Tolerancing analysis determines optimum configurations
Although the level of innovation in fiberoptic components over recent years has been unprecedented, the reality is that many manufacturing processes for key components have not evolved significantly in the journey from laboratory to production line. In particular, the manual assembly processes of many micro-optic components have not been optimized in terms of component performance or manufacturing costs.
The breathing space experienced by the industry through the current downturn is an opportunity not just for envisioning next-generation components but also an opportunity to develop optimum designs and manufacturing processes to improve performance, consistency, and cost. This certainly applies to relatively simple crystal-based components including isolators, circulators, and interleavers, which will be key building blocks in future optical networks.
Currently, specifications for the individual elements that make up these passive components, such as waveplates and beam displacers, vary widely between different component manufacturers. As an example, for the same part, the specification for stress birefringence varies by two orders of magnitude from three leading vendors. The consequence of overspecifying is increased cost, while underspecifying leads to suboptimal performance.
Automation is regularly promoted as the main path to improved manufacturing efficiencies. However, the first step in this process is to understand how individual elements in micro-optic assemblies impact overall component performance. Tolerancing analyses can be applied to determine the optimum configuration. Tolerancing allows us to build up a realistic set of performance parameters for crystal elements and to determine the assembly tolerances of the ancillary optical elements. Factors that can be modeled include crystal length, wedge angle/parallelism, optical axis alignment, stress birefringence, wave-front distortion, dispersion, and required fiber positioning accuracy. Symmetry effects also can be used in new designs to significantly dilute tolerances, thereby improving production costs and yields.
Birefringent crystal-based fiberoptic devices can be divided into two main classes, namely phase retardance components and those that make use of the fact that when the optical axis is correctly oriented, the o-ray and e-ray propagate in different directions. The first effect can be used to fabricate devices such as half and quarter waveplates and optical interleavers, while components that make use of the second effect include circulators and optical isolators.
Although the operation principles of these devices are well known, there is a lack of data related to their tolerances. Thus, the development of modeling software is vital to determining the optimum fabrication and assembly conditions for such birefringent-based devices.
We used the commercially available ray-tracing program, Zemax, to analyze the ray propagation characteristics of three devices: an optical circulator, a simple optical interleaver, and an optical isolator. The software allows the user to build up a system of optical elements including lenses, fibers, birefringent crystals, prisms, and diffractive elements, and then trace a series of rays through the system. Data can be entered using a spreadsheet format or a more flexible programming language that allows for automation of any particular analysis.
The optical software has a fiber coupling-efficiency option that allows the user to define an input and output fiber having a specified numerical aperture. The coupling efficiency of an o-ray or e-ray propagating through the optical system can therefore be modeled for a variety of optical components, making it possible to determine fabrication, assembly, and alignment tolerances of the various optical elements. This capability is important because in many cases birefringent-crystal fabrication errors can only be compensated for by realigning the position of the output optical fiber.
The ray-tracing engine used in this program is only capable of supporting uniaxial birefringent crystals.1 However, for the purpose of this analysis we assumed that all birefringent crystals were yttrium vanadate (YVO4), which is a uniaxial crystal. Vanadate crystals are ideal for applications in fiberoptics because of their high birefringence (0.2039 at 1550 nm) and mechanical stability.2
A key challenge in general is to relate material or fabrication specifications of micro-optic elements to overall component performance. Tolerancing is an ideal way to define this relationship by modeling element specifications as a function of component performance metrics such as insertion loss and polarization dependent loss. Insertion loss (IL) is defined by
and the polarization-dependent loss (PDL) is defined by
Let us first consider a simple optical circulator (see Fig. 1). There were several interesting outcomes from the analyses for the modeled beam displacer specification requirements. The typical vendor specification for error in crystal length (~±50 µm) is close to the modeled optimum to achieve the target contribution to component IL and PDL. However, parallelism (typically ±10 arcsec) and optic axis alignment (typically ±0.1°) are significantly overspecified, while wavefront distortion is underspecified.
As an example of how modeling can be used to improve component design, consider the optical isolator (see Fig. 2). Of key importance to the operation of the isolator is the accuracy to which the wedge angle of the crystals must be fabricated. For completeness, we must consider the main wedge angles, α1 and α2 (tilt about the x-axis), and the tilts about the y-axis, β1 and β2. The accuracy can be determined in the context of PDL and IL.
If we consider the wedges to be independent, they must be fabricated to exceptionally challenging tolerances so that the insertion loss is minimized (see Fig. 3). The variation in insertion loss as a function of wedge angle error of the last crystal is shown for a system where the output fiber is adjusted to minimize the polarization dependent loss. The PDL can always be reduced to close to zero by aligning the translational position and/or the tilt of the output fiber such that it is centered between the focused ordinary and extraordinary wavefronts.
To minimize the IL contribution from variation in the wedge angle from the ideal, a fabrication specification of <±0.1° is required in both axes. In this case, the modeled specification approximately matches the typical vendor requirement (which is only specified in one plane). Achieving this angle tolerance with high yield is almost impossible using current fabrication technology and processes.
By carrying out a series of tolerancing analyses using the software, we found that the optimum configuration was one where both wedge angles were identical (α1 = α2). Standard wedge-sorting tools already exist. The variation in IL as a function of wedge angle is also shown in Fig. 3, where again the fiber is aligned to minimize the PDL. As can be seen, the roll-off in IL is almost negligible over a wide range, thereby simplifying the fabrication process.
The tilts about the y-axis must still be controlled accurately because they do not compensate in a system where the two vanadate crystals are fabricated as described above. To reduce the insertion-loss variation to below 0.2 dB, the wedge angle about the y-axis must be controlled to better than ±0.15°. However, we have now reduced the fabrication problem to one where the wedge in only one direction must be accurately controlled.
The third device analyzed was the interleaver (see Fig. 4). Modeling phase retardance devices such as interleavers is less straightforward in Zemax, and for the purposes of this analysis a series of Matlab-based models were written to calculate the sensitivity of interleaver response to various fabrication errors.
Care must be taken when relating a given input polarization state to the o-ray or e-ray induced. In general, for each direction of propagation in an anisotropic medium, two mutually orthogonal eigenwaves with different phase velocities and polarization directions exist. Moreover, in the case of a nonabsorbing medium, these eigenwaves are linearly polarized because all components in the dielectric tensor are real.
For a single crystal, an arbitrary polarized incident beam will be split into two linearly polarized beams—the o-ray and e-ray. However, in the case of a multiple birefringent-crystal-based ideal system, the o-ray leaving the first crystal may be resolved into a new o-ray and e-ray, and similarly for the e-ray exiting the first crystal. In other words, the polarization state of the light incident on the second crystal does not exactly match the eigenmode. Thus, rather than the two beams propagating in the second crystal designed for, we will have four beams. This is particularly important when there are fabrication errors associated with the crystals—an effect that can be corrected for by using symmetry conditions.
WDM data streams consist of a series of high-speed digital signals spaced uniformly across the frequency spectrum. Standard frequency spacings are 100, 50, and 25 GHz, all defined with respect to the ITU grid. An interleaver is a device that separates rates even and odd signals, thereby increasing the spacing by a factor of two. This simplifies the tolerances on subsequent optical WDM components in an optical network. As a birefringent-based interleaver makes use of phase retardance effects, it is highly sensitive to errors in the birefringence, crystal length, surface flatness, and the presence of wedges/nonparallelism between the front and rear surface of such a device.
A series of Matlab/Zemax models were developed to calculate the dependence of the position of the WDM transmission spectrum, crosstalk, and extinction ratio on these parameters. Of particular interest is the variation in crosstalk of the system as a function of these errors. To analyze this we assumed that the WDM data pulses had a Gaussian pulse profile, and then calculated the crosstalk by integrating over the pulse in frequency space.
The ideal length for the vanadate uniaxial crystals is 14.703 mm for an interleaver device centered on the C-band. A comparison of the spectral response of a perfect device, and one where the length of the crystal is out by 1 µm reveals a significant shift in the position of the passband for such small errors in crystal length (see Fig. 5). To keep the shift to less than 7.5 GHz, the crystal length must be controlled to better than 0.6 µm. The variation in the position of the passband as a function of vanadate birefringence dictates that we must control the birefringence of the vanadate to better than 1 × 10–5.
These tolerances will be difficult to meet in a mass-production environment. Thus, in the next stage of this research, we shall investigate the ability of angular tuning to compensate for such fabrication errors. We believe that by tilting the vanadate crystal with respect to the incident optical axis, the effective phase retardation can be adjusted to optimize performance. By combining the ray-tracing abilities of the software program with the analytical abilities of Matlab we believe that more realistic fabrication limits can be determined.
We hope that this analysis shows that rigorous tolerancing of birefringent-based telecommunication components can be used to determine which parameters must be most tightly controlled, and that symmetry considerations can allow significant relaxation on certain key dimension and material values. Future work will concentrate on improving these models and developing new compensation techniques with the aim of simplifying the fabrication of high-performance birefringent crystals.
John Nicholls is CEO of Photonic Materials, Strathclyde Business Park, Bellshill ML4 3BF, Scotland; and Brian Robertson is a senior research associate at University of Cambridge, Cambridge, England. John Nicholls can be reached at email@example.com.
- Q-T Liang, Appl. Opt. 29(7) 1008 (1990).
- J. Nicholls, WDM Solutions (December 2001).