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Collimation & C-LENS SelectionCoupling Optics Design

Size the spot on the emit side, pick the lens on the receive side — both steps of a coupling design on one page.

chip θ collimator f D₀ working distance wd C-LENS (R) fiber (MFD)
Emit side (Tab A): θ → D. Receive side (Tab B): pick C-LENS radius R by the spot at working distance
Chip divergence + focal length → collimated spot
D1/e² = θ1/e²(rad) · f 1/e² dia.FWHM dia. = 1√(½·ln2) ≈ 1.6986 capture = 1 − e−2T², T = NAlensNAbeam

Emit side: geometric projection, wavelength-free

The chip's far field is a diverging cone; the collimated spot diameter is simply divergence (radians) × focal length — a small-angle geometric projection with no wavelength in it. Datasheets usually quote FWHM full angles while coupling design needs the 1/e² aperture: the ratio is the fixed Gaussian constant 1.6986. When choosing collimator NA, "enough is enough": capture rises with T = NAlens/NAbeam and saturates near T≈1.5 (>99%); more NA adds no coupling but more spherical aberration and tighter alignment tolerance — our measurements on 20–30° chips show an NA 0.5 collimator out-coupling an NA 0.71 one (typical result).

Receive side: diffraction limit + aberration correction

As a receive/collimating lens, the C-LENS spot follows the Gaussian diffraction limit D₀ = 2λf/(π·w_f), with focal length set by the radius through f = R/(n−1). Large-R lenses fill their aperture and edge spherical aberration shortens the effective focal length, making real spots smaller than ideal — the correction factor k(R) on this page comes from our full-series measurements at 1550 nm. Within the Rayleigh range z_R the spot barely changes; beyond it, it grows hyperbolically — so select by "spot at working distance closest to target".

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※ Formulas on this page assume ideal models; all device parameters shown are typical values — refer to the datasheet and the serialized factory test report shipped with each unit. For selection support, contact sales@lncetek.com.