Achromatic doublets using group indices of refraction

Abstract

One main function of short pulses is to concentrate energy in time and space [1]. The use of refractive lenses allows us to concentrate energy in a small volume of focusing around the focal point of the lens. When using refractive lenses, there are three effects that affect the concentration of energy around the focal point of the lens. These are the group velocity dispersion (GVD), the propagation time difference (PTD), and the aberrations of the lens. In this paper, we study lenses which are diffraction limited so that the monochromatic aberrations are negligible; the group velocity dispersion and the propagation time difference are the main effects affecting the spreading of the pulse at the focus. We will show that for 100-fs pulses the spatial spreading is larger than the temporal spreading of the pulse. It is already known that the effect of spatial spreading of the pulse due to PTD can be reduced by using achromatic optics. We use the theory proposed by A. Vaughan to analyze simple lenses and normal achromatic doublets, where normal means doublets that we can buy from catalogs. We then use the Vaughan theory to design achromatic doublets in phase and group, which produce no spatial spreading of the pulse, i.e., PTD = 0, when the doublet is designed for the carrier of the pulse. We compare these phase and group achromatic doublets with normal achromatic doublets. Finally, we show that apochromatic optics can give a much better correction of PTD than using normal achromatic doublets.