The most common type of beam expander is derived from the Galilean telescope which usually has one negative input lens and one positive output lens, as shown in Figure 1. The input lens presents a virtual beam focus at the output. For low expansion ratios (1.3-20?), the Galilean telescope is most often employed due to its simplicity, small package size, and low cost.
Figure 1: Diagram of a beam expander As shown in Figure 1, the lens M3 focuses the laser beam onto the front focus plane and divergence angle q? can be represented as
and the new beam waist w?0
where w(l) is the radius of the beam entering the lens M3, l is the distance between the lens M3 and the beam waist w0 from the laser generator, and f3 is the focal length of the lens M3.
Since w0? lies on the back focus plane of the lens M 4 with a longer focal length, f4, the Gaussian beam with a beam waist w?0 will be collimated by the beam expander. collimation ratio of the beam expander for a Gaussian beam is as follows The
(4) where T1 = f4/f3. The beam waist w?0 and divergence angle q? after the beam expander are
(6) Substituting Equation (1) into Equation (5), the following expression can be obtained
(7) From Equations (4)-(7), it is concluded that the beam expansion ratio and the collimation ratio for a Gaussian beam depend not only on the specifications of the beam expander, but also on the laser beam parameters as well as the positions of the optical lenses. The function of a beam expander is to reduce the divergence angle of laser beams and thus make the focused beam diameter smaller.
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