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Optics Express

  • Editor: J. H. Eberly
  • Vol. 7, Iss. 12 — Dec. 4, 2000
  • pp: 381–394
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Tolerancing of polarization losses in free-space optical interconnects.

Frédéric Lacroix, Michael H. Ayliffe, and Andrew G. Kirk  »View Author Affiliations


Optics Express, Vol. 7, Issue 12, pp. 381-394 (2000)
http://dx.doi.org/10.1364/OE.7.000381


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Abstract

A study of polarization losses in free-space optical interconnects is presented. A generic method is used for the prediction of optical power losses originating from fabrication errors in the polarization characteristics of components or light sources in free-space optical systems. The impact of polarization errors is evaluated on an individual level by a sensitivity analysis and on a system level by a Monte-Carlo analysis. The method is demonstrated by application to an optical interconnect example and validated by comparison with experimental results. The simultaneous interaction of multiple tolerance parameters (commonly known as “tolerance stackup”) is shown to have a significant impact on polarization losses.

© Optical Society of America

1. Introduction

Two dimensional optical interconnects are widely seen as potential solutions to present and future bandwidth bottlenecks in massively parallel electronic systems [1

1. D. A. B. Miller, “Physical reasons for optical interconnection,s” International Journal of Optoelectronics , 11, 155–168 (1997).

,2

2. D. J. Goodwill, “Free-space optical interconnect for Terabit network elements,” Proceedings of Optics in Computing (Snowmass, Colorado, 1999).

]. One of the major hurdles impeding their widespread acceptance is linked to concerns over the cost and manufacturability of the optics and optomechanics that are used in such systems [3

3. F. A. P. Tooley, “Challenges in Optically Interconnecting Electronics,” IEEE Journal of Selected Topics in Quantum Electronics , Vol. 2, No. 1, pp. 3–13, April 1996. [CrossRef]

]. Cost and manufacturability issues arise because of the severe optical and optomechanical component fabrication tolerances that are required to insure proper alignment of the optical components and guarantee that a maximum of the light emitted from the source falls on the appropriate detector.

Optical power losses limit system performance as receiver switching speeds are energy dependent [4

4. T.K. Woodward, A. V. Krishnamoorthy, A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, L. A. D’Asaro, M. F. Chirovsky, S. P. Hui, B. Tseng, D. Kossives, D. Dahringer, and R. E. Leibenguth, “1-Gb/s Two-Beam Transimpedance Smart-Pixel Optical Receivers Made from Hybrid GaAs MQW Modulators Bonded to 0.8µm Silicon CMOS,” IEEE Photonics Technology Letters , Vol. 8, No. 3, pp. 422–424, March 1996. [CrossRef]

] and the semiconductor lasers which are used as light sources possess limited output powers [5

5. F. Tooley, P. Sinha, and A. Shang, “Time-differential operation of an optical transceive,r” Optics in Computing. 1997 Technical Digest Series Vol.8. Postconference Edition, Topical Meeting on Optics in Computing - OC97, Incline Village, NV, USA, pp. 73–75, 18–21 March 1997. [CrossRef]

]. Losses can originate from numerous sources such as Fresnel reflections at optical surfaces, the limited diffraction efficiency of diffractive optical elements (DOEs) used for beam collimation/focusing and fanout operations, leakage due to the non-ideal polarization properties of the input laser source and polarization components (polarizers, retarders, etc.), insertion losses associated with electro-absorption modulators and beam clipping due to misalignments of the optical or optoelectronic components with respect to the system optical axis, among others.

While some effort has been spent on tolerancing the optomechanical aspects of optical interconnects [6

6. D. Zaleta, S. Patra, V. Ozguz, J. Ma, and S. H. Lee, “Tolerancing of board-level-free-space optical interconnects,” Appl. Opt. 35, 1317–1327 (1996). [CrossRef] [PubMed]

, 7

7. S. P. Levitan, T. P. Kurzweg, P. J. Marchand, M. A. Rempel, D. M. Chiarulli, J. A. Martinez, J. M. Bridgen, C. Fan, and F. B. McCormick, “Chatoyant: a computer-aided-design tool for free-space optoelectronic systems,” Appl. Opt. 37, 6078–6092 (1998). [CrossRef]

, 8

8. D. T. Neilson, “Tolerance of optical interconnections to misalignment,” Appl. Opt. 38, 2282–2290 (1999). [CrossRef]

], little information is available in the literature on the tolerancing of other system aspects. In particular, polarization losses in optical interconnects have rarely drawn much attention (see [9

9. F.B. McCormick, T. J. Cloonan, F. A. P. Tooley, A. L. Lentine, J. M. Sasian, J. L. Brubaker, R. L. Morrison, S. L. Walker, R. J. Crisci, R. A. Novotny, S. J. Hinterlong, H. S. Hinton, and E. Kerbis, “Six-Stage digital free-space optical switching network using symmetric self-electro-optic-effect devices,” Appl. Opt. 32, 5153–5171 (1993). [CrossRef] [PubMed]

, 10

10. G. C. Boisset, M. H. Ayliffe, B. Robertson, R. Iyer, Y. S. Liu, D. V. Plant, D. J. Goodwill, D. Kabal, and D. Pavlasek, “Optomechanics for a four-stage hybrid-self-electro-optic-device-based free-space optical backplane,” Appl. Opt. 36, 7341–7358 (1997). [CrossRef]

, 11

11. M.H. Ayliffe and D. V. Plant, “A Generalized Method for Tolerancing Polarization Losses in Free-Space Optical Interconnects,” Optics in Computing. 1997 Technical Digest Series Vol.8. Postconference Edition, Topical Meeting on Optics in Computing - OC97, Incline Village, NV, USA, pp. 221–223, 18–21 March 1997.

] for some discussion of the topic) and the mechanisms of accumulation of polarization losses (“tolerance stackup”) in a complex optical interconnect system have not, to the author’s knowledge, been previously investigated. The question then arises as to whether the tolerances commonly specified for the polarization-based components (which are often determined by what is standard for the optical shop) are appropriate.

Polarization-based beam combination and routing techniques have been employed in a large majority of the demonstration systems implemented by various research groups [9

9. F.B. McCormick, T. J. Cloonan, F. A. P. Tooley, A. L. Lentine, J. M. Sasian, J. L. Brubaker, R. L. Morrison, S. L. Walker, R. J. Crisci, R. A. Novotny, S. J. Hinterlong, H. S. Hinton, and E. Kerbis, “Six-Stage digital free-space optical switching network using symmetric self-electro-optic-effect devices,” Appl. Opt. 32, 5153–5171 (1993). [CrossRef] [PubMed]

, 10

10. G. C. Boisset, M. H. Ayliffe, B. Robertson, R. Iyer, Y. S. Liu, D. V. Plant, D. J. Goodwill, D. Kabal, and D. Pavlasek, “Optomechanics for a four-stage hybrid-self-electro-optic-device-based free-space optical backplane,” Appl. Opt. 36, 7341–7358 (1997). [CrossRef]

, 12

12. D. T. Neilson, S. M. Prince, D. A. Baillie, and F. A. P. Tooley, “Optical Design of a 1024-channel free-space sorting demonstrator,” Appl. Opt. 36, 9243–9252 (1997). [CrossRef]

, 13

13. F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hintelong, R. J. Crisci, R. A. Novotny, and H. S. Hinton, “Five-Stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt. 33, 1601–1618 (1994). [CrossRef] [PubMed]

, 14

14. M. Yamaguchi, T. Yamamoto, K. Yukimatsu, S. Matsuo, C. Amano, Y. Nakano, and T. Kurokawa, “Experimental investigation of a digital free-space photonic switch that uses exciton absorption reflection switch arrays,” Appl. Opt. 33, 1337–1343 (1994). [CrossRef] [PubMed]

]. The fact that polarization losses in free-space optical interconnects have received so little attention is surprising considering the fact that in systems that use polarizing beam splitter quarter-wave plate (PBS/QWP) assemblies (figure 1) to perform beam combination functions, the optical power losses can easily amount up to 5% or more of the input light per pass per PBS/QWP assembly when commercial grade components are used. Losses are thus likely to accumulate rapidly in a system employing multiple PBS/QWP assemblies.

Figure 1. Diagram of PBS/QWP assembly.

The dotted arrows in figure 1 illustrate the leakage paths resulting from polarization losses in a PBS/QWP assembly. This polarization leakage is likely to degrade the contrast ratio of the modulated beams by interfering coherently with them or cause instabilities when reflecting back to a laser source [15

15. S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “Influence of External Optical Feedback on Threshold and Spectral Characteristics of Vertical-Cavity Surface-Emitting Lasers,” Photonics Technology Lett6, (1994).

]. Polarization losses originate from two factors:

1) Deviations from specifications in polarization based components.

2) Imperfections in the polarization of input light sources.

There is thus a need to rigorously study polarization losses in optical interconnects. This would be useful for a number of reasons:

1) Allow the system designer to calculate a polarization tolerance budget. This budget can be divided into two parts:

i) calculate the tolerances of polarization-based components (extinction ratio of PBS, retardance accuracy of QWPs, etc.) and verify whether commercial tolerances are sufficient to ensure the intended level of performance for a given system.

ii) calculate the tolerances for the polarization properties of the source and delivery system (diode laser, polarization maintaining (PM) fiber, Vertical Cavity Surface Emitting Laser (VCSEL) array).

2) Determine the effect of tolerance stackup, i.e. what polarization loss penalty must be included in the power budget once the source and component tolerances have been set. To perform this analysis, a Monte-Carlo simulation is necessary as the throughput as a function of the polarization components parameters is non-linear (see [16

16. R.M.A Azzam and W.M. Bashara, Ellipsometry and Polarized Light, (North-Holland Editor, Amsterdam, 1977).

] for some example throughput response functions) and so the moments of the function such as the mean and standard deviation cannot be evaluated analytically [17

17. S. D. Nigam and J. U. Turner, “Review of statistical approaches to tolerance analysis,” Computer-Aided Design 27, 6–15 (1995). [CrossRef]

].

The methodology illustrated in figure 2 is used to respond to the needs outlined above.

Figure 2. Flowchart of tolerancing method.

An initial system design is converted to a parametric mathematical model by using the Stokes vectors and Mueller matrix representation of polarization states. A thorough treatment of mathematical methods in polarization analysis can be found in [16

16. R.M.A Azzam and W.M. Bashara, Ellipsometry and Polarized Light, (North-Holland Editor, Amsterdam, 1977).

]. A sensitivity analysis is then performed. This is an analysis of the impact of the independent system parameters on the system throughput and is used to determine a tolerance budget for these parameters. These tolerances must then be judged to be acceptable or not from a manufacturing standpoint. They are then input into a Monte-Carlo analysis in order to predict the probable loss penalty when using those components to construct an actual system. If the loss penalty is deemed acceptable, the design cycle ends. However, if the probable loss penalty exceeds the allocated polarization loss margin, the tolerances must be modified and another iteration made.

The methodology is illustrated with the help of an application example consisting of a free-space optical interconnect designed for board-to-board applications. Other possible applications of this method include the tolerancing of compact disc pickup heads, telecommunication isolators or circulator components and any free-space optical system that uses polarization-based components.

A description of the optical interconnect, characterization data for the components used in building the system, a sensitivity analysis for the various parameters in order to delimit acceptable tolerance ranges and finally Monte-Carlo simulations of the probable throughputs when using such components to build a system are presented. A simulation of the optical interconnect using the measured data is also presented to validate the proposed method.

2. Application Example: A Free-Space Optical Interconnect

A free-space optical interconnect designed for board-to-board applications was chosen as an application example of the tolerancing process. The details of the optical design have already been published [18

18. B. Robertson, “Design of an optical interconnect for photonic backplane applications,” Appl. Opt. 37, 2974–2984 (1998). [CrossRef]

].

The design is a modulator-based system and employs two cascaded PBS/QWP assemblies in order to route arrays of optical beams between optoelectronic chips. Figure 3 shows a schematic layout of the interconnect with the various polarization states indicated as the light propagates from the input of the first PBS/QWP assembly to the output at stage 2.

Figure 3. Schematic layout of the interconnect with polarization states.

The components that modify the state of polarization of the beams propagating in the interconnect (PBSs and QWPs) were modeled using Mueller matrices. The optoelectronic reflection modulators only change the handedness of the polarization upon reflection and were therefore modeled as mirrors. Polarization aberrations that could be introduced in the beams by the other optical elements such as the diffractive fanouts and minilens arrays were ignored due to the use of slow, f/16 beams in the system [19

19. J. L. Pezzanti and R. A Chipman, “Angular dependence of polarizing beam-splitter cubes,” Appl. Opt. 33, 1916–1928 (1994). [CrossRef]

]. The angular position of the PBSs was assumed to be perfect with respect to the rest of the system. This is a necessary assumption as mechanical tolerances are not the subject of this paper and the angular mechanical alignment tolerances of a PBS are usually much smaller than a degree [20

20. F. K. Lacroix, “Analysis and Implementation of a Clustered, Scaleable and Misalignment Tolerant Optical Interconnect,” Chpt 3, Master of Engineering Thesis, McGill University, Montréal, Canada, 1999.

] whereas the angular field of view for a commercial component is equal to ±2° [19

19. J. L. Pezzanti and R. A Chipman, “Angular dependence of polarizing beam-splitter cubes,” Appl. Opt. 33, 1916–1928 (1994). [CrossRef]

]. This signifies that the power losses caused by tilt introduced into the beams upon reflection from a misaligned PBS cause power losses that are much more significant than the associated polarization leakage losses. Figure 4 is a schematic drawing representing the components included in the Mueller matrix model.

Figure 4. Schematic diagram of system model.

2.1 Component Characterization Results

Figure 5 shows the setup used to perform characterization of the components. A 50/50 beam splitter pellicle was mounted at 45° relative to a collimated 2ω o=1200µm diameter beam output from a single-mode polarization maintaining fiber (PM) - collimating lens assembly. Excellent linearity in the output polarization is ensured by placing a polarizer after the PM fiber (specified to at least a 10, 000:1 extinction ratio). The beam reflected from the pellicle was used as a reference to decrease the influence of power fluctuations of the input light source (about ±2%) on the power meter readings. All power measurements were done using a dual-channel power meter.

Figure 5. Diagram of setup used for component characterization.

2.1.1 Quarter-Wave Plates (QWPs)

The quarter-wave plates used were composed of a layer of thin birefringent quartz sandwiched between two fused silica or BK7 optical windows that provide mechanical support. The quartz layer must be 23.4µm thick for the plate to function as a zero-order quarter-wave plate at 852nm. Deviations from the nominal quartz thickness will translate into retardance variations for the wave propagating in the crystal. The quarter-wave plates were specified to a ±l/200 tolerance. This means that the thickness must be controlled to a tenth of a micron to respect the specified tolerance.

The QWPs used in this system were fabricated as a single batch which means that a large sheet of quartz was polished and then diced to provide multiple components. It can therefore be assumed that all the QWPs used in the system possess a uniform retardance value. This assumption was experimentally confirmed by measuring the retardance of many QWPs as described below.

The differential retardance of the QWPs could not be measured directly. The indirect method used for characterization consists in sending a linearly polarized beam into the QWP and varying its rotation angle such that the output polarization is as close to circular as possible [21

21. P. A. Williams, A. H. Rose, and C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36, 6466–72 (1997). [CrossRef]

]. From the measurement of the extinction ratio the retardance can be calculated with the following formula:

δ=sin1(2ηη2+1)
(1)

where δ is the differential retardance of the quarter-wave plate and η is the ratio of the amplitudes (not intensity) of both axes of the light output from the QWP.

The precision of this measurement depends on the polarization linearity of the light delivered at the input and the precision of the angular alignment of the retarder fast or slow axis with respect to the input polarization. The linear polarization at the QWP input was measured to have an extinction ratio better than (12,000:1) which can be assumed to be infinite. The QWP rotational position can be adjusted to about ±1° (estimated manual adjustment sensitivity).

The average circularity at the output was measured to be 1.5:1 (for four QWPs). The maximum variation on the ellipticity measurement for each QWP was 0.05. These numbers translate into a λ/33 differential retardance error from the perfect λ/4 when using equation 1. The QWPs in the system thus possess a retardance of either λ/4+λ/33 or λ/4-λ/33. This does not respect the specified tolerance of ±λ/200 and represents a serious fabrication error. The uncertainty on the measurement is estimated to be equal to ±λ/350.

2.1.2 PBS/QWP Assembly

The PBS/QWP assemblies were pre-assembled by the commercial vendor. They were characterized to determine the throughput coefficients. The PBS/QWP assemblies were characterized in both transmit and reflect modes. The throughput was measured to be 90%±1 in the transmit mode and 95%±1 in the reflect mode. Two assemblies were then cascaded in order to measure the total throughput. This was measured to be 85% ±1. The measured throughput is 5% lower than calculated from the manufacturers specifications ((kp(1-ks))2=(0.96(1-0.01))2=0.95). The difference is attributable to the poor quality of the QWPs used in the system. Pairs of crossed plates will tend to partially compensate their individual retardance errors and produce polarization of reasonably good quality. This is an interesting result as it signifies that the QWPs in PBS/QWP assemblies do not need to possess a very precise 90 degree retardance value: they only need to have uniform retardances.

2.2 Demonstration of the Method

2.2.1 Sensitivity Analysis

A sensitivity analysis was performed. This is a study of the effect of the variation of the independent parameters on the system performance and is useful to establish acceptable tolerance ranges for each parameter. It also informs the designer as to which parameters of which components most affect throughput. Note that only one parameter is varied at a time while the others are kept constant. A critical part of the sensitivity analysis consists in selecting a power falloff metric to delimit the tolerable variation range. A relaxed metric will mean that components might be easier to fabricate but might provide lower performance in the assembled system due to accumulated losses. A more severe metric will mean that tolerances are tighter, providing a lower loss but also increasing fabrication cost. The number of parameters to simulate is large: each QWP and PBS in the interconnect has two independent parameters for a total of fourteen parameters as shown in equation 2.

MSystem=f(θ1,δ1,θ2,δ2,θ3,δ3,θ4,δ4,θ5,δ5,Kp1,Ks1,Kp2,Ks2)
(2)

Where θ and δ represent the orientation of a QWP fast axis and its retardance value, respectively. Kp and Ks are the PBS transmission coefficients for p and s polarization. Following the sensitivity analysis, two metrics (1% and 10% power falloffs) are used to delimit tolerance ranges for the parameters. Two metrics were chosen in order to compare the loss penalties associated with the choice of a conservative metric (1%) or a more relaxed metric (10%).

2.2.1.1 Effect of Imperfect PBS.

2.2.1.2 Effect of Quarter-wave Plates Retardance Errors.

A sensitivity analysis of the QWPs retardance on the throughput was performed. Figure 6 shows a plot of throughput versus retardance deviation from the perfect 90° for the five QWPs in the system. Perfectly linear p-polarization is assumed at the input.

Figure 6. Plot of throughput versus retardance deviation.

2.2.1.3 Effect of QWPs Rotational Misalignment

Figure 7 shows a plot of throughput versus QWP rotational misalignment. The curves follow the same order as on figure 6.

Figure 7. Throughput versus QWP rotational misalignment.

Figure 7 shows that there is a certain similarity between having a rotationally misaligned perfect QWP and a well-aligned imperfect QWP as the two situations will impart a deviation from the nominal λ/4 retardance on the wave traversing it.

2.2.1.4 Input Polarization Azimuthal Orientation

Figure 8 shows a plot of throughput versus the azimuthal orientation of the input p-polarization. Such a variation in the input azimuthal angle would result, for example, from having a rotationally misaligned PM fiber fast or slow axis with respect to the system axis. It shows that power will drop by about 1% when the input linear polarization is rotated by ±6°.

Figure 8. Throughput versus azimuthal orientation of input P-polarization.

2.2.1.5 Input Polarization Ellipticity

Figure 9 plots the throughput versus ellipticity for right-hand elliptically polarized light launched from the source. Note that the ellipticity is defined as the intensity ratio of the s axis over the p axis. An ellipticity of 0 thus represents perfectly linear p-polarization.

Figure 9. Throughput versus ellipticity at input.

2.2.2 Summary of Sensitivity Analysis

A set of tolerances for two falloff metrics (1% and 10%) calculated from the above graphs as well as the commercial tolerances available for each component are presented in table 1.

Table 1. Summary of tolerances

table-icon
View This Table

Note that the commercial specifications are better than the tolerances calculated with a 1% power loss metric in almost all cases except for the PBS transmission coefficients. However, it is necessary to investigate the impact of the accumulation of these tolerances in the system. This requires a Monte-Carlo analysis.

2.3 Monte-Carlo Analysis

A Monte-Carlo analysis was performed. The set of tolerances calculated above was used to delimit the range of the input tolerance probability distributions. When performing such an analysis, it is important to understand the impact that the input probability distributions have on the final Monte-Carlo distribution. A proper distribution for each parameter must be chosen in order to obtain useful results. The precise shape of these distributions is highly coupled to the manufacturing process. In this case, after communicating with the manufacturer, it was decided to use a truncated Gaussian distribution with its peak at the midway point between the nominal value and the high side tolerance to represent the retardance value distribution of the QWPs as there is a tendency of optical shops to leave elements on the high side of the thickness tolerance. Truncated Gaussian distributions with the peak located at the nominal value were used to represent the QWP angular alignment and PBS transmission coefficient distributions. Both distributions were truncated at the 3s points, which lie at the tolerance limits. These probability distributions are thought to be representative of common optical shop practices (see [22

22. CODE V Version 8.30 Reference Manual, Chapter 6, pp. 65–67, Optical Research Associates, 3280 East Foothill Boulevard, Pasadena, California, California 91107, August 1999.

] for more details). A hundred and fifty thousand samples were used to obtain stable results and a good accuracy. The calculation necessitated about 5 hours of CPU time on a SunSparc 20 station.

2.3.1 Monte-Carlo Analysis for 1% Falloff Metric

The tolerances for each parameter calculated with the 1% power falloff metric were input into the Monte-Carlo analysis. The source ellipticity was assumed to vary between 0 and 0.01. Figure 10 shows a graph of the resulting throughput histogram distribution.

Figure 10. Histogram of number of samples versus throughput for tolerances calculated using 1% falloff metric.

Notice that the distribution is not normal in shape but is skewed towards higher values. The mean of the distribution is located at 97.9% and the standard deviation is 0.94. The 99% confidence interval cutoff value of the distribution was calculated to be located at a throughput value of 94.9% (i.e. 99% of the systems built with components using those tolerances would possess a throughput value greater than 94.9%).

2.3.2 Monte-Carlo Analysis for 10% Falloff Metric

The tolerances for each parameter calculated with the 10% power falloff metric were input into a Monte-Carlo analysis. The source ellipticity was allowed to vary between 0 and 0.11. Figure 11 shows a graph of the resulting throughput distribution.

Figure 11. Histogram of number of samples versus throughput for tolerances calculated using 10% falloff metric.

The distribution now occupies a much larger interval of values (from 35 to 92%). The mean is equal to 76.4% and the standard deviation is 8.7. The 99% confidence interval cutoff is now located at a throughput value of 50%. The use of a more relaxed tolerance metric has led to a severe degradation in the confidence interval cutoff value.

2.3.3 Monte-Carlo Analysis for Commercial Tolerances

The effect of using standard commercial grade components was studied. The emitter was modeled as a polarization maintaining (PM) fiber emitting linear p-polarized light possessing a nominal contrast ratio of 30dB (0.001 intensity ratio) with an arbitrary ±0.002 s-polarized noise factor superposed 90 degrees in phase (in effect producing right-hand circularly polarized light) to model random mode coupling between the axes of the fiber due to stress or environmentally induced birefringence. This represents the type of source used in this system. The resulting polarization ellipse is assumed to rotate by ±2° around the p-axis (commercial specification for alignment of the fiber fast axis relative to the connector ferrule).

Figure 12 shows the resulting Monte-Carlo analysis results. Again, 150000 samples were calculated. The mean of the distribution is equal to 91.1% and the standard deviation is equal to 0.37%. The 99% confidence interval boundary is located at 90.4%.

Figure 12. Histogram of number of samples versus throughput for commercial tolerances.

As can be seen on figure 12, standard commercial grade polarization components should guarantee that a worst-case power falloff of slightly less than 10% should be obtained.

2.3.4 Monte-Carlo Analysis for Optical Interconnect

The effects of using the components characterized in section 2.1 to construct an actual system were investigated. Commercial grade components were assumed except that QWPs having a uniform λ/33 error in the retardance value (as measured) were modeled.

Figure 13. Histogram of number of samples versus throughput distribution for demonstrator system.

Figure 13 demonstrates that the experimentally measured throughput of 85% ±1 falls comfortably within the calculated distribution. The mean of the distribution is equal to 84.3%. This result validates the simulation method.

3 Conclusions

This paper has presented a method to rigorously calculate polarization losses and tolerance polarization-based components in free-space optical interconnect systems. This is necessary in order to accurately quantify power losses resulting from the use of components or sources having imperfect polarization characteristics and answers the needs outlined in the introduction:

1) To specify tolerances of polarization-based components.

2) To specify tolerances for the polarization properties of the source.

3) To determine the effect of tolerance stackup, i.e. the polarization loss penalty that must be included in the power budget.

The method was demonstrated with the help of a free-space optical interconnect application example. The availability of measured data for the interconnect throughput verified the validity of the simulation model. The throughput measured when using components possessing commercial tolerances was found to fall within the simulation result distribution.

A detailed sensitivity analysis for the free parameters in the interconnect was presented. The throughput falloff curves were used to delimit tolerance ranges for the parameters according to two different power falloff metrics (1% and 10%). Table 1 presents a list of tolerances calculated from the throughput curves.

It was found that using pairs of crossed wave plates as present on the PBS/QWP assemblies acts as a partial compensation mechanism for the fabrication errors in the QWPs retardance. Using wave plates possessing equal retardances insures that the power losses due to polarization leakage caused by fabrication errors in the wave plates are kept to a minimum. It is thus preferable to use wave plates manufactured in the same batch when fabricating PBS/QWP assemblies.

The output Monte-Carlo distributions for graphs 10 and 11 (1% and 10% falloff metrics) look very similar in general shape except that the mean and standard deviations of the distribution calculated using a 10% metric are very different from the distribution calculated using a 1% metric: the mean is about 20% less and the standard deviation is roughly 9 times greater for the distribution calculated using a 10% falloff metric compared to the distribution calculated using a 1% falloff metric. But perhaps more importantly, the confidence interval cutoff value of the two distributions (the value that is included in the power budget to evaluate polarization losses) are also very different: 94.9% for the 1% falloff metric compared to 50% for the 10% falloff metric. Clearly then, the choice of a more relaxed metric has led to a severe and rapid degradation of the probable throughput. This confirms the importance of tolerance stackup in a complex system employing many polarization-based components: this must be taken into account when selecting a throughput falloff metric to set fabrication tolerances.

Commercial tolerances are superior for all parameters (except the PBS transmission coefficients for the p and s polarizations) to the set of tolerances calculated using a 1% power falloff metric. There is then little sense in specifying tolerances calculated using a metric that translate to tolerances looser that commercially available. The cutoff value for the Monte-Carlo distribution calculated using commercial tolerances is 90.4%. The difference between this value and the cutoff for the distribution calculated using the 1% set of tolerances is entirely due to the lower transmission coefficients of the PBS. Commercial tolerances seem to be sufficient to obtain an adequate level of performance in most cases for this type of system.

The decrease in the cutoff value of the distribution does not seem to be linear with the number of PBS/QWP assemblies used. This means that a very severe power falloff metric (≪10%) must be used to set tolerances for a system cascading three or more PBS/QWP assemblies. Commercial specifications might not be good enough in this case.

Note that the above analysis remains largely valid for a VCSEL-based system employing the same basic optical layout. Replacing the modulators with a VCSEL array would probably slightly increase the tolerances for the source azimuthal orientation and ellipticity. Feedback to the active devices due to polarization leakage might cause power or wavelength fluctuations of the VCSEL output [15

15. S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “Influence of External Optical Feedback on Threshold and Spectral Characteristics of Vertical-Cavity Surface-Emitting Lasers,” Photonics Technology Lett6, (1994).

]. This might degrade system performance and should be considered in the system design.

Acknowledgements

This research was supported by a grant from the Canadian Institute for Telecommunications Research under the National Centres of Excellence program of Canada. In addition A. Kirk acknowledges support from the National Sciences and Engineering Research Council (NSERC-OG0194547) and Fonds pour la formation et l’aide à la recherche (FCAR-NC-1778).

References and Links

1.

D. A. B. Miller, “Physical reasons for optical interconnection,s” International Journal of Optoelectronics , 11, 155–168 (1997).

2.

D. J. Goodwill, “Free-space optical interconnect for Terabit network elements,” Proceedings of Optics in Computing (Snowmass, Colorado, 1999).

3.

F. A. P. Tooley, “Challenges in Optically Interconnecting Electronics,” IEEE Journal of Selected Topics in Quantum Electronics , Vol. 2, No. 1, pp. 3–13, April 1996. [CrossRef]

4.

T.K. Woodward, A. V. Krishnamoorthy, A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, L. A. D’Asaro, M. F. Chirovsky, S. P. Hui, B. Tseng, D. Kossives, D. Dahringer, and R. E. Leibenguth, “1-Gb/s Two-Beam Transimpedance Smart-Pixel Optical Receivers Made from Hybrid GaAs MQW Modulators Bonded to 0.8µm Silicon CMOS,” IEEE Photonics Technology Letters , Vol. 8, No. 3, pp. 422–424, March 1996. [CrossRef]

5.

F. Tooley, P. Sinha, and A. Shang, “Time-differential operation of an optical transceive,r” Optics in Computing. 1997 Technical Digest Series Vol.8. Postconference Edition, Topical Meeting on Optics in Computing - OC97, Incline Village, NV, USA, pp. 73–75, 18–21 March 1997. [CrossRef]

6.

D. Zaleta, S. Patra, V. Ozguz, J. Ma, and S. H. Lee, “Tolerancing of board-level-free-space optical interconnects,” Appl. Opt. 35, 1317–1327 (1996). [CrossRef] [PubMed]

7.

S. P. Levitan, T. P. Kurzweg, P. J. Marchand, M. A. Rempel, D. M. Chiarulli, J. A. Martinez, J. M. Bridgen, C. Fan, and F. B. McCormick, “Chatoyant: a computer-aided-design tool for free-space optoelectronic systems,” Appl. Opt. 37, 6078–6092 (1998). [CrossRef]

8.

D. T. Neilson, “Tolerance of optical interconnections to misalignment,” Appl. Opt. 38, 2282–2290 (1999). [CrossRef]

9.

F.B. McCormick, T. J. Cloonan, F. A. P. Tooley, A. L. Lentine, J. M. Sasian, J. L. Brubaker, R. L. Morrison, S. L. Walker, R. J. Crisci, R. A. Novotny, S. J. Hinterlong, H. S. Hinton, and E. Kerbis, “Six-Stage digital free-space optical switching network using symmetric self-electro-optic-effect devices,” Appl. Opt. 32, 5153–5171 (1993). [CrossRef] [PubMed]

10.

G. C. Boisset, M. H. Ayliffe, B. Robertson, R. Iyer, Y. S. Liu, D. V. Plant, D. J. Goodwill, D. Kabal, and D. Pavlasek, “Optomechanics for a four-stage hybrid-self-electro-optic-device-based free-space optical backplane,” Appl. Opt. 36, 7341–7358 (1997). [CrossRef]

11.

M.H. Ayliffe and D. V. Plant, “A Generalized Method for Tolerancing Polarization Losses in Free-Space Optical Interconnects,” Optics in Computing. 1997 Technical Digest Series Vol.8. Postconference Edition, Topical Meeting on Optics in Computing - OC97, Incline Village, NV, USA, pp. 221–223, 18–21 March 1997.

12.

D. T. Neilson, S. M. Prince, D. A. Baillie, and F. A. P. Tooley, “Optical Design of a 1024-channel free-space sorting demonstrator,” Appl. Opt. 36, 9243–9252 (1997). [CrossRef]

13.

F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hintelong, R. J. Crisci, R. A. Novotny, and H. S. Hinton, “Five-Stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays,” Appl. Opt. 33, 1601–1618 (1994). [CrossRef] [PubMed]

14.

M. Yamaguchi, T. Yamamoto, K. Yukimatsu, S. Matsuo, C. Amano, Y. Nakano, and T. Kurokawa, “Experimental investigation of a digital free-space photonic switch that uses exciton absorption reflection switch arrays,” Appl. Opt. 33, 1337–1343 (1994). [CrossRef] [PubMed]

15.

S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, “Influence of External Optical Feedback on Threshold and Spectral Characteristics of Vertical-Cavity Surface-Emitting Lasers,” Photonics Technology Lett6, (1994).

16.

R.M.A Azzam and W.M. Bashara, Ellipsometry and Polarized Light, (North-Holland Editor, Amsterdam, 1977).

17.

S. D. Nigam and J. U. Turner, “Review of statistical approaches to tolerance analysis,” Computer-Aided Design 27, 6–15 (1995). [CrossRef]

18.

B. Robertson, “Design of an optical interconnect for photonic backplane applications,” Appl. Opt. 37, 2974–2984 (1998). [CrossRef]

19.

J. L. Pezzanti and R. A Chipman, “Angular dependence of polarizing beam-splitter cubes,” Appl. Opt. 33, 1916–1928 (1994). [CrossRef]

20.

F. K. Lacroix, “Analysis and Implementation of a Clustered, Scaleable and Misalignment Tolerant Optical Interconnect,” Chpt 3, Master of Engineering Thesis, McGill University, Montréal, Canada, 1999.

21.

P. A. Williams, A. H. Rose, and C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36, 6466–72 (1997). [CrossRef]

22.

CODE V Version 8.30 Reference Manual, Chapter 6, pp. 65–67, Optical Research Associates, 3280 East Foothill Boulevard, Pasadena, California, California 91107, August 1999.

OCIS Codes
(200.2610) Optics in computing : Free-space digital optics
(200.4650) Optics in computing : Optical interconnects
(260.5430) Physical optics : Polarization

ToC Category:
Research Papers

History
Original Manuscript: September 19, 2000
Published: December 4, 2000

Citation
Frederic Lacroix, Michael Ayliffe, and Andrew Kirk, "Tolerancing of polarization losses in free-space optical interconnects," Opt. Express 7, 381-394 (2000)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-7-12-381


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References

  1. D. A. B. Miller, "Physical reasons for optical interconnection,s" International Journal of Optoelectronics, 11, 155-168 (1997).
  2. D. J. Goodwill, "Free-space optical interconnect for Terabit network elements," Proceedings of Optics in Computing (Snowmass, Colorado, 1999).
  3. F. A. P. Tooley, "Challenges in Optically Interconnecting Electronics," IEEE Journal of Selected Topics in Quantum Electronics, Vol. 2, No. 1, pp. 3-13, April 1996. [CrossRef]
  4. T.K. Woodward, A. V. Krishnamoorthy, A. L. Lentine, K. W. Goossen, J. A. Walker, J. E. Cunningham, W. Y. Jan, L. A. D'Asaro, M. F. Chirovsky, S. P. Hui, B. Tseng, D. Kossives, D. Dahringer and R. E. Leibenguth, "1-Gb/s Two-Beam Transimpedance Smart-Pixel Optical Receivers Made from Hybrid GaAs MQW Modulators Bonded to 0.8�m Silicon CMOS," IEEE Photonics Technology Letters, Vol. 8, No. 3, pp. 422-424, March 1996. [CrossRef]
  5. F. Tooley, P. Sinha and A. Shang, "Time-differential operation of an optical transceive,r" Optics in Computing. 1997 Technical Digest Series Vol.8. Postconference Edition, Topical Meeting on Optics in Computing - OC97, Incline Village, NV, USA, pp. 73-75, 18-21 March 1997. [CrossRef]
  6. D. Zaleta, S. Patra, V. Ozguz, J. Ma and S. H. Lee, "Tolerancing of board-level-free-space optical interconnects," Appl. Opt. 35, 1317-1327 (1996). [CrossRef] [PubMed]
  7. S. P. Levitan, T. P. Kurzweg, P. J. Marchand, M. A. Rempel, D. M. Chiarulli, J. A. Martinez, J. M. Bridgen, C. Fan and F. B. McCormick, "Chatoyant: a computer-aided-design tool for free-space optoelectronic systems," Appl. Opt. 37, 6078-6092 (1998). [CrossRef]
  8. D. T. Neilson, "Tolerance of optical interconnections to misalignment," Appl. Opt. 38, 2282-2290 (1999). [CrossRef]
  9. F.B. McCormick, T. J. Cloonan, F. A. P. Tooley, A. L. Lentine, J. M. Sasian, J. L. Brubaker, R. L. Morrison, S. L. Walker, R. J. Crisci, R. A. Novotny, S. J. Hinterlong, H. S. Hinton and E. Kerbis, "Six-Stage digital free-space optical switching network using symmetric self-electro-optic-effect devices," Appl. Opt. 32, 5153-5171 (1993). [CrossRef] [PubMed]
  10. G. C. Boisset, M. H. Ayliffe, B. Robertson, R. Iyer, Y. S. Liu, D. V. Plant, D. J. Goodwill, D. Kabal and D. Pavlasek, "Optomechanics for a four-stage hybrid-self-electro-optic-device-based free-space optical backplane," Appl. Opt. 36, 7341-7358 (1997). [CrossRef]
  11. M.H. Ayliffe and D. V. Plant, "A Generalized Method for Tolerancing Polarization Losses in Free-Space Optical Interconnects," Optics in Computing. 1997 Technical Digest Series Vol.8. Postconference Edition, Topical Meeting on Optics in Computing - OC97, Incline Village, NV, USA, pp. 221-223, 18-21 March 1997.
  12. D. T. Neilson, S. M. Prince, D. A. Baillie and F. A. P. Tooley, "Optical Design of a 1024-channel free-space sorting demonstrator," Appl. Opt. 36, 9243-9252 (1997). [CrossRef]
  13. F. B. McCormick, T. J. Cloonan, A. L. Lentine, J. M. Sasian, R. L. Morrison, M. G. Beckman, S. L. Walker, M. J. Wojcik, S. J. Hintelong, R. J. Crisci, R. A. Novotny and H. S. Hinton, "Five-Stage free-space optical switching network with field-effect transistor self-electro-optic-effect-device smart-pixel arrays," Appl. Opt. 33, 1601-1618 (1994). [CrossRef] [PubMed]
  14. M. Yamaguchi, T. Yamamoto, K. Yukimatsu, S. Matsuo, C. Amano, Y. Nakano and T. Kurokawa, "Experimental investigation of a digital free-space photonic switch that uses exciton absorption reflection switch arrays," Appl. Opt. 33, 1337-1343 (1994). [CrossRef] [PubMed]
  15. S. Jiang, Z. Pan, M. Dagenais, R. A. Morgan and K. Kojima, "Influence of External Optical Feedback on Threshold and Spectral Characteristics of Vertical-Cavity Surface-Emitting Lasers," Photonics Technology Lett 6, (1994).
  16. R.M.A Azzam and W.M. Bashara, Ellipsometry and Polarized Light, (North-Holland Editor, Amsterdam, 1977).
  17. S. D. Nigam and J. U. Turner, "Review of statistical approaches to tolerance analysis," Computer-Aided Design 27, 6-15 (1995). [CrossRef]
  18. B. Robertson, "Design of an optical interconnect for photonic backplane applications," Appl. Opt. 37, 2974-2984 (1998). [CrossRef]
  19. J. L. Pezzanti and R. A Chipman, "Angular dependence of polarizing beam-splitter cubes," Appl. Opt. 33, 1916- 1928 (1994). [CrossRef]
  20. F. K. Lacroix, "Analysis and Implementation of a Clustered, Scaleable and Misalignment Tolerant Optical Interconnect," Chpt 3, Master of Engineering Thesis, McGill University, Montr�al, Canada, 1999.
  21. P. A. Williams, A. H. Rose, C. M. Wang, "Rotating-polarizer polarimeter for accurate retardance measurement," Appl. Opt. 36, 6466-72 (1997). [CrossRef]
  22. CODE V Version 8.30 Reference Manual, Chapter 6, pp. 65-67, Optical Research Associates, 3280 East Foothill Boulevard, Pasadena, California, California 91107, August 1999.

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