We investigate the characteristics of crossing and branching nodes in monolayer soft-lithography-based polymer optical interconnects with experimental and theoretical analysis. The theoretical crosstalk, as calculated by a function of crossing angle, was determined for a set of interconnect pairs with varying cross-sections, and was compared with experimental measurements. Furthermore, a suitable branching angle was found for branching node and the effects of short-distance mode scrambling in highly multimode polymer waveguides were studied in detail. It was found that mode-filling occurred within a propagation distance of 1.5mm for a 50×50μm2 cross-section for VCSEL coupling; however, complete scrambling of ray direction required a propagation distance of more than 5 mm.
© 2007 Optical Society of America
With the debut of 25Gb/s board-level interconnects, optical interconnects have demonstrated their ability to provide communications infrastructure for next-generation computing [1, 2]. In the domain of very-high-bandwidth short-range communications, light-based waveguides have consistently demonstrated higher placement density, more packaging flexibility, and superior alignment reliability than their electrical counterparts [1–3]. In recent years, a strong focus of optical computing technology has been placed upon optics-embedded printed circuit boards (PCBs) [4,5], or hybrid electro-optical PCBs [6,7], in which the optical and electrical layers are integrated into one board, as their fabrication can take advantage of existing PCB manufacturing processes.
The vertical coupling and in-plane connections form the two core components of monolayer chip-to-chip optical interconnections (Fig. 1). We have previously designed a soft-lithography based coupling structure with a 45° total internal reflector (TIR), a beam duct, and a polymer waveguide in order to vertically couple light beams between transmitter, receiver, and the waveguide layer ; this structure has demonstrated higher misalignment tolerances than competing designs utilizing micro-lens arrays. However, as optical interconnects will inevitably cross in-plane when used heavily within circuits and PCBs, cross-over or branching nodes are necessary for signal crossing, splitting, or isolation, and the performance of these nodes in the circuit becomes critical in determining the overall quality of optical signal transmission. Moreover, multimode waveguides exhibit many special transmission properties over short-range (mm to cm) applications [9, 10], such as mode scrambling and shifting of the center of beam intensity. A thorough study of these characteristics may serve as future guidelines in the layout of interconnects that minimize crosstalk and optimize propagation.
This paper devotes a detailed theoretical analysis to the above phenomena, and the calculated result is compared to experimental measurements in interconnection circuits fabricated by soft lithography techniques, which was utilized to “print” proposed in-plane interconnect structures at a high efficiency and low cost [11, 12].
2. Crossing and Branching of Light guides in In-plane Interconnects
2.1 General layout and fabrication
Regardless of the vertical coupling structure used , most PCB implementations with multiple board-level, in-plane optical waveguides will require cross-over and branching. Figures 2(a) and 2(b) show 2×2 cross-over and 1×2 branching waveguides, respectively; they are representative of two possible node configurations for in-plane interconnects. Due to the confinement nature of light inside a finite-sized waveguide, light beams can permeate into the counterpart waveguide. As such, layout of an interconnect is required to follow certain guidelines in order to ensure a low-BER transmission. Furthermore, as short-range multimode optical interconnects feature a length of only millimeters to centimeters, it suffers from phenomena negligible or non-existent in conventional long-range single mode fiber connections. The most significant is that of angled mode distribution, in which a light beam passing through either a curved or split waveguide changes its mode distribution from a uniform one to a slanted, or vise versa, in both its intensity and propagation direction profile. As a result, crosstalk in crossing waveguides is strongly dependent on the location of intersection.
As an effort to search for a novel manufacture means for optical interconnection on PCB, we have been prototyped the in-plane circuits including the crossing and branching nodes by using soft lithography, a known efficient optoelectronic and microelectronic fabrication method that can produce satisfactorily the required features in both the horizontal and vertical directions for the proposed polymeric three-dimensional tapered waveguides .
Soft-lithographic techniques adopted to fabricate the optical interconnection circuits are low in capital cost, and straightforward and accessible in implementation [11, 12]. They can circumvent the diffraction limitations of projection photolithography, provide access to quasi-three-dimensional structures and generate patterns, and also can be used with a wide variety of materials and surface chemistries, marking it as a promising solution for the creation of optoelectronic devices varying from a few micrometers to several hundreds of micrometers. We report here the fabrication of the integrated optical in-plane interconnection circuits.
For fabrication of the cross-over prototypes, a series of cross-over circuits were micro-engraved on a brass substrate using a computer controlled engraver with a step size of 0.8μm, including 4 sets of crossing structure with a cross section of 50×50, 100×100, 200×200, 300×300μm2, respectively. The master was then surface-polished and a silicone elastomer (Sylgard® 184, Dow Corning) was applied in a vacuum container to eliminate possible bubbles during the process. The elastomer was cured at 80°C for two hours to form a minimal-shrinkage negative mold of the master. The elastomer negative mold is partially UV transparent, allowing it to be capable of pattern printing with UV polymers. In our fabrication process, a UV-curable polyurethane acrylate prepolymer (DeSolite® optical fiber secondary coating, DSM Desotech) with a refractive index of 1.50 was poured into the negative, and subsequent UV exposure cured the DeSolite®. The finished structure may then be detached from the elastomer negative mold to form the desired crossing structure, a precise replica of the original micro-machined positive master. The hard-polymer final product may be subsequently cladded with a softer prepolymer, DeSolite® optical fiber primary coating with a refractive index of 1.48
This technique can be used to print 3-D structures of any UV or heat-curable optical polymer-based thin film material that often cannot be fabricated by conventional lithographic approaches. Examples of the fabricated cross-over and branching structure before cladding with primary coating are shown in Fig. 3. Experimental measurements conducted on fabricated cross-over prototypes are displayed in Figs. 4(a) and 4(b) along with calculated result to be described in the following section. In comparison with calculated result, the measured crosstalk in strong confinement is slightly higher for small crossing angles ranging from 10° to 35°, but lower for angles above 35°. The main reason for the discrepancy is that the printout of soft lithography usually leaves a thin remnant layer on substrate depending on pressure during print. This layer plays as a connecting channel that increases crosstalk at small crossing angles when separation between input and crossing light guide are close up, whereas it has a little influence for crossing angles between 20° and 45°. In addition, the power leakage through the remnant layer forms a background of about -25dB, making the sharp drop in cross-talk above 50° unobserved. In that case the accuracy of crosstalk primarily determined by surface roughness, responsible for leakage in the vicinity of crossing joint. For the case of weak confinement a similar situation was observed at crossing angles between 5° and 12°. It is believed that a fined polished or chromium electroplated master plate will provide a more satisfactory result.
2.2 Crossing Node
For the cross-over node, as shown in Fig. 2(a), crosstalk is usually required to be as low as 20-30dB for a reliable data communications. Considering the multimode nature of the waveguides for on-board optical interconnections, we utilized both wide-angle BPM and ZEMAX® to simulate the efficiency of polymer rectangular waveguide by varying cross angle, while the output from the waveguide was monitored. The results are shown in Figs. 4(a) and 4(b) for both strong-confinement and weak-confinement core/clad assemblies, respectively. As shown in Fig. 4, crosstalk as a function of cross angle was calculated and compared to experimental measurement for four selected cross sections of 50×50μm2, 100×100μm2, 200×200μm2, and 300×300μm2, with a cross angle ranging from 10° to 55° for strong-confinement assembly (core 1.50, cladding 1.00) and 5°~12.5° for weak-confinement (core 1.50, cladding 1.48). For weak confinement, it is found that the crosstalk decreases linearly with crossing angle from 5° to 9°, and then exhibits a faster-than-exponential attenuation when cross angle increases from 9° to 12°; when above 12°, a crosstalk of less than -30dB is obtained. For strong confinement, however, a greater crossing angle of about 52° is needed to achieve a -30dB crosstalk. It is also noted in Fig. 4 that the -20dB cross angle, as denoted with dotted blue lines, increases slightly with waveguide cross-section for both strong and weak confinement conditions. It is understood that as cross-section increases, the size of the crossing joint also increases, and so does the window of leakage to adjoining waveguide, therefore it takes a greater cross angle to achieve the same crosstalk.
Portions of BPM simulation figures are displayed in Fig. 5 (left), where leakage and crossing beams at angles of 5°, 10° and 12.5° are shown for a weak-confinement waveguide with a cross-section of 50×50μm2. It is clearly shown that light beams traveling into the adjoining waveguide decreases with the cross angle, and that at a cross angle of greater than ~12.5°, nearly all beams are confined to propagate in the original waveguide.
For comparison we traced 200,000 ray trajectories in Monte Carlo simulations using Zemax® with an uniform modal distribution of the beam at junction, and portions of simulation figures are displayed in Fig. 5 (right). The software defines this type of ray tracing with non-sequential components, or NSC, which is different from non-sequential surfaces, or NSS, which supports the definition and placement of multiple light sources, multiple objects, and multiple detectors in space, with the automatic processing of diffraction, reflection, refraction, and total internal reflection (TIR) for a wide range of objects and materials.
As current VCSELs exhibit a beam divergence ranging from 8° to 15° (e.g., 8°, single-mode from Lasermate® and 15°, multimode from Truelight®), a beam divergence of 10° was chosen in calculation. Parameters used in the simulation are listed in Table 1.
An interesting phenomenon was observed by comparing Fig. 5 (left) and Fig. 5 (right): BPM calculation exhibits leaking waves coming from both sides of crossing node, whereas ray tracing result shows only leaking rays from one direction between two crossing waveguides. An insertion loss caused by leaking waves ranges from 0 to 0.8dB in weak confinement, while up to 0.5dB in strong confinement; averaged results from BPM calculation are listed in Table 2 for various cross-sections for both confinement conditions. Weak-confinement waveguides suffer a higher insertion loss for great cross angles due to a small acceptance angle, compared to strong-confinement waveguides. The ZEMAX® result, however, shows a slightly lower crosstalk, with an insertion loss of up to 0.4dB.
2.3 Branching Node
Highly multimode Y-branching deserves special attention for its possible applications in polymer interconnects, particularly due to the special phenomenon of beam center shift in post-branching waveguides, which significantly affects their crossing characteristics. We took the case of weak-confinement assemblies and calculated power leakage in BPM simulation for both 50×50μm2 and 100×100μm2 cross-sections as a function of branching angles at the Y-junction, as shown in Fig. 6 (left), for a branching angle varying from 1° to 18°. By using BPM simulation we found that until a branching angle of 7° is reached, the leakage for 50×50μm2 light guides is negligible. In the range of 7° ~ 12°, the leakage suffers a linear increase from 0 to 100%, and remains at a constant for angles beyond 12°. The phenomenon is partly explained by Fig. 6 (right), which shows part of leaking waves in Y-branching at 3°, 8°, and 15°. For Y-branching with a cross-section of 100×100μm2, the leakage range of angle “smears”, or otherwise widen, to a range of 6.5° to 16°, mainly due to the relatively large volume of branching joints that allows multimode beams to zig-zag more than once within the joint region. Five sets of polymer branching prototypes were fabricated using soft lithography and measured result agrees reasonably well with BPM calculation, as shown in Fig. 6 (left), one printout of polymer branching node is also displayed in Fig. 3 (right).
In order to result in predictable power in interconnect circuits, it is desirable for the light propagating through the Y branching to have a uniform distribution in each branching arm when it enters into sequential waveguides. Thus, optimizing for the uniformity of light traveling in the branching arms with the shortest propagation length was investigated. We define the position of peak intensity in light guide as the beam center shift, which can be obtained in ZEMAX® calculations through curve fitting. By recording the deviation of the beam center in transversal directions of a branching arm, the oscillation in beam center was monitored and shown in Fig. 7, for waveguides with cross-sections of 50×50μm2 and 100×100μm2, under a weak-confinement condition, and with the branching angle at 3° and 6° so that the leakage from the branching circuit is negligible. We found that the period of the oscillation increases with branching angle as well as a decreasing cross-section. The insets in Fig. 7 describe the phenomenon that the beam center oscillates from one side to another side and eventually centers. It is important to note that beam scrambling takes actually much longer distance than a few millimeters to settle down, especially for great branching angles, which needs to be taken into account if a subsequent crossing or branching node is needed in the interconnect layout.
2.4. Mode scrambling Dependence
To simplify analysis, all input beams used in both the calculations and experiments above have been sufficiently pre-scrambled before entering the waveguides, as it is found in our research that mode scrambling is a prerequisite to make propagated power in interconnects predictable. VCSEL has been the most popular source for optical interconnects due to its innumerable advantages such as high efficiency, high speed operation, and the simplicity of forming two-dimensional arrays . Though multimode VCSEL is available in the market, homochromatic and single mode VCSELs are often used to couple into interconnection circuits, which are composed of multimode waveguides in most cases. Thus the single-mode beam from VCSEL is transformed into multimode within a short distance before its further propagation in the optical layer. In our practical layout designs, it was found that a nonuniform mode distribution would influence follow-up circuit output by a great deal and makes it nearly impossible to predict output power from final terminals. A mode scrambler is thus a necessity in order to make beam output as planned. In case of board-level interconnection, however, instead of a particularly designed structure or a coil of fibers, a short segment of polymer rectangular waveguide with a suitable length can serve as the scrambler.
To obtain a good estimation of the shortest propagation length needed to scramble a VCSEL beam, we conducted an analysis of beam mode scrambling in terms of intensity profile as well as distribution of ray directionality. We define VCSEL beam filling factor as the fraction of FWHM (full width at half maximum) of intensity profile over waveguide width:
Where I(u) is a function of intensity distribution inside the waveguide, ω is the width of the waveguide and I(0) denotes peak intensity under the assumption of symmetric profiles. For two typical cross-sections of waveguides used in interconnects, 50×50μm2 and 100×100μm2, the beam filling factor was calculated as a function of propagation distance using Monte Carlo simulation and result is shown in Fig. 8 (left), it follows that minimum lengths of 1.3mm and 2.5mm are needed, respectively, for the beam to uniformly fill up the 50×50 or 100×100μm2 waveguides in terms of intensity regardless of incident direction. Four profiles of VCSEL beam filling factor of 10%, 25%, 40%, and 80% are shown in the insets of Fig. 8 (left).
However, in further calculation and experimental measurements, we found a very interesting phenomenon: it actually takes a much longer propagation distance for ray direction to become completely scrambled. To demonstrate the effect, we calculated crosstalk at a 9° cross angle as a function of straight distance between a single mode VCSEL and crossing point and the result is displayed in Fig. 8 (right), in which a peak in crosstalk from below -11dB to -9dB was shown at 1.05mm and 2.38mm for 50×50 and 100×100μm2 light guide respectively, followed with three satellite peaks spanning to 15mm of propagation distance.
Taking the example of the 50×50μm2, the relationship between the crosstalk fluctuation peaks in crossing light guide and the length of propagation can be explained as follows: when the input VCSEL beam reaches the waveguide for the first time, a portion of the rays find a chance to migrate into the opposing waveguide at small cross angles comparable with VCSEL divergent angle, which occurs at 1.05mm in Fig. 8 (right); thus the pitch of zig-zag movement of rays inside light guide is approximately 1mm, whereas the second peak located at 3.00mm results from the third bounce of light rays on the side wall of waveguide. The fifth bounce gives a peak at 5.5mm due to partial scrambling, and followed by a few lower peaks of odd-number of bounces and increased scrambling until all ray directions are fully scrambled. Based on the same principle, it can be estimated that a minimum of five zig-zag changes are needed to scramble the rays in the Y-branching arm after splitting, which, depending on the branching angle, signifies a propagation distance of about 5-7mm. This scrambling length is longer than expected, and may find useful application in the layout of interconnects where a crosstalk of crossing waveguide is concerned.
The 2×2 cross-over circuit, as detailed in this paper, can achieve acceptable crosstalk at a cross angle of greater than 12° in weak confinement. We have also obtained suitable branching angle of a 1×2 branching node for the purpose of reducing leakage in the Y-junction. We have finally found proper lengths of propagation in a branching arm for the consideration of distribution uniformity of light rays. Prototypes of in-plane circuits have been fabricated and tested, and the experimental performance results are in accordance with the simulation. The results have a high degree of applicability to future optics-integrated PCBs featuring soft-lithography-fabricated interconnect structures.
This research is supported by the China National Science Foundation under grants No. 6047719 and No. 60577025.
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