García-Martínez L, Rosete-Aguilar M, Garduño-Mejia J
Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Cd. Universitaria, México City, México.
Appl Opt. 2012 Jan 20;51(3):306-15. doi: 10.1364/AO.51.000306.
We analyze the spatio-temporal intensity of sub-20 femtosecond pulses with a carrier wavelength of 810 nm along the optical axis of low numerical aperture achromatic and apochromatic doublets designed in the IR region by using the scalar diffraction theory. The diffraction integral is solved by expanding the wave number around the carrier frequency of the pulse in a Taylor series up to third order, and then the integral over the frequencies is solved by using the Gauss-Legendre quadrature method. The numerical errors in this method are negligible by taking 96 nodes and the computational time is reduced by 95% compared to the integration method by rectangles. We will show that the third-order group velocity dispersion (GVD) is not negligible for 10 fs pulses at 810 nm propagating through the low numerical aperture doublets, and its effect is more important than the propagation time difference (PTD). This last effect, however, is also significant. For sub-20 femtosecond pulses, these two effects make the use of a pulse shaper necessary to correct for second and higher-order GVD terms and also the use of apochromatic optics to correct the PTD effect. The design of an apochromatic doublet is presented in this paper and the spatio-temporal intensity of the pulse at the focal region of this doublet is compared to that given by the achromatic doublet.
我们利用标量衍射理论，分析了载波波长为810nm、脉宽小于20飞秒的脉冲沿红外区域设计的低数值孔径消色差和复消色差双合透镜光轴的时空强度。通过在脉冲载波频率附近将波数展开为泰勒级数至三阶来求解衍射积分，然后使用高斯 - 勒让德求积法求解频率积分。通过取96个节点，该方法的数值误差可忽略不计，与矩形积分法相比，计算时间减少了95%。我们将表明，对于在810nm波长下通过低数值孔径双合透镜传播的10飞秒脉冲，三阶群速度色散（GVD）不可忽略，其影响比传播时间差（PTD）更重要。然而，最后这个效应也很显著。对于脉宽小于20飞秒的脉冲，这两种效应使得必须使用脉冲整形器来校正二阶及更高阶GVD项，并且还需要使用复消色差光学器件来校正PTD效应。本文给出了一个复消色差双合透镜的设计，并将该双合透镜焦区的脉冲时空强度与消色差双合透镜给出的强度进行了比较。
