Laser Beam Expander Calculator

A laser beam expander is an afocal optical system that increases beam diameter while reducing angular divergence. It commonly uses two lenses arranged like a telescope. The expansion ratio, also called magnification, is the output beam diameter divided by the input beam diameter. In an ideal system it also equals the magnitude of the second lens focal length divided by the first lens focal length. A five-times expander turns a 2 mm input beam into a 10 mm output beam. Conservation of optical throughput explains the corresponding divergence change. Ignoring aberrations, clipping, and diffraction introduced by finite apertures, angular divergence decreases by the expansion ratio. A 1 mrad input beam passing through a five-times expander ideally leaves with 0.2 mrad divergence. This tradeoff is useful for long-distance propagation, lidar, interferometry, materials processing, alignment, and applications where a narrow far-field spot is important. This calculator reports the expanded diameter, ideal output divergence, and required magnitude of the second lens focal length. It accepts the magnitude of the first focal length so the same arithmetic supports both common layouts. A Keplerian expander uses two positive lenses separated by approximately the sum of their focal lengths. It forms an internal focus, can spatially filter a beam, and inverts the image. A Galilean expander uses a negative first lens and positive second lens separated by approximately the difference in focal-length magnitudes. It is shorter and has no internal focus, which can be advantageous at high power. Practical design requires more than paraxial ratios. Lens clear apertures need margin beyond the nominal beam diameter, commonly several beam radii depending on acceptable clipping. Coatings must match wavelength and power, and lens materials must tolerate the pulse energy or continuous intensity. Aberrations, input collimation, lens spacing, beam quality, and alignment affect the achieved divergence. The result is therefore an ideal first-pass specification rather than a complete optical prescription. Use it to compare expansion options and focal-length pairs, then verify the design with Gaussian propagation, aperture checks, damage thresholds, mechanical tolerances, and measured beam parameters.