Abstract

We introduce here a simple method of integrating 45° total internal reflection micro-mirrors with polymer optical waveguides by an improved tilted beam photolithography on printed circuit boards to provide surface normal light coupling between waveguides and optoelectronic devices for optical interconnects. De-ionized water is used to couple ultraviolet beam through the waveguide core polymer layer at 45° angle during the photo exposure process. This technique is compatible with PCB manufacturing facility and suitable to large panel board-level manufacturing. The mirror slope is controlled accurately (within ± 1°) with high repeatability. The insertion loss of an uncoated micro-mirror is measured to be 1.6 dB.

© 2009 OSA

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2008 (2)

N. Hendrickx, J. Van Erps, E. Bosman, C. Debaes, H. Thienpont, and P. Van Daele, “Embedded micromirror inserts for optical printed circuit boards,” IEEE Photon. Technol. Lett. 20(20), 1727–1729 (2008).
[CrossRef]

F. Wang, F. Liu, G. K. Chang, and A. Adibi, “Precision Measurements for Propagation Properties of High Definition Polymer Waveguides by Imaging of Scattered Light,” Opt. Eng. 47(2), 024602 (2008).
[CrossRef]

2007 (1)

N. Herdrickx, J. V. Erps, G. V. Steenberge, H. Thienpont, and P. V. Daele, “Laser ablated micromirrors for printed circuit board integrated optical interconnections,” IEEE Photon. Technol. Lett. 19(11), 822–824 (2007).
[CrossRef]

2006 (3)

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

A. V. Krishnamoorthy and D. A. B. Miller, “Scaling optoelectronic-VLSI circuits into the 21st century: A technology roadmap,” IEEE J. Sel. Top. Quantum Electron. 2(1), 55–76 (2006).

T. Yoshimura, M. Miyazaki, Y. Miyamoto, N. Shimoda, A. Hori, and K. Asama, “Three-dimensional optical circuits consisting of waveguide films and optical z-connections,” J. Lightwave Technol. 24(11), 4345–4352 (2006).
[CrossRef]

2005 (4)

M. Moyniham, B. Sicard, and T. Ho, “etc., “Progress toward board-level Optical Interconnect technology,” Proc. SPIE 5731, 50–62 (2005).
[CrossRef]

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. T. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[CrossRef]

A. L. Glebov, J. Roman, M. G. Lee, and K. Yokouchi, “Optical interconnect modules with fully integrated reflector mirrors,” IEEE Photon. Technol. Lett. 17(7), 1540–1542 (2005).
[CrossRef]

S. Han, I. Cho, S. Hwang, W. Lee, and S. Ahn, “A high-density two-dimensional parallel optical interconnection module,” IEEE Photon. Technol. Lett. 17(11), 2448–2450 (2005).
[CrossRef]

2004 (1)

J. T. Kim, B. C. Kim, M. Jeong, and M. Lee, “Fabrication of a micro-optical coupling structure by laser ablation,” J. Mater. Process. Technol. 146(2), 163–166 (2004).
[CrossRef]

2001 (1)

2000 (1)

S. Lehmacher and A. Neyer, “Integration of polymer optical waveguides into printed circuit boards,” Electron. Lett. 36(12), 1052–1053 (2000).
[CrossRef]

1999 (1)

S. Garner, S.-S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. Steier, and L. Dalton, ““Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron. 35(8), 1146–1155 (1999).
[CrossRef]

1994 (1)

M. Li and S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109(3–4), 239–245 (1994).
[CrossRef]

1984 (1)

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72(7), 850–866 (1984).
[CrossRef]

Adibi, A.

F. Wang, F. Liu, G. K. Chang, and A. Adibi, “Precision Measurements for Propagation Properties of High Definition Polymer Waveguides by Imaging of Scattered Light,” Opt. Eng. 47(2), 024602 (2008).
[CrossRef]

Ahn, S.

S. Han, I. Cho, S. Hwang, W. Lee, and S. Ahn, “A high-density two-dimensional parallel optical interconnection module,” IEEE Photon. Technol. Lett. 17(11), 2448–2450 (2005).
[CrossRef]

Asama, K.

Athale, R. A.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72(7), 850–866 (1984).
[CrossRef]

Baks, C. W.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Bi, H.

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. T. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[CrossRef]

Bosman, E.

N. Hendrickx, J. Van Erps, E. Bosman, C. Debaes, H. Thienpont, and P. Van Daele, “Embedded micromirror inserts for optical printed circuit boards,” IEEE Photon. Technol. Lett. 20(20), 1727–1729 (2008).
[CrossRef]

Bour, D. P.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Budd, R. A.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Chang, G. K.

F. Wang, F. Liu, G. K. Chang, and A. Adibi, “Precision Measurements for Propagation Properties of High Definition Polymer Waveguides by Imaging of Scattered Light,” Opt. Eng. 47(2), 024602 (2008).
[CrossRef]

Chen, A.

S. Garner, S.-S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. Steier, and L. Dalton, ““Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron. 35(8), 1146–1155 (1999).
[CrossRef]

Chen, R. T.

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. T. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[CrossRef]

Chiniwalla, P.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Cho, I.

S. Han, I. Cho, S. Hwang, W. Lee, and S. Ahn, “A high-density two-dimensional parallel optical interconnection module,” IEEE Photon. Technol. Lett. 17(11), 2448–2450 (2005).
[CrossRef]

Choi, J.

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. T. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[CrossRef]

Chuyanov, V.

S. Garner, S.-S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. Steier, and L. Dalton, ““Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron. 35(8), 1146–1155 (1999).
[CrossRef]

Daele, P. V.

N. Herdrickx, J. V. Erps, G. V. Steenberge, H. Thienpont, and P. V. Daele, “Laser ablated micromirrors for printed circuit board integrated optical interconnections,” IEEE Photon. Technol. Lett. 19(11), 822–824 (2007).
[CrossRef]

Dalton, L.

S. Garner, S.-S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. Steier, and L. Dalton, ““Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron. 35(8), 1146–1155 (1999).
[CrossRef]

Dangel, R.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Debaes, C.

N. Hendrickx, J. Van Erps, E. Bosman, C. Debaes, H. Thienpont, and P. Van Daele, “Embedded micromirror inserts for optical printed circuit boards,” IEEE Photon. Technol. Lett. 20(20), 1727–1729 (2008).
[CrossRef]

Doany, F. E.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Dolfi, D. W.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Erps, J. V.

N. Herdrickx, J. V. Erps, G. V. Steenberge, H. Thienpont, and P. V. Daele, “Laser ablated micromirrors for printed circuit board integrated optical interconnections,” IEEE Photon. Technol. Lett. 19(11), 822–824 (2007).
[CrossRef]

Garner, S.

S. Garner, S.-S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. Steier, and L. Dalton, ““Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron. 35(8), 1146–1155 (1999).
[CrossRef]

Glebov, A. L.

A. L. Glebov, J. Roman, M. G. Lee, and K. Yokouchi, “Optical interconnect modules with fully integrated reflector mirrors,” IEEE Photon. Technol. Lett. 17(7), 1540–1542 (2005).
[CrossRef]

Goodman, J. W.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72(7), 850–866 (1984).
[CrossRef]

Guckenberger, D.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Han, S.

S. Han, I. Cho, S. Hwang, W. Lee, and S. Ahn, “A high-density two-dimensional parallel optical interconnection module,” IEEE Photon. Technol. Lett. 17(11), 2448–2450 (2005).
[CrossRef]

Hegde, S.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Hendrickx, N.

N. Hendrickx, J. Van Erps, E. Bosman, C. Debaes, H. Thienpont, and P. Van Daele, “Embedded micromirror inserts for optical printed circuit boards,” IEEE Photon. Technol. Lett. 20(20), 1727–1729 (2008).
[CrossRef]

Herdrickx, N.

N. Herdrickx, J. V. Erps, G. V. Steenberge, H. Thienpont, and P. V. Daele, “Laser ablated micromirrors for printed circuit board integrated optical interconnections,” IEEE Photon. Technol. Lett. 19(11), 822–824 (2007).
[CrossRef]

Ho, T.

M. Moyniham, B. Sicard, and T. Ho, “etc., “Progress toward board-level Optical Interconnect technology,” Proc. SPIE 5731, 50–62 (2005).
[CrossRef]

Hori, A.

Horst, F.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Hwang, S.

S. Han, I. Cho, S. Hwang, W. Lee, and S. Ahn, “A high-density two-dimensional parallel optical interconnection module,” IEEE Photon. Technol. Lett. 17(11), 2448–2450 (2005).
[CrossRef]

Ito, H.

Jeong, M.

J. T. Kim, B. C. Kim, M. Jeong, and M. Lee, “Fabrication of a micro-optical coupling structure by laser ablation,” J. Mater. Process. Technol. 146(2), 163–166 (2004).
[CrossRef]

Jiang, W.

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. T. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[CrossRef]

John, R. A.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Kagami, M.

Kash, J. A.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Kawasaki, A.

Kim, B. C.

J. T. Kim, B. C. Kim, M. Jeong, and M. Lee, “Fabrication of a micro-optical coupling structure by laser ablation,” J. Mater. Process. Technol. 146(2), 163–166 (2004).
[CrossRef]

Kim, J. T.

J. T. Kim, B. C. Kim, M. Jeong, and M. Lee, “Fabrication of a micro-optical coupling structure by laser ablation,” J. Mater. Process. Technol. 146(2), 163–166 (2004).
[CrossRef]

Krishnamoorthy, A. V.

A. V. Krishnamoorthy and D. A. B. Miller, “Scaling optoelectronic-VLSI circuits into the 21st century: A technology roadmap,” IEEE J. Sel. Top. Quantum Electron. 2(1), 55–76 (2006).

Kucharski, D.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Kuchta, D. M.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Kung, S.-Y.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72(7), 850–866 (1984).
[CrossRef]

Kwark, Y. H.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Lee, M.

J. T. Kim, B. C. Kim, M. Jeong, and M. Lee, “Fabrication of a micro-optical coupling structure by laser ablation,” J. Mater. Process. Technol. 146(2), 163–166 (2004).
[CrossRef]

Lee, M. G.

A. L. Glebov, J. Roman, M. G. Lee, and K. Yokouchi, “Optical interconnect modules with fully integrated reflector mirrors,” IEEE Photon. Technol. Lett. 17(7), 1540–1542 (2005).
[CrossRef]

Lee, S.-S.

S. Garner, S.-S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. Steier, and L. Dalton, ““Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron. 35(8), 1146–1155 (1999).
[CrossRef]

Lee, W.

S. Han, I. Cho, S. Hwang, W. Lee, and S. Ahn, “A high-density two-dimensional parallel optical interconnection module,” IEEE Photon. Technol. Lett. 17(11), 2448–2450 (2005).
[CrossRef]

Lehmacher, S.

S. Lehmacher and A. Neyer, “Integration of polymer optical waveguides into printed circuit boards,” Electron. Lett. 36(12), 1052–1053 (2000).
[CrossRef]

Leonberger, F. J.

J. W. Goodman, F. J. Leonberger, S.-Y. Kung, and R. A. Athale, “Optical interconnects for VLSI systems,” Proc. IEEE 72(7), 850–866 (1984).
[CrossRef]

Li, M.

M. Li and S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109(3–4), 239–245 (1994).
[CrossRef]

Libsch, F. R.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Lin, C.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Liu, F.

F. Wang, F. Liu, G. K. Chang, and A. Adibi, “Precision Measurements for Propagation Properties of High Definition Polymer Waveguides by Imaging of Scattered Light,” Opt. Eng. 47(2), 024602 (2008).
[CrossRef]

Miller, D. A. B.

A. V. Krishnamoorthy and D. A. B. Miller, “Scaling optoelectronic-VLSI circuits into the 21st century: A technology roadmap,” IEEE J. Sel. Top. Quantum Electron. 2(1), 55–76 (2006).

Miyamoto, Y.

Miyazaki, M.

Moyniham, M.

M. Moyniham, B. Sicard, and T. Ho, “etc., “Progress toward board-level Optical Interconnect technology,” Proc. SPIE 5731, 50–62 (2005).
[CrossRef]

Neyer, A.

S. Lehmacher and A. Neyer, “Integration of polymer optical waveguides into printed circuit boards,” Electron. Lett. 36(12), 1052–1053 (2000).
[CrossRef]

Nyikal, H.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Nystrom, M.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Offrein, B. J.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Patel, C. S.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Pepeljugoski, P. K.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Roman, J.

A. L. Glebov, J. Roman, M. G. Lee, and K. Yokouchi, “Optical interconnect modules with fully integrated reflector mirrors,” IEEE Photon. Technol. Lett. 17(7), 1540–1542 (2005).
[CrossRef]

Rosner, J.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Schares, L.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Schaub, J. D.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Schow, C. L.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Schuster, C.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Shan, L.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Sheard, S. J.

M. Li and S. J. Sheard, “Waveguide couplers using parallelogramic-shaped blazed gratings,” Opt. Commun. 109(3–4), 239–245 (1994).
[CrossRef]

Shimoda, N.

Sicard, B.

M. Moyniham, B. Sicard, and T. Ho, “etc., “Progress toward board-level Optical Interconnect technology,” Proc. SPIE 5731, 50–62 (2005).
[CrossRef]

Steenberge, G. V.

N. Herdrickx, J. V. Erps, G. V. Steenberge, H. Thienpont, and P. V. Daele, “Laser ablated micromirrors for printed circuit board integrated optical interconnections,” IEEE Photon. Technol. Lett. 19(11), 822–824 (2007).
[CrossRef]

Steier, W.

S. Garner, S.-S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. Steier, and L. Dalton, ““Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron. 35(8), 1146–1155 (1999).
[CrossRef]

Tan, M. R. T.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Tandon, A.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Thienpont, H.

N. Hendrickx, J. Van Erps, E. Bosman, C. Debaes, H. Thienpont, and P. Van Daele, “Embedded micromirror inserts for optical printed circuit boards,” IEEE Photon. Technol. Lett. 20(20), 1727–1729 (2008).
[CrossRef]

N. Herdrickx, J. V. Erps, G. V. Steenberge, H. Thienpont, and P. V. Daele, “Laser ablated micromirrors for printed circuit board integrated optical interconnections,” IEEE Photon. Technol. Lett. 19(11), 822–824 (2007).
[CrossRef]

Trewhella, J. M.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Trott, G. R.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Tsang, C. K.

L. Schares, J. A. Kash, F. E. Doany, C. L. Schow, C. Schuster, D. M. Kuchta, P. K. Pepeljugoski, J. M. Trewhella, C. W. Baks, R. A. John, L. Shan, Y. H. Kwark, R. A. Budd, P. Chiniwalla, F. R. Libsch, J. Rosner, C. K. Tsang, C. S. Patel, J. D. Schaub, R. Dangel, F. Horst, B. J. Offrein, D. Kucharski, D. Guckenberger, S. Hegde, H. Nyikal, C. Lin, A. Tandon, G. R. Trott, M. Nystrom, D. P. Bour, M. R. T. Tan, and D. W. Dolfi, “Terabus: terabit/second-class card-level optical interconnect technologies,” IEEE J. Sel. Top. Quantum Electron. 12(5), 1032–1044 (2006).
[CrossRef]

Van Daele, P.

N. Hendrickx, J. Van Erps, E. Bosman, C. Debaes, H. Thienpont, and P. Van Daele, “Embedded micromirror inserts for optical printed circuit boards,” IEEE Photon. Technol. Lett. 20(20), 1727–1729 (2008).
[CrossRef]

Van Erps, J.

N. Hendrickx, J. Van Erps, E. Bosman, C. Debaes, H. Thienpont, and P. Van Daele, “Embedded micromirror inserts for optical printed circuit boards,” IEEE Photon. Technol. Lett. 20(20), 1727–1729 (2008).
[CrossRef]

Wang, F.

F. Wang, F. Liu, G. K. Chang, and A. Adibi, “Precision Measurements for Propagation Properties of High Definition Polymer Waveguides by Imaging of Scattered Light,” Opt. Eng. 47(2), 024602 (2008).
[CrossRef]

Wang, L.

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. T. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[CrossRef]

Wang, X.

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. T. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[CrossRef]

Yacoubian, A.

S. Garner, S.-S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. Steier, and L. Dalton, ““Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron. 35(8), 1146–1155 (1999).
[CrossRef]

Yokouchi, K.

A. L. Glebov, J. Roman, M. G. Lee, and K. Yokouchi, “Optical interconnect modules with fully integrated reflector mirrors,” IEEE Photon. Technol. Lett. 17(7), 1540–1542 (2005).
[CrossRef]

Yoshimura, T.

Appl. Phys. Lett. (1)

L. Wang, X. Wang, W. Jiang, J. Choi, H. Bi, and R. T. Chen, “45° polymer-based total internal reflection coupling mirrors for fully embedded intraboard guided wave optical interconnects,” Appl. Phys. Lett. 87(14), 141110 (2005).
[CrossRef]

Electron. Lett. (1)

S. Lehmacher and A. Neyer, “Integration of polymer optical waveguides into printed circuit boards,” Electron. Lett. 36(12), 1052–1053 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Garner, S.-S. Lee, V. Chuyanov, A. Chen, A. Yacoubian, W. Steier, and L. Dalton, ““Three-dimensional integrated optics using polymers,” IEEE J. Quantum Electron. 35(8), 1146–1155 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

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Figures (6)

Fig. 1
Fig. 1

Schematic of titled beam photolithography. (α and θ being the incident angles in air and in the polymer respectively)

Fig. 2
Fig. 2

Microscope image of a cleaved 50 μm thick polymeric waveguide core layer with a 31.5° negative tapered mirror integrated at the end on silicon substrate by using the air-polymer tilted beam (52.7°) contact photolithography.

Fig. 3
Fig. 3

Schematic of improved UV photolithography on PCB substrate. (α and θ being the incident angles in water and polymer respectively)

Fig. 4
Fig. 4

Microscope images of a 50μm × 50μm polymer waveguide with a 45° (a) positive and (b) negative tapered mirror facet at the end on FR4 substrate.

Fig. 5
Fig. 5

Surface profile of the positive tapered mirror (as in Fig. 4(a)) at the waveguide end measured by the contact surface profiler (DekTek 303).

Fig. 6
Fig. 6

SEM images showing the top views of (a) positive tapered and (b) negative tapered 45° micro-mirrors at the ends of 50 × 50μm multimode waveguides on PCB substrate.

Equations (1)

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n1sinα=n2sinθ

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