Diode to Single-mode Fiber Problem

This is one of the few problems well suited to the ray-trace based coupling efficiency calculations. This problem requires collimating an elliptical Gaussian beam with an asphere and then coupling it back into a single-mode fiber. The purposes of this problem are to probe elliptical-to-circular coupling and to force a shift from a standard wavelength. The fiber MFD in the prescription was calculated in OpTaliX, since the wavelength conversion is handled automatically. Because the beam is elliptical, the beam waists move at significantly different rates. The only point where the x and y beam waists are at the same location is when the asphere BFL is approximately 3.29644 mm, as illustrated in Figure 1. The distance from the asphere to the collimator lens is on the order of 10-20 mm, so that lens is also nearly at paraxial focus. The dominant loss mechanism in this problem is due to the beam ellipticity, not the precision of locating the beam waists. The general methodology that we have used to find the optimal solution is to put a paraxial focus solve on the length of the collimator lens and then to plot the coupling efficiency vs. radius of surface 4 (the collimator lens) (Figure 2). Armed with the radius information, a catalog collimator of the desired effective focal length can be selected.

Figure 1: Location of the diode fast and slow axis beam waists as a function of the asphere BFL.

Figure 2: Coupling efficiency versus collimator lens radius of curvature as predicted by the OpTaliX CEF

The optical prescription for this problem is:

FILE = DIODE-ASPHERE-COLLIMATOR

Wavelength:  1.5000 microns

Object X coordinate:  0.00000

Object Y coordinate:  0.00000

Object Space NA = 0.628, telecentric emitter. Source Gaussian waist x = 0.565 microns, Source Gaussian waist y = 1.265 microns. Image Space NA = 0.14. Fiber Mode Field Diameter on surface 5 is 10.14 microns.

   # TYPE        RADIUS     DISTANCE  GLASS          INDEX    SEMI-DIAMETER

 OBJ S         Infinity      0.329644             1.000000     0.00 

   1>A           0.9305      1.00000  PBH71       1.870424     0.35  Geltech 370880/

                                                                           Asahi LDIFA-101A

 STO A          -0.8802     10.00000              1.000000     0.56

   3 S         Infinity     10.00000              1.000000    

   4 A           1.5690      5.10400  HERASIL     1.444724     0.625 Use this lens as the starting point

 IMG S         Infinity                           1.000000     0.625

Aspheres:

Surface #    Conic      4^th Order Term   6^th Order Term  8^th Order Term   10^th Order Term

   1      0.0000000000 -0.84612666E+00  0.71082591E+01 -0.22483601E+02 -0.29039367E+02

   2      0.0000000000  0.29493664E+00  0.80678523E+00 -0.45362290E+00  0.10529315E+02

   4     -0.48

März offers an expression for the minimum coupling loss possible for an elliptical-to-circular- mode coupling problem ⁽¹⁾ :

where m _x/m _y is the beam ellipticity ratio. For this example, given the ellipticity in this example of 2.24, the equation predicts and optimal IL of 0.68 dB. One alternate technique-a back-of-the envelope estimate-is to picked the collimator based on the average of the major and minor beam diameters exiting the asphere.

Access to experimental data was limited. The parameters used in this problem resulted in reasonable beam ellipticity, but the diode beam sizes and wavelength were arbitrary. However, using the same technique described above with a real, commercially available diode, OpTaliX predicted a coupling efficiency that differed from the experimental data by one percent. Note that IL vs. radius response curve in Figure 2 is quite flat; hence the different predicted optima produce quite similar end results and may not be experimentally distinguishable..

One other pont of reference is found in a paper by Milster and Chen ⁽²⁾ in which they used Matlab to map the coupling efficiency response surface of a specific diode-ball lens-fiber problem originally described by Sumida and Takemoto ⁽³⁾ .

ZEMAX: To avoid unreasonably fine grids, rays were used to propagate through the asphere (which has a lot of aberration on its first surface). Because the system is quite fast, "Use Polarization" setting was used so that I could explicitly see the magnitude of the polarization effects. The results were determined via manual adjustment of the collimator radius because the POP coupling was not yet available as a merit function call (remedied in the current version). The agreement between POP and FICL was excellent. DIODE-ASPHERE-COLLIMATOR.ZIP

OpTaliX: CEF worked quite efficiently; I was not able to get BPM to report reasonable values, even though the beam showed no obvious problems. DIODE-ASPHERE-COLLIMATOR.OTX

OSLO: The Premium version is required in order to input the elliptical beam parameters into the source definition. Note that the IL prediction appears to be an outlier compared to the other programs. DIODE-ASPHERE-COLLIMATOR.LEN

CODE V: No data available. DIODE-ASPHERE-COLLIMATOR.SEQ

FRED: No data available.

ASAP: No data available. Contact BRO customer support.

1. Reinhard März, Integrated Optics: Design and Modeling (Artech House: Boston, 1995)., equation 5.25.

2. Tom D. Milster and Zhiyong Chen, "Combination of ray-trace and diffraction modeling to describe coupling laser diodes to fibers and waveguides," Proc. SPIE 2610, pp. 194-202 (1996).

3. M. Sumida abd T. Takemoto, "Lens coupling of laser diodes to single-mode fibers," J. Lightwave Tech. LT-2, pp. 305-311 (1984).