We present a systematic study of the optical absorption coefficient (OAC) and refractive index change (RIC) for a symmetric semiconductor nanostructure. We derived the OAC and RIC following two approaches, one without approximations, besides the usual ones (rotating-wave approximation and application of a two-level model), and the other using an approximation keeping only the contribution of the linear and third-order nonlinear terms. In the derivation we consider properly the contribution of the population decay time and the dephasing time, which may be different to each other, in general, in semiconductor nanostructures, extending previous works. We also apply the derived formulae for the calculation of the OAC and RIC in a specific semiconductor quantum well with position-dependent mass and compared the results obtained from the derived formulae. We find that while for low light intensities the different formulae for OAC and RIC give similar results for higher light intensities only the formulae obtained without approximations can lead to correct physical results. We also present a critical intensity below which the different formulae for OAC and RIC give practically the same results. This critical intensity can be used for obtaining correct behavior for the OAC and RIC in any symmetric semiconductor nanostructure.

我们目前对对称半导体纳米结构的光吸收系数（OAC）和折射率变化（RIC）进行系统研究。我们通过以下两种方法得出OAC和RIC，一种是除常规方法（旋转波逼近和两级模型的应用）外没有近似值，另一种方法是仅保留线性和三阶贡献的近似值非线性项。在推导过程中，我们会适当考虑总体衰减时间和移相时间的贡献，这在半导体纳米结构中通常可能会有所不同，从而扩展了以前的工作。我们还将导出的公式应用于位置依赖质量的特定半导体量子阱中的OAC和RIC的计算，并比较了从导出的公式获得的结果。我们发现，对于低光强度，对于高光强度，OAC和RIC的不同公式给出了相似的结果，只有获得的近似公式才能得出正确的物理结果。我们还提出了一种临界强度，在该临界强度以下，OAC和RIC的不同公式给出的结果几乎相同。该临界强度可用于在任何对称半导体纳米结构中获得OAC和RIC的正确行为。我们发现，对于低光强度，对于高光强度，OAC和RIC的不同公式给出了相似的结果，只有获得的近似公式才能得出正确的物理结果。我们还提出了一种临界强度，在该临界强度以下，OAC和RIC的不同公式给出的结果几乎相同。该临界强度可用于在任何对称半导体纳米结构中获得OAC和RIC的正确行为。我们发现，对于低光强度，对于高光强度，OAC和RIC的不同公式给出了相似的结果，只有获得的近似公式才能得出正确的物理结果。我们还提出了一种临界强度，在该临界强度以下，OAC和RIC的不同公式给出的结果几乎相同。该临界强度可用于在任何对称半导体纳米结构中获得OAC和RIC的正确行为。