Yetzbacher Michael K, Belabas Nadia, Kitney Katherine A, Jonas David M
Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0215, USA.
J Chem Phys. 2007 Jan 28;126(4):044511. doi: 10.1063/1.2426337.
Using a solution of Maxwell's equations in the three-dimensional frequency domain, femtosecond two-dimensional Fourier transform (2DFT) spectra that include distortions due to phase matching, absorption, dispersion, and noncollinear excitation and detection of the signal are calculated for Bloch, Kubo, and Brownian oscillator relaxation models. For sample solutions longer than a wavelength, the resonant propagation distortions are larger than resonant local field distortions by a factor of approximately L/lambda, where L is the sample thickness and lambda is the optical wavelength. For the square boxcars geometry, the phase-matching distortion is usually least important, and depends on the dimensionless parameter, L sin(2)(beta)Deltaomega/(nc), where beta is the half angle between beams, n is the refractive index, c is the speed of light, and Deltaomega is the width of the spectrum. Directional filtering distortions depend on the dimensionless parameter, (Deltaomega)w(0) sin(beta)/c, where w(0) is the beam waist at the focus. Qualitatively, the directional filter discriminates against off diagonal amplitude. Resonant absorption and dispersion can distort 2D spectra by 10% (20%) at a peak optical density of 0.1 (0.2). Complicated distortions of the 2DFT peak shape due to absorption and dispersion can be corrected to within 10% (15%) by simple operations that require knowledge only of the linear optical properties of the sample and the distorted two-dimensional spectrum measured at a peak optical density of up to 0.5 (1).
利用三维频域中的麦克斯韦方程组解，针对布洛赫、久保和布朗振子弛豫模型，计算了飞秒二维傅里叶变换（2DFT）光谱，这些光谱包含由于相位匹配、吸收、色散以及信号的非共线激发和检测而产生的畸变。对于长度超过一个波长的样品溶液，共振传播畸变比共振局部场畸变大约大L/λ倍，其中L是样品厚度，λ是光波长。对于方形箱形几何结构，相位匹配畸变通常最不重要，并且取决于无量纲参数Lsin²(β)Δω/(nc)，其中β是光束之间的半角，n是折射率，c是光速，Δω是光谱宽度。方向滤波畸变取决于无量纲参数[(Δω)w(0)sin(β)/c]²，其中w(0)是焦点处的光束腰宽。定性地说，方向滤波器会抑制非对角振幅。在峰值光密度为0.1（0.2）时，共振吸收和色散会使二维光谱畸变10%（20%）。由于吸收和色散导致的2DFT峰形的复杂畸变可以通过仅需了解样品的线性光学性质和在高达0.5（1）的峰值光密度下测量的畸变二维光谱的简单操作校正到10%（15%）以内。
