Kovachev Lubomir M, Kovachev Kamen L
Institute of Electronics, Bulgarian Academy of Sciences, Sofia, Bulgaria.
J Opt Soc Am A Opt Image Sci Vis. 2008 Sep;25(9):2232-43. doi: 10.1364/josaa.25.002232.
We present a systematic study of linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media, and vacuum. The applied method of amplitude envelopes makes it possible to estimate the limits of the slowly varying amplitude approximation and to describe an amplitude integrodifferential equation governing propagation of optical pulses in the single-cycle regime in solids. The well-known slowly varying amplitude equation and the amplitude equation for the vacuum case are written in dimensionless form. Three parameters are obtained defining different linear regimes of optical pulse evolution. In contrast to previous studies we demonstrate that in the femtosecond region the nonparaxial terms are not small and can dominate over the transverse Laplacian. The normalized amplitude nonparaxial equations are solved using the method of Fourier transforms. Fundamental solutions with spectral kernels different from those according to Fresnel are found. Exact unidirectional analytical solution of the nonparaxial amplitude equations and the 3D wave equations with initial conditions compatible with Gaussian light bullets are obtained also. One unexpected new result is the relative stability of light bullets (pulses with spherical and spheroidal spatial form) when we compare their transverse enlargement with paraxial diffraction of light beams in air. It is important to emphasize here the case of light disks, i.e., pulses whose longitudinal size is small with respect to the transverse one, which in some partial cases are practically diffractionless over distances of a thousand kilometers. A new formula that calculates the diffraction length of optical pulses is suggested. Finally, propagation of single-cycle pulses in air and vacuum was investigated, and a coronal (semispherical) form of diffraction at short distances was observed.
我们对超短激光脉冲在具有色散的介质、无色散介质和真空中的线性传播进行了系统研究。所应用的振幅包络方法使得能够估计缓变振幅近似的极限，并描述一个振幅积分微分方程，该方程支配着固体中光学脉冲在单周期 regime 下的传播。著名的缓变振幅方程和真空情况下的振幅方程被写成无量纲形式。获得了定义光学脉冲演化不同线性 regime 的三个参数。与先前的研究不同，我们证明在飞秒区域非傍轴项不小，并且可以超过横向拉普拉斯算子。使用傅里叶变换方法求解归一化振幅非傍轴方程。找到了具有不同于菲涅耳光谱核的基本解。还获得了非傍轴振幅方程和具有与高斯光子弹兼容的初始条件的三维波动方程的精确单向解析解。一个意想不到的新结果是，当我们将光子弹（具有球形和椭球形空间形式的脉冲）的横向扩展与光束在空气中的傍轴衍射进行比较时，光子弹具有相对稳定性。在此强调光盘的情况很重要，即纵向尺寸相对于横向尺寸较小的脉冲，在某些部分情况下，它们在一千公里的距离上实际上是无衍射的。提出了一个计算光学脉冲衍射长度的新公式。最后，研究了单周期脉冲在空气和真空中的传播，并观察到短距离处的日冕（半球形）衍射形式。
