124
L. Parameswar
iq 2x + q 2tt + 2(α|q 1 |
2
+ β|q 1 |
2
)q 2 = 0
( 1 0 )
iq 1x + q 1tt + 2(α|q 1 |
2
+ β|q 2 |
2
)q 1 = 0
This model is not only useful to describe soliton propagation in optical fibers, but
can also be used to describe incoherent soliton-beam propagation in the so-called
photorefractive materials. These materials can often exhibit high nonlinearity with
very low intensity optical pulses, even with milliWatt power lasers or incandescent
bulbs. Examples of such photorefractive materials include lithium niobate (Li N bO 3 )
and strontium barium niobate (Sr Ba N bO 3 ) crystals. The coupled-beam propagation
through photorefractive media is investigated using the theory of two-beam coupling
[3] and the possibility of formation of dark as well as bright soliton is studied subject
to some parametric conditions.
6 Photorefractive Solitons
Segev et al. [9] have shown that the photorefractive media can support a new type of
soliton in which the mixing of two waves or self scattering is balanced by diffraction.
The photorefractive (PR) soliton possess the property of independence absolute high
intensity and can experience, absorption with no change in the transverse structure.
The shape of the soliton modulates the refractive index via photorefractive (PR)
effect, which results in exact compensation for the effect of diffraction and causes
the light beam to propagate with an unvarying profile. The PR solitons have become
a subject of increased interest for the past few years [9–13]. Chen et al. [14] showed
that two mutually incoherent beams of same polarization can form coupled steadystate spatial solitons pair in a biased photorefractive medium. In general a coupled
PR soliton pair is analogous to a Manakov soliton, in which both beams are mutually
trapped [15]. It was also shown that a system of incoherently coupled equations may
possess general solutions for coupled solitary waves. The condition in which two
beams of light of slightly different frequencies interact in such a manner that energy
is transferred from one beam to another is known as “two-beam coupling”. CNLSE is
used to describe the possibility of soliton-like propagation in PR media. The method
used is two-beam coupling. Starting from the wave equation, the CNLSE is derived.
We found that under certain conditions, this equation possesses soliton solutions.
7 Two-Beam Coupling Using Solitons
Consider two beams of light (which in general have different frequencies) interacting in a photorefractive material. To describe this process mathematically, the total
electric field within the nonlinear medium is described as [11]
L. Parameswar
iq 2x + q 2tt + 2(α|q 1 |
2
+ β|q 1 |
2
)q 2 = 0
( 1 0 )
iq 1x + q 1tt + 2(α|q 1 |
2
+ β|q 2 |
2
)q 1 = 0
This model is not only useful to describe soliton propagation in optical fibers, but
can also be used to describe incoherent soliton-beam propagation in the so-called
photorefractive materials. These materials can often exhibit high nonlinearity with
very low intensity optical pulses, even with milliWatt power lasers or incandescent
bulbs. Examples of such photorefractive materials include lithium niobate (Li N bO 3 )
and strontium barium niobate (Sr Ba N bO 3 ) crystals. The coupled-beam propagation
through photorefractive media is investigated using the theory of two-beam coupling
[3] and the possibility of formation of dark as well as bright soliton is studied subject
to some parametric conditions.
6 Photorefractive Solitons
Segev et al. [9] have shown that the photorefractive media can support a new type of
soliton in which the mixing of two waves or self scattering is balanced by diffraction.
The photorefractive (PR) soliton possess the property of independence absolute high
intensity and can experience, absorption with no change in the transverse structure.
The shape of the soliton modulates the refractive index via photorefractive (PR)
effect, which results in exact compensation for the effect of diffraction and causes
the light beam to propagate with an unvarying profile. The PR solitons have become
a subject of increased interest for the past few years [9–13]. Chen et al. [14] showed
that two mutually incoherent beams of same polarization can form coupled steadystate spatial solitons pair in a biased photorefractive medium. In general a coupled
PR soliton pair is analogous to a Manakov soliton, in which both beams are mutually
trapped [15]. It was also shown that a system of incoherently coupled equations may
possess general solutions for coupled solitary waves. The condition in which two
beams of light of slightly different frequencies interact in such a manner that energy
is transferred from one beam to another is known as “two-beam coupling”. CNLSE is
used to describe the possibility of soliton-like propagation in PR media. The method
used is two-beam coupling. Starting from the wave equation, the CNLSE is derived.
We found that under certain conditions, this equation possesses soliton solutions.
7 Two-Beam Coupling Using Solitons
Consider two beams of light (which in general have different frequencies) interacting in a photorefractive material. To describe this process mathematically, the total
electric field within the nonlinear medium is described as [11]