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Neglecting divergence due to poor beam quality, the divergence of a laser beam is proportional to its wavelength and inversely proportional to the diameter of the beam at its narrowest point. For example, an ultraviolet laser that emits at a wavelength of 308 nm will have a lower divergence than an infrared laser at 808 nm, if both have the ...
From the above expression for divergence, this means the Gaussian beam model is only accurate for beams with waists larger than about 2λ/π. Laser beam quality is quantified by the beam parameter product (BPP). For a Gaussian beam, the BPP is the product of the beam's divergence and waist size w 0. The BPP of a real beam is obtained by ...
The beam of a single transverse mode (gaussian beam) laser eventually diverges at an angle that varies inversely with the beam diameter, as required by diffraction theory. Thus, the "pencil beam" directly generated by a common helium–neon laser would spread out to a size of perhaps 500 kilometers when shone on the Moon (from the distance of ...
The beam divergence of a laser beam is a measure for how fast the beam expands far from the beam waist. It is usually defined as the derivative of the beam radius with respect to the axial position in the far field, i.e., in a distance from the beam waist which is much larger than the Rayleigh length. This definition yields a divergence half-angle.
In laser science, the beam parameter product (BPP) is the product of a laser beam's divergence angle (half-angle) and the radius of the beam at its narrowest point (the beam waist). [1] The BPP quantifies the quality of a laser beam, and how well it can be focused to a small spot.
The beam quality of a laser beam is characterized by how well its propagation matches an ideal Gaussian beam at the same wavelength. The beam quality factor M squared (M 2) is found by measuring the size of the beam at its waist, and its divergence far from the waist, and taking the product of the two, known as the beam parameter product.
Beams with power well out in the "tails" of the distribution have M 2 much larger than one would expect. In theory, an idealized tophat laser beam has infinite M 2, although this is not true of any physically realizable tophat beam. For a pure Bessel beam, one cannot even compute M 2.
Laser physicists typically choose to make θ the divergence of the beam: the far-field angle between the beam axis and the distance from the axis at which the irradiance drops to e −2 times the on-axis irradiance. The NA of a Gaussian laser beam is then related to its minimum spot size ("beam waist") by