The coherent light interacting with a direct band-gap semiconductor is modelled as two coupled harmonic oscillators with Kerr-type nonlinearity in one of the oscillators. By considering the nonlinearity in the exciton mode, we derive approximate analytical solutions of the coupled differential equations involving two bosonic modes. For both photon and exciton modes which are in initial coherent states, we calculate the phase fluctuation parameters due to Carruthers and Nieto. We have used the Pegg–Barnett formalism for defining the useful phase operators. We report the increase and decrease of phase fluctuation parameters of input radiation field compared to its initial values. Effects of vacuum field on the phase fluctuation parameters are found distinctly different from their counterparts without vacuum. The complete analytical approach of the present investigation is substantiated by the numerical calculations based on QuTip.

与直接带隙半导体相互作用的相干光被建模为两个耦合谐波振荡器，其中一个振荡器具有克尔型非线性。通过考虑激子模式的非线性，我们推导出涉及两个玻色模的耦合微分方程的近似解析解。对于处于初始相干状态的光子和激子模式，我们计算了由于 Carruthers 和 Nieto 引起的相位波动参数。我们已经使用 Pegg-Barnett 形式主义来定义有用的相位运算符。我们报告了输入辐射场的相位波动参数与其初始值相比的增加和减少。发现真空场对相位波动参数的影响与没有真空的情况明显不同。