The dual fiber collimator problem is designed to probe
short-range performance of the coupling efficiency algorithms, gradient-index
glass and errors tracking sign reversal after a mirror. When the problem was
selected, the assumption was that Wagner and Tomlinson-based algorithms should
be able to handle this problem. The coupling efficiency errors will be due more
substantially to angular misalignment of the beam and the receiving fiber than
the waist location. Commercially this problem is interesting because dual-fiber
collimators are used extensively in many multi-port device designs.
Figure 1: Dual fiber collimator in x-z plane showing that the natural stop (mirror location) is uniquely one focal length from the front principal plane. |
The problem, illustrated in Figure 1, consists of
light being transmitted from an off-axis SMF-28 fiber, through a TL1.80AB25-8
lens (GRADIUM® G23SF glass, 1.8 mm diameter, 1.97 mm focal length, “quarter
pitch” lens with an eight degree angle on the plano surface, 1310/1550 nm DBAR
coated), reflected from a mirror, and being captured by a second, off-axis
SMF-28 fiber. This example uses the
0.25 pitch lens design. Other gradient index lenses from NSG, Grintech,
or Corning, all of the more common radial gradient variety, could also be used
as well as a homogeneous lens. Geometrically, we would expect significant
cancellation of the odd aberrations and low spherical aberration because of the
high-index convex lens surface. The lowest insertion loss should be reported
when (1) the Gaussian beam waist is at the mirror and (2) when the mirror is
placed at the telecentric stop location, i.e. the location where the beams from
surface normal emitters (the off-axis fibers) naturally cross, as depicted in
Figure 1. This location is one focal length in front of the front principal
plane. The front principal plane is the apex of the convex surface on a TL lens
and somewhere inside a radial-gradient lens. Because the principal plane is
inside a radial gradient lens, the telecentric stop location is very close to
the front lens facet. The fiber facets and the lens plano surface are polished
at an eight degree angle in the x-y plane to suppress back reflections. The
fiber centers are located at x="62.5 microns, y=0
microns; the fibers are parallel to the optical axis. The optical prescription
follows:
FILE = MIRRORED DUAL-FIBER
Wavelength: 1.55000 microns
Object X coordinate: 0.06250
Object Y coordinate: 0.00000
Image X coordinate: -0.06250
Image Y coordinate: 0.00000
Object Space NA = 0.140000.
Image Space NA = 0.140000. Beam is deviated from normal emission because of the
8 degree polish on the fiber and the lens. Fiber Mode Field Diameter on
surfaces 0 and 9 is 10.4 microns. Surfaces 1, 2, 7 and 8 are angled at 8
degrees.
Units in mm.
# TYPE RADIUS DISTANCE
GLASS INDEX SEMI-DIAMETER
OBJ SD Infinity 0.0000
SMF-28 1.468100
1>SD
Infinity 0.00900 1.000000
2 SDI Infinity 3.30000
G23SFP 1.652594 0.90 GRADIUM TL1.80AB25-8 Lens
DELTA Z = 2.40000
3 S -1.4000 1.97000 1.000000
0.90
STO SM Infinity 0.00000
MIRROR -1.000000 (Natural Stop Location & Gaussian
Beam Waist)
5 S Infinity -1.97000 -1.000000
The thickness of this surface is a pickup from surface 3
6 SI -1.4000 -3.30000
G23SFN -1.710411 0.90 GRADIUM TL1.80AB25-8 Lens
DELTA Z = 3.70000
7 SD Infinity -0.00900 -1.000000
0.90
8 SD Infinity 0.00000
SMF-28 -1.468100
IMG S Infinity -1.000000
Decenter / Tilts :
# XDE YDE ZDE ADE BDE CDE TLM TSEQ
0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0 XYZABC
1 0.0000 0.0000
0.0000 -8.0000 0.0000 0.0000
0 XYZABC
2 0.0000 0.0000 0.0000 -8.0000 0.0000 0.0000 0 XYZABC
GRIN 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
7 0.0000 0.0000 0.0000 -8.0000 0.0000 0.0000 0 XYZABC
8 0.0000 0.0000 0.0000 -8.0000 0.0000 0.0000 0 XYZABC
Because ZEMAX only models GRADIUM® as a surface,
rather than a glass, it is not possible to put a wedge on the front surface
(surface 2 in the optical prescription). Therefore that surface must either be
modeled as a plano surface or the lens must be shortened and a thin wedge of
N-SF8 used to put the angled surface in the system. N-SF8 happens to have the
closest refractive index properties to the back side of the TL lens of any
catalog glass that I have noticed. However, not only is the physical length of
the lens shortened, but the delta z value on surface 2 must be increased by the
center thickness of the wedge. This inability to model the wedge is not an
issue with radial gradient lenses of the NSG type (GRIN9 surface).
As a side note, many programs generate incorrect
Gaussian beam data for this problem. One issue is that the angled surfaces
distort the paraxial calculations. Problems with the paraxial Gaussian beam
calculations have been noted in ZEMAX, OSLO and OpTaliX.
RESULTS: Dual
Fiber.xls
ZEMAX: The fiber coupling (FICL) worked perfectly. I
was unable to get POP to give a reasonable result. This may be due to the
inhomogeneous material, which must be handled by ray trace. Dual Fiber.zip
OpTaliX: CEF failed to provide meaningful results
(Wagner-Tomlinson algorithm). BPM (a.k.a. POP) was also unable to produce
reasonable results. The PSF-based CEF introduced in approximately v. 5.02 does better than the old algorithm.Mirrored
Dual-Fiber Collimator.otx
OSLO: Fiber coupling is based on Wagner-Tomlinson algorithm and
failed to provide meaningful results. Mirrored
Dual-Fiber Collimator-tilt x.len
CODE V: No data available. Mirrored
Dual-Fiber Collimator.seq
FRED: No data available.
ASAP: No data available. Contact BRO customer assistance.