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Near-Field vs. Far-Field Divergence

Unlike conventional light beams, Gaussian beams do not diverge linearly. Near the laser, the divergence angle is extremely small; far from the laser, the divergence angle approaches the asymptotic limit described above. The Raleigh range (zR), defined as the distance over which the beam radius spreads by a factor of the square-root of 2, is given by

At the beam waist (z = 0), the wavefront is planer (R(0) = ∞). Likewise, at z = ∞, the wavefront is planer (R(∞) = ∞). As the beam propagates from the waist, the wavefront curvature, therefore, must increase to a maximum and then begin to decrease, as shown in the figure below. The Raleigh range, considered to be the dividing line between near-field divergence and mid-range divergence, is the distance from the waist at which the wavefront curvature is a maximum. Far-field divergence (the number quoted in laser specifications) must be measured at a distance much greater than zR (usually >10 ?nbsp;zR will suffice). This is a very important distinction because calculations for spot size and other parameters in an optical train will be inaccurate if near- or mid-field divergence values are used. For a tightly focused beam, the distance from the waist (the focal point) to the far field can be a few millimeters or less. For beams coming directly from the laser, the far-field distance can be measured in meters.

Changes in wavefront radius with propagation distance