Application of the ABCD ray matrix method for the design of a refractive 2.5× beam expander–focuser used for coupling laser beams into a 5 × 4 fiber-optic array: Comparison with Zemax Gaussian and geometrical optics calculations

In this article, an approach for the design and construction of a refractive 2.5× Galilean beam expander–focuser system which incorporates a two-axis galvanometer for coupling non-collinear laser beams into a 5×4200 μm core diameter fiber-optic array is discussed. M2 Gaussian beam waist and beam waist location computations using the ABCD ray matrix and Zemax® paraxial Gaussian optics methods are given. Using the described optical system a 532 nm and 637 nm laser beams are coupled noncollinearly into 200 μm core diameter fiber array by focusing down the laser beams to 71.26 ± 3.18 m and 90.32 ± 4.28 μm diameter spots, respectively. Furthermore, an experimental validation for the focused beam size calculations using a knife-edge profilemeter is provided. The measured average transmission for the fibers in the fiber-optic array is 92.54 ± 3.78% (maximum FCE (fiber coupling efficiency): 99%; minimum FCE: 82%). Whereas the Zemax® calculated geometric ray-optics fiber coupling efficiency for the beam expander-focuser into a 200 μm core diameter fiber using uncoated lenses and without accounting for Fresnel reflections and bulk absorption effects is 100%. Geometric ray-optics calculations indicate that Fresnel reflections and bulk absorption effects account for 7% of the 100% FCE value. The described optical switching scheme which incorporates a galvanometer is used for exciting asynchronously 20 PCR (Polymerase Chain Reaction) vessels in high throughput DNA/RNA amplification systems.