Four-wave mixing reflectivity of silicon at 1.06 μm: Influence of free-carrier absorption

The phase-conjugate reflectivity obtainable by degenerate four-wave mixing in silicon at a 1.06 m is calculated including free-carrier absorption. A maximum reflectivity of more than 100% is possible. The dependence of the reflectivity on the signal and pump energy densities up to 70 mJ/cm² is measured and found to agree with theory. The wave-front-correction property of DFWM is demonstrated with a lens in the signal beam.     

Hölder estimate for the solution of degenerate parabolic equations

Consider the degenerate parabolic equations of the type $$u_t = div A(x,t,u,Du) + b(x,t,u,Du)$$ which is of the same nature as $$u_t = div|Du|^p Du + |Du|^{p + 2} (p > 2).$$ This paper is to study the \(C^{1 + \alpha } ,\frac{{1 + \alpha }}{2}\) Hölder continuity of a class of degenerate parabolic equations and the existence and uniqueness of the initial boundary value problem.     

Bang-bang optimal control for the dam problem

The dam problem with general geometry is considered. Fluid is drawn from the bottomS ₁ at a ratek where 0 k N, _{S 1} k M; the objective is to minimize the total pressure of the fluid in the dam. A bang-bang principle is established for any optimal controlk ₀, that is,k ₀ = 0 on a setA andk ₀ =N on the complement setS ₁ A. In the case of a rectangular dam the structure ofA is determined and the uniqueness of the minimizerk ₀ is established.This work is partially supported by National Science Foundation Grants DMS-8501397 and DMS-8420896.     

Vibrational modes and infrared absorption of interstitial oxygen in silicon

A quasi-linear Si₂O molecule model (QLMM) is suggested from an analysis of the configuration and the interactions of an isolated oxygen atom with its neighbor silicon atoms. The vibrational modes are assigned and the infrared absorption spectra are calculated in detail with the model. The theoretical results are in reasonably good agreement with reported experimental values. This agreement shows that for the analysis of the vibrational modes of the interstitial oxygen atom in silicon crystals it is not necessary to consider the coupling of the molecule with the rest of the lattice. The interaction of the oxygen atom with its six second-nearest silicon atoms only causes the level separation of the ₂ mode and the formation of the fine structure.