含义Meaning
散射光与激发光的波数差等于分子振动（转动）波数，与激发波长无关。斯托克斯线（低频侧）比反斯托克斯线强，比值可用于测温。
The wavenumber difference between scattered and incident light equals a molecular vibrational (rotational) wavenumber, independent of the laser. Stokes lines are stronger than anti-Stokes lines; their ratio gives temperature.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(\Delta\tilde\nu\) | 拉曼位移Raman shift | cm⁻¹ |
| \(\lambda_0, \lambda_s\) | 激发光、散射光波长laser and scattered wavelengths | cm |
| \(\tilde\nu_m\) | 振动波数vibrational wavenumber | cm⁻¹ |
推导Derivation
光子与分子非弹性碰撞：能量守恒 \(h\nu_s = h\nu_0 \mp h\nu_m\)。
Inelastic scattering conserves energy: \(h\nu_s = h\nu_0 \mp h\nu_m\).
经典图像：诱导偶极 \(\mu = \alpha E\)，若极化率随振动调制 \(\alpha = \alpha_0 + (\partial\alpha/\partial Q)Q\)，散射光含 \(\nu_0 \pm \nu_m\) 频率——拉曼活性要求 \(\partial\alpha/\partial Q \ne 0\)。
Classically, a vibration-modulated polarisability produces \(\nu_0 \pm \nu_m\); Raman activity needs \(\partial\alpha/\partial Q \ne 0\).
反斯托克斯来自已激发的振动态，布居按玻尔兹曼因子较少；散射强度还 \(\propto \nu^4\)。
Anti-Stokes starts from excited levels (Boltzmann-depleted); intensity also scales as ν⁴.
适用条件与局限Assumptions & limitations
拉曼散射很弱（约 10⁻⁶–10⁻⁸ 的入射光）；荧光会掩盖拉曼信号（可改用近红外激发）。
Raman scattering is weak (~10⁻⁶–10⁻⁸); fluorescence can swamp it (use NIR excitation).
例题Worked example
CCl₄ 的 459 cm⁻¹ 带：532 nm 激发时斯托克斯线在 545.3 nm。
CCl₄ 459 cm⁻¹ band: with 532 nm excitation the Stokes line is at 545.3 nm.