Abstract

We present a CMOS compatible mass manufacturable, compact Si/SiO2 multilayer GRIN lens mode size converter from standard single mode fiber to 300nm-thick Si waveguide. The fiber-to-GRIN lens coupling loss is 2.6 ± 0.3dB (coupling efficiency: 51~60%) with optimized focal length of 11.6~11.8μm and Si/SiO2 multilayer thickness of 7.4μm.

© 2012 OSA

1. Introduction

Silicon photonic nano-wire waveguide with cross-sectional dimensions in the sub-0.5μm holds potential for high-density circuit integration of electronic, optoelectronics, and optical devices on a chip for providing optical functionalities in high-speed optical interconnect infrastructures [14]. By building such electronics/photonics integrated circuits (EPIC) on silicon-on-insulator (SOI) platform, exploiting the use of mainstream low-cost silicon IC manufacturing process for its fabrication [5], and devising a low cost interface of such EPIC to external environment through standard single-mode fiber (SMF), are crucial for its successful deployment in the emerging optical interconnect mass market. The great disparity in optical mode sizes of standard SMF (core diameter: 9~10μm) and sub-0.5μm Si-wire waveguide requires an efficient mode-size converter (MSC) to couple SMF to Si-wire waveguide. Various kinds of MSCs have been reported [619]. Low cost requirement does not favor the use of discrete ball lens coupler and active alignment method [6] since it results in tight tolerance to misalignment, high cost and low manufacturing yield. Although vertical coupling approach of SMF end-face butt-terminated to on-chip grating coupler has been widely employed [79], its coupling efficiency is wavelength dependent and may require active alignment since there is no natural self-alignment mechanism to fix the fiber position. On-chip horizontal MSC reported so far include Si up-taper [10], Si down-taper [11,12], amorphous Si coupler [13], hydrated SiOx graded-index (GRIN) lens coupler [14,15], SiON GRIN lens [16], and cascaded linear/non-linear Si up-taper [17,18]. Another approach is employing multilayer thin films of alternating TiO2/SiO2 to form parabolic refractive index profile in a GRIN lens to form horizontal MSC [19]. In all these methods, mode size conversion from standard SMF of core diameter 9~10μm to sub-0.5μm thick Si-wire waveguide has not been achieved. Recently, we have reported a compact 19~20μm-long a-Si/SiO2 multilayer GRIN lens MSC to couple 9~10μm diameter optical mode to 0.26μm-thick Si-wire waveguide [20,21]. This achievement was made possible by the combined utilization of multilayer bi-materials [19] and the high index contrast of a-Si/SiO2. However, the method to fabricate such a-Si/SiO2 multilayer GRIN (ML-GRIN) lens in [20] on Si-wire waveguide was by the lift-off of a-Si/SiO2 multilayer. The GRIN lens longitudinal length that determines the beam focusing action was determined by die-edge polishing which has significant lens length error [20]. This method does not give predictable MSC coupling efficiency, and is not useful for low cost and mass fabrication to meet market demand.

In this paper, we report the integration of a-Si/SiO2 ML-GRIN lens MSC to Si-wire waveguide using a fabrication process compatible with conventional processing technologies widely used in Complementary Metal-Oxide Semiconductor (CMOS) fabrications. And it is suited for integration with other optoelectronic devices or electronic circuits on SOI wafer. In addition, the GRIN lens focal length for best coupling is further shortened to 11.6~11.8μm for a-Si/SiO2 multilayer thickness of 7.4μm.

2. Fabrication process

The proper working of the a-Si/SiO2 ML-GRIN lens relies on accurate positioning of the output surface, which determines the focal length of the fabricated lens. In this work, the position of the output surface is defined by photolithography and vertical side-wall etching of a-Si/SiO2 multilayer by inductive-coupled plasma reactive ion etching (ICP/RIE) using C4F8-O2 chemistry. Figure 1 shows the schematic of the fabrication process flow.

 

Fig. 1 Schematic of the fabrication process flow of integrating a-Si/SiO2 ML-GRIN lens to Si-wire waveguide.

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Fabrication began by low-pressure chemical vapor deposition (LPCVD) of 200nm of silicon nitride (SiNx) on 4-inch Si-on-insulator (SOI) substrate which consists of 1μm-thick buried oxide (BOX) and 300nm-thick SOI. The BOX functions as bottom cladding layer for Si-waveguide. Multi-mode Si-waveguides were first defined on SOI substrate by contact mode photolithography of AZ5214E positive photo-resist using mask-1. The Si-waveguide patterns were transferred to the SiNx hard-mask by RIE. Without removing the photo-resist, the Si-waveguides were formed by ICP/RIE etching of the SOI using fluorine-based chemistry. The photo-resist was removed by O2-plasma etching and SiNx was removed by dipping wafer in boiling phosphoric acid. Subsequently, the Si-waveguide was protected by blanket deposition of 400nm of SiO2 by plasma-enhanced chemical vapor deposition (PECVD) and, then, 50nm of Al etch-stop (ES) layer by electron-beam evaporation. Physical openings of dimension 60μm(w)x40μm(l) were made at the Si-waveguide tips by photolithography of mask-2. Al, and subsequently, the underlying SiO2 were removed by dry etching to expose the Si-waveguide tips. The exposed Si-waveguide tips were removed by ICP/RIE so that Si-waveguides can be butt-coupled to the a-Si/SiO2 multilayer to be deposited later. After removal of photo-resist and substrate solvent cleaning, a-Si/SiO2 multilayer was blanket deposited onto the substrate.

The a-Si/SiO2 multilayer differs from previous run [20] in that its total thickness is 7.4μm. Its structure is given in the following section. The first layer of the multilayer stack is a-Si. Al etch-stop layer not only provides adhesion for the a-Si/SiO2 multilayer, it also prevents over-etching into the underlying Si-waveguide during the etching of a-Si/SiO2 multilayer. Al was chosen for the ES-layer because it provides good adhesion to Si or SiO2, and it also has low etch-rates in fluorine based RIE etching chemistry so that it can function as a good etch-stop. No peeling of a-Si/SiO2 multilayer was observed after its deposition. To form Ni hard-mask, a-Si/SiO2 multilayer deposited substrate is blanket deposited with a thin layer of Cr/Au seed metals. Rectangular openings of dimension 50μm(w)x30μm(l) overlapping second-mask openings were made at the tip of the Si-waveguide using SU-8 negative photo-resist using mask-3 photolithography. The extent of this overlap in the openings between second and third masks in the longitudinal direction defines the LGRIN of the ML-GRIN lens. Sufficiently thick Ni was electroplated into the openings of the SU-8 photo-resist. The electroplated-Ni conformed to the side-wall profile of the SU-8 photo-resist. After Ni electroplating, SU-8 can be removed by either dry etching or dipping whole sample into boiling Remover-PG solvent for several minutes. Using the Ni as hard-mask, the a-Si/SiO2 multilayer was etched in ICP/RIE with vertical side-wall using C4F8-O2 chemistry [22]. After the etching stopped on underlying Al-ES, the Al-ES was removed by low power Cl2/BCl3 RIE. The Ni hard-mask was removed by dipping the wafer in Pirahna solution. In the final step, 1~1.5μm-thick passivation oxide was deposited by PECVD to protect the devices. Figure 2(a) and Fig. 2(b) shows the final form of the fabricated ML-GRIN lens integrated to Si-waveguide.

 

Fig. 2 (a) Scanning electron micrograph (SEM) of the fabricated Si/SiO2 multilayer GRIN lens integrated to Si-waveguide. (b) SEM image of the front side view of the ML-GRIN lens, showing the etched output surface.

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3. Fabricated device structure

3.1 Fabricated device

Figure 2(a) shows the scanning electron micrograph (SEM) of the fabricated a-Si/SiO2 ML-GRIN lens monolithically integrated to the Si-waveguide. LGRIN refers to the length from the Si-waveguide tip to the ML-GRIN lens output surface. There is a 10μm overlap of the a-Si/SiO2 multilayer with the output tip of the Si-waveguide. Figure 2(b) shows the output surface of the ML-GRIN lens by SEM. Good coupling efficiency of the ML-GRIN lens depends to a large extent on well-defined and reproducible LGRIN which ICP/RIE is capable of, and to a lesser extent on the output surface smoothness. The smoothness of the etched output surface can be further improved in future by optimizing the process condition of SU-8 photo-resist. This will result in better smoothness of the electroplated Ni hard-mask side-wall and the output surface of the ML-GRIN lens. Figure 3 shows a schematic of the ML-GRIN lens MSC. The Si-waveguide has dimension of 0.3μm(t)x3μm(w). 3μm-wide Si-waveguide was chosen because this is the minimum achievable lateral width in contact mode photolithography. Although this resulted in multimode waveguide, this does not obviate the primary purpose to demonstrate vertical mode size conversion for the ML-GRIN lens. The optical MSC is based on cascade of lateral Si up-taper that transforms the mode horizontally from 3μm-wide Si-waveguide to 6~7μm-wide slab waveguide at the output, and ML-GRIN lens that transforms the mode vertically from 0.3μm to 7~8μm. The optical beam that emerged from the 7~8μm output facet and propagated through LGRIN across the ML-GRIN medium remained fairly non-divergent as verified by simulations [21]. In this test chip, the lateral Si up-taper has a length of LTaper = 500μm. LTaper can be shortened to 50μm while maintaining low loss [11] to minimize Si area consumption during its practical implementation in EPIC.

 

Fig. 3 Schematic diagram of MSC that consists of ML-GRIN lens in cascade with Si up-taper.

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Figure 4 shows the cross-sectional schematic view of Si-waveguide tip integrated to ML-GRIN lens. As a result of the fabrication process and mask design, there exists an overlap of the a-Si/SiO2 multilayer stack on the Si-waveguide tip. The overlap ensures that Si-waveguide tip butt-couples to the ML-GRIN lens medium. In contrast to ML-GRIN lens fabricated by lift-off method [20], this overlapping resulted in distortion of the multilayer medium due to the Si-waveguide- passivation oxide tip step which is about 755nm in height. In Fig. 4, since the thickness of the first a-Si layer was 1.59μm, lightwave emitted from the waveguide tip, entered the distorted ML-GRIN lens medium uninterrupted. Lightwave propagated through the homogeneous a-Si region, entered the undistorted multilayer region and experienced lensing action. Simulation results [23] have shown that lensing action is solely determined by LGRIN (refer to Fig. 4) and is independent of the distorted segment length L’. The position of the ML-GRIN lens output surface is designed to be ~15μm away from the edge of the die to prevent damage due to dicing action. In coupling to standard single-mode fiber, the facet of the single mode fiber is butt-terminated to the diced edge. The 15μm allowance does not degrade the coupling efficiency since the output optical beam from ML-GRIN lens is collimated and has longitudinal fiber placement tolerance of up to 30μm [20].

 

Fig. 4 Schematic diagram of cross-section of the ML-GRIN lens integrated to Si-waveguide tip.

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3.2 Si/SiO2 multilayer stack for ML-GRIN lens

The ML-GRIN lens consists of multi-layers of a-Si and SiO2 in alternation. The refractive indices of a-Si and SiO2 are 3.2 and 1.46, respectively, which has been determined by ellipsometry on single layer of the respective materials. The theory to derive the thicknesses of a-Si and SiO2 to achieve near-parabolic refractive index profile for aberration-free medium has been reported in [20,21]. The total thickness of the a-Si/SiO2 multilayer for this particular work was measured to be about 7.4μm by surface profiler scan of the device above the passivated Si-waveguide surface. Figure 5 shows the effective refractive index of the GRIN lens medium, the thicknesses of a-Si and SiO2 thin films for each slice against distance from the bottom of the stack.

 

Fig. 5 Computed effective RI (solid curve) of the ML-GRIN lens medium, the computed thicknesses of a-Si (red-square) and SiO2 (blue triangle) against vertical distance from the bottom of the a-Si/SiO2 multilayer stack.

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The a-Si thickness decreases to 101nm from bottom to top of the stack, and the thickness of SiO2 increases from 6nm to 211nm toward the top of the stack in a near-parabolic manner. There are altogether 21 pairs of practical a-Si/SiO2 bi-layers in the ML-GRIN lens. The solid curve shows the effective refractive index of the ML-GRIN lens medium.

4. Measurement results

The experimental data are presented to verify that the fabrication is successful. In addition, the optimized LGRIN and the coupling efficiency to standard single-mode fiber are also reported.

4.1 Optical mode expansion

The total length of Si-waveguide from input to output end inclusive of the ML-GRIN lens is 2228.5μm. 500μm-long horizontal Si up-taper transforms the optical mode size horizontally from 3μm to 6μm at the output. Figure 6 shows the optical micrograph of the arrangement. The LGRIN of the ML-GRIN lenses from one to other end of the die increases from 7μm to 15μm in steps of either 1μm or 0.5μm. Si-waveguides of similar termination widths at input and output but without ML-GRIN lens are fabricated adjacent to ones with ML-GRIN lens for reference during each device measurement. The vertical flat front facet of the single-mode optical fiber can be made in contact to the die edge to couple the light from the ML-GRIN lens.

 

Fig. 6 Optical micrograph of Si-waveguides with output butt-terminated with a-Si/SiO2 ML-GRIN lenses for LGRIN varying from 7μm to 15μm in steps of 0.5μm or 1μm. Objective lenses (magnification: 60X, NA: 0.65) were used for input optical coupling and output imaging.

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Discrete objective lens of 60X magnification and numerical aperture (NA) of 0.65 was utilized to couple randomly polarized IR laser light at wavelength of 1550nm into the Si-waveguide at the input end, and similar objective lens was utilized to image the optical near-field pattern of the mode at the ML-GRIN lens output surface and recorded on IR-camera. Figure 7(a) shows the optical mode at the output of 6μm-wide termination with the ML-GRIN lens which has LGRIN of 11.6~11.8μm. Figure 7(b) shows the optical mode at the output surface of 6μm-wide termination without the ML-GRIN lens. The optical mode expanded equally both horizontally by lateral Si up-taper and vertically by the ML-GRIN lens by about 7~8μm.

 

Fig. 7 (a) Optical output image from 6μm-wide Si-waveguide with a butt-terminated ML-GRIN lens. (b) Optical output image from 6μm-wide Si-waveguide termination without ML-GRIN lens.

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4.2 Optical mode compression (focusing)

To demonstrate that the ML-GRIN lens can focus or compress the optical mode vertically, IR-laser light of random polarization at 1550nm was coupled into the ML-GRIN lens from SMF placed with its core (diameter: 9~10μm) in proximity to the output surface of the ML-GRIN lens. ML-GRIN lenses with various LGRINs were tested. The right column of Fig. 8(a) to (c) shows the optical modes imaged at the waveguide input-ends by discrete lens objective (magnification: 60X, NA:0.65) for ML-GRIN lenses with LGRIN’s of 11.6~11.8μm, 12.0~12.6μm, and 10.0~10.5μm. The ML-GRIN lens with LGRIN = 11.6~11.8μm gives the brightest optical output at the Si-waveguide input-end. Optical output becomes dim as LGRIN decreases to 10.0~10.5μm or increases to 12.0~12.6μm (Fig. 8(b) and Fig. 8(c)).

 

Fig. 8 (a) to (c) shows the coupling of SMF into ML-GRIN lenses for LGRIN of 11.6~11.8μm, 12~12.6μm and 10~10.5μm. The optical emission at the waveguide input-end was imaged by 60X lens. (d) Optical mode of single-mode fiber imaged by 30X objective lens with its output facet placed at the same object plane as the waveguide input-end. (e) Optical mode imaged at waveguide input-end by using 30X objective lens for LGRIN = 11.6~11.8μm.

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Using 30X objective lens, Fig. 8(d) shows the imaged optical mode of SMF for 1550nm-wavelength IR-light at power of 100μW with its output facet placed at the same object plane as the Si-waveguide input-end. Figure 8(e) shows the optical mode at the Si-waveguide input-end for illuminated ML-GRIN lens with LGRIN = 11.6~11.8μm. The comparison of Fig. 8(d) and Fig. 8(e) shows an almost ten times vertical mode size reduction. Since the optical mode diameter of the fiber core is 9~10μm, the vertical size of the optical mode in Fig. 8(e) should be about 1μm. As reported in [18], the optical spot diameter as imaged by the optical imaging system is always larger than the true spot diameter due to limitation of objective lens N.A. of 0.4. Since the optical emission in Fig. 8(e) comes from Si-waveguide of 0.3μm in thickness, there is, therefore, about 30 times vertical mode size reduction due to the ML-GRIN lens.

4.3 Estimation of SMF to ML-GRIN lens coupling loss

Conical-tip lensed fiber probe (N.A. better than 0.5) was used to couple randomly polarized IR-laser light at 1550nm into 3μm-wide Si-waveguide input. The standard SMF was placed with its core in proximity to the ML-GRIN lens output surface to couple the light out from it. The ML-GRIN lens to standard SMF coupling loss can be evaluated by subtracting the fiber-probe input coupling loss and the propagation loss through the Si-waveguide from the overall insertion loss from fiber-probe to standard SMF [20]. Discrete lens objectives (60X, NA = 0.65) were used to couple light into and out of the straight 3μm-wide Si-waveguide. From the peak-valley ratios of Fabry-Perot spectra as shown in Fig. 9 , TE, TM and random polarized lights propagation loss were evaluated to be 19.5 ± 1dB/cm, 24 ± 1dB/cm and 23 ± 1dB/cm, respectively [23,24]. For Si-waveguide length of 2228.5μm (inclusive of the ML-GRIN lens) the power loss due to propagation was 5dB for random polarized light.

 

Fig. 9 Fabry-Perot resonance spectra of straight 3μm-wide Si-waveguide without tapers at both ends using lens objectives to couple light into/out of the Si-waveguide.

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To evaluate the fiber-probe to waveguide coupling loss, tunable IR-laser light was coupled into and out of the straight Si-waveguide using conical-tip (N.A. better than 0.5) lensed fiber-probes as shown at the insert of Fig. 10 . The insertion loss spectrum of the 3μm-wide 2228.5μm-long Si-waveguide was measured to be 26.4~27.6dB, as shown in Fig. 10. Since the propagation power loss for the same length is 5dB, the coupling loss of lensed fiber-probe to Si-waveguide at the input is ((26.4~27.6dB) – 5dB)/2 = 10.7~11.3dB, by symmetry of the arrangement. Figure 11 shows the insertion-loss spectrum of the ML-GRIN lens loaded Si-waveguide. Its insert shows the experimental set-up. Conical-tip lensed fiber-probe was used for input coupling and standard SMF was used for out-coupling of light from ML-GRIN lens. The average insertion loss of the ML-GRIN lens loaded Si-waveguide was 18.6dB. The insertion loss was evaluated by dividing the transmitted optical power through the Si-waveguide with ML-GRIN lens by the total transmitted power without the device. The coupling loss from output surface of ML-GRIN lens to standard SMF was evaluated to be (18.6dB –5dB (propagation) – 10.7~11.3dB (input-coupling loss)) = 2.3~2.9dB. This is equivalent to coupling efficiency of 51~60%. This corroborates well with the theoretical calculation results in Fig. 5 of Ref [25]. Within this coupling loss from ML-GRIN lens to standard SMF, Fresnel reflection loss accounts for about 1.8dB. This is estimated from the Fresnel equations [26] for normal incidence light that passes through ML-GRIN lens/air and air/SMF interfaces. Hence, if anti-reflection coatings are deposited on ML-GRIN/air and air/SMF interfaces to minimize Fresnel loss, the estimated coupling loss from ML-GRIN lens to standard SMF is 0.5~1dB, which is equivalent to coupling efficiency of 80~89%. Figure 8 of Ref [25] shows that coupling efficiency from ML-GRIN lens to SMF can be improved to better than 90% with anti-reflection coatings deposited on both interfaces. We believe that by improving the smoothness of the output surface of the ML-GRIN lens and utilizing anti-reflection coatings for both interfaces, the practical coupling efficiency from ML-GRIN lens to SMF can be further improved to more than 90%. In addition, Fig. 11 also shows that the insertion loss of the ML-GRIN lens is wavelength insensitive, although Fabry-Perot resonance peaks due to multiple reflections between ML-GRIN lens and SMF surfaces appeared.

 

Fig. 10 Insertion loss spectra of 3μm-waveguide using lensed fiber-probes to couple light into/out of the Si-waveguide. (Insert: schematic of the experimental set-up).

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Fig. 11 Insertion-loss spectrum of 3μm-wide, 2228.5μm-long Si-waveguide, with 500μm-long Si up-taper at the output and butt-terminated with ML-GRIN lens. Lensed fiber-probe was used for input-coupling and standard SMF was used for output-coupling.

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5. Conclusion

Given the experimental results which demonstrated the mode size conversion from SMF to 0.3μm-thick Si wire-waveguide and SMF to ML-GRIN lens coupling efficiency of 51~60%, the proposed CMOS compatible process for monolithic integration of a-Si/SiO2 ML-GRIN lens MSC to Si-waveguide based on SOI substrate is a working solution toward mass fabrication. The ML-GRIN lens has a multilayer stack thickness of 7.4μm and it must have a length (LGRIN) of 11.5~11.8μm to give optimized mode size conversion from standard SMF to 0.3μm-thick Si-waveguide. In contrast to previous fabrication method which employed multilayer lift-off process and die-edge polishing, the ML-GRIN lens length in this work has been defined by photolithography and vertical side-wall etching by ICP/RIE of the a-Si/SiO2 multilayer. This method has the advantage of predictability in the LGRIN, which is crucial for predictable SMF to Si-waveguide coupling efficiency for application in fiber-to-chip assembly.

Acknowledgments

The authors would like to thank Centre for Ion-Beam Applications of National University of Singapore for providing electroplating facility.

References and links

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References

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  1. R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE 81(12), 1687–1706 (1993).
    [CrossRef]
  2. C. Gunn, “CMOS photonics for high-speed interconnects,” IEEE Micro 26(2), 58–66 (2006).
    [CrossRef]
  3. D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88(6), 728–749 (2000).
    [CrossRef]
  4. A. Shachem, K. Bergman, and L. P. Carloni, “On the design of a photonic Network-on-chip,” in Proceedings of International Symposium on Network-on-Chip (NOCS), Princeton, NJ, Paper 2.1, May 2007.
  5. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
    [CrossRef]
  6. Q. X. Zhang, Y. Du, C. W. Tan, J. Zhang, M. B. Yu, W. G. Yeoh, G. Q. Lo, and D. L. Kwong, “A silicon platform with MEMS active alignment functions and its potential application in Si-photonics packaging,” IEEE J. Sel. Top. Quantum Electron. 16, 101–105 (2010).
  7. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguide,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
    [CrossRef]
  8. V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, T. F. Krauss, and R. Baets, “Compact ad highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
    [CrossRef]
  9. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, and R. Baets, “An out-pf-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
    [CrossRef]
  10. A. Sure, T. Dillon, J. Murakowski, C. Lin, D. Pustai, and D. W. Prather, “Fabrication and characterization of three-dimensional silicon tapers,” Opt. Express 11(26), 3555–3561 (2003).
    [CrossRef] [PubMed]
  11. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
    [CrossRef] [PubMed]
  12. T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
    [CrossRef]
  13. A. Delâge, S. Janz, B. Lamontagne, A. Bogdanov, D. Dalacu, D. X. Xu, and K. P. Yap, “Monolithically integrated asymmetric graded and step-index couplers for microphotonic waveguides,” Opt. Express 14(1), 148–161 (2006).
    [CrossRef] [PubMed]
  14. K. Shirashi and C. S. Tsai, “A micro light-beam spot-size converter using a hemispherical GRIN-slab tip with high index contrast,” J. Lightwave Technol. 23(11), 3821–3826 (2005).
    [CrossRef]
  15. H. Yoda, H. Ikedo, T. Ketsuka, A. Irie, K. Shirashi, and C. S. Tsai, “A high performance micro-GRIN-chip spot-size converter formed with focused ion-beam,” IEEE Photon. Technol. Lett. 18(14), 1554–1556 (2006).
    [CrossRef]
  16. R. Sun, V. Nguyen, A. Agarwal, C. Y. Hong, J. Yasaitis, L. Kimerling, and J. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90(20), 201116 (2007).
    [CrossRef]
  17. K. Shiraishi, H. Yoda, A. Ohshima, H. Ikedo, and C. S. Tsai, “A silicon-based spot-size converter between single-mode fibers and Si-wire waveguides using cascaded tapers,” Appl. Phys. Lett. 91(14), 141120 (2007).
    [CrossRef]
  18. H. Yoda, K. Shiraishi, A. Ohshima, T. Ishimura, H. Furuhashi, H. Tsuchiya, and C. S. Tsai, “A two-port single-mode fiber-silicon wire waveguide coupler module using spot-size converters,” J. Lightwave Technol. 27(10), 1315–1319 (2009).
    [CrossRef]
  19. Y. Huang and S. T. Ho, “Superhigh numerical aperture (NA > 1.5) micro gradient-index lens based on a dual-material approach,” Opt. Lett. 30(11), 1291–1293 (2005).
    [CrossRef] [PubMed]
  20. T. H. Loh, Q. Wang, J. Zhu, K. T. Ng, Y. C. Lai, Y. Huang, and S. T. Ho, “Ultra-compact multilayer Si/SiO2 GRIN lens mode-size converter for coupling single-mode fiber to Si-wire waveguide,” Opt. Express 18(21), 21519–21533 (2010).
    [CrossRef] [PubMed]
  21. Q. Wang, Y. Huang, T. H. Loh, K. T. Ng, and S. T. Ho, “Application and optimization of dual-materials approach in graded-index optics,” Opt. Express 18, 4574–4589 (2010).
    [CrossRef] [PubMed]
  22. X. Li, L. Li, X. Hua, M. Fukasawa, G. S. Oehrlein, M. Barela, and M. Anderson, “Effects of Ar and O2 additives on SiO2 etching in C4F8-based plasma,” J. Vac. Sci. Technol. A 21(1), 284–293 (2003).
    [CrossRef]
  23. R. G. Walker, “Simple and accurate loss measurement technique for semiconductor optical waveguide,” Electron. Lett. 21(13), 581–583 (1985).
    [CrossRef]
  24. G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
    [CrossRef]
  25. Q. Wang, T. H. Loh, K. T. Ng, and S. T. Ho, “Design and analysis of optical coupling between silicon nanophotonics waveguide and standard single-mode fiber using an integrated asymmetric Super-GRIN lens,” IEEE J. Sel. Top. Quantum Electron. 17(3), 581–589 (2011).
    [CrossRef]
  26. E. Hecht, Optics (Addison Wesley, 1998), Chap. 4.

2011 (1)

Q. Wang, T. H. Loh, K. T. Ng, and S. T. Ho, “Design and analysis of optical coupling between silicon nanophotonics waveguide and standard single-mode fiber using an integrated asymmetric Super-GRIN lens,” IEEE J. Sel. Top. Quantum Electron. 17(3), 581–589 (2011).
[CrossRef]

2010 (3)

2009 (1)

2007 (3)

R. Sun, V. Nguyen, A. Agarwal, C. Y. Hong, J. Yasaitis, L. Kimerling, and J. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90(20), 201116 (2007).
[CrossRef]

K. Shiraishi, H. Yoda, A. Ohshima, H. Ikedo, and C. S. Tsai, “A silicon-based spot-size converter between single-mode fibers and Si-wire waveguides using cascaded tapers,” Appl. Phys. Lett. 91(14), 141120 (2007).
[CrossRef]

V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, T. F. Krauss, and R. Baets, “Compact ad highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[CrossRef]

2006 (5)

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguide,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

C. Gunn, “CMOS photonics for high-speed interconnects,” IEEE Micro 26(2), 58–66 (2006).
[CrossRef]

B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. 24(12), 4600–4615 (2006).
[CrossRef]

A. Delâge, S. Janz, B. Lamontagne, A. Bogdanov, D. Dalacu, D. X. Xu, and K. P. Yap, “Monolithically integrated asymmetric graded and step-index couplers for microphotonic waveguides,” Opt. Express 14(1), 148–161 (2006).
[CrossRef] [PubMed]

H. Yoda, H. Ikedo, T. Ketsuka, A. Irie, K. Shirashi, and C. S. Tsai, “A high performance micro-GRIN-chip spot-size converter formed with focused ion-beam,” IEEE Photon. Technol. Lett. 18(14), 1554–1556 (2006).
[CrossRef]

2005 (2)

2003 (3)

2002 (2)

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, and R. Baets, “An out-pf-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[CrossRef]

2000 (1)

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88(6), 728–749 (2000).
[CrossRef]

1993 (2)

R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE 81(12), 1687–1706 (1993).
[CrossRef]

G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
[CrossRef]

1985 (1)

R. G. Walker, “Simple and accurate loss measurement technique for semiconductor optical waveguide,” Electron. Lett. 21(13), 581–583 (1985).
[CrossRef]

Agarwal, A.

R. Sun, V. Nguyen, A. Agarwal, C. Y. Hong, J. Yasaitis, L. Kimerling, and J. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90(20), 201116 (2007).
[CrossRef]

Almeida, V. R.

Anderson, M.

X. Li, L. Li, X. Hua, M. Fukasawa, G. S. Oehrlein, M. Barela, and M. Anderson, “Effects of Ar and O2 additives on SiO2 etching in C4F8-based plasma,” J. Vac. Sci. Technol. A 21(1), 284–293 (2003).
[CrossRef]

Ayre, M.

V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, T. F. Krauss, and R. Baets, “Compact ad highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[CrossRef]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguide,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

Baets, R.

V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, T. F. Krauss, and R. Baets, “Compact ad highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[CrossRef]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguide,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, and R. Baets, “An out-pf-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[CrossRef]

Barela, M.

X. Li, L. Li, X. Hua, M. Fukasawa, G. S. Oehrlein, M. Barela, and M. Anderson, “Effects of Ar and O2 additives on SiO2 etching in C4F8-based plasma,” J. Vac. Sci. Technol. A 21(1), 284–293 (2003).
[CrossRef]

Bienstman, P.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguide,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, and R. Baets, “An out-pf-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[CrossRef]

Bogaerts, W.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguide,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, and R. Baets, “An out-pf-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[CrossRef]

Bogdanov, A.

Daele, P. V.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, and R. Baets, “An out-pf-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[CrossRef]

Dalacu, D.

Delâge, A.

Dillon, T.

Du, Y.

Q. X. Zhang, Y. Du, C. W. Tan, J. Zhang, M. B. Yu, W. G. Yeoh, G. Q. Lo, and D. L. Kwong, “A silicon platform with MEMS active alignment functions and its potential application in Si-photonics packaging,” IEEE J. Sel. Top. Quantum Electron. 16, 101–105 (2010).

Fathpour, S.

Fukasawa, M.

X. Li, L. Li, X. Hua, M. Fukasawa, G. S. Oehrlein, M. Barela, and M. Anderson, “Effects of Ar and O2 additives on SiO2 etching in C4F8-based plasma,” J. Vac. Sci. Technol. A 21(1), 284–293 (2003).
[CrossRef]

Furuhashi, H.

Gunn, C.

C. Gunn, “CMOS photonics for high-speed interconnects,” IEEE Micro 26(2), 58–66 (2006).
[CrossRef]

Ho, S. T.

Hong, C. Y.

R. Sun, V. Nguyen, A. Agarwal, C. Y. Hong, J. Yasaitis, L. Kimerling, and J. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90(20), 201116 (2007).
[CrossRef]

Hua, X.

X. Li, L. Li, X. Hua, M. Fukasawa, G. S. Oehrlein, M. Barela, and M. Anderson, “Effects of Ar and O2 additives on SiO2 etching in C4F8-based plasma,” J. Vac. Sci. Technol. A 21(1), 284–293 (2003).
[CrossRef]

Huang, Y.

Ikedo, H.

K. Shiraishi, H. Yoda, A. Ohshima, H. Ikedo, and C. S. Tsai, “A silicon-based spot-size converter between single-mode fibers and Si-wire waveguides using cascaded tapers,” Appl. Phys. Lett. 91(14), 141120 (2007).
[CrossRef]

H. Yoda, H. Ikedo, T. Ketsuka, A. Irie, K. Shirashi, and C. S. Tsai, “A high performance micro-GRIN-chip spot-size converter formed with focused ion-beam,” IEEE Photon. Technol. Lett. 18(14), 1554–1556 (2006).
[CrossRef]

Irie, A.

H. Yoda, H. Ikedo, T. Ketsuka, A. Irie, K. Shirashi, and C. S. Tsai, “A high performance micro-GRIN-chip spot-size converter formed with focused ion-beam,” IEEE Photon. Technol. Lett. 18(14), 1554–1556 (2006).
[CrossRef]

Ishimura, T.

Jalali, B.

Janz, S.

Karthe, W.

G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
[CrossRef]

Ketsuka, T.

H. Yoda, H. Ikedo, T. Ketsuka, A. Irie, K. Shirashi, and C. S. Tsai, “A high performance micro-GRIN-chip spot-size converter formed with focused ion-beam,” IEEE Photon. Technol. Lett. 18(14), 1554–1556 (2006).
[CrossRef]

Kimerling, L.

R. Sun, V. Nguyen, A. Agarwal, C. Y. Hong, J. Yasaitis, L. Kimerling, and J. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90(20), 201116 (2007).
[CrossRef]

Krauss, T. F.

V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, T. F. Krauss, and R. Baets, “Compact ad highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, and R. Baets, “An out-pf-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[CrossRef]

Kwong, D. L.

Q. X. Zhang, Y. Du, C. W. Tan, J. Zhang, M. B. Yu, W. G. Yeoh, G. Q. Lo, and D. L. Kwong, “A silicon platform with MEMS active alignment functions and its potential application in Si-photonics packaging,” IEEE J. Sel. Top. Quantum Electron. 16, 101–105 (2010).

Laere, F. V.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguide,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

Laere, V.

Lai, Y. C.

Lamontagne, B.

Li, L.

X. Li, L. Li, X. Hua, M. Fukasawa, G. S. Oehrlein, M. Barela, and M. Anderson, “Effects of Ar and O2 additives on SiO2 etching in C4F8-based plasma,” J. Vac. Sci. Technol. A 21(1), 284–293 (2003).
[CrossRef]

Li, X.

X. Li, L. Li, X. Hua, M. Fukasawa, G. S. Oehrlein, M. Barela, and M. Anderson, “Effects of Ar and O2 additives on SiO2 etching in C4F8-based plasma,” J. Vac. Sci. Technol. A 21(1), 284–293 (2003).
[CrossRef]

Lin, C.

Lipson, M.

Lo, G. Q.

Q. X. Zhang, Y. Du, C. W. Tan, J. Zhang, M. B. Yu, W. G. Yeoh, G. Q. Lo, and D. L. Kwong, “A silicon platform with MEMS active alignment functions and its potential application in Si-photonics packaging,” IEEE J. Sel. Top. Quantum Electron. 16, 101–105 (2010).

Loh, T. H.

Mesel, K. D.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, and R. Baets, “An out-pf-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[CrossRef]

Michel, J.

R. Sun, V. Nguyen, A. Agarwal, C. Y. Hong, J. Yasaitis, L. Kimerling, and J. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90(20), 201116 (2007).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88(6), 728–749 (2000).
[CrossRef]

Moerman, I.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, and R. Baets, “An out-pf-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[CrossRef]

Morita, H.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[CrossRef]

Murakowski, J.

Ng, K. T.

Nguyen, V.

R. Sun, V. Nguyen, A. Agarwal, C. Y. Hong, J. Yasaitis, L. Kimerling, and J. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90(20), 201116 (2007).
[CrossRef]

Oehrlein, G. S.

X. Li, L. Li, X. Hua, M. Fukasawa, G. S. Oehrlein, M. Barela, and M. Anderson, “Effects of Ar and O2 additives on SiO2 etching in C4F8-based plasma,” J. Vac. Sci. Technol. A 21(1), 284–293 (2003).
[CrossRef]

Ohshima, A.

H. Yoda, K. Shiraishi, A. Ohshima, T. Ishimura, H. Furuhashi, H. Tsuchiya, and C. S. Tsai, “A two-port single-mode fiber-silicon wire waveguide coupler module using spot-size converters,” J. Lightwave Technol. 27(10), 1315–1319 (2009).
[CrossRef]

K. Shiraishi, H. Yoda, A. Ohshima, H. Ikedo, and C. S. Tsai, “A silicon-based spot-size converter between single-mode fibers and Si-wire waveguides using cascaded tapers,” Appl. Phys. Lett. 91(14), 141120 (2007).
[CrossRef]

Panepucci, R. R.

Prather, D. W.

Pustai, D.

Richter, B.

G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
[CrossRef]

Roelkens, G.

Schrauwen, J.

Shiraishi, K.

H. Yoda, K. Shiraishi, A. Ohshima, T. Ishimura, H. Furuhashi, H. Tsuchiya, and C. S. Tsai, “A two-port single-mode fiber-silicon wire waveguide coupler module using spot-size converters,” J. Lightwave Technol. 27(10), 1315–1319 (2009).
[CrossRef]

K. Shiraishi, H. Yoda, A. Ohshima, H. Ikedo, and C. S. Tsai, “A silicon-based spot-size converter between single-mode fibers and Si-wire waveguides using cascaded tapers,” Appl. Phys. Lett. 91(14), 141120 (2007).
[CrossRef]

Shirashi, K.

H. Yoda, H. Ikedo, T. Ketsuka, A. Irie, K. Shirashi, and C. S. Tsai, “A high performance micro-GRIN-chip spot-size converter formed with focused ion-beam,” IEEE Photon. Technol. Lett. 18(14), 1554–1556 (2006).
[CrossRef]

K. Shirashi and C. S. Tsai, “A micro light-beam spot-size converter using a hemispherical GRIN-slab tip with high index contrast,” J. Lightwave Technol. 23(11), 3821–3826 (2005).
[CrossRef]

Shoji, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[CrossRef]

Soref, R. A.

R. A. Soref, “Silicon-based optoelectronics,” Proc. IEEE 81(12), 1687–1706 (1993).
[CrossRef]

Sun, R.

R. Sun, V. Nguyen, A. Agarwal, C. Y. Hong, J. Yasaitis, L. Kimerling, and J. Michel, “High performance asymmetric graded index coupler with integrated lens for high index waveguides,” Appl. Phys. Lett. 90(20), 201116 (2007).
[CrossRef]

Sure, A.

Taillaert, D.

V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, T. F. Krauss, and R. Baets, “Compact ad highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[CrossRef]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguide,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, and R. Baets, “An out-pf-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38(7), 949–955 (2002).
[CrossRef]

Tan, C. W.

Q. X. Zhang, Y. Du, C. W. Tan, J. Zhang, M. B. Yu, W. G. Yeoh, G. Q. Lo, and D. L. Kwong, “A silicon platform with MEMS active alignment functions and its potential application in Si-photonics packaging,” IEEE J. Sel. Top. Quantum Electron. 16, 101–105 (2010).

Thourhout, D. V.

V. Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. V. Thourhout, T. F. Krauss, and R. Baets, “Compact ad highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
[CrossRef]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguide,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

Tittelbach, G.

G. Tittelbach, B. Richter, and W. Karthe, “Comparison of three transmission methods for integrated waveguide propagation loss measurement,” Pure Appl. Opt. 2(6), 683–700 (1993).
[CrossRef]

Tsai, C. S.

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T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
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[CrossRef]

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Q. X. Zhang, Y. Du, C. W. Tan, J. Zhang, M. B. Yu, W. G. Yeoh, G. Q. Lo, and D. L. Kwong, “A silicon platform with MEMS active alignment functions and its potential application in Si-photonics packaging,” IEEE J. Sel. Top. Quantum Electron. 16, 101–105 (2010).

Yoda, H.

H. Yoda, K. Shiraishi, A. Ohshima, T. Ishimura, H. Furuhashi, H. Tsuchiya, and C. S. Tsai, “A two-port single-mode fiber-silicon wire waveguide coupler module using spot-size converters,” J. Lightwave Technol. 27(10), 1315–1319 (2009).
[CrossRef]

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[CrossRef]

H. Yoda, H. Ikedo, T. Ketsuka, A. Irie, K. Shirashi, and C. S. Tsai, “A high performance micro-GRIN-chip spot-size converter formed with focused ion-beam,” IEEE Photon. Technol. Lett. 18(14), 1554–1556 (2006).
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Q. X. Zhang, Y. Du, C. W. Tan, J. Zhang, M. B. Yu, W. G. Yeoh, G. Q. Lo, and D. L. Kwong, “A silicon platform with MEMS active alignment functions and its potential application in Si-photonics packaging,” IEEE J. Sel. Top. Quantum Electron. 16, 101–105 (2010).

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Figures (11)

Fig. 1
Fig. 1

Schematic of the fabrication process flow of integrating a-Si/SiO2 ML-GRIN lens to Si-wire waveguide.

Fig. 2
Fig. 2

(a) Scanning electron micrograph (SEM) of the fabricated Si/SiO2 multilayer GRIN lens integrated to Si-waveguide. (b) SEM image of the front side view of the ML-GRIN lens, showing the etched output surface.

Fig. 3
Fig. 3

Schematic diagram of MSC that consists of ML-GRIN lens in cascade with Si up-taper.

Fig. 4
Fig. 4

Schematic diagram of cross-section of the ML-GRIN lens integrated to Si-waveguide tip.

Fig. 5
Fig. 5

Computed effective RI (solid curve) of the ML-GRIN lens medium, the computed thicknesses of a-Si (red-square) and SiO2 (blue triangle) against vertical distance from the bottom of the a-Si/SiO2 multilayer stack.

Fig. 6
Fig. 6

Optical micrograph of Si-waveguides with output butt-terminated with a-Si/SiO2 ML-GRIN lenses for LGRIN varying from 7μm to 15μm in steps of 0.5μm or 1μm. Objective lenses (magnification: 60X, NA: 0.65) were used for input optical coupling and output imaging.

Fig. 7
Fig. 7

(a) Optical output image from 6μm-wide Si-waveguide with a butt-terminated ML-GRIN lens. (b) Optical output image from 6μm-wide Si-waveguide termination without ML-GRIN lens.

Fig. 8
Fig. 8

(a) to (c) shows the coupling of SMF into ML-GRIN lenses for LGRIN of 11.6~11.8μm, 12~12.6μm and 10~10.5μm. The optical emission at the waveguide input-end was imaged by 60X lens. (d) Optical mode of single-mode fiber imaged by 30X objective lens with its output facet placed at the same object plane as the waveguide input-end. (e) Optical mode imaged at waveguide input-end by using 30X objective lens for LGRIN = 11.6~11.8μm.

Fig. 9
Fig. 9

Fabry-Perot resonance spectra of straight 3μm-wide Si-waveguide without tapers at both ends using lens objectives to couple light into/out of the Si-waveguide.

Fig. 10
Fig. 10

Insertion loss spectra of 3μm-waveguide using lensed fiber-probes to couple light into/out of the Si-waveguide. (Insert: schematic of the experimental set-up).

Fig. 11
Fig. 11

Insertion-loss spectrum of 3μm-wide, 2228.5μm-long Si-waveguide, with 500μm-long Si up-taper at the output and butt-terminated with ML-GRIN lens. Lensed fiber-probe was used for input-coupling and standard SMF was used for output-coupling.

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