Numerical Aperture | previous | next | feedback |
(Acronym: NA)
Definition: sine of the maximum angle of an incident beam of some optical device, or the sine of the acceptance angle of a waveguide or fiber
The term numerical aperture (NA) is used with two rather different meanings, depending on the context, which may be fiber optics or imaging optics.
Numerical Aperture of an Optical Fiber or Waveguide
In a ray picture, a light beam can be considered which propagates in air and hits the core of a (perpendicularly cut) step-index fiber with large mode area. The numerical aperture (NA) of the fiber is the sine of the maximum angle of an incident ray with respect to the fiber axis, so that the transmitted beam is guided in the core. The NA is determined by the refractive index difference between core and cladding, more precisely by the relation
which can be derived from the requirement that the transmitted beam at the core/cladding interface propagates with the critical angle for total internal reflection.
In a similar way, the NA can also be defined for other kinds of waveguides with cylindrical symmetry.
For small core areas (e.g. for single-mode fibers), the wave nature of the beams becomes essential, and ray picture becomes invalid. (The beam divergence can then no longer be ignored.) The above equation may still be used to define the NA via the refractive indices. The concept becomes questionable for non-rectangular refractive index profiles, i.e., for non-step-index fibers.
A high numerical aperture usually relates to a large beam divergence for the fundamental mode exiting the fiber end, but this beam divergence also depends on the core diameter. For fibers other than step-index fibers (where the core does not have a constant refractive index), an effective numerical aperture may be defined based on an equivalent step-index profile, which leads to rather similar mode properties.
For a single-mode fiber, the NA is typically of the order of 0.1, but can vary roughly between 0.05 and 0.4. Multimode fibers typically have a higher numerical aperture of e.g. 0.3. Very high values are possible for photonic crystal fibers.
A higher numerical aperture has the following consequences:
- For a given mode area, a fiber with higher NA is more strongly guiding, i.e., it will tentatively support a larger number of modes.
- Single-mode guidance requires a smaller core diameter. The corresponding mode area is smaller, and the divergence of the beam exiting the fiber is larger. The fiber nonlinearity is correspondingly increased. (Conversely, a large mode area single-mode fiber must have a low NA.)
- Bend losses are reduced; the fiber can be more strongly bent before bend losses become significant.
- The sensitivity of the guidance to random refractive index fluctuations is reduced. (For large mode area low-NA single-mode fibers, it can be a problem.)
- The higher doping concentration of the core (e.g. with germanium), as required for increasing the refractive index difference, may increase scattering losses. The same can be caused by irregularities of the core/cladding interface, which are more important for a larger index difference.
Numerical Aperture of a Lens
The NA of a lens (or a microscope objective, which is a combination of lenses) is defined as the sine of the angle of the marginal ray coming from the focal point, multiplied by the refractive index of the medium from which the input beam comes. The NA of a lens (and not its focal length) is what limits the size of a beam waist which can be formed with that lens. In a microscope, the NA limits the obtainable image resolution. It can be increased by using some immersion oil with large refractive index between sample and objective lens, so that the numerical aperture can be greater than 1.
Lenses with high numerical aperture are also required for collimating laser beams which originate from small apertures. For example, this is the case for low-power single-mode laser diodes. When a lens with too low NA is used, the resulting collimated beam can be distorted (→ beam aberrations) or even truncated.
Bibliography
| [1] | Article on numerical aperture and resolution, http://microscopy.fsu.edu/primer/anatomy/numaperture.html, of the Optical Microscopy Primer |
See also: fibers, single-mode fibers, waveguides, fiber core, V number, focal length
Categories: fibers and other waveguides, general optics
