N-SF11 Plano-Concave Lenses, AR Coated for 350 - 700 nm

Mounting High-Curvature Optics

Thorlabs' retaining rings are used to secure unmounted optics within lens tubes or optic mounts. These rings are secured in position using a compatible spanner wrench. For flat or low-curvature optics, standard retaining rings manufactured from anodized aluminum are available from Ø5 mm to Ø4". For high-curvature optics, extra-thick retaining rings are available in Ø1/2", Ø1", and Ø2" sizes.

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As an application example, consider a Newport R- HeNe Laser with beam diameter 0.63 mm and a divergence of 1.3 mrad. Note that these are beam diameter and full divergence, so in the notation of our figure, y1 = 0.315 mm and θ1= 0.65 mrad. To expand this beam ten times while reducing the divergence by a factor of ten, we could select a plano-concave lens KPC043 with f1 = -25 mm and a plano-convex lens KPX109 with f2 = 250 mm. Since real lenses differ in some degree from thin lenses, the spacing between the pair of lenses is actually the sum of the back focal lengths BFL1 + BFL2 = -26.64 mm + 247.61 mm = 220.97 mm.

The expanded beam diameter is: 2y3 = 2y1f2/|-f1| = 2(0.315 mm)(250 mm)/|-25 mm|= 6.3 mm. 

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The divergence angle is: θ3 = θ1|-f1|/f2 = (0.65 mrad)|-25 mm|/250 mm = 0.065 mrad.

For minimal aberrations, it is best to use a plano-concave lens for the negative lens and a plano-convex lens for the positive lens with the plano surfaces facing each other. To further reduce aberrations, only the central portion of the lens should be illuminated, so choosing oversized lenses is often a good idea. This style of beam expander is called Galilean.

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