formation. The occurrence of modulational instability
(MI) in fibers had been first suggested by Hasegawa and
Brickman [72] and experimentally verified by Tai et al.
[73]. The effects of MI which occurs when a perturbed
continuous wave experiences an instability that leads to
an exponential growth of its amplitude or phase during
the course of propagation in optical fibers due to an in-
terplay between the nonlinearity and group velocity dis-
persion (GVD) act in opposition. THE studies on modu-
lational instability (MI) have some impacts on solitons
[8,74,75].
The researchers recently have realized the potential
applications of these solitons in fiber Bragg grating for
all-optical switching [67,76,77], pulse compression
[69,71,78], limiting [80], and logic operations [81,84],
also promising for the fiber-sensing technology [79],
especially important for the optical communication sys-
tems [78,82]. One would hope to achieve zero velocity
by a clever tailoring of the Bragg grating. This research
goes beyond its intellectual value; all optical buffers and
storing devices can be based on such fibers. About logic
operations, for the first time to our knowledge, an all-
optical ‘AND’ gate based on a configuration proposed by
S. Lee and S.T. Ho [84]. The operation of the gate relies
on the formation and propagation of coupled gap solitons
by two orthogonally polarised high intensity input b eams
incident within the bandgap of a FBG [81]. Recently
Nuran Dogru was pursueing for the hybrid soliton pulse
source (HSPS) developed as a pulse source for the soli-
ton transmission system [88–92]. In a Bragg grating
SPM results in the transmission being bistable with one

X. L. LI ET AL.
47
state (high power) having a transmission of unity while
in the other (low power) the transmission is vanishingly
small [31]. For strong optical pulses this behavior can
result in all-optical switching. The all- optical switching
of a fiber Bragg grating (FBG) was first seen by La-
Rochelle et al. in 1990 [67] using a self-written grating
centered at 514 nm. In their experiment the probe beam
was centered on the grating, while the pump beam had a
wavelength of 1064 nm. It was in this vein that Radic,
George and Agrawal suggested the use of l/4 phase-
shifted gratings for use in optical switching [77]. Ju Han
Lee [85–87] demonstrate the use of a superstructured
fiber Bragg grating obtain more optimal operation of
nonlinear all-optical switches [85], all-optical modula-
tion and demultiplexing systems [86], tunable optical
pulse source [87]. In long distance communications, that
a third-order nonlinear effect is together with anomalous
dispersion, can result in the formation of bright temporal
optical solitons. Beacause of the shape-preserving prop-
erty of the bright and dark solitons, they have received
considerable attention from optical communication in-
dustries. Solitons are particularly desirable for dtra-long
distance communication system and high-bit-rate fiber
communications. A challenging possibility is to use fiber
gratings for the creation of pulses of slow light, which is
a topic of great current interest. A possible way to trap a
zero-velocity soliton is to use an attractive finite-size or
local defect [83] in BG. The interaction of the soliton
with an attractive defect in the form of a local suppres-
sion of BG was studied recently in Refs [78,79].
4. Conclusions
My attempt on this article is to giv e a survey and update
some of fiber Bragg grating solitons. There have been
two papers for summarizing to Bragg solions [93] and
gap solitons [20], gave readers insight into a series of
working methods and results before these generalize.
Clearly grating solitons have played an important role in
past and ongoing nonlinear optical research in fiber
Bragg grating, and we bel i eve fiber Bragg grati ng sol i ons
to have their greatest impact in the years to come.
5. Acknowledgements
This work was supported by the National Natural Science
Foundation of China (No. 40571097) and the National
Program on Key Basic Research Project (973 Program)
(No. 2009CB724001)
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