The macroscopic behavior of a semiconductor laser medium is described by use of modified rate equations. The model, valid on time scales greater than 10 Ϫ13 s, explicitly treats carrier temperature as a dynamic variable and includes the nonlinear dependence of the gain function on carrier density and temperature. Gain suppression that is due to carrier heating is a natural consequence of the model and gives a qualitative explanation of subpicosecond gain dynamics experiments without introducing gain nonlinearity phenomenologically. We demonstrate the temperature behavior of the laser during transient dynamics near and well above threshold. By including carrier temperature as a dynamic variable we show that the laser response to an external perturbation exhibits a noticeable change in the damped oscillations of the photon density compared with that in models without temperature dynamics. Variation in the evolution of the gain function for different external pulse energies is also demonstrated.
A theoretical model that predicts difference frequency pressure within the interaction region of a parametric array is presented. Linear and nonlinear attenuation are neglected, and it is assumed that the primary signals are spherically spreading throughout the interaction region. It is shown that with these assumptions the three-dimensional scattering integral can be reduced to a single integral if the primary pressure fields are axially symmetric. Analyses of the error introduced by assuming the primary fields are spherically spreading and by neglecting linear attenuation are presented. Theoretical results compare favorably to p’revious experimental results. The results indicate that diffraction effects are more important than attenuation when the observation point is within the interaction region and when primary signal level reduction is due more to spherical spreading than attenuation. Subject Classification: 25.35; 20.30, 20.15.
Results are reported of an investigation of the reflection of parametric radiation from a finite planar target. The interference of the difference frequency sound generated after reflection with the reflected difference frequency sound is considered. Amplitude and phase were measured before and after reflection from a polyfoam target. Target size ranged from slightly larger than the beamwidth to smaller than the beamwidth. The results are compared with calculations based on equations describing the linear radiation and the parametric radiation. These equations are derived using the parabolic approximation.
The three-dimensional integral solution for the secondary sound produced by a parametric array is formulated in a manner useful for the consideration of broadband or transient primary signals. It is shown that when the primary pressure field can be modeled as spherically spreading from the origin, the low-frequency secondary sound can be expressed as the convolution of the "input" to the parametric array with the "impulse response" of the parametric array. By modeling the primary directivity functions as Gaussian, the impulse response is reduced to a single integral. The "frequency response" of the parametric array is derived and /shown to be the Fourier transform of the impulse response. For the special case of an observer on the axis of symmetry, an exact analytic result for the frequency response is obtained and is compared with previous theories and with experiment. A Fourier transform of secondary pressure field a primary pressure field directivity parameter for Gaussian directivity C = •SR•õ exp(2aRo)•/(2poCo 4) Co small signal sound speed D•, 2 primary pressure field directivity functions
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