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Flip-chip optical couplers with scalable I/O count for silicon photonics

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Abstract

A scalable and tolerant optical interfacing method based on flip-chip bonding is developed for silicon photonics packaging. Bidirectional optical couplers between multiple silicon-on-insulator waveguides and single-mode polymer waveguides are designed and fabricated. Successful operation is verified experimentally in the 1530-1570 nm spectral window. At the wavelength of 1570 nm, the coupling loss is as low as 0.8 dB for both polarization states and the planar misalignment loss is less than 0.6 dB for TE and 0.3 dB for TM polarization in a lateral silicon-polymer waveguide offset range of ± 2 µm. The coupling loss does not exhibit any temperature dependence up to the highest measurement point of 70°C.

©2013 Optical Society of America

1. Introduction

Low-cost packaging technologies are necessary to facilitate widespread deployment of silicon photonics in optical interconnections. Optical coupling between the photonic chip and the external world is among the most significant challenges especially for high-index-contrast silicon-on-insulator (SOI) waveguides. There has been extensive research on efficient coupling to SOI waveguides, most of which utilize on-chip spot size converters or diffraction gratings [113]. Research efforts have almost completely focused on fiber coupling up to now as a valid approach for applications, such as in transceivers for optical fiber communications. Silicon photonics also offers excellent prospects for integrating optical communications into servers and high-performance computing systems [14, 15]. Here the boundary conditions are different as large numbers of optical channels have to be distributed throughout the system. Optical waveguides embedded in the backplane and/or on the printed circuit board (PCB) have the potential to offer a more cost-effective and scalable solution for optical interconnects [16]. Especially polymer waveguides are promising building blocks for optical interconnects owing to their relatively low processing and material cost, along with their compatibility with large-area processing [1719]. Silicon photonics may be integrated into this ecosystem by using single-mode polymer waveguides embedded in the processor package [20]. Figure 1 shows the schematic picture of an envisioned packaging concept that makes use of optical waveguides on the carrier substrate to interface silicon photonics chips with board-level optical waveguides and optical fibers. The polymer waveguides enable simultaneous interfacing of many optical signal ports between the silicon chip and the system.

 figure: Fig. 1

Fig. 1 Envisioned packaging concept that includes photonic chips connected to the optical printed circuit board (PCB) and the optical backplane through optical waveguides on the chip carrier. The figure is not to scale. The optical coupling mechanism between the chip and the carrier, between the carrier and the PCB and between the PCB and the backplane are not shown in the figure.

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We have been conducting research on bidirectional optical coupling between multiple SOI waveguides and single-mode polymer waveguides, which function analogous to electrical bond pads by achieving multichannel coupling simultaneously using a single bonding step. Coupling between polymer and SOI waveguides is provided by adiabatic mode transformation. This method is based on positioning the cores of SOI and polymer waveguides in contact or close proximity and tapering the SOI waveguide gradually, so that the supermodes (eigenmodes of the coupled waveguide system) evolve adiabatically along the coupler [21,22]. The coupler has reciprocity, which means that both SOI-to-polymer and polymer-to-SOI coupling are possible with equal efficiencies. Unlike directional couplers, adiabatic couplers do not rely on mode beating. Therefore, they can be designed to have a relatively high tolerance to variations of waveguide dimensions, refractive index, temperature, and wavelength. Adiabatic inter-waveguide couplers have been used for spot size conversion and active-passive integration in monolithic and hybrid photonic integrated circuits of different types [6,10,2327]. However, to our knowledge, the utilization of this method for flip-chip coupling between photonic chips and optical carriers has only been investigated in a theoretical study [28].

The present paper reports the design, fabrication and characterization of proof-of-concept multichannel couplers for silicon photonic chips flip-chip-bonded on polymer waveguides. The adiabatic couplers are designed to facilitate low-loss optical coupling with a high tolerance to misalignment. A low-cost process is developed to realize single-mode polymer waveguides. An assembly process is established for flip-chip bonding the silicon photonic chip on the polymer waveguide core. The wavelength and polarization dependence of the couplers, along with their misalignment tolerance and temperature dependence, are measured in the wavelength range of 1530-1570 nm. The following sections describe these design, fabrication and characterization results, respectively.

2. Design of the couplers

Figure 2(a) shows the cross sectional view of a silicon chip, flip-chip bonded to the substrate with polymer waveguides, i.e., at the end of the assembly process. The lower side of the assembly consists of the polymer waveguide core and cladding layers, deposited on a substrate. On the upper side, the chip containing the SOI waveguides is positioned upside down, so that the SOI waveguide cores are in contact with the polymer waveguide cores. The underfill material between the chips functions as a cladding material for both waveguides and improves the integrity of the assembly. Figure 2(b) shows the simplified schematic top view of the SOI and polymer waveguides in a coupler. The SOI waveguide width is tapered along the coupler length, whereas the other geometrical design parameters are constant. The even supermode of the coupled waveguide system is confined in the SOI waveguide core at the input (top) of the taper, whereas it is confined in the polymer waveguide core at the output of the taper. When the adiabaticity condition is met, the field distribution is defined by a certain supermode profile (even supermode in the present case) throughout the taper. This is achieved by preventing coupling to the other supermodes and to the radiation modes [22].

 figure: Fig. 2

Fig. 2 (a) Schematic cross section of the flip-chip-bonded silicon photonics assembly. (b) Simplified top view of the SOI and polymer waveguide cores in a coupler. The figures are not to scale.

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The cross section of the polymer waveguides is designed to achieve relatively high coupling efficiency and misalignment tolerance within the boundary conditions imposed by the currently available polymer waveguide materials and process conditions. Nevertheless, an ultimate optimization of the coupler design is out of scope for the present study. We employ single-mode polymer waveguides for silicon photonics packaging. In adiabatic inter-waveguide couplers, the shortest distance required to obtain a certain coupling efficiency is inversely proportional to the amplitude spatial overlap (coupling strength), κ, of the coupled waveguide system [29]. According to the coupled mode theory, κ increases as the refractive index perturbation of the polymer waveguide increases [21]. Under single-mode operation, a higher refractive index corresponds to smaller cross sectional dimensions, i.e., smaller size mismatch between the waveguides. On the other hand, wider polymer waveguides lead to a higher lateral misalignment tolerance because of the laterally extended guided mode. Therefore, rectangular polymer waveguide core geometries that are larger in the lateral axis than the vertical axis are preferable to obtain couplers with a high misalignment tolerance and a compact design.

We consider these general design rules to choose the polymer waveguide materials and design the waveguide dimensions. We use a photopatternable inorganic-organic hybrid polymer pair (ORMOCER®) to process the single-mode polymer waveguides. These materials have an optical loss of 0.6 dB/cm at 1550 nm [30]. Moreover, waveguides made of these materials passed a reliability test with 100 cycles of thermal shock from −20°C to + 125°C [31]. At the wavelength of 1550 nm, the refractive indices of the cladding and core materials are 1.517 and 1.535 respectively. The underfill is a thermally curable epoxy, which has a refractive index of 1.46 (EPO-TEK® 305 by Epoxy Technology). The width and the thickness of the polymer waveguide are designed to be 7 µm and 3.5 µm to provide laterally-extended single-mode operation. In the silicon waveguide chip, the thicknesses of the SOI layer and the buried oxide layer are 220 nm and 3 µm respectively.

The supermodes of the coupled-waveguide structure are calculated for different values of the SOI waveguide width. Figure 3(a) shows the refractive index distribution applied in the mode calculations. Figures 3(b)-3(e) show the even transverse electric (TE) supermode profiles of the coupled waveguides in the cases of an SOI width of 425 nm, 185 nm, 150 nm and 75 nm respectively. The fundamental TE mode profiles of the SOI waveguide alone and the polymer waveguide alone are shown in Figs. 3(f)-3(g) for comparison. In the case of an SOI width of 425 nm, the even supermode profile matches the fundamental mode profile of the individual SOI waveguide very well (power overlap of 99.97%) because the refractive index difference between the cladding and the core of the polymer waveguide is a negligible perturbation compared to the high refractive index contrast of the SOI waveguide. As the SOI width reduces, the overlap of the even supermode in the polymer waveguide core increases. In the case of the SOI width of 185 nm, the power is approximately equally distributed between the SOI and polymer cores. When the SOI width is 150 nm, the even supermode of the coupled waveguides matches the individual polymer waveguide mode with a power overlap of 99.05%. The overlap increases to 99.97% as the SOI width reduces to 75 nm.

 figure: Fig. 3

Fig. 3 (a) Refractive index distribution used for the supermode calculation, where the width of the SOI core (pink rectangle) varies. TE-polarized even supermode of the SOI-polymer waveguide system in the case of an SOI core width of (b) 425 nm, (c) 185 nm, (d) 150 nm, and (e) 75 nm. For comparison, the fundamental TE mode profiles of the (f) SOI waveguide alone, and (g) polymer waveguide alone are also shown.

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It is known that linear tapers are not the most efficient design for couplers of this type because the rate of modal transformation is a nonlinear function of the SOI waveguide width [32]. The fastest transformation occurs around the point, where the modal power is equally distributed between the two individual waveguides. The sensitivitiy of the supermode profile to the SOI waveguide width reduces towards both ends of the taper. Therefore, in an optimal design, the transition rate of the taper should be the lowest at the equilibrium point and should increase monotonously towards the ends. As a simplified approximation to this nonlinear design, we use tapers that consist of three linear segments as follows: Segment 1 tapers from 75 nm to 150 nm in a length of 50 µm; Segment 2 tapers from 150 nm to 250 nm in a length of 500 µm; Segment 3 tapers from 250 nm to 425 nm in a length of 150 µm. According to our simulations based on the three-dimensional finite-difference beam propagation method (FD-BPM), this design has a theoretical coupling loss lower than 0.2 dB. In addition, we have 800-µm-long couplers that consist of a single linear taper between 75 nm and 425 nm for comparison.

Figure 4 schematically shows the layouts of the SOI and polymer waveguides. At the input on the left, light is coupled into a polymer waveguide. It is then adiabatically coupled to the SOI waveguide. The SOI waveguide transports the signal to the adjacent polymer waveguide channel through an S bend. The second adiabatic coupler transfers the signal from the SOI waveguide to the second polymer waveguide, which is 100 µm away from the first polymer waveguide. For each input port, the transmission is measured at the corresponding straight and cross ports. Straight polymer waveguides that do not have any SOI waveguides in their proximity are also available in the layout (reference waveguide in Fig. 4). In order to characterize the alignment tolerance of the couplers, the planar misalignment between SOI and polymer waveguides (in the transverse axis) is scanned between values of −3 µm and + 3 µm with a step size of 1 µm.

 figure: Fig. 4

Fig. 4 Layouts of the SOI (red) and polymer (blue) waveguides used for the characterization of the couplers (Ref: reference). The figure is not to scale.

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3. Fabrication and assembly process

Figure 5 presents the process flow that we use to realize the polymer waveguides. The process of each layer (lower cladding and core) consists of spin coating, soft bake, ultraviolet (UV) exposure, and post-exposure bake, respectively. The soft bake step (80°C/2 min) removes the residual solvent in the thin film after spin coating. A UV exposure starts the photoinitiation of the polymerization process, which is completed with a post-exposure bake (130°C/10 min). The oxygen plasma treatment at the end of the lower cladding process improves the wetting and adhesion of the core layer. The lower cladding is an unpatterned film, so it is subject to flood exposure using a mercury lamp. On the other hand, we apply selective exposure on the core material by direct laser writing. This maskless method makes use of a laser beam, which follows a predefined path on the sample. A frequency-tripled Nd:YAG laser emission (355 nm) with a circular beam diameter of 7 µm is used to write the single-mode polymer waveguide core. These waveguides are written at a speed of 30-40 mm/s. If necessary, the writing speed can be increased by using higher laser intensity, which makes it possible to write large-scale circuits in a short time. Both flood exposure of the cladding and laser writing of the core are implemented in a nitrogen chamber with a quartz top cover to prevent oxygen inhibition. After the post-exposure bake, the core material is developed in a solvent bath (OrmoDev®) to remove the unexposed material. Figure 6(a) shows the top view microscope image of an array of straight polymer waveguides with a pitch of 100 µm, taken after development. A large number of polymer waveguides can be processed without significant defects and particles. According to our measurements using the cut-back method, polymer waveguides that are used in the bonding experiments have a propagation loss of ~0.8 dB/cm at 1550 nm and a single-mode fiber coupling loss of ~1.5 dB. Both propagation and fiber coupling losses do not exhibit any significant polarization dependence.

 figure: Fig. 5

Fig. 5 Process flow of the lower cladding and core layers of the polymer waveguides.

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 figure: Fig. 6

Fig. 6 (a) Top view microscope image of an array of straight polymer waveguides that have a pitch of 100 µm. (b) Dark-field microscope image of an array of SOI waveguides.

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The SOI waveguides are structured using electron beam lithography and anisotropic dry etching. A 140-nm-thick hydrogen silsesquioxane (HSQ) film is used as a negative-tone electron beam resist. The entire SOI layer outside the waveguides is etched using HBr:O2 gases in an inductively coupled plasma (ICP) reactive ion etching (RIE) chamber. After silicon etching, HSQ is removed using buffered hydrofluoric acid (BHF). To prevent contamination of the silicon chip in the dicing process, it is covered by a protection layer, such as a photoresist. After singulation of the dies, the protection layer is removed using acetone and the sample is cleaned by a piranha (H2SO4/H2O2) treatment followed by a rinse in de-ionized water. Figure 6(b) shows the dark-field micrograph of an array of SOI waveguides at the end of the process. SOI dies with two different dimensions (10.0 mm × 6.0 mm and 6.5 mm × 2.7 mm) are used in the experiments.

The SOI chip is flip-chip bonded on the polymer waveguides by thermocompression bonding without any adhesive materials. An automated flip-chip bonder (FC150 by Smart Equipment Technology) is used for this purpose. The silicon and polymer waveguide samples are parallelized and aligned to each other visually. Thermocompression bonding is implemented by applying a temperature of 80°C for 60 seconds and a force of 10 N on the 6.5 mm × 2.7 mm die (corresponding to a pressure of ~125 N/mm2 assuming that the contact area equals the total surface area of the SOI waveguides and the silicon alignment structures) for a total duration of 160 seconds including the temperature ramp up and ramp down times of 50 seconds. After thermocompression bonding, the thermally curable epoxy is applied as an underfill. The sample is heated up to a temperature of 65°C and subsequently the epoxy is applied by drop casting. At this temperature, the viscosity of the epoxy is significantly lower than its room temperature value of 150-350 cPs. The epoxy underfills the gap between the lower cladding of the polymer waveguides and the buried oxide layer quickly through capillary forces. A one-hour-long bake at 65°C is applied to cure the epoxy.

By dicing multiple samples at random locations and inspecting the cross section using an optical microscope, it is confirmed that the epoxy fills the cavities completely. Figure 7(a) shows the cross sectional microscope image of the assembly after wafer saw dicing. Figure 7(b) shows the zoomed cross sectional image of a polymer waveguide under illumination from the back side. The bright rectangular region at the center is the core of the polymer waveguide. Both the buried oxide and the underfill appear dark in this image because they have significantly lower refractive indices than the polymer waveguide materials, causing the microscope illumination to radiate out of these layers.

 figure: Fig. 7

Fig. 7 (a) Microscope image of the cross section of the assembly after underfilling and wafer saw dicing. (b) Microscope image of the cross section of a polymer waveguide under illumination from the back side.

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4. Characterization of the optical couplers

The couplers are characterized optically across the 1530-1570 nm wavelength range. A tunable laser and a polarization state adjuster are used at the input side of the measurement setup. Light is coupled to/from the polymer waveguides using standard single-mode fibers. The insertion loss of the input-to-cross channel (Fig. 4) is measured for different coupler designs and offset values between the polymer and SOI waveguides. This measurement is performed with two samples that have identical designs of adiabatic couplers, polymer waveguides and SOI waveguides, the only difference being the length of the SOI waveguides (1.7 mm vs 5.0 mm between the narrow ends of the SOI tapers in Sample 1 and Sample 2 respectively). Both samples include reference channels, which are straight polymer waveguides as shown in Fig. 4. The fiber-to-fiber loss components of the input-to-cross channel and the reference channel in these samples are listed in Table 1. The polymer-to-SOI waveguide coupling loss is equal to the SOI-to-polymer waveguide coupling loss because of reciprocity, and it is given by

αcoupl(dB)=αic(dB)αref(dB)αSOIexc(dB)2,
where αic is the loss of the input-to-cross channel, αref is the loss of the reference channel, and αSOI-exc is the excess propagation loss of the SOI waveguide over that of the polymer waveguide of equal length. The propagation loss of the SOI waveguides is estimated to be ~5.1 dB/cm according to the fiber-to-fiber loss difference between Sample 1 and Sample 2. Thus, αSOI-exc is 0.43 dB in Sample 1 based on the 0.8 dB/cm propagation loss of the polymer waveguide and the 1.0 mm length of the SOI waveguide. The propagation loss of the SOI waveguides is higher than the state of the art because a process optimization has not been performed to reduce the loss of these SOI waveguides, which is out of scope for this study.

Tables Icon

Table 1. Components of the fiber-to-fiber loss in the input-to-cross and reference channels of Sample 1 and Sample 2 (numbers in parentheses are the lengths of the waveguides under the assumption that half of the taper contributes to the SOI waveguide length and the other half contributes to the polymer waveguide length)

The coupling loss corresponding to different offset values and taper types is extracted using Eq. (1). Figure 8 shows the coupler loss as a function of the lateral alignment offset between the SOI and the polymer waveguides for two taper designs, i.e., the three-segment and single-segment layouts as described in Section 2. The measurements are performed at the wavelengths of 1530, 1550 and 1570 nm. Note that the initially designed offset range of −3 µm to + 3 µm is normalized to −2 µm to + 4 µm because of an estimated bonding misalignment of ~1 µm, based on the symmetry of the data points. The error bars of ± 0.1 dB represent the estimated uncertainty in the experiments, based on the variation of the fiber-to-fiber loss among identical waveguides, in addition to the uncertainty of the actual propagation loss difference between the SOI and polymer waveguides. To facilitate the interpretation of the measurement data, Table 2 and Table 3 list the lowest coupling loss and the highest misalignment loss of the three-segment and the one-segment tapers within an offset range of ± 2 µm. The three-segment taper has a clearly higher alignment tolerance and a lower polarization dependent loss (PDL) than the one-segment taper although its total length is smaller because it has a slower variation in the critical width range of 150-250 nm, leading to a better suppression of scattering to the other modes. For the three-segment taper, coupling loss as low as 0.8 dB and a misalignment loss (in ± 2 µm) as low as 0.3 dB are measured at 1570 nm. At the same wavelength, the lowest fiber-to-fiber loss of Sample 1 at the input-to-cross channel is 5.2 dB for the three-segment taper and 5.0 dB for the one-segment taper, whereas the fiber-to-fiber loss at the reference channel is 3.2 dB.

 figure: Fig. 8

Fig. 8 Loss per coupler vs offset between SOI and polymer waveguides at the wavelength of (a) 1530 nm, (b) 1550 nm, and (c) 1570 nm.

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Tables Icon

Table 2. Lowest coupling loss and the highest misalignment loss within an offset range of ± 2 µm in the case of the three-segment taper

Tables Icon

Table 3. Lowest coupling loss and the highest misalignment loss within an offset range of ± 2 µm in the case of the one-segment taper

For both taper types, the coupling efficiency and alignment tolerance increase gradually towards longer wavelengths. The reason of this smooth wavelength dependence is the influence of wavelength on the mode field diameter of individual waveguide modes, which affects the amplitude spatial overlap, κ, according to the coupled mode theory [21]. These results also indicate that the couplers perform slightly better in TM polarization than in TE polarization. This is attributed to the polarization dependence of the modal distributions, which is especially pronounced when the contrast between the width and the thickness of the SOI waveguide increases. The significantly better performance of the three-segment taper underlines the importance of efficient taper design. Note that the three-segment linear taper in this example is not the most efficient taper design, and the waveguide cross sections are not optimized to achieve the highest coupling efficiency. For an ultimate optimization, the refractive indices and the dimensions of the polymer waveguide have to be designed to obtain the highest value of κ, and a nonlinear taper geometry has to be designed to maintain a low level of scattering to the other modes throughout the coupler [22]. Therefore, it is possible to increase the efficiency and alignment tolerance of these couplers by further optimization, which will provide adiabatic coupling in the entire wavelength range of interest.

One anticipated application of the silicon photonics couplers is in a processor package. Consequently the optical interface may experience substantial temperature variations during operation. The temperature dependence of coupling loss is characterized by using a Peltier element and repeating the measurements at different temperatures. Figure 9 shows the loss of two randomly chosen one-segment and three-segment couplers as a function of temperature. The loss at 24°C is normalized to zero for easier visualization of temperature-dependent loss. For both one-segment and three-segment tapers, no significant temperature-dependent loss is measured up to the highest measurement point of 70°C. The couplers in the present work exhibit low temperature sensitivity because they do not rely on resonant operating conditions. A temperature increase leads to a change of the refractive indices of the materials, but the adiabatic coupler continues to function as long as the polymer waveguide has a higher refractive index than the buried oxide. The effects of the coefficient of thermal expansion (CTE) mismatch between the silicon photonics chip and the carrier are not investigated in this experiment because the polymer waveguides are located on a silicon substrate.

 figure: Fig. 9

Fig. 9 Normalized loss per coupler as a function of temperature in the case of a one-segment and three-segment taper. The data corresponds to 1550 nm wavelength and TM polarization.

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5. Conclusion

In this paper, we presented a photonic chip optical coupling method based on flip-chip bonding on polymer waveguides. We designed optical couplers between SOI and polymer waveguides based on the principle of adiabatic mode transformation. We fabricated single-mode polymer waveguides using a low-cost maskless and etchless process and established a flip-chip bonding process. The optical characterization of the proof-of-concept sample revealed a coupling loss of 0.8-1.1 dB for TE polarization and 0.8-1.3 dB for TM polarization in the 1530-1570 nm wavelength range. At the wavelength of 1550 nm, the loss caused by a lateral misalignment of ± 2 µm was lower than 0.6 dB for TE polarization and 0.3 dB for TM polarization, demonstrating moderate alignment accuracy requirements. The coupling efficiency and the alignment tolerance were higher at longer wavelengths. No significant temperature-dependent coupling loss was measured between room temperature and 70°C. We expect that the coupling efficiency and misalignment tolerance can be increased further by optimization of the coupler design parameters. Owing to the relatively low material and processing costs of polymer waveguides and the relatively high alignment tolerance of flip-chip coupling, this coupling concept is a promising building block for future photonic packaging.

Acknowledgments

We would like to thank Kevin Lister for contributing to the processing of SOI waveguides, Yassir Madhour and Folkert Horst for the valuable discussions. This work was partially supported by the European Union Seventh Framework project, FIREFLY (Multilayer Photonic Circuits Made by Nano-Imprinting of Waveguides and Photonic Crystals).

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Figures (9)

Fig. 1
Fig. 1 Envisioned packaging concept that includes photonic chips connected to the optical printed circuit board (PCB) and the optical backplane through optical waveguides on the chip carrier. The figure is not to scale. The optical coupling mechanism between the chip and the carrier, between the carrier and the PCB and between the PCB and the backplane are not shown in the figure.
Fig. 2
Fig. 2 (a) Schematic cross section of the flip-chip-bonded silicon photonics assembly. (b) Simplified top view of the SOI and polymer waveguide cores in a coupler. The figures are not to scale.
Fig. 3
Fig. 3 (a) Refractive index distribution used for the supermode calculation, where the width of the SOI core (pink rectangle) varies. TE-polarized even supermode of the SOI-polymer waveguide system in the case of an SOI core width of (b) 425 nm, (c) 185 nm, (d) 150 nm, and (e) 75 nm. For comparison, the fundamental TE mode profiles of the (f) SOI waveguide alone, and (g) polymer waveguide alone are also shown.
Fig. 4
Fig. 4 Layouts of the SOI (red) and polymer (blue) waveguides used for the characterization of the couplers (Ref: reference). The figure is not to scale.
Fig. 5
Fig. 5 Process flow of the lower cladding and core layers of the polymer waveguides.
Fig. 6
Fig. 6 (a) Top view microscope image of an array of straight polymer waveguides that have a pitch of 100 µm. (b) Dark-field microscope image of an array of SOI waveguides.
Fig. 7
Fig. 7 (a) Microscope image of the cross section of the assembly after underfilling and wafer saw dicing. (b) Microscope image of the cross section of a polymer waveguide under illumination from the back side.
Fig. 8
Fig. 8 Loss per coupler vs offset between SOI and polymer waveguides at the wavelength of (a) 1530 nm, (b) 1550 nm, and (c) 1570 nm.
Fig. 9
Fig. 9 Normalized loss per coupler as a function of temperature in the case of a one-segment and three-segment taper. The data corresponds to 1550 nm wavelength and TM polarization.

Tables (3)

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Table 1 Components of the fiber-to-fiber loss in the input-to-cross and reference channels of Sample 1 and Sample 2 (numbers in parentheses are the lengths of the waveguides under the assumption that half of the taper contributes to the SOI waveguide length and the other half contributes to the polymer waveguide length)

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Table 2 Lowest coupling loss and the highest misalignment loss within an offset range of ± 2 µm in the case of the three-segment taper

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Table 3 Lowest coupling loss and the highest misalignment loss within an offset range of ± 2 µm in the case of the one-segment taper

Equations (1)

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α coupl (dB)= α ic (dB) α ref (dB) α SOIexc (dB) 2 ,
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