# Single-mode and PM fiber Coupling

## Coupling into single-mode and polarization-maintaining fibers

For fiber coupling, either the laser beam couplers type 60SMS or the collimators of type 60FC can be used.

If a collimator is selected then it can be used for fiber-coupling by using it in reverse mode and placing it in an adjustable mirror mount (or other mechanics providing the same degrees of freedom). This gives all degrees of freedom to achieve a high coupling efficiency.

For even more details please refer to the articles a general article about fiber coupling you can find here and an article on how measured fiber parameters help to choose the best coupling and collimation optics here.

### Selection of coupling focal length for a circular beam

Beam path of a beam that is coupled into a single-mode fiber with angled connector FC APC.

Maximum coupling efficiency is achieved for an ideal Gaussian beam (M2 = 1, no astig­ma­tism) when the convergence of the focused, circular beam equals the effective NAe2 of the fiber. Then the laser spot on the ­fiber end face equals the mode field diameter MFD of the single mode fiber.
Except for an 8% loss from Fresnel reflection at the ­entrance into and exit from the fiber, an ideal Gaussian beam is transported completely.
For a specified effective fiber NAe2 the optimum focal length of the laser beam coupler at a given beam diameter Øbeam (defined at its 1/e2-level) is given by

{!{!{f'=\frac{0.5\cdot\emptyset_{beam}}{{\rm NA}_{e^2}}}!}!}

If the effective NAe2 of the fiber is not known, then the optimum focal length f’ can be calculated from the nominal numerical aperture NA by
{!{!{f'=\frac{F_{NA}\cdot\emptyset_{beam}}{{\rm NA}}}!}!}

The nominal fiber NA corresponds to the Gaussian angle distribution at a 1% - 5 % level requiring the factor FNA to correct for the different definitions of the NA.

### Factor FNA

Factor FNA depending on nominal %-level

LevelFNA
1 %0.76
3 %0.66
5 %0.61

### Example:

Beam diameter: Øbeam = 1.0 mm
Effective numerical aperture of fiber: NAe2 = 0.08
Focal length: f’ = 0.5 · 1.0 mm/0.08 = 6.25 mm
Therefore, select e.g. lens A6.2S with f’ = 6.2 mm