Lens design using group indices of refraction

Abstract

An approach to lens design is described in which the ratio of the group velocity to the speed of light (the group index) in glass is used, in conjunction with the more familiar phase index of refraction, to control certain chromatic properties of a system of thin lenses in contact. It is shown that, at the wavelength of a maximum or minimum (where the phase power of a lens is locally independent of wavelength), the group power is equal to the phase power. It is further shown that, in a lens consisting of three or more elements, the phase and group powers can be constrained to be both equal and independent of wavelength (achromatic) at one or more wavelengths. In the neighbourhood of such wavelengths, both the first and the second derivatives of phase power with respect to wavelength are zero, giving this type of lens (in principle) an exceptionally high degree of achromatism not previously described, herein called group achromatism. The first-order design of thin-lens systems is illustrated by examples with the help of a computer program incorporating the methods described.