A 0.4 dB excess loss, 0.01 dB output channel imbalance polymer 1 x 3 MMI power splitter is modeled having linearly tapered input section suitable for use in an optical backplane connector. The device design was additionally optimized using FD-BPM to have a good tolerance to source lateral misalignments

Rashed, AM

Selviah, DR

English

UCL Discovery

Modeling of a Polymer 1 u 3 MMI Power Splitter for Optical Backplane Atef M. Rashed and David R. Selviah  Department of Electronic and Electrical Engineering University College London, Torrington Place, London WC1E 7JE, United Kingdom Telephone: +44 20 7679 3056, Fax: +44 20 7388 9325 Email: a.rashed@ee.ucl.ac.uk Email: d.selviah@ee.ucl.ac.uk Abstract—A 0.4 dB excess loss, 0.01 dB output channel imbalance polymer 1 u 3 MMI power splitter is modeled having linearly tapered input section suitable for use in an optical backplane connector. The device design was additionally optimized using FD-BPM to have a good tolerance to source lateral misalignments.Keywords - polymer MMI; power splitter; optical backplane; multimode tapered waveguide; spot size converter; FD-BPM; source misalignmen; optical connector I. INTRODUCTIONLarge electronic systems are generally constructed as racks of many dismountable printed circuit boards (PCBs) plugged into a larger PCB at the back of the rack, known as the backplane or motherboard. The backplane has data buses to interconnect the PCBs at high data rates using copper tracks. At current data rates of 10 Gb/s [1] copper tracks can only be used over short distances and this requires complex signal shaping to overcome attenuation and distortion due to high frequency parasitics and limited bandwidth [1]. High bandwidth optical polymer waveguides integrated within the FR4 PCB layer offer a low cost and compact approach to overcome the limitations of copper track interconnects [2, 3]. Due to the complex layout of interconnects on the PCBs and on the backplane, there is a growing need for polymer waveguide devices integrated onto the optical backplane for optical signal processing and distribution. Multimode interference (MMI) optical power splitters [4] are an important example of such devices for signal distribution to aid routing on the optical backplane.Vertical cavity surface emitting lasers (VCSELs)  used as signal sources on the dismountable PCBs must be aligned to the optical backplane at optical connectors. However, low cost connectors may suffer from some misalignment of the VCSEL relative to the waveguide.. Therefore, the waveguide should be designed to provide uniform and preferably high source coupling efficiency even when the optical source is offset [5]. This can be achieved for lateral offsets using laterally tapered input waveguides [6] as part of the optical connector. In this paper FD-BPM [7] is used to design a polymer 1 × 3 MMI power splitter with tapered input waveguide for use in the optical connector. II. PRINCIPLE OF MMI SPLITTERMMI devices are useful photonic components because they can reproduce images of an input beam at periodic intervals along the propagation direction due to interference of the waveguide modes. This self-imaging principle [8] causes the input field to be reproduced as either single or multiple images at regular intervals along the length of the MMI device. In a straight-sided MMI device, single and double images of the input field occur at integer and odd half-integer multiples of 3LS, respectively [8]. 3-fold images of the input field also occur at L SwhereLS is the beat length of the two lowest-order modes in the MMI device and is defined to be [8]: LS=4nW2/3Owhere n is the waveguide core refractive index, W is the width of the MMI region and O is the free space wavelength. The length of the MMI device can be reduced without compromising the performance by considering structures with a smaller or a parabolically tapered width that still offer a uniform output power distribution [9].  III. 1  u3 MMI POWER SPLITTEROur final waveguide design after optimization using FD-BPM has a 21 Pm wide input waveguide that tapers down linearly with a half taper angle of 1.6º over a length of 250 Pm. It joins our 292 Pm long, non-uniform width MMI  section at the centre of its input port. Our MMI section width is 23 Pm at both input and output edges and narrows to a 19 Pm waist at the middle of the structure. The side walls of the MMI section are circular arcs with radii of curvature of 6 mm that make an angle of up to 1.4º with the optical propagation axis as shown in Fig. 1(a). The MMI section is followed by three output waveguides arranged in a fan, each of 7 Pm width. One output waveguide is 258 Pm long and is aligned to the longitudinal axis of the device. The outer two waveguide centers are positioned symmetrically at ±15 Pm either side of the central COMMAD 04 0-7803-8820-8/05/$20.00  2005 IEEE 281axis with ±0.7º tilt angle to the longitudinal axis and their endsare aligned with the end of the central waveguide. The waveguides have core and cladding refractive indices of 1.54and 1.52, respectively. The material loss of the waveguide istaken to be 0.03 dB/cm at 850 nm wavelength. These figuresare typical values for waveguide polymers used in opticalbackplanes such as Truemode™ polymer [10].X(Pm)30 - 20 - 10 - 0 10 20 30Z(Pm)02004006008001000X(Pm)30 - 20 - 10 - 0 10 20 30Z(Pm)02004006008001000VCSELs for optical backplanes operating at 10 Gb/s often have 7 Pm diameter apertures [1]. In our modeling we chosesuch a VCSEL emitting in its fundamental transverse mode as the input source. The input field used in the simulation, shownin the inset of Fig. 2, is TE-polarized with a width of 7 Pm ate-1 intensity. The input field is launched initially at the centre ofthe input aperture of the input waveguide along the opticalpropagation z-axis direction. Fig. 1(a) shows the layout of thewaveguide structure with simulation results for discreteintensity profiles of the propagating optical field at intervalsalong the propagation direction. Fig. 1(b) shows thecorresponding intensity contour map of the propagating field.Following our FD-BPM optimization procedure our MMIsection is 8% shorter than that in the corresponding straight-sided device. This was achieved by adjusting the devicedimensions to give the minimum imbalance corresponding tothe greatest uniformity between the outputs of the three outputwaveguides whilst maintaining only a small angle between theside walls of the MMI section and the propagation axis of thedevice [9] to minimize excess loss.IV. NUMERICALMODELThe numerical model used 2-dimensional semi-vectorialFD-BPM (2D SV FD-BPM). The 2D SV wave equation for theTE-polarized optical field, u, [11] omits the dependence on thetransverse direction, y, due to the structures uniformity in thisdirection:¿¾½¯®­¸¹· ¨©§   » ¼º« ¬ªwwww wwu k k u nx n x kizu 2 2 2212(2)where x and z are the coordinates corresponding to the lateral and propagation directions, respectively. k is the reference wavenumber and k = (2SO) n(x, z) is the spatially dependentwavenumber. Since the waveguide structure supportsmultimode propagation the wide-angle form of SV FD-BPMincorporating the Padé approximation is employed to overcomethe paraxial nature of the wave equation [12, 13]. The Padé (1,1) approximant has been used and transparent boundaryconditions (TBC) [14] were implemented in the calculations toeliminate spurious reflections at the edges of the computationdomain [15]. This modeling technique only considers forwardpropagating waves and does not take into account reflectedwaves.00.10.20.30.40.50.60.7-40 -30 -20 -10 0 10 20 30 40X (Pm)Intensity(au)00.10.20.30.40.50.60.7-40 -30 -20 -10 0 10 20 30 4000.10.20.30.40.50.60.7-40 -30 -20 -10 0 10 20 30 40X (Pm)Intensity(au)A 2D mesh with step sizes of 'x = 50 nm and 'z = 1 Pm wasused for calculations and (2) was integrated forwards in z by replacing the partial derivatives with their finite differenceapproximations [16]. The step sizes were chosen to besufficiently small that they gave consistent solutions as thoseobtained for smaller step sizes, and that  they  were  sufficiently(a) (b)Figure 1. (a) 1 u 3 MMI splitter with intensity profiles of the optical field (b) Contour map of the propagating field intensitylarge to minimize computational time. The optical field wassuccessively calculated at each longitudinal step, 'z untilreaching the end of the waveguide structure. The total power within the waveguide was determined by computing theintegral of the power in the field at the corresponding z-position over the waveguide cross sectional area. V. DISCUSSION AND RESULTSFig. 2 shows the near field at the end of the tilted fannedwaveguides showing the uniformity of the power in the threebranches. 7 Pm wide extension long straight waveguidesparallel to the device longitudinal z-axis were added in the simulation to each output branch to monitor the uniformity of the splitter as a function of propagation distance as  signals willtravel longer distances on a backplane. Fig. 3 shows the outputpower normalized to the input power as a function of thepropagation distance. The device achieves a uniform splittingratio of 30% in each branch. This is close enough to the ideal value of 33.3% and does not change over the propagationdistance from the splitter output. However, the splitting ratiocan be improved at the expense of uniformity by changing thedesign slightly.The excess loss of the splitter is defined as [17]:EL = -10 log10(Pout/Pin)   (3)Figure 2. Output near field with inset of input field282Figure 3. Normalized output power versus propagation distance where Pout is the total output power of the three ports and Pin is the input power. The calculated EL is found to be as low as 0.4dB at the end of the fanned output waveguides. A slightlyhigher EL value of 0.6 dB was calculated at the end of theextension waveguides due to the modal mismatch between theparallel extension waveguides and the fanned waveguides.However, in practice smooth bends would be used to join theseto reduce such loss. These computed EL values also include thematerial loss that accumulates with distance. The imbalance of the splitter can be defined as [18]:IB = -10 log10(1-Vp) (4)where Vp is the standard deviation of the power at the outputports normalized to one third of the input power.A very small IB of 0.01 dB at the splitter output was calculated.Hence our design achieves lower excess loss and betteruniformity than the corresponding parabolic-sided one [17].However, our circular arc-sided MMI section is 15% longerthan the equivalent parabolic-sided design since the average width of the circular arc-sided design is larger than that of theparabolic-sided design and there is a direct proportionalitybetween the average width, W and the beat length, LSof theMMI section,. This slight increase in the length of ourdesign has been traded-off for less loss since losses increases asthe curvature of the sides becomes sharper as in the case of theparabolic-sided design.The effect of source lateral misalignment on the splitteroutput imbalance for a tapered input waveguide and a straightinput waveguide of 7 Pm width was compared. Fig. 4 showsthat the splitter with the tapered input waveguide has lessimbalance by up to 0.4 dB than the splitter with the straightinput waveguide over a source lateral misalignment range of 28Pm.VI. CONCLUSIONSA 0.4 dB excess loss, 0.01 dB output channel imbalancepolymer 1 u 3 MMI power splitter is modeled using FD-BPM.The splitter has a linearly tapered input section that provides a good tolerance to source lateral misalignments when used inoptical backplane.Figure 4. Imbalance versus source lateral offset ACKNOWLEDGMENTUK EPSRC, DTI and Xyratex, Havant are acknowledgedfor support through the LINK Storlite project.REFERENCES[1] F. Mederer, R. Michalzik, J. Guttmann, H.-P. Huber, B. Lunitz, J.Moisel, and D. Wiedenmann, “10 Gb/s data transmission with TO-packaged multimode GaAs VCSELs over 1 m long polymer waveguidesfor optical backplane applications,” Opt. Comms., vol. 206, pp. 309–312,June 2002.[2] D. Israel, R. Baets, M. J. Goodwin, N. Shaw, M. D. Salik, and C. J. Groves-Kirkby, “Comparison of different polymeric multimode star couplers for backplane optical interconnect,” J. Lightwave Technol., vol.13, No. 6, pp. 1057-1064, June 1995.[3] J. Moisel, “Optical backplane for avionic applications using polymermultimode waveguides,” Proc. Of IEEE LEOS Conf., Paper WT1, vol. 2, pp. 567-568, 2000.[4] M. L. Mašanoviü, E. J. Skogen, J. S. Barton, J. M. Sullivan, D. J. Blumenthal, and L. A. Coldren, “Multimode interference-based two-stage 1 × 2 light splitter for compact photonic integrated circuits,” IEEEPhoton. Technol. Lett., vol. 15, No. 5, pp. 706-708, May 2003.[5] W. B. Joyce, and B. C. DeLoach, “Alignment of Gaussian beams,” Appl.Opt., vol.23, No. 23, pp. 4187-4196, Dec. 1984.[6] A. M. Rashed, and D. R. Selviah, “Modelling of polymer taper waveguides for optical backplane,” Proc. Of Semiconductor andIntegrated Optoelectronics Conf., Cardiff, Paper 40, April 2004.[7] A. M. Rashed, K. A. Williams, P. J. Heard, R. V. Penty, and I. H. White,“Tapered waveguide with parabolic lens: theory and experiment,” Opt.Eng., vol. 42, No. 3, pp. 792-797, March 2003.[8] L. B. Soldano, and E. C. M. Pennings, “Optical multi-mode interferencedevices based on self-imaging: principles and applications,” J.Lightwave Technol., vol. 13, No. 4, pp. 615-627, April 1995.[9] D. S. Levy, R. Scarmozzino, and R. M. Osgood, Jr., “Length reductionof tapered N u N MMI devices,” IEEE Photon. Technol. Lett., vol. 10,No. 6, pp. 830-832, June 1998.[10] C. Berger, R. Beyeler, G.-L. Bona, R. Dangel, L. Dellmann, P. Dill, F.Horst, M. A. Kossel, C. Menolfi, T. Morf, B. Offrein, M. L. Schmatz, T.Toifl, and J. Weiss, “Optical links for printed circuit boards,” Proc. OfIEEE LEOS Conf., vol. 1, pp. 61-62, 2003.[11] A. M. Rashed, and D. R. Selviah, “Modelling of the effects of thermalgradients on optical propagation in polymer multimode taperedwaveguides in optical backplanes,” SPIE Proc. of Software andModelling in Optics, Photonics North 2004, Paper 5579B-54, Canada, Sept. 2004.[12] I. Iliü, R. Scarmozzino, and R. M. Osgood, Jr., “Investigation of the Padé approximant-based wide-angle beam propagation method for283accurate modeling of waveguideng circuits,” J. Lightwave Technol., vol. 14, No. 12, pp. 2813-2822, Dec. 1996. [13] Y.-P. Chiou, and H.-C. Chang, “Analysis of optical waveguide discontinuities using the Padé approximants,” IEEE Photon. Technol. Lett., vol. 9, No. 7, pp. 964-966, July 1997. [14]  G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron., vol. 28, pp. 363-367, 1992. [15] I.  Iliü, R. Scarmozzino, R. M. Osgood, Jr., J. T. Yardley, K. W. Beeson, and M. J. McFarland, “Modeling multimode-input star couplers in polymers,” J. Lightwave Technol., vol. 12, No. 6, pp. 996-1003, June 1994. [16] Y. Chung, and N. Dagli, “An assessment of finite difference beam propagation method,” IEEE J. Quantum Electron., vol. 26, No. 8, pp. 1335-1339, Aug. 1990. [17]  H. Wei, J. Yu, Z. Liu, X. Zhang, W. Shi, and C. Fang, “Fabrication of 4 u 4 tapered MMI coupler with large cross section,” IEEE Photon. Technol. Lett., vol. 13, No. 5, pp. 466-468, May 2001. [18]  J. A. Besley, J. D. Love, and W. Langer, “A multimode planar power splitter,” J. Lightwave Technol., vol. 16, No. 4, pp. 678-684, April 1998.  284

10 Gb/s data transmission with TOpackaged multimode GaAs VCSELs over 1 m long polymer waveguides for optical backplane applications,”

A multimode planar power splitter,”

An assessment of finite difference beam propagation method,”

Analysis of optical waveguide discontinuities using the Padé approximants,”

Comparison of different polymeric multimode star couplers for backplane optical interconnect,”

Investigation of the Padé approximant-based wide-angle beam propagation method for 283accurate modeling of waveguideng circuits,”

Length reduction of tapered

Modeling multimode-input star couplers in polymers,”

Modelling of polymer taper waveguides for optical backplane,”

Modelling of the effects of thermal gradients on optical propagation in polymer multimode tapered waveguides in optical backplanes,”

Multimode interference-based twostage

Optical backplane for avionic applications using polymer multimode waveguides,”

Optical links for printed circuit boards,”

Optical multi-mode interference devices based on self-imaging: principles and applications,”

tapered MMI coupler with large cross section,”

Tapered waveguide with parabolic lens: theory and experiment,”

Transparent boundary condition for the beam propagation method,”

Modeling of a polymer 1x3 MMI power splitter for optical backplane

Modeling of a polymer 1x3 MMI power splitter for optical backplane

Abstract

Similar works

Full text

Available Versions

UCL Discovery