We study how the effects of finite pulse durations modify the fifth-order two-quantum two-dimensional (2Q-2D) and three-dimensional (3D) optical spectra. Instead of directly calculating the time domain polarization, the equivalent approach in frequency domain significantly simplifies the calculations and delivers exact expressions for the 2Q-2D and 3D spectra. Our results minimize the number of numerical integrations needed. We also derive simple analytical formulas for practically important situations when the laser pulses are short on the timescale of nuclear motion as well as short (or long) on the timescale of electronic dephasing. These formulas evaluate the measured spectra by multiplying the spectral response function by a factor depending on the spectral pulse envelopes.

我们研究有限脉冲持续时间的影响如何修改五阶二维量子（2Q-2D）和三维（3D）光谱。代替直接计算时域极化，频域中的等效方法显着简化了计算并提供了2Q-2D和3D光谱的精确表达式。我们的结果使所需的数值积分数量最少。当激光脉冲在核运动的时间尺度上短而在电子移相的时间尺度上短（或长）时，我们还为实际重要的情况推导了简单的解析公式。这些公式通过将光谱响应函数乘以取决于光谱脉冲包络的因子来评估测得的光谱。