Single-mode Equations Research Articles

Relative contribution of carrier diffusion and spontaneous emission to the strength and damping of relaxation oscillations in InGaAsP/InP lasers

The damping and strength of relaxation oscillations in BH long-wavelength lasers have been investigated. In addition to previously published papers, the relative contribution of carrier diffusion effects and spontaneous emission is analysed. At moderate pumping rates, the calculated damping factor, using singlemode rate equations and a constant spontaneous carrier lifetime, is found to be in good agreement with experimental results if the finite rise time of the pulse generator is introduced. It is also shown that the overshoot depends mainly on the spontaneous emission factor. However, in general, for the calculated spontaneous emission factor, the predicted overshoot is greater than the measured one. Possible reasons for this disagreement are discussed.

The Influence of Vertical Vorticity on Thermal Convection

The single-mode equations of Boussinesq thermal convection have been modified to include the vertical component of vorticity, which has led, in certain parameter ranges, to a new family of solutions for stationary convection in the absence of external constraints. The features of these solutions are discussed and a comparison with the family of solutions possessing zero vertical vorticity, which are also solutions of the equations, is presented. Specifically, these new solutions are characterized by a lower vertical velocity and heat flux, nonzero vertical vorticity thereby giving them a helical structure and considerably reduced thermal boundary layers in comparison with the family of solutions with zero vertical vorticity. It is to be stressed that this new family of solutions is not due to externally applied influences such as rotation or a magnetic field, the only driving force present being that due to buoyancy.

Microwave Circuit Models of Semiconductor Injection Lasers

Small-signal two-port circuit models of packaged commerical broad-stripe and buried-heterojunction AlGaAs laser diodes are presented. The models are based on the single-mode rate equations, and include the heterojunction I-V and space-charge characteristics. Also included are package and substrate parasitic. The models agree well with measured reflection coefficient and modulation frequency response data, and can be incorporated in standard microwave circuit analysis programs.

Nonlinear Anelastic Modal Theory for Solar Convection

AbstractPreliminary solar envelope models have been computed using the single-mode anelastic equations as a description of turbulent convection. This approach provides estimates for the variation with depth of the largest convective cellular flows, akin to giant cells, with horizontal sizes comparable to the total depth of the convection zone. These modal nonlinear treatments are capable of describing compressible motions occurring over many density scale heights. Single-mode anelastic solutions have been constructed for a solar envelope whose mean stratification is nearly adiabatic over most of its vertical extent because of the enthalpy (or convective) flux explicitly carried by the big cell; a sub-grid scale representation of turbulent heat transport is incorporated into the treatment near the surface. The single-mode equations admit two solutions for the same horizontal wavelength, and these are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is striking that the upward directed flows experience large pressure effects when they penetrate into regions where the vertical scale height has become small compared to their horizontal scale. The fluctuating pressure can modify the density fluctuations so that the sense of the buoyancy force is changed, with buoyancy braking actually achieved near the top of the convection zone. The pressure and buoyancy work in the shallow but unstable H+ and He+ ionization regions can serve to decelerate the vertical motions and deflect them laterally, leading to strong horizontal shearing motions. It appears that such dynamical processes may explain why the amplitudes of flows related to the largest scales of convection are so feeble in the solar atmosphere.

Stellar convection theory. III - Dynamical coupling of the two convection zones in A-type stars by penetrative motions

The thermal convection occurring over many density scale heights in an A-type star outer envelope, encompassing both the hydrogen and helium convectively unstable zones, is examined by means of anelastic modal equations. The single-mode anelastic equations for such compressible convection display strong overshooting of the motions into adjacent radiative zones, which would preclude diffusive separation of elements in the supposedly quiescent region between the two unstable zones. In addition, the anelastic solutions reveal that the two zones of convective instability are dynamically coupled by the overshooting motions. The two solutions that the nonlinear single-mode equations admit for the same horizontal wavelength are distinguished by the sense of the vertical velocity at the center of the three-dimensional cell. It is suggested that strong horizontal shear flows should be present just below the surface of the star, and that the large-scale motions extending into the stable atmosphere would appear mainly as horizontal flows.

Boundary-layer solutions of single-mode convection equations

Nonlinear thermal convection between two stress-free horizontal boundaries is studied using the modal equations for cellular convection. Assuming a large Rayleigh number R the boundary-layer method is used for different ranges of the Prandtl number σ. The heat flux F is determined for the values of the horizontal wavenumber a which maximizes F. For a large Prandtl number, σ [Gt ] R⅙(log R)−1, inertial terms are insignificant, a is either of order one (for $\sigma \geqslant R^{\frac{2}{3}}$) or proportional to $R^{\frac{1}{3}}\sigma^{-\frac{1}{2}}$ (for $\sigma \ll R^{\frac{2}{3}}$) and F is proportional to $R^{\frac{1}{3}}$. For a moderate Prandtl number, \[ (R^{-1}\log R)^{\frac{1}{9}} \ll \sigma \ll R^{\frac{1}{6}}(\log R)^{-1}, \] inertial terms first become significant in an inertial layer adjacent to the viscous buoyancy-dominated interior, and a and F are proportional to R¼ and \[ R^{\frac{3}{10}}\sigma^{\frac{1}{5}} (\log\sigma R^{\frac{1}{4}})^{\frac{1}{10}}, \] respectively. For a small Prandtl number, $R^{-1} \ll \sigma \ll (R^{-1} \log R)^{\frac{1}{9}}$, inertial terms are significant both in the interior and the boundary layers, and a and F are proportional to ($R \sigma)^{\frac{9}{32}} (\log R\sigma)^{-\frac{1}{32}}$ and ($R \sigma)^{\frac{5}{16}} (\log R \sigma)^{\frac{3}{16}}$, respectively.

Nonperiodic oscillations of Langmuir waves

It is shown that the single-mode equations derived from Zakharov’s model for Langmuir turbulence in a plasma in the presence of an external spatially homogeneous electric field oscillating at the electron plasma frequency has nonperiodic chaotic solutions whose power spectra have turbulence-like features. Bounds for these chaotic solutions are derived. Typical numerical results are presented for the one-dimensional case.

Investigation of the stability of a periodic train of pulses emitted by a solid-state laser

A study is made of the stability of the emission of a high-frequency train of pulses by a solid-state laser with periodic Q switching. Generation of a single pulse is analyzed theoretically by single-mode rate equations. The point mapping method is employed in a study of the stability of a periodic train of pulses characterized by different periods and pumping rates, and also of a periodic train consisting of a few pulses of different durations. The results are compared with the experimental data.

Effects of lateral mode and carrier density profile on dynamic behaviors of semiconductor lasers

Dynamic behaviors of the semiconductor lasers have been investigated both theoretically and experimentally. A single-mode rate equation, which takes account of the lateral mode profile and the carrier density profile, has been solved numerically. Effects of the carrier and lateral mode confinement have been clarified. The lateral mode deformation in lasers without a built-in mode confinement structure greatly enhances the relaxation oscillations. In lasers whose stripe width is narrower than \sim10 \mu m, the carrier diffusion is found to play an important role in suppressing the relaxation oscillations, especially for lasers without a lateral carrier confinement structure. On the other hand, the fraction of the spontaneous emission going into the lasing mode is significant for lasers with a lateral carrier confinement structure. The slow increase of the laser output at the transient is confirmed to be due to the carrier diffusion.

Effects on spontaneous emission on dynamic characteristics of semiconductor lasers

Dynamic characteristics of semiconductor lasers are calculated with single-mode rate equations, taking into account spontaneous emission factor β and bias current

Numerical solutions of single-mode convection equations

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Stability of an intracavity frequency-doubled Nd:YAG laser

Single-mode rate equations are solved in the small-signal limit to determine the oscillation frequency and decay constant for relaxation oscillations in an intracavity frequency-doubled Nd:YAG laser. It is found that improved stability is noted for nonlinear coupling constants greater than 10-5. Eventually, cavity perturbations become critically damped with increased coupling, and oscillatory behavior disappears.

Effect of spatial dependence in the single-mode laser rate equations

Effect of spatial dependence in the single-mode laser rate equations