## Effective Numerical Aperture

### Effective numerical aperture NAe2

For fiber-coupling purposes an effective fiber NAe^{2} defined at the 1/e^{2}-level is more convenient than the nominal fiber NA defined by the refractive indices since Gaussian beams generally are defined by their 1/e^{2} diameter, also.

Schäfter+Kirchhoff defines an effective fiber NA which corresponds to the divergence of the power distribution emitted by the fiber taken at the 1/e^{2}-level of the Gaussian angle distribution.

This NA value is the designated effective numerical aperture NAe^{2}. For a typical single-mode fiber the value is NAe^{2} = 0.075.

For single-mode fibers and for polarization-maintaining fibers, the effective NAe^{2} typically decreases slightly with increasing wavelength λ.

1 Single-mode fiber

2 Core diameter

3 Mode-field diameter

4 Intensity level (13.5% or 1/e2-level)

5 Intensity level (e.g. 5%)

6 2xNA (e.g. 5%)

7 2xNAe^{2} (13.5% or 1/e^{2}-level)

### Typical Values for the effective numerical Aperture

Please find here some measured (averaged) values for the effective numerical aperture NAe^{2} for common fibers at their respective cut-off wavelength.

**When purchasing a fiber from Schäfter+Kirchhoff, the fiber is delivered with more accurate measurements of the effective numerical aperture NAe ^{2}. Schäfter+Kirchhoff determines the NAe^{2} of the fiber for each fiber batch by measuring the divergence of the emitted radiation in the far field. Due to the wavelength dependence of the NAe^{2}, this is done for several typical wavelengths in the working range of the fiber. **

**An articel on how measured fiber parameters help to choose the best coupling and collimation optics can be found here.**

### Nominal Numerical Aperture NA

_{co}and n

_{cl}as the refractive indices of fiber core and cladding, respectively.

### Fiber Coupling

### Collimation

_{beam}is a function of the collimating focal length f’ and the numerical aperture NA of the single-mode fiber.