Modeling draws a bead on manufacturing tolerances

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Joe Shiefman

Using modeling software, designers can move from a basic concept to a polished design that meets criteria. This iterative process determines manufacturing tolerances by varying alignments and material properties of elements within a component and then by examining the effects on specifications.

Significant drops in spending and increased competition have made the optical telecommunications components market a very difficult place to do business. Once spending levels rebound, the winners will not necessarily be those companies with the cleverest component concepts because, for most component types, there will be many companies offering products with specifications that meet the market's needs. From within these companies, those with the most inexpensive and most manufacturable designs will be the winners.

How does one get from a basic concept, formulated in some sort of component block diagram, to a polished design that achieves the necessary cost and manufacturing criteria? The answer is by performing an iterative procedure, which starts by finding the manufacturing tolerances of the original design.

This tolerancing is accomplished by varying alignments, shapes, and material properties of the system elements. The resulting effects on system specifications, such as polarization-dependent loss, insertion loss, return loss, crosstalk, and polarization-mode dispersion, are then examined. Tolerancing procedures highlight weaknesses in the original design. The next step is to change the original design to remove these problems. This iterative process of alternating tolerancing and design revisions continues until the most "buildable" design is obtained.

What is the best way to perform the tolerancing? There are two possible solutions. One is to build a prototype of the latest design in a lab and then vary the elements of that system while measuring the component output with external measurement equipment. The second approach is to use optical-modeling software to construct that latest design, vary the system elements, and calculate the output.

Modeling software has several advantages. Building and modifying a model is usually much faster in software than in a lab. In the lab it is not only time-consuming to assemble the system elements, it also takes significant time to obtain them. Additionally, modeling the system in software is less expensive since it does not involve purchasing the system elements or the support equipment necessary to hold and align them, and to measure the system input and output. The parameters of both the system elements and the state of the light going into the system are also more controllable in software than in the lab. In particular, the issues of time and expense become magnified in such an iterative approach.

SOFTWARE SHORTCUTS
Breault Research Organization's ASAP optical-system software was used to determine a single system tolerance on a hypothetical, single-channel, 1 x 2 optical switch designed for the purposes of this article. This analysis is detailed to demonstrate how the software tolerancing procedure is performed. Using two sketches of the system (one for each switch mode), light propagating in the Z direction from the input fiber gets collimated by the input collimator and then split into ordinary and extraordinary polarization components by calcite #1.

It then enters a half-wave plate, which is the switching element. If the optic axis of the wave plate is aligned in a direction halfway between the two polarization components that emerge from calcite #1 (a rotation of 45°), the ordinary polarization (X-pol) will switch to extraordinary (Y-pol) and vice versa (see path #1 in Fig. 1). In this case, both beams will exit calcite #2, reflect off the two right-angle prisms, and be directed to the top output collimator, which focuses the beam into its companion fiber.

On the other hand, if the optic axis of the wave plate is aligned in the same direction as one of the two polarization components that emerge from calcite #1 (a rotation of 0°), the polarization of the two beams will be unchanged and they will continue to move further apart as they propagate through calcite #2 (see path #2 in Fig. 1). In this case, both beams miss the right-angle prisms, get recombined by calcite #3, and are fed back into the path #2 output fiber by its collimating lens. The compensating glass that is positioned just before calcite #3 is introduced to add additional path length to the bottom beam in path #2, which has a shorter optical path through the rest of the system than the top beam in path #2.

The software tolerancing procedure is demonstrated by examining the effect of a rotation of the optic axis (OA) in calcite #1 on the system insertion loss. The OA in calcite #1 is nominally in the Y-Z plane. The type of OA rotation examined here is for a rotation of the OA out of its nominal Y-Z plane such that it acquires some X component.

This rotation of the OA, relative to its nominal location in the system Y-Z plane, can arise either from the OA not being oriented correctly, relative to the reference side of the calcite block, or from a mechanical misalignment where the block is mounted with a rotation relative to its nominal system orientation. The mechanical misalignment can be due to any of several possible causes—such as bad mechanical parts, poor assembly of those parts, or the assembly method used to fix the calcite block to the mechanical fixture.

These results can then be plotted (see Fig. 2). The insertion loss in this study is limited only to that due to the calcite OA rotation. It does not include Fresnel losses due to surface reflections. The beam propagation was started in the collimated space after the input collimating lens and the coupling overlap integral was calculated in the collimated space just before the output collimating lens. Therefore, the insertion loss also does not include losses due to aberrations in the beam from the collimating lenses. Certainly, both of these other factors contribute to the insertion loss and also must be toleranced and budgeted into the design check process.

The insertion losses for this design are 0.1 dB for +1.25° and -1.34° of OA rotation, 0.2 dB for +1.77° and -1.96° of OA rotation, 0.3 dB for +2.17° and -2.46° of OA rotation, and 0.4 dB for +2.52° and -2.90° of OA rotation.

Therefore, since it does not include other sources of insertion loss, for most components the acceptable tolerance on this type of OA rotation in calcite #1 will be in the 1° to 3° range. To determine how easy it is to achieve 1° to 3° of OA rotation, the optical engineer must obtain a specification on the accuracy of the OA orientation relative to the reference side of the calcite block from its manufacturer. The reference side of the calcite block is determined by how it is mounted in the component.

Additionally, the optical engineer must determine specifications for the flatness and rotation of the mechanical reference surface onto which the calcite block mounts. The method of mounting is also important since this can also induce rotation. Once these questions are answered one can determine whether this rotation of 1° to 3° of OA is easily achievable, or whether it will require expensive parts or difficult assembly, or lead to a low yield. If there is a problem, the design will have to be modified and retoleranced.

UNDERSTANDING FOR REDESIGN
As part of the process of generating the component tolerances for each of the possible errors, it is also important to follow the optical field through the element being toleranced all the way to the output fiber. This process serves two purposes.

First it ensures that the numbers obtained in the tolerancing run are valid. For instance, in the example at hand, one would like to know why the plot (in Fig. 2) shows an asymmetry of insertion loss between plus and minus rotations.

This analysis also helps to understand the mechanisms by which the error is generated. In the current example, this corresponds to understanding how the optic-axis rotation gives rise to insertion loss. Often the understanding of the problem derived in this fashion can lead to a better redesign.

The following analysis looks at the case of 10° of OA rotation and an input beam of 45° polarization using a picture of the energy emerging from calcite #1 (see Fig. 3, top). The original beam has split into two beams after exiting the calcite. The beams are separated not only in Y but also in X, and the bottom beam contains 73% of the total energy.

The corresponding polarization for the same two beams can be plotted (see Fig. 3, center). The result shows a top beam that is polarized at 13.8° off from horizontal and a bottom beam polarized at 13.8° off from vertical. If there were no OA rotation, there would be two beams of equal flux, both located at X = 0 but still separated in Y. The top beam would be pure horizontal polarization and the bottom beam would be pure vertical.

The explanation for the difference between the OA rotated and unrotated cases is that because of the OA rotation, the normal polarization modes for a beam traveling in the Z direction into calcite #1 are no longer X and Y, but instead lie along a set of orthogonal, but rotated, axes. Since the mode axes are rotated, the incident 45° polarized beam will decompose more strongly into one of the modes than the other, as indicated in the resulting picture. The upper and lower beams swap polarization after passing through the half-wave plate rotated at 45° (see Fig. 3, bottom). The amount of flux in each of the two beams stays essentially the same.

FIGURE 3. Starting with 45° polarized light, the energy in a plane just after calcite #1 (top) is greater in the bottom of two beams for the case of +10° OA rotation. Both beams emerge in linear states rotated by 13.8° from their nominal X and Y states (center). After passing through the half-wave plate, the polarization states of the two beams get flipped about the 45° axis (bottom).

Since the OA of calcite #2 is not rotated out of its nominal position, the normal polarization modes for a beam traveling in the Z direction into calcite #2 are X and Y. Therefore, the two beams entering calcite #2 each split into their X and Y components, which gives rise to four beams exiting calcite #2.

A logarithmic picture shows the energy in the four beams that exit from calcite #2 (see Fig. 4, left). The reason for the log scale is to show all four beams clearly, even though there are large differences in the relative amounts of energy in the four beams. In fact, the percentage of the total flux in each of the four beams, given from top to bottom, is 1.5%, 69.0%, 25.3%, and 4.2%. It also makes sense that the two beams with the least flux would be located at the two extremes in Y, while the two beams with the most flux will be located at Y positions in between the two.

To understand this, notice that the polarization plot for the beams after exiting the wave plate shows the top beam polarized primarily in Y and the bottom beam in X. Combine this with the fact that in calcite #2 the X polarization corresponds to the ordinary beam and Y polarization to the extraordinary beam: it implies that the larger portion of the top beam incident on calcite #2 will be displaced down in Y while the larger portion of the bottom incident beam will not be displaced in Y, and therefore the larger portions of both incident beams will exit calcite #2 at nearly the same Y value and the smaller portions of each beam will be at the two Y extremes.

FIGURE 4. A logarithmic picture (left) of the energy in a plane located just after calcite #2, for the case of +10° of OA rotation in calcite #1, shows four beams. The four beams are generated by calcite #2, which breaks the two beams that exit the wave plate into their X and Y polarization components (right).

The polarization map of the four beams exiting calcite #2 also supports this argument (see Fig. 4, right). This map also shows that the two beams that touch in the center Y region are out of phase with each other. This is why the polarization map shows an elliptical polarization state in the overlap region rather than some intermediate linear state.

At this point one can also see that the two beams at the extreme +/- Y values will miss the right-angle prism and will not arrive at the path #1 output as intended for this switch mode. This 5.7% (1.5% + 4.2%) of the flux that is lost at this point is the first contributor to insertion loss due to the OA rotation.

The remaining two beams at the entrance plane to the path #1 output collimator are also pictured (see Fig. 5, top). As given previously, the X polarized beam has 69% of the original energy and the Y polarized beam has 25.3% of the original energy. Unfortunately, because the two beams are displaced relative to one another, it is impossible to couple all of this 94.3% of the original flux into the output fiber.

This is the second contributor to insertion loss due to the optic axis rotation. For this +10° of OA rotation only 31.5% of the original flux couples into the output fiber (insertion loss = 5.02). For the 10° of OA rotation only 71.2% of the original flux couples into the output fiber (insertion loss = 1.47).

The reason for the asymmetry of insertion loss as a function of OA rotation is that for the +10° rotation case, the beam with the lesser flux arrives at the output collimator with the same (X, Y) coordinates as an ideal beam with no OA rotation. Therefore, this beam with the lesser flux couples perfectly into the fiber while the beam with the greater flux couples poorly. For the -10° rotation case, it is the beam with the greater flux that arrives at the output collimator with the same (X, Y) coordinates as an ideal beam with no OA rotation. Therefore, there is less insertion loss for minus OA rotations than for the plus OA rotations (the asymmetry seen in Fig. 2).

FIGURE 5. In the presence of +10° of calcite #1 OA rotation, the energy in a plane just prior to the collimating lens of path #1 shows two beams (top). The beam with the least energy is located in the nominal position and therefore couples well into the output fiber. The beam with the most energy is displaced from the nominal position and therefore couples poorly into the output fiber. The two beams are in orthogonal X and Y polarization states (bottom) and have different phases.

In this example, no attempt to improve the coupling into the output fiber was made. In most components, coupling improvement could be obtained during component assembly by translating the output collimator/fiber pair as a group. This coupling improvement by translating the output collimator/fiber pair could easily have been added to the model.

Software analysis is extremely informative and useful. It not only tells what the change in performance is, but why it is changing. The analysis in this article represents less than one day of work by an experienced user and no material or equipment expense beyond the cost of the software and a computer. Clearly, in the process of arriving at a best design, there are significant cost and time benefits to analyzing and tolerancing telecom components using software.

Joe Shiefman is an optical consultant with Shiefman Consulting, 2530 N. Falling Water Court, Tucson, AZ 85749. He can be reached at shiefman@theriver.com.

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