This paper investigates the effect of the linewidth
enhancement factor on the operation and intensity noise
fluctuations of 980-InGaAs/InP fiber grating lasers operating
under strong optical feedback. The analyses are performed in
terms of the temporal trajectory of the laser intensity, bifurcation
diagram and relative intensity noise. The influence of intrinsic
fluctuations in the intensity and optical phase of the lasing field on
the laser dynamics were taken into account. The laser diode
operates in pulsation under strong optical feedback and at small
and relatively large values the linewidth enhancement factor. The
optical feedback noise is found to be as low as the quantum noise
level when the laser is operated in pulsing region and at relatively
large values of the linewidth enhancement factor

This paper investigates influence of the
linewidth enhancement factor on the output of
980-InGaAs/InP fiber grating lasers operating under strong
optical feedback. The study is based on intensive numerical
integration of an improved time-delay rate equations of
semiconductor lasers over wide ranges of the linewidth
enhancement factor and ratio of the grating reflectivity to
that of the anti-reflecting front facet. The results show that
the laser operates in continuous wave and pulsation at small
values of the linewidth enhancement factor. Under large
values of the factor, the laser happens to exhibits chaos and
pulsation. However, such pulsation is predicted to be more
stable due to locking of the laser oscillation at the external
cavity resonance frequency

This paper investigates dynamics of
semiconductor lasers under optical feedback during
transitions to chaos. Influence of the external-cavity length
on the route-to-chaos is elucidated. The study is based on
numerical solution of a time-delay model of rate equations.
The route to chaos is period doubling when the ratio of the
relaxation frequency to the external-cavity resonance
frequency is less than unity. The route is sub-harmonic
when the frequency ratio is slightly higher than unity, and
is quasi-periodic characterized by the compound-cavity
frequency and the relaxation frequency as well as their
difference when the ratio is far above unity

This paper investigates numerically influence of the external-cavity length on the type of the route-to-chaos
of semiconductor lasers under external optical feedback. The study is based on numerical solution of a
time-delay model of rate equations, and the solutions are employed to construct bifurcation diagrams and
to examine the Fourier frequency spectrum of the laser output. The ratio of the relaxation frequency to the
external-cavity resonance frequency is employed to measure the influence of the length of the external
cavity. The route-to-chaos is period doubling when this frequency ratio is less than unity. The route is subharmonic
when the frequency ratio increases up to 2.25. When the frequency ratio increases further, the
transition to chaos becomes quasi-periodic characterized by the compound-cavity frequency and the
relaxation frequency as well as their difference.

Influence of the linewidth-enhancement factor on the output and operations of InGaAs/InP pumping
lasers emitting at a wavelength of 980nm under strong optical feedback is investigated numerically. The
investigations are performed based on intensive numerical integration of an improved time-delay rate
equations of semiconductor lasers over wide ranges of the linewidth-enhancement factor and optical
feedback strength. The results show that the semiconductor laser operates under strong optical feedback in
continuous wave and pulsation at small values of the linewidth-enhancement factor. Under large values of
the linewidth-enhancement factor, the laser happens to exhibit chaos and pulsation. We predict that
semiconductor laser subjected to strong optical feedback exhibits much more stable pulsing operation
under higher values of the linewidth-enhancement factor, which indicates that the laser is locked at the
external cavity frequency.

The jump problem and problems with defects on the type change line for model mixed-type equations in the mixed domains are investigated. The explicit solutions of the jump problem are obtained by the method of integral equations and by the Fourier transformation method. The problems with defects are reduced to singular integral equations. Some results for the solution of the equation under consideration are discussed concerning the existence and uniqueness for the solution of the suggested problem.