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A laser beam profiler captures, displays, and records the spatial intensity profile of a laser beam at a particular plane transverse to the beam propagation path. Since there are many types of lasers— ultraviolet , visible , infrared , continuous wave , pulsed, high-power, low-power—there is an assortment of instrumentation for measuring ...
Tophat beams are often used in industry, for example for laser drilling of holes in printed circuit boards. They are also used in very high power laser systems, which use chains of optical amplifiers to produce an intense beam. Tophat beams are named for their resemblance to the shape of a top hat.
The equations below assume a beam with a circular cross-section at all values of z; this can be seen by noting that a single transverse dimension, r, appears.Beams with elliptical cross-sections, or with waists at different positions in z for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of w 0 and of the z = 0 location for ...
The beam is imaged by a lens, effecting a Fourier transform, whose intensity is represented in this picture The functions are a basis defined over the circular support area, typically the pupil planes in classical optical imaging at visible and infrared wavelengths through systems of lenses and mirrors of finite diameter.
is the centroid of the beam profile in the x direction. When a beam is measured with a laser beam profiler, the wings of the beam profile influence the D4σ value more than the center of the profile, since the wings are weighted by the square of its distance, x 2, from the center of the beam. If the beam does not fill more than a third of the ...
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p is the associated Laguerre polynomial of order p and index l, and w is the spot size of the mode corresponding to the Gaussian beam radius. Cylindrical transverse mode with p=2, l=1. With p = l = 0, the TEM 00 mode is the lowest order. It is the fundamental transverse mode of the laser resonator and has the same form as a Gaussian beam.
The diameter of the multimode beam is then M times that of the embedded Gaussian beam everywhere, and the divergence is M times greater, but the wavefront curvature is the same. The multimode beam has M 2 times the beam area but 1/M 2 less beam intensity than the embedded beam. This holds true for any given optical system, and thus the minimum ...