Design curves for insertion loss of multimode polymer waveguide 90° bends are reported as a function of bend radius for several waveguide widths. For the first time, to our knowledge, in multimode rectangular waveguides the insertion loss is resolved into its components of transition, radiation and propagation loss, in order of decreasing strength, separating them from input and output coupling loss by calibration and comparison of experimentally measured and beam propagation method (BPM) modeled curves. We used the method of nested bends for the first time in multimode polymer waveguides to calculate the propagation loss on a small substrate without using destructive cut-back. The lowest loss of 0.74 dB occurred for a 50 μm square cross section, Δn=0.0296, 13.5 mm radius waveguide bend.
©2007 Optical Society of America
The insertion loss of waveguide bends has been thoroughly studied in single mode (SM) rectangular waveguides [1,2], however, limited research has been reported for the special case of multimode (MM) waveguides with a higher refractive index polymer core surrounded by a lower refractive index polymer cladding, fabricated on FR4 printed circuit boards (PCBs) for use in large area backplane interconnects [3,4], [5–7]. The insertion loss of straight polymer multimode waveguides is determined by the bulk material loss and the side wall roughness which also causes modal coupling and which may depend on the fabrication method. The modes in waveguide bends tend to have their energy shifted towards the outside of the bend and are inherently lossy. However bends are not used alone and are usually attached to other, for example, straight waveguides resulting in a modal mismatch and additional loss at this transition point. The different types of loss radiate in different directions from the waveguide. The relative strengths of the various types of loss must be found so that other waveguides on the backplane can be arranged to reduce crosstalk. The waveguides may also capture light strongly in the opposite direction from which they emit. For example two waveguide bends placed back to back so that they are mirror images of one another may experience strong crosstalk due to transition loss at the joint between input straight waveguides and the bends. Therefore, carefully arranged experiments must be designed to separate the total bend loss from the input and output coupling loss after which the relative magnitudes of the various loss components can be found by exploiting a comparison with computer modeled loss. The propagation loss can be found and removed by the method of nested bends . We chose to use Beam Propagation Method (BPM) which has the advantage that it is very effective in calculating how efficiently the modes in one waveguide are coupled in to the modes of another to find transition loss although it does not model reflected light and can be time consuming unless correctly implemented. The design curves will allow engineers to choose the appropriate bend radius and to layout the waveguides to minimize crosstalk.
Section 2 details the various loss mechanisms in a waveguide bend. Section 3 describes experimental measurements of loss in waveguide bends. Section 4 describes the BPM modeling. Section 5 analyzes the results and compares the experimental results and those from BPM modeling. Finally section 6 concludes.
2. Waveguide loss components
Figure 1(a) shows a schematic diagram of the waveguide bend structure used in the experiments. Four types of loss occur in these waveguide bends: input and output coupling, transition, radiation and propagation loss.
2.1 Input and output coupling loss
Coupling loss occurs between an incoming multimode fiber and the waveguide and also between the waveguide exit and a photodetector in our experiments and consists of:
- (i) Fresnel reflection loss due to reflection at the interface between different refractive index media with a magnitude that depends strongly on whether an air gap exists between the waveguide and adjacent external components.
- (ii) Scattering loss caused by a rough waveguide end face which scatters light forwards and backwards into a wide range of angles.
- (iii) Mode mismatch loss due to the circular cross section input waveguide meeting the rectangular cross section waveguide.
In Fig. 1(a) coupling loss occurs along plane I, at the input to the waveguides and along plane O at the output. The coupling loss is given by the variables, CouplI and CouplO.
2.2 Waveguide transition loss or joint loss
Transition loss occurs due to mode mismatch at the junction between waveguiding structures supporting different modes. The field across the waveguide cross section emerging from the first waveguide cannot be expanded and fully represented as a weighted combination of only the propagating modes of the waveguide into which the light travels. The modal field expansion must also include radiation modes to match the field distribution fully. Transition loss occurs along line A, at the interface between the straight and the waveguide bends, TransA and along line B at the interface between the waveguide bend and the straight waveguide, TransB.
2.3 Bend radiation loss
Waveguide bends cannot support perfectly bound modes but instead they host leaky modes, which radiate energy continuously around a bend causing radiation loss, RL. Each propagating mode loses power at a unique rate determined by its mode number and waveguide parameters such as numerical aperture, physical dimensions and radius of curvature [9,10].
2.4 Propagation loss
Propagation loss, PL, is caused by the scattering of energy from propagating to radiation modes due to the rough waveguide side walls and also direct loss due to material absorption. The core layer is spun as a liquid onto the wafer so the upper and lower surfaces of the waveguide are flat. However the vertical side walls are formed by lithographic UV exposure using a photomask and cause side wall roughness which may be the main reason for the measured total propagation loss . The scattering of guided modes at the rough side walls not only causes loss by radiation but also redistributes energy between guide modes .
2.4 Total bend insertion loss
The total loss, TL, in our device can, from the above, be resolved into the following components:
These loss components can be clearly identified in Fig. 1(b) which shows red light from a Helium-Neon laser passing through an input standard 50/125 μm multimode fiber butt coupled to one waveguide of Fig. 1(a). A small bend radius was chosen to give a high loss so that the directions of the lost light can be clearly seen. The light from the glowing input fiber can first be seen to scatter at the rough input face of the waveguide after which it traverses the straight waveguide and emerges as a narrow beam due to transition loss at the joint between the straight waveguide and the waveguide bend. As the light travels around the bend tangentially emitted light due to bend radiation loss can be discerned. No light can be discerned due to transition loss at the joint between the bend and the straight waveguide. Finally as the light exits the waveguide light backscattered from the rough waveguide output face can be seen. The slanted fringes are due to scattering from the top surface of the PCB below the lower cladding of the waveguide due to the weave and weft of the FR4 material. Although Fig. 1(b) was obtained for red light for convenience similar results occur for infra red light more often used in optical backplanes.
3.1 Waveguide fabrication and structure
The waveguides were formed photolithographically on a 7” diameter FR4 wafer. A photosensitive acrylate polymer, TruemodeTM from Exxelis Limited , was used for the core and the cladding with slightly different formulations to give the core a higher refractive index. TruemodeTM has a reported  absorption at 850 nm of <0.04 dB/cm which is compatible with readily available 10 Gb/s VCSELs used in low cost OPCB backplanes [3,4]. A circular 800 μm thick, FR4 wafer, one side of which was coated with a 17 μm thick copper layer was initially planarized by spinning a ∼50 μm layer of cladding polymer. The core polymer precursor (99% core monomer / 1% photoinitiator) was then spun for 30 sec at 230 rpm, to obtain a thickness of 50 μm and exposed to UV light (for 15 sec, UV light intensity 15 mW/cm2) through a dark field laser written photomask which is somewhat lower cost than an e-beam mask. The polymer precursor layers were spun on wet, the mask was placed ∼100 μm above the layer and the gap was flushed with dry nitrogen at atmospheric pressure to eliminate the presence of oxygen during exposure to avoid oxidation. Once the unexposed core material was washed off a second layer of cladding was spun over the core and lower cladding to a depth of ∼50 μm above the top of the core layer. After each polymerizing step the wafer was cured in an oven for 30 min at 100 °C. The refractive index of the core was ncore = 1.556 and that of the cladding was nclad = 1.5264, measured by the prism coupler method of frustrated total internal reflection, giving a numerical aperture of NAwg = 0.302. A large NA was chosen to ensure low coupling loss to similar NA multimode fibers, low radiation loss and low crosstalk between adjacent waveguides. The thicknesses of the lower- and upper-cladding layers were large enough to ensure that the waveguide modes had no energy at the air and FR4 interfaces shown in Fig. 2 which shows a photograph of the end face of a 50 μm × 50 μm waveguide cross section recorded with an infrared sensitive CCD camera.
The mask pattern was designed, Fig. 1(a), to have three sets of 90° circular arc waveguide bends aligned to straight waveguides at each end. In each set the waveguides ranged from a radius, R = 5.5 mm to 34.5 mm with a difference between two adjacent arcs of ΔR = 1 mm, giving N = 30 waveguide bends in each set. The input straight section of length, lin = 11.5 mm and the output section of length, lout = 24.5 mm were introduced to investigate transition loss between straight and waveguide bends (line A) and between curved and straight waveguides (line B) and to allow tolerance for the positioning of a dicing saw to cut through the polymer, copper and FR4 layers in a low cost approach without polishing the waveguide end face. After fabrication the thicknesses of the lower and upper claddings and waveguide cores were each 50 μm. Three sets of waveguides with this thickness but different widths, w = 50 μm, 75 μm, and 100 μm were fabricated on the same wafer. Widths were chosen to give low coupling loss to 50/125 μm and 62.5/125 μm MM fibers.
3.2 Experimental measurement technique
Light from an 845 nm VCSEL was launched into a standard 50/125 μm step index MM fiber with NAfibre = 0.2 < NAwg. The fiber was wound sufficient times around a drum to couple the modes so that after mode scrambling a large number of transverse modes filled the solid angle of the numerical aperture. The fiber was aligned and butt-coupled to one of the waveguides. This was achieved by mounting the fiber end on a system of one manual rotation stage and three motorized translation stages with sub-micrometer precision for accurate alignment in x, y, and z directions and adjusting them respectively to maximize the light through the waveguide. Light from the waveguide output was spatially filtered by a 150 μm diameter circular pinhole to exclude much of the light traveling through the cladding and coupled into and traveling through adjacent waveguides. A large area integrating sphere photodetector (PD) was placed beyond the output pinhole to measure the integrated output optical power so avoiding inconsistencies due to laser speckle and spatial variation of efficiency across the photodiode detector. The pinhole diameter was chosen to simulate the aperture of the photodetector chosen for use in the final practical system demonstrator . Index matching fluid (n = 1.4911 at 845 nm) was applied to both MM fiber - waveguide and waveguide -pinhole interfaces to reduce coupling loss.
3.3 Experimental measurement results
The power Pbend(w,R) measured at the output of each bend was calibrated by subtracting the power, Pstr at the output of three straight waveguides fabricated on the same wafer and having the same cross-sectional dimensions as those of the waveguide bends to give Pnorm1(dB) = Pbend(w,R)-Pstr(dBm). Pstr corresponds to the input power (Pin), from the multimode fiber which was coupled to the VCSEL, after being attenuated due to two types of loss Pstr(dBm)=Pin(dBm)-[CouplI(dB) + CouplO(dB)]-α(w)lstr(dB). In the previous equation α(w) (dB/mm), is the propagation loss rate in the straight waveguides.. The power at the output of the MM fiber was set to be Pin = 0 dBm and the output power from the straight waveguide Pstr, was measured to be -0.78 ± 0.18 dBm for the 50 μm × 50 μm waveguide, -0.69 ± 0.11 dBm for the 75 μm × 50 μm waveguide and -0.63 ± 0.09 dBm for the 100 μm × 50 μm waveguide so these values also represent the loss since the input power is 0 dBm. The experimental error given for each Pstr, is the standard deviation calculated from three repeated measurements. The loss for the 50 μm × 50 μm waveguide has more experimental error than that for the other two waveguides perhaps because this waveguide’s width is identical to the fiber’s diameter and therefore any uncertainty such as lateral misalignment or angular displacement causes a partial illumination of the waveguide aperture giving a larger effect in this case. All three straight waveguides were of length lstr = 65.5 mm which were the longest straight waveguides we could fit onto the mask.
This first normalization only partially compensated for the propagation loss but totally compensated for the coupling loss in the bends. A fuller compensation of the propagation loss is carried out in section 5.1. The normalized results for the calibrated waveguide radiation loss, Pnorm1, as a function of the radius of curvature, R, are shown in Fig. 3 for the three sets with different waveguide widths.
For R < 20 mm and all three widths as expected [5–7], [9,10] loss decreases as the radius of curvature increases. The wider waveguides have consistently higher insertion loss. The loss reaches a minimum at R ∼ 15 mm in all cases as shown in Table 1. A low order (5th order) polynomial was fit to the data in Fig. 3 and minimum loss values in Table 1 were calculated from the fitted curves. At larger radii for all widths the loss again increases. As the radius of curvature increases beyond the minimum loss value for each waveguide bend, propagation loss (PL) becomes more significant than the combination of transition and radiation loss since the larger radius bends have longer lengths.
4. Beam Propagation Method (BPM) waveguide modeling
The waveguide bends were modeled using BPM on a three dimensional mesh. Since direct simulation of a 90° bend could not be performed due to the inherent paraxial limitations of the BPM algorithm, we divided our 90° waveguide bend into a number of smaller radial sectors within which the paraxial approximation was valid. The initial field profile was propagated through one segment and the amplitude and phase of the field profile at the end was stored and used as the initial field for the next segment, Fig. 4. After a set of trial simulations using increasingly larger segments we concluded that we could accurately analyze segments turning through an angle of up to 10° before the output of several cascaded sections changed. After another set of test simulations using fully-vectorial BPM we found that the scalar version of BPM gave indistinguishable results for the loss of TE and TM waveguide modes through a 10° segment and was much faster so this was used in subsequent calculations. Table 2 lists the parameters used in the simulations.
Two input fields were investigated. In the first case waveguides were excited by the modes of a multimode fiber with a fully filled NA and in the latter by a three dimensional field consisting of many waveguide modes filling the waveguides NA, all with equal amplitudes. In both cases each mode was given a random phase to model the effect of the mode scrambler for fiber modes and the effect of wall roughness for waveguide modes. To avoid inadvertently chosen special cases three different modal phase profiles were created for the two cases (MM fiber, waveguide modes) by a Monte-Carlo random number generator. After generation, all three fields were summed and launched into the first rectangular straight waveguide segment. The total number of modes generated was found to be in excess of 300 by performing a mode transform on the cross sectional field in the waveguide.
4.2 Simulation results
After propagating 1 mm inside the straight waveguide, the amplitude and the phase of the field were saved. The input straight waveguide was 11.5 mm in length but it was sufficient to only model a 1 mm section as we found that the total power and the distribution of power between modes at the end of the short (1 mm) and the long (11.5 mm) straight waveguides were identical. This was because wall roughness and the resultant intermodal coupling were not included in the model. This saved field was then launched into the first 10° waveguide bend segment. Typical radial field profiles are shown in Fig. 4 for the first and a later segment. After the strong initial radiation mainly caused by transition loss, seen in Fig 4(a) beyond the outside of the bend, radiation loss eventually remains and can only just be seen in Fig. 4(b) again on the outside of the bend. This is seen more clearly in Fig. 5 where the power has been integrated along the radius across the waveguide and all 9 segments have been plotted continuously as a function of angle traversed together with this curve’s derivative for one case of interest w = 75 μm, R = 5 mm, but similar curves can be drawn for all cases. From the power derivative plot we can easily identify three regions namely region 1, 2 and 3 where the contribution of transition and radiation loss varies. The high rate of increasing loss within a small angle ∼8°, of the waveguide entrance (region 1) between 0.04 dB/° and 0.11 dB/° is due to a combination of transition loss, TransA which dominates and radiation loss, RL. As we progress from region 1 to region 2, energy is lost at a decreasing rate due to the weakened contribution of TransA but both types of loss are important. Finally at larger angles >33° (region 3) the much slower rate of increase of loss of 0.016 dB/° is the RL since the model did not include propagation loss. In other waveguides region 1 was seen to extend over a much larger angular region. By subtracting the radiation loss, RL found by fitting a line to the curve in region 3, from the total loss we can find and separate out the transition loss, TransA. Finally, we launch the field at the end of the 90° bend into a straight waveguide, and similarly calculate the TransB loss component.
5. Analysis and discussion
5.1 Loss component separation
Figure 6 shows the simulation results for the two input fields compared to normalized experimental results for the 50 μm width of waveguide. Similar results were also obtained for the other waveguide widths. The modeled loss when a fiber is butt-coupled to the straight waveguide as in the experiments is significantly lower than that when the input is considered to come from a fully excited waveguide. If a fiber with an NAfibre = 0.2 is aligned to a square waveguide with NAwg = 0.302 it only excites a fraction of the waveguide modes which in the model maintain their relative powers throughout the straight waveguide section until they reach the start of the bend since there is no mixing mechanism such as wall roughness to couple them. On the other hand an input fully filled straight waveguide excites all of the straight waveguide modes.
The normalized experimental results in Fig. 6 were obtained from those in Fig. 3 by completely subtracting the propagation loss, α(w). This was found by fitting a line to the curves in Fig. 3 for radii beyond 20 mm to make sure that propagation loss was the dominant loss component, and finding the slope, α exp(w). Note that experimental results contain both propagation and radiation loss. In order to separate them we fit a line to the fully filled waveguide launch modeled curves in Fig. 6 beyond a 20 mm radius to find the slope, α BPM(w) which corresponds to RL as stated in Fig. 5. Both α exp(w) and α BPM(w) are given in Table 3. The units of these slopes are in dB per mm change in the radius of curvature but they can easily be converted to loss in dB per cm of waveguide length. If we assume that the slope of the BPM modeled curves is accurate then we can subtract the two slopes to find the propagation loss rate, α(w). Assuming that the propagation loss rate α(w) in the straight waveguide sections is the same as that in the bend the propagation loss becomes:
where lbend is the length of each curved section. PL, can then be used to renormalize the experimental results using (3):
writing the power Pbend measured at the output of each bend as:
we obtain from the definition of Pnorm1 and after substituting (1), (2) and (4) in (3):
So the final normalized experimental curve in Fig. 6 consists only of combined transition and radiation losses.
Figure 7 shows all of the loss components after being separated. Wider waveguides appear to have higher transition and radiation loss but less propagation loss. The higher transition loss and higher radiation loss of the wider waveguides agrees with the theoretically obtained results for slab waveguides in [9,10]. Table 3 shows that the wider waveguides have slightly less propagation loss which agrees with  but the large experimental error means this cannot be asserted with confidence.
5.2 Accounting for the differences between experiments and simulations
Figure 6 compares the total loss calculated by BPM with the normalized experimental loss after removal of propagation loss. The BPM loss curves have a very similar shape to the experimental curves but the experiment shows a slightly increased loss always lying above the modeled curves. The best agreement with experiment occurs for the BPM model using the fully filled waveguide modes launch condition despite the fully filled fiber modes field more closely resembling the experiments performed. This suggests that a mode coupling process is occurring and there are two possible processes. Although the matching fluid refractive index is close to the core index there is still some mismatch. Therefore the relatively rough front waveguide surface couples light into more waveguide modes than for a polished entry surface due to scattering and causes additional scattering loss. In addition, the side-wall roughness redistributes energy between bound modes.
Figure 6 shows the experimental results to agree with the BPM fully filled waveguide modes launch simulation to within experimental error for radii above about 10 mm but to increasing deviate for radii below this to give a 1 dB difference at a radius of 5 mm with an increased experimental loss more than the simulation. The main differences between simulations and experiments which may account for the slight differences are:
- a) Direct implementation of waveguide wall roughness is difficult in BPM since it requires a very fine grid to capture the highest spatial frequency components of the roughness leading to unpractically long simulation times. The facet roughness was also not included directly in the theoretical model although the choice of fully filled modal launch conditions partially accounted for it and for wall roughness to some extent.
- b) Alignment in experiments was not perfect as in the theory and was estimated to be angular misalignment <1° and lateral and axial misalignment <5 μm.
- c) The dicing cut at the entrance and exit of the straight waveguides was not always at exactly 90° to the waveguide which would affect the symmetry of mode coupling and predominant propagation direction.
- d) The photograph of the end face of the waveguide (Fig. 2) shows a slight spreading of the field to the sides of the waveguide core at its lowest level which was not included in the simulations.
- e) The waveguide layout was digitized onto a grid with a resolution of ∼39.7 nm (68,000 dpi) in order to form the photomask. This quantization error would result in a rough wall to the waveguide bend which might be worse than for an e-beam mask made using a finer mesh.
The loss of multimode polymer waveguide bends was measured and calculated by BPM modeling for a range of radii of curvature and for several waveguide widths to establish design curves to aid optical waveguide interconnect backplane designers. The design curves of loss as a function of bend radius were plotted after separating out the propagation loss. The experimental results were obtained for waveguides having a refractive index difference of Δn=0.0296 (=1.9% of core index) and having relatively rough diced end faces which are commonly used in OPCB backplane applications [3,4]. The trends in the results are also more widely applicable. The optimum bend radius for polymer waveguide backplanes, Fig. 3, Table 1, is 13.5 mm for 50 μm × 50 μm, is 15.3 mm for 75 μm × 50 μm and is 17.7 mm for 100 μm × 50 μm waveguide cores as these provides a balance of transition and radiation loss versus propagation loss. Results in [5,6], agree reasonably well with the results in Fig. 3, for the insertion loss of our 50 μm × 50 μm waveguide, which is most commonly used in backplanes. However in both [5,6] they did not report the increase of loss in the long radii range due to propagation loss domination nor separated the loss components from each other. Insertion loss in  is significantly lower compared to this study or to [5,6] but in that case out-of-plane 180° bends were investigated on flexible polymer circuits which makes any direct comparison difficult.
The various components making up the total loss were separated with the help of BPM modeling to separate the radiation loss from the transition loss. The wider waveguides have higher transition loss than radiation loss and less propagation loss, Fig. 7. For the smallest radii the transition loss from the first straight waveguide to the waveguide bend was the most important. As the radius increased the transition and radiation loss decreased while the propagation loss increased so that at a radius of ∼15 mm they were all of equal importance. Finally at radii larger than 20 mm the propagation loss was the most important. Fig. 7 can be used as a design curve to establish the loss for the link power budget calculation. Moreover, since transition loss was the most serious, a design rule can be specified in order to avoid crosstalk that an input straight waveguide entering a bend should not be aligned to an output straight waveguide following a bend. This situation occurs in back to back mirrored bends and so this work suggests that these should be avoided.
We used the method of nested bends for the first time in multimode polymer waveguides to calculate the propagation loss. Since the radii of successive waveguide bends differ by a fixed amount, by plotting the loss for each waveguide as a function of radius and fitting a linear curve the propagation loss can be extracted which is more convenient, uses less substrate area and is less destructive than using the conventional cut-back method since the uncertainties involved in the successive dicing of a waveguide wafer are eliminated.
The authors thank Navin Suyal, Exxelis for preparation of the TruemodeTM polymer and for supplying the details of the waveguide fabrication technique, Dave Milward, Ken Hopkins, Richard Pitwon, Xyratex Technology Ltd. and Frank Tooley, Photonix for fruitful discussions. The authors thank UK funding council EPSRC for financial support through the LINK Storlite research project and through a Doctoral Training Award and thank Xyratex Technology for financial support. We also thank the reviewers for their useful comments
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