Single-mode to Single-mode Fiber Collimator Problem
This problem is typical of the modeling required to design many of the MEMS-based optical switches. Because the working distance is large, only POP-based fiber coupling approaches are expected to succeed. Calculating the insertion loss versus separation for 0 to 300 mm should allow us to see the minimum match the paraxial Gaussian design of 200 mm; also, the 0 to 100 mm range takes us very close to the edge of the Rayleigh range; some programs will need to alter the sampling grid at some point in this range. Other than the range, this is the generic single-mode-fiber-to-single-mode-fiber coupling problem. Since the fiber is fused to the lens for thermal stability and power handling, no additional modeling of the fiber is required other than to simply place the source at surface 1.
The specific example chosen is the LightPath T4300 design, a long working distance collimator for which data from engineering samples was available. The prescription is:
FILE = T43XX SMF-28 PAIR
Wavelength: 1.55000 micronsObject Space NA = 0.140000, telecentric emitter. Image Space NA = 0.140000. Fiber Mode Field Diameter on surfaces 1 and 5 is 10.4 microns.
Units in mm.
# TYPE RADIUS
DISTANCE GLASS INDEX Semi-Diameter
OBJ S
Infinity 0.0000 1.000000
1 S
Infinity 5.14600 HERASIL
1.444132 0.625
STO A
-1.5690 100.55026 1.000000
0.625
3 S
Infinity 100.55026 1.000000 (Gaussian beam waist)
4 A 1.5690
5.14600 HERASIL 1.444132 0.625
IMG S
Infinity 1.000000 0.625
Aspheres (surface type = A): conic constant = -0.48 on surfaces 2 and 4.
The thicknesses of surfaces 2 and 3 above put the paraxial Gaussian beam waist at surface 3. For our modeling work, the thickness of surface 2 was set to 0 and the thickness of surface 3 ranged from 0 to 300 mm. As a class, geometric algorithms perform poorly on this problem.
Results: Single-mode to Single-mode.xls
A theoretical expression for the expected shape of the insertion loss curve in this case is referenced by März (1):
where zr is the Rayleigh range and Dz is the WD change from the IL minimum. Obviously, this expression returns a value of 0 at the minimum, so there will be some offset between this curve and experimental data. In this particular case, we find that the shape of the theoretical curve tracks experiment only if we multiply the theoretical values by 2.4; we have seen other cases where the multiplier is approximately 1.4. This suggests some physics in the experiment not captured by the model of a propagating Gaussian beam.
ZEMAX: Fiber Coupling Efficiency or POP can be used "out of the box" for a Gaussian beam. For more accurate modeling with the actual fundamental fiber mode, load the fundamental fiber mode .dll into the ZEMAX/POP/dll folder to make the dll available. Beta versions had some IL discontinuities that no longer appear when running this problem. POP works well; FICL does not. T4300 SMF28 PAIR.ZIP
OSLO: Fiber coupling is only possible with Gaussian beam and the Wagner-Tomlinson approach. Thus OSLO does not perform well on this problem. T4300 SMF28 PAIR.LEN
OpTaliX: The Gaussian mode is selectable for POP (aka BPM). Select the Gaussian as the mode to propagate from the BPM dialog box AND the select the Gaussian mode and fiber type (all the parameters are automatically calculated for listed fibers) from the coupling efficiency dialog box. When doing CEF only, the fundamental mode is selectable; just enter the appropriate waveguide radius and refractive indices. POP works well; geometric CEF does not. T4300 SMF28 PAIR.OTX.
CODE V: Version 9.20 SR2 PC. Excellent results for gaussian and fundamental mode calculations for POP; the geometric algorithm fails. T4300 SMF28 PAIR.SEQ
FRED: The algorithm is similar to the ASAP Gaussina beamlet approach. The curves were similar but FRED predicted the highest IL. T4300 SMF28 PAIR.FRD.
ASAP: This problem was run with the fundamental mode parameters. Contact BRO customer support for the files and technical support needed.
Reinhard März, Integrated Optics: Design and Modeling (Artech House: Boston, 1995), p. 140, equation 5.26.