We developed photodefined, multimode-fiber compatible waveguides based on epoxies. The waveguides showed losses <0.06 dB/cm at 832 nm and 633 nm. Propagation and bending losses are calculated and experimentally verified. The minimum allow-able radius that can be connected to a straight waveguides are modeled and experimentally verified

Diemeer, Mart

Driessen, A.

Hilderink, L.T.H.

Kelderman, H.

English

We developed photodefined, multimode-fiber compatible waveguides based on epoxies. The waveguides showed losses &lt;0.06 dB/cm at 832 nm and 633 nm. Propagation and bending losses are calculated and experimentally verified. The minimum allow-able radius that can be connected to a straight waveguides are modeled and experimentally verified

University of Twente Research Information

Bends in Polymeric Multimode WaveguidesHenry Kelderman, Mart B.J. Diemeer, Lucy T.H. Hilderink, and Alfred DriessenUniversity of Twente, Integrated Optical MicroSystems (IOMS) h.kelderman@ewi.utwente.nlAbstract: We developed photodefined, multimode-fiber compatible waveguides based on epoxies. Thewaveguides showed losses < 0.06 dB/cm at 832 nm and633 nm. Propagation and bending losses are calcu-lated and experimentally verified. The minimum allow-able radius that can be connected to a straight waveg-uides are modeled and experimentally verified.IntroductionThe continuous increase of the microprocessor clock-rate (expected clockfrequency ∼ 1010 Hz in 2011),in addition to the continuous increase of data ratesin optical transmission systems, has created a bottle-neck in high- end systems like servers, and telecomswitches, at the interconnect between cards over theirPCB (Printed Circuit Board) backplane. In those sys-tems, aggregate data rates of multiple Tbps have to betransported via the backplanes over a typical distanceof about 0.5 m. With such bandwidth-distance prod-ucts, electrical data transmission through a copper lineis touching its fundamental limit around 20 Gbps.Optical transmission via waveguides offers the poten-tial of a much larger capacity. Therefore, there isworldwide an intense research activity ongoing to re-alize Optical Backplanes. These are backplanes withan embedded multimode polymeric optical waveguidelayer, equipped with in- and output couplers, fabri-cated with PCB compatible, low-cost fabrication tech-niques [1]. In [2] we reported on a photodefinableepoxy formulation with attractive properties for Opti-cal Backplane applications. This paper shows propaga-tion losses obtained from spiral structures and bendinglosses from U-shaped bends.Waveguide Definition and Cross SectionThe core of the waveguides presented in this paper isabout 45 × 45 μm. The core material used in the spiralswas spun directly on the Pyrex substrate. This simpli-fies processing, but also introduces an asymmetry inthe index below and surrounding the other sidewallsof the core. For the U-bends a bottom cladding wasapplied, resulting in a more symmetrical modal profile-as far as we can speak of modal profile in these highlymultimodal waveguides- and subsequently a lower re-fractive index contrast can be used. Figure 1 showsa cross section of the several waveguides used in theU-bends.For the U-bends the refractive index in the cladding is1.514 and the core is 1.528 leading to an index contrastof 0.014. In the spirals a higher index contrast of 0.03was used.Fig. 1: Cross section of 5 waveguides used in U-bends.RminreferenceFig. 2: Schematic layout of an Archimedean spiralwith two reference waveguides.Archimedean SpiralPropagation losses in the order of 0.1 dB/cm are dif-ficult to measure by cut-back measurements. Sincedifferences in chiplength are typically centimeters, thedifferences in loss are in the same order as the fiber-chip coupling variation.Therefore, we decided to create a waveguide of signif-icantly longer length by curling it up in a spiral andcomparing its losses to an on-chip shorter referencewaveguide. The contribution of the bending loss willbe limited when the curvature of the spiral and espe-cially the S-bend in the middle is chosen appropriatelyi.e., the radius of curvature chosen large enough. Thesmallest radius will be found in the s-bend.The mismatch of modes from connecting differentcurved waveguides e.g., in the center of the s-bend hasbeen disregarded since improving it by adiabaticallyconnecting different curvatures will result in a largeroverall structure for which there was no space. Thefollowing section will show that this presumption didnot introduce significant additional losses, which is aThD1500 600 700 800 900wavelength (nm)0.00.10.20.30.4loss(dB/cm)Fig. 3: Spectral dependence of propagation loss ob-served in spiral waveguideresult of the relatively high contrast used and the rela-tively large core dimensions.An Archimedean spiral is defined by:r = aθ1/p (1)We have set a = 1.0 and p = 1.1, and scaling appro-priately to obtain more or less equidistant windings.The minimum radius used in the s-bend also definesthe minimum radius in the spiral (2Rmin). We have setRmin to 15mm leading to an approximate single wind-ing length of 2 × 2πRmin ∼ 188mm, where the pitchfrom winding to winding has been disregarded.Equation 1 has been discretisized in θ leading to anarray of points (r, θ). After transforming these to carte-sian coordinates, these points have been connected bypieces of straight waveguides. Thus the curvature hasbeen approximated by segmented lines. If the stepsizeΔθ is chosen small enough this will be barely notice-able in the photomask.The low contrast used (NA = 0.2) also allowed to usein-house laser beam written masks that typically havean edge roughness of ∼150 nm. Propagation losses de-picted here include scattering losses and an easy, albeitcostly, improvement could be to use e-beam writtenphotomasks.Propagation LossTo allow for accurate propagation loss measurements,a very long (103.6 cm) coiled up waveguide, com-bined with a short (7.2 cm) reference waveguide wasmade on a 4” Pyrex wafer. The long waveguide is anArchimedean spiral as shown in Figure 2.Figure 3 shows the spectral dependance of the prop-agation loss in the spiral by subtracting the insertionloss for the reference waveguide and the spiral and ac-counting for the difference in propagation length.To verify these losses we took a picture of a part of thespiral as shown in Figure 4. By integrating the inten-sity of the pixels over a small rectangle that capturesjust one waveguide, an estimate for the local power isFig. 4: Scattered light as observed from the top at 633nm-50 -25 0 25 50propagation distance (cm)5556575859straylightintensity(dB)L=0.042x+57.274Fig. 5: Observed local intensity as function of propa-gated length in spiral.obtained. This is done for the four waveguides that areclose together and represent the four windings of thespiral. Since it is known how far the light propagatedfrom one winding to the next, also accounting for theS-bend in the center, the intensity of each local areacontaining one waveguide can be set out versus its rel-ative propagation length. Figure 5 shows the local scat-tered intensity versus the relative propagation length inthe spiral, from that we can determine the propagationloss at 633 nm to be about 0.04 dB/cm. Which com-pares well to the values we found earlier.Bend lossThe size of a spiral is determined by the radius of thearc used in the S-bend in the middle of the spiral wherethe losses are still acceptable. In order to find that ‘cut-off’ radius a sample has been made with varying radii.As depicted schematically in Figure 6 we choose a U-shaped bend where the total angle traveled is 360◦.Note that the vertical section on the right hand side hasbeen prolonged. This served two goals. Firstly it cre-ates an offset between the input and the output. Sec-ondly it was used to make the total propagation lengthin all U-bends exactly the same. Note that although inThD1RFig. 6: Schematic ‘U’-shaped bendFig. 7: Mask design showing multiple U-bends withvarying radii.Figure 6 only one U-bend has been shown, the radiushas been varied from 1 to 19 mm in steps of 1 mm. SeeFigure 7 for resulting mask layout.To determine the propagation loss, six straight refer-ence waveguides have been placed on the same sample.The difference in length between U-bend and referenceis 40 mm, which is expected to lead to an difference isloss of about 0.4 dB.Figure 8 shows the insertion loss of the U-bends minusthe loss found in the reference waveguide as functionof the radius. Note that this introduces a systematicerror of about 0.4 dB at wavelengths larger than 600nm.Reducing the bend radius gradually increases losses,until a certain cut-off is met, where losses increaserapidly. The transmission in the waveguides with thesmallest radii seems to increase. This is an artifact thatcan be explained as follows; the light lost in the bend isnot absorbed, and hence will find its way to the back-side of the sample, leading to a background level of in-tensity. Especially in smaller radii where more light islost, this effect is more predominant and makes align-ment hard. The higher loss at 532 nm can partially beexplained by the higher losses at that wavelength (cf.Figure 3).The modeled response in Figure 8 can be calculatedfrom [3]:L = 10 ·10 log(1 − t2R− t22R2− t32R3− t42R4)(2)0 5 10 15 20radius (mm)-40-30-20-100loss(dB). . .... . .. . . . . . . . . . .Eq. (2). 532 nm633832850Fig. 8: Observed losses in ‘U’-shaped bends at fourdifferent wavelengths.RR+w/2αFig. 9: A ray traveling in the middle of the waveguidecoming from the right, would strike the normal to thetangent of the outer perimeter of the bend at an angleα.where t = (n2corew)/(NA)2, w is the width of the wave-guide and NA is the Numerical Aperture. The modelfails when t/R < 0.5, but adequately describes theexperimental results as shown in [4]. The offset inthe cut-off region in our experimental data can be ex-plained by the fact that in the U-bend eight straight-bend coupling areas are introduced, and the model in-cludes only the effects of a circular bend.Further inspection revealed that light is escaping thebend predominantly in the first part of the curved sec-tion, and not continuously over the entire bend asmight have been suspected.This can partially be explained by the angle at which aray strikes the outer perimeter of the bend as shown inFigure 9. Suppose we were to look at a ray travelingin the middle of the straight waveguide. It would strikethe outer perimeter at an angle α to the normal of thetangent described by:α = arcsin(RR + w/2)(3)If we use this angle in the Fresnel equation for s-ThD10 5 10 15 20radius (mm)0.00.10.20.30.40.50.60.70.80.91.0Reflectionsmiddle of straightupper perimeter of straightFig. 10: Reflection coefficient from a ray travelling inthe middle of the straight waveguide striking the outerperimeter of the curved section as function of the ra-dius. Also shown is the reflection of a ray travelingalong the upper boundary of the straight waveguide.polarisation:Rs =ncore sinα − ncladding sin θ2ncore sinα − ncladding sin θ2 (4)where θ2 can be obtained from Snell’s law of refrac-tion. we obtain Figure 10. Although not shown here,p-polarisation will result in almost the same fractionof light reflected. Without taking into account that theactual angles of the rays will vary, this simple descrip-tion accurately estimates the minimum radius that canbe connected without loss to a straight waveguide.This argument does not directly explain the non-continuous loss through the bend. If we were to con-sider a ray traveling along the tangent of the innerperimeter of the bend, which is the ray that has thesmallest angle to the normal and hence experience thelowest reflection. This specific ray would have been re-flected at an earlier point in the bend at the same angle,therefore its power would have been reduced signifi-cantly upon the first reflection, provided the angle issufficiently small.ConclusionWe have presented multimode photodefinable waveg-uides for Optical Backplane applications. A propaga-tion loss of <0.06 dB/cm at 850 and 633 nm has beenmeasured in spirals using two methods; 1) from the dif-ference in length and the obtained insertion loss thereofand 2) from analysis of the scattered light of differentlocations in the spiral. For a refractive index contrastof 0.014 (NA=0.2) we experimentally found that theminimum usable radius is 10 mm and verified this bysimple calculation of Fresnel reflection and also com-pared this to a model by Israel et al. It has been shownthat within the wavelength region measured (530-850nm) the loss in bends as function of radius is indepen-dent of wavelength.AcknowledgmentsThe authors acknowledge the financial support ofDutch Foundation STW (project TOE 6986) and wishto thank Anton J.F. Hollink for his support.References[1] C. Berger, R. Beyeler, G.-L. Bona, R. Dangel, L.Dellmann, P. Dill, F. Horst, M. Kossel, C. Menolfi,T. Morf, B. J. Offrein, M. L. Schmatz, T. Toifl, andJ. Weiss, ”Optical links for printed circuit boards,”in 16th Ann. Meeting of IEEE Lasers & Electro-Optics Soc., October 26-30, Tucson, AZ, USA,2003.[2] Mart Diemeer, Lucie Hilderink, Ronald Dekkerand Alfred Driessen, ”Low-cost and low-lossmultimode waveguides of photodefinable epoxy”,IEEE Photon. Technol. Lett., vol. 18, no. 15, pp.1624-1626, 2006.[3] D. Israel, R. Baets, N. Shaw, and M.J. Goodwin,Techn. Digest MOC/GRIN, 1993.[4] Sami Musa, Albert Borreman, A.A.M Kok, M.B.J.Diemeer, and Alfred Driessen, ”Experimentalstudy of multimode optical waveguides”, Appl.Optics, vol. 43 no. 40, October 2004.ThD1

Bends in polymeric multimode waveguides

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