Coupling an Extended Source Into a Multimode Fiber

Beam Parameter Product or Etendue

When coupling the radiation of an extended source into a multimode fiber, there are principle limitations.

An extended source, e.g. a LED source or a plasma typically emits a beam from a large area and with a large angular spectrum. This beam characteristics (area x angle) is given by the so-called beam parameter product BPM or, more precisely, the étendue.

The multimode fiber however -as every fiber type - only has a limited acceptance angle and core area (defined by the numerical aperture and the core diameter, respectively). Only light that is focused with the right angle (⇾numerical aperture) and focus size (⇾core diameter) is coupled into the fiber, everything else is not transmitted. The multimode fiber accepts beams with the corresponding BPM.

Every components has different BPMs it emits or accepts (source, optics, as well as fiber).

In classical optics, this BPM is an invariant, which means that it is not possible to change the BPM of an optical system by means of optical imaging.

An extended source, e.g. a LED source or a plasma emits a beam that automatically has a large BPM as both the emitter area as well as the angular spectrum is large. This also means that you need to choose a fiber that accepts a large BPM (large NA, large core diameter) in order to couple as much light as possible into the fiber.

Choosing the right coupling optics for an extended ligth source

It is unimportant, if you use an optics with a small focal length (smaller spot, wide angle) or a longer focal length (larger spot, smaller angle), as the main limitation is the non-changeable BPM and the ratio of BPM to the BPM accepted by the fiber.

This is as long as the optics fulfills the following criteria:

  • It is coated with an AR-coating for the appropriate wavelength
  • It has a numerical aperture larger than the one of the multimode fiber (otherwise more light is lost)

In other words: There is no optimum focal length when choosing the right coupling optics, the NA of the optics needs to be large enough.

Note: Single-mode fibers have a smaller NA and a smaller MFD. 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. Thus single-mode fibers accept a much smaller BPM compared to multimode fibers. It is impossible to couple a significant amount of light emitted by an extended source into a single-mode fiber.