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Chapter 6:
Lenses for Laser Applications
The aberration theory that we use in the design of "€œwhite-light" systems is applicable to the design of lenses that are intended for use in instruments involving lasers. However, for most designs the laser can be regarded as monochromatic, so that chromatic aberrations need not be considered. We also need to be aware of the intensity profile of the laser beam. This will affect lens apertures and the position of optimum focus, especially in conditions of very low numerical aperture, when the basic geometrical optics approximations break down. A Gaussian beam is formed as the lowest-order transverse mode in a stable laser resonator with spherical mirrors, and in most of these cases it has a circular cross section. On the other hand, a Gaussian beam with an elliptical cross section often describes light emitted by laser diodes. The energy of a Gaussian beam is concentrated into a narrow cone and its transverse amplitude distribution is a Gaussian, with its center on the beam axis. The width of a Gaussian distribution is minimal in the position of maximum contraction of the beam—in its center—and the width increases in both directions with distance from the center. The center of a Gaussian beam is known as the beam waist. In the vicinity of the waist, constant phase surfaces are nearly plane. As distance from the beam waist increases these phase surfaces become increasingly curved; for very large distances from the beam waist they become nearly spherical, with curvature centering on the beam waist center. The parameters of Gaussian beams are usually given at the 1/e fraction of maximum amplitude, which corresponds with 1/e2 level of maximum energy in the beam cross section. When a Gaussian beam passes through a lens, it is important to ensure that all energy within the 1/e2 level passes through without obstruction. If this condition is not met, then the outgoing beam from the lens cannot be described as Gaussian, and Gaussian calculations will not apply. It should be noted that the 1/e2 requirement is an absolute minimum, and in many applications (e.g. when considering the coupling efficiency of a Gaussian beam into a single-mode optical fiber) a greater fraction of the energy must be transmitted without obstruction.
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