The transmission properties of one dimensional PT-symmetric photonic crystal (PC) structure with gain and loss regions are presented. Obtained characteristics illustrate the influence of the structures parameters such as the ratio of the PC period to the operating wavelength, the number of the primitive cells creating PC, the loss and gain level (imaginary part of the refractive indices) on reflection and transmission coefficients. It demonstrates strong nonreciprocal response of the structure.
In this paper, a method of designing a Raman laser structures with Bragg mirrors used to coupling pump signal, forming
a resonator and lead-out laser signal outside is presented. The Raman laser is SOI waveguide structure (such as "rib,"
i.e. ridge waveguide) with built-in reverse biased p-i-n diode, wherein the optical gain is generated by stimulated Raman
effect in the waveguide. Our way of designing is based on the effective refractive index method. Design of Raman laser
with Bragg mirrors consists of two main stages: the first step is the choice of the optimum size and shape of the rib
waveguide; the second step is the selection of Bragg gratings parameters. Our method of designing such Raman laser
structures is a design tool, which uses analytical dependences and allows specifying optimal geometric parameters of one
mode laser.
This paper describes an approximate analysis of Raman generation in silicon-on-insulator (SOI) rib waveguide with
DBR/F-P resonator and an integrated p-i-n (PIN) junction, taking into account spatial field distribution and nonlinear
effects involved in silicon. These effects comprise especially, stimulated Raman scattering (SRS), free-carrier absorption
(FCA), degenerate two-photon absorption (i.e. the pump-pump TPA) and non-degenerate two-photon absorption (i.e. the
pump-Stokes TPA and the Stokes-pump TPA). Applying the reverse biased PIN junction allows to reduce the nonlinear
optical losses due to TPA-induced FCA. The model is based on the semiclassical approach and an energy theorem. In
threshold analysis of steady-state Raman laser operation, an analytical formula relating input pump power to the system
parameters is obtained. It allows analyzing the influence of all physical and geometrical parameters on the threshold
pump power. The analysis of the above threshold operation is based on the exact energy conservation relation, in which
the approximated pump and Stokes field distributions are used. The Stokes field distributions are approximated by that
existing at the threshold, whereas the approximate pump field distributions are obtained by integrating the equations for
the pump signal using the linear (threshold) pump field distributions and the threshold Stokes field distributions. We
obtain an approximate, semi-analytical expression related the Raman output power to the pump power and system
parameters.
An approximate method of modeling of Raman generation in silicon-on-insulator(SOI) rib waveguide with DBR/F-P
resonator including nonlinear effects such as Raman amplification and free-carrier absorption (FCA), is presented. In our
detailed theoretical model, we consider coupled set of differential equations for pump signal and Stokes signal inside the
laser cavity. In threshold analysis of steady-state Raman laser operation, we assume that the pump signal distribution is
determined from linear equations. An analytical formula relating threshold pump power to the system parameters is
obtained. The analysis of the above threshold operation is based on an energy theorem and threshold field
approximation. In exact energy conservation relation, we approximate the pump and Stokes field distributions by these
proportional to linear field distribution existing at the threshold, obtaining an approximate, semi-analytical expression
related the Raman output power (i.e. the output power of Stokes lasing) to the pump power and system parameters. With
this formula, the laser characteristics revealing the optimal rib waveguide geometry and the optimal coupling
coefficients, which provide the maximal power efficiency, can be obtained.
In this paper, we present an analysis of light generation in various lasers based on photonic crystal structures. In our
theoretical model, we take into account the gain saturation effect, transverse and longitudinal field distribution. That
model allows defining in easy way the influence of the real structures parameters (for example photonic crystal cell
geometry) on the normalized small signal gain, spontaneous emission, relaxation oscillation parameters, and 3dB
modulation bandwidth.
In this paper, we present a semi analytical, approximate model of relaxation oscillation of Nd3+:YAG DBR (Distributed Bragg Reflector) laser with one dimensional photonic crystals (1D PC). In our theoretical model, we take into account the gain saturation effect, transversal and longitudinal field distribution. With the help of time dependent laser rate equations, we obtain an approximate formulas relating the damping rate and frequency of relaxation oscillations to the output power and laser parameters such as photonic crystal geometry, losses, and reflectivity coefficient of laser mirror. With this approximate formulas, we obtain the laser characteristics, which reveal an optimal feedback strength for DBR cavity laser structure.
In this paper, for the first time we present semi analytical, approximate model of dynamic operation of one dimensional photonic crystal Nd3+:YAG laser. In our theoretical model, we take into account the gain saturation effect and longitudinal field distribution. With the help of time dependent laser rate equations, we obtain an approximate formulas relating the damping rate and frequency of relaxation oscillations and modulation bandwidth to the output power and laser parameters such as photonic crystal geometry, losses, and value of reflection coefficient of laser mirror. With this approximate formulas, we obtain the 1D photonic crystal laser characteristics, which reveal an optimal feedback strength for F-P cavity laser structure. With the help of this model it is possible to defined optimal geometry of the laser structures, which provides maximal modulation bandwidth for given pumping level (characterized by small signal gain).
We present semi analytical, approximate model of nonlinear operation of planar waveguide laser manufactured on the base of 2D photonic crystal. We consider laser structure with F-P cavity and take into account the gain saturation effect, transverse as well as longitudinal field distribution. Our model, based on energy theory, allows to investigate in relatively easy way the influence of the real structure parameters such as photonic crystal geometry, waveguide geometry, losses as well as strength of feedback (i.e. cavity parameters) on output power level. The laser characteristics obtained reveal optimal feedback strength for given laser structure, which provide maximal power efficiency for given pumping level.
We analyze dynamic operation of planar circular grating DFB/DBR laser with phase shift. In our theoretical model, we take into account the spatial hole burning effect, the transverse and longitudinal field distribution. It is found the proper value and position of additional phase shift affects the parameters of relaxation oscillations: damping rate coefficient and frequency, and the 3-dB modulation bandwidth. Moreover, for certain geometry of the structure the mode selectivity can be improved.
In this paper, for the first time we present an analysis of the nonlinear operation of the F-P and DFB lasers based on photonic crystal structure. In our theoretical mode, we take into account the gain saturation effect, transverse and longitudinal field distribution. That model allows to define in easy ways the influence of the real structures parameters (for example photonic crystal cell geometry) on the normalized small signal gain.
In this paper, we present an analysis of relaxations oscillations in planar circular grating DFB and DBR lasers. In our theoretical model, we take into account the transverse and longitudinal field distribution. That model allows to study the influence of the real structures parameters on the relaxation oscillations.
A model of bistable operation of dielectric planar laser with one and two photon nonlinear absorber is presented. The equations of the small-signal gain coefficient for the planar structures with one and two photon nonlinear absorber are derived. Dependence of the waveguide width, transverse mode number, the saturation parameter and position of the active medium is discussed in detail.
An influence of the gain saturation effect and spatial hole burning effect on the dynamic operation of distributed feedback (DFB) lasers with the complex coupling coefficient is analyzed. The strong dependence of the nonlinear effects on the dynamic operation is shown for two different dielectric laser structures with the loss coupling and gain coupling.
An analysis of the dynamic operation in distributed feedback (DFB) lasers is shown. In particular, the influence of the spatial field distribution, the gain saturation effect, and spatial hole burning effect on the relaxation oscillations and modulation bandwidth is discussed for two different dielectric lasers structures, i.e. planar and fiber waveguide lasers. We consider two cases: the dynamic model of DFB laser with pure index modulation and with the complex coupling coefficient.
The effects of the gain saturation of the active medium and spatial hole burning, and system parameters such as loss coefficient, coupling coefficient, and waveguide geometry on the 3-dB modulation bandwidth in planar and fiber distributed feedback lasers is discussed for various transverse laser modes. Additionally, the effect of the amplitude and phase of the end reflectivity on the modulation bandwidth is analyzed for both structures. The characteristics revealing competition between the Fabry-Perot resonator and the distributed feedback resonator are presented.
The influence of the gain saturation of the active medium and system parameters such as loss coefficient, coupling coefficient, and waveguide geometry on the 3 dB modulation bandwidth in fiber distributed feedback lasers is discussed for various transverse laser modes. Additionally, the effect of the amplitude and phase of the end reflectivity is taken into account. The characteristics revealing competition between the Fabry-Perot resonator and the distributed feedback resonator are presented.
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