ZEMAX Development Corporation thanks Dr. Reinhard Voelkel of Suss MicroOptics SA for the experimental data used in this article.

This article is also available in Japanese.

This article describes a commercial fiber coupler, which couples two pieces of Corning SMF-28e Fiber using SUSS MicroOptics FC-Q-250 microlens arrays:

A schematic of the system we will model

The manufacturers' data is as follows:

 Single Mode Fiber, Corning SMF-28e 1

  
 Numerical Aperture  0.14
 Core Diameter  8.3 µm
 Mode Field Diameter @1.31 µ  9.2 ± 0.4 µm

 Microlens Array, SUSS MicroOptics SMO399920 2  
 Substrate material  Fused Silica
 Substrate thickness  0.9 mm
 Internal Transmission  >0.99
 Lens Diameter  240 µm
 Lens Pitch  250 µm
 Radius of Curvature  330 µm
 Conic Constant  0
 Numerical Aperture  0.17

The file single mode coupler.zmx in the attached zip file (which can be downloaded from the last page of this article) shows how to implement this system. Please note the following:

  • The object/lens and lens/image distance has been set by hand to 0.1 mm as this is approximately the right value. This number is to be computed by the optimization routine later
  • A pick-up solve is used to make the final lens-image thickness the same as the initial object-lens image. Since the lenses and fibers are identical (within manufacturing tolerances), the optical system should work either way round, and should therefore by symmmetric
  • The separation of the two lenses is set to 2 mm, as this is the experimental distance used. Again, this distance will be computed by rigorous optimization later
  • The system aperture is set using float by stop size on the rear face of the first lens. This means that the system aperture is set by the physical aperture of the lens. The fiber mode we propagate through this system can be clipped by this physical aperture. In this case, the fiber mode is significantly smaller than the physical aperture
  • Be wary of the multiple definitions of the term "numerical aperture". It may use the sine of the marginal ray angle, the sine of the angle at which the intensity has fallen to 1/e2 (both definitions are used in different calculations in ZEMAX, as we shall see) or the sine of the angle at which the intensity has fallen to 1% of peak, as used by Corning. Definitions matter!
  • A Gaussian apodization has been applied to the aperture definition to highlight the Gaussian distribution of light. This is currently only approximate. The calculations we shall use later will be precise
  • The lens is diffraction limited across most of its aperture, and is diffraction limited across the region illuminated by the fiber mode

The first-pass layout