Soliton Propagation Through Photorefractive Media
121
3 Optical Solitons
Nonlinear optics is the study of phenomena that occur as a consequence of the
modification of the optical properties of a material system by the presence of light.
The beginning of the field of nonlinear optics is often taken to be the discovery of
second harmonic generation by Franken et al. in 1961, shortly after the demonstration
of the first working of laser by Maiman in 1960 [4]. Nonlinear optical phenomena
are nonlinear in the sense that they occur when the response of a material system
to an applied optical field depends in a nonlinear manner upon the strength of the
optical field.
After the invention of lasers, nonlinear optics has emerged as one of the most
sought-after subjects in all the frontiers of science by both theoreticians and experimentalists. Nonlinear optics has stirred many phenomena like fabrication of new
nonlinear materials, harmonic generations, optical solitons, parametric amplification, stimulated Raman scattering, self-induced transparency, modulation instability,
etc. which find a myriad of applications ranging from high data transmission in
optical communication, switching amplifiers, pulse reshaping, pulse compression,
tunable lasers to encoded message transmission. Notable among them is the concept of optical soliton pioneered by Hasegawa of Japan [5]. It revolutionalized the
scope of telecommunication world and solitons are nowdays perceived to be carriers of communication signals in near future. Optical solitons were first observed by
Mollenaeur and his group in 1980s in optical fibers [6].
Optical solitons fall into two categories (1) Spatial optical solitons and (2) Temporal optical solitons [7]. Spatial solitons are optical beams that can propagate in a
nonlinear medium without diffraction, that is, their beam diameter remains invariant
during propagation. A spatial soliton represents an exact balance between diffraction
and nonlinearity induced self lensing or self defocusing effects. Spatial solitons have
become one of the research areas in optics and nonlinear science. A temporal soliton
is formed when group velocity dispersion (GVD) is totally counteracted by temporal self-focusing or self-phase modulation (SPM) effects [4, 5]. Optical temporal
solitons have become a candidate for optical communication networks.
All optical solitons require a strong enough nonlinear interaction between themselves and the material in which they propagate. This interaction requires the socalled diffraction length for the spatial case or dispersion length for temporal (fiber)
case which is comparable to a nonlinear length that characterizes self-focusing in
the medium. In fibers low losses allow propagation distance of kilometers, and as
a result, the very weak glass nonlinearity becomes cumulatively sufficient for soliton formation. In spatial case, however, the sample sizes are typically limited to
centimeters, and thus, either the nonlinearities or the operator powers need to be
larger. Therefore dimensionality is the factor that counterparts spatial solitons from
fiber. Fiber solitons are described by (1+1) dimensional creatures. The higher dimensionalities of spatial solitons lead to host of interesting phenomena and processes,
which have no analogue whatsoever in temporal case. These include, for example,
121
3 Optical Solitons
Nonlinear optics is the study of phenomena that occur as a consequence of the
modification of the optical properties of a material system by the presence of light.
The beginning of the field of nonlinear optics is often taken to be the discovery of
second harmonic generation by Franken et al. in 1961, shortly after the demonstration
of the first working of laser by Maiman in 1960 [4]. Nonlinear optical phenomena
are nonlinear in the sense that they occur when the response of a material system
to an applied optical field depends in a nonlinear manner upon the strength of the
optical field.
After the invention of lasers, nonlinear optics has emerged as one of the most
sought-after subjects in all the frontiers of science by both theoreticians and experimentalists. Nonlinear optics has stirred many phenomena like fabrication of new
nonlinear materials, harmonic generations, optical solitons, parametric amplification, stimulated Raman scattering, self-induced transparency, modulation instability,
etc. which find a myriad of applications ranging from high data transmission in
optical communication, switching amplifiers, pulse reshaping, pulse compression,
tunable lasers to encoded message transmission. Notable among them is the concept of optical soliton pioneered by Hasegawa of Japan [5]. It revolutionalized the
scope of telecommunication world and solitons are nowdays perceived to be carriers of communication signals in near future. Optical solitons were first observed by
Mollenaeur and his group in 1980s in optical fibers [6].
Optical solitons fall into two categories (1) Spatial optical solitons and (2) Temporal optical solitons [7]. Spatial solitons are optical beams that can propagate in a
nonlinear medium without diffraction, that is, their beam diameter remains invariant
during propagation. A spatial soliton represents an exact balance between diffraction
and nonlinearity induced self lensing or self defocusing effects. Spatial solitons have
become one of the research areas in optics and nonlinear science. A temporal soliton
is formed when group velocity dispersion (GVD) is totally counteracted by temporal self-focusing or self-phase modulation (SPM) effects [4, 5]. Optical temporal
solitons have become a candidate for optical communication networks.
All optical solitons require a strong enough nonlinear interaction between themselves and the material in which they propagate. This interaction requires the socalled diffraction length for the spatial case or dispersion length for temporal (fiber)
case which is comparable to a nonlinear length that characterizes self-focusing in
the medium. In fibers low losses allow propagation distance of kilometers, and as
a result, the very weak glass nonlinearity becomes cumulatively sufficient for soliton formation. In spatial case, however, the sample sizes are typically limited to
centimeters, and thus, either the nonlinearities or the operator powers need to be
larger. Therefore dimensionality is the factor that counterparts spatial solitons from
fiber. Fiber solitons are described by (1+1) dimensional creatures. The higher dimensionalities of spatial solitons lead to host of interesting phenomena and processes,
which have no analogue whatsoever in temporal case. These include, for example,