# 超快激光 — 超快相干性的基本原理

##### 图 2:通过锁模产生超短脉冲（产生波长带宽很宽但时间宽度超短的脉冲）的基本概念

(1)$$\phi = \sum{a_n \varphi_n}$$

(2)$$a_n = C \langle \varphi_n | \chi_0 \rangle \int^{+ \infty}_{- \infty} \exp{\left[ - \frac{i \left( E_n - E_0 \right) t }{\hslash} \right]} \cdot \exp{\left( \frac{-t^2}{\alpha \tau^2} \right)} \cdot \cos{\left( \omega t \right)} \, \text{d} t$$

(3)$$a_n = C \langle \varphi_n | \chi_0 \rangle \cdot \exp{\left[ \frac{- \left( \omega_n - \omega \right)^2 \alpha \tau^2}{4} \right]}$$

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