Abstract

The stable one-time tuning of silicon-photonic directional couplers, over a broad range of coupling ratios, is achieved through the selective photo-removal of an upper cladding layer of chalcogenide glass. Analysis shows that the coupling coefficient per unit length between two parallel fully-etched silicon waveguides may be changed by 45%. The power coupling ratio of a 50 µm-long directional coupler between two such waveguides may be tuned arbitrarily between 0 and 1, with weak residual wavelength dependence. Smaller modifications in the coupling coefficient per unit length are obtained between two partially-etched ridge waveguides, on the order of 10%. The proposed procedure is demonstrated in the post-fabrication tuning of transmission notches of a race-track resonator, from over-coupling through critical coupling to weak coupling. The extinction ratio of specific resonances is varied between 4 and 40 dB. The coupling ratio of a tuned device remains stable following three months of storage.

© 2015 Optical Society of America

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References

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    [Crossref]

2014 (1)

2013 (1)

2012 (2)

2011 (2)

2010 (2)

2009 (3)

H. L. Lira, S. Manipatruni, and M. Lipson, “Broadband hitless silicon electro-optic switch for on-chip optical networks,” Opt. Express 17(25), 22271–22280 (2009).
[Crossref] [PubMed]

L. Zhou, K. Okamoto, and S. J. B. Yoo, “Athermalizing and trimming of slotted silicon microring resonators with UV-sensitive PMMA upper-cladding,” IEEE Photonics Technol. Lett. 21(17), 1175–1177 (2009).
[Crossref]

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (1)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

2005 (1)

T. Yasuda, Y. Tsuji, and M. Koshiba, “Tunable light propagation in photonic crystal coupler filled with liquid crystal,” IEEE Photonics Technol. Lett. 17(1), 55–57 (2005).
[Crossref]

2004 (3)

1997 (1)

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

1992 (1)

G. D. Maxwell, R. Kashyap, B. J. Ainslie, D. L. Williams, and J. R. Armitage, “UV written 1.5 µm reflection filters in single mode planar silica guides,” Electron. Lett. 28(22), 2106–2107 (1992).
[Crossref]

1985 (1)

A. E. Owen, A. P. Firth, and P. J. S. Ewen, “Photo-induced structural and physico-chemical changes in amorphous chalcogenide semiconductors,” Philosoph. Mag. Part B 52(3), 347–362 (1985).
[Crossref]

1964 (1)

B. T. Kolomiets, “Vitreous semiconductors I,” Phys. Status Solidi 7(2), 359–372 (1964).
[Crossref]

1953 (1)

Adam, J.-L.

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

Adibi, A.

Agarwal, A.

Ainslie, B. J.

G. D. Maxwell, R. Kashyap, B. J. Ainslie, D. L. Williams, and J. R. Armitage, “UV written 1.5 µm reflection filters in single mode planar silica guides,” Electron. Lett. 28(22), 2106–2107 (1992).
[Crossref]

Armitage, J. R.

G. D. Maxwell, R. Kashyap, B. J. Ainslie, D. L. Williams, and J. R. Armitage, “UV written 1.5 µm reflection filters in single mode planar silica guides,” Electron. Lett. 28(22), 2106–2107 (1992).
[Crossref]

Asghari, M.

Askari, M.

Atabaki, A. H.

Baets, R.

Bakish, I.

Beeckman, J.

Califa, R.

Calvez, L.

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

Canciamilla, A.

Cardenas, J.

Chen, A.

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

Cheung, S.

Chuyanov, V.

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

Cunningham, J. E.

Dalton, L. R.

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

Danziger, S.

De Cort, W.

Ding, Z.

Djordjevic, S. S.

Dong, P.

Eftekhar, A. A.

Ewen, P. J. S.

A. E. Owen, A. P. Firth, and P. J. S. Ewen, “Photo-induced structural and physico-chemical changes in amorphous chalcogenide semiconductors,” Philosoph. Mag. Part B 52(3), 347–362 (1985).
[Crossref]

Feng, D.

Firth, A. P.

A. E. Owen, A. P. Firth, and P. J. S. Ewen, “Photo-induced structural and physico-chemical changes in amorphous chalcogenide semiconductors,” Philosoph. Mag. Part B 52(3), 347–362 (1985).
[Crossref]

Fontaine, N. K.

Frerichs, R.

Gadret, G.

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

Garner, S.

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

Genish, H.

Grillanda, S.

Guan, B.

Guillevic, E.

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

Guilloux-Viry, M.

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

Haeiwa, H.

H. Haeiwa, T. Naganawa, and Y. Kokubun, “Wide range center wavelength trimming of vertically coupled microring resonator filter by direct UV irradiation to SiN ring core,” IEEE Photonics Technol. Lett. 16(1), 135–137 (2004).
[Crossref]

Hill, C. M.

Hô, N.

Ibrahim, S.

Kaganovskii, Y.

Kashyap, R.

G. D. Maxwell, R. Kashyap, B. J. Ainslie, D. L. Williams, and J. R. Armitage, “UV written 1.5 µm reflection filters in single mode planar silica guides,” Electron. Lett. 28(22), 2106–2107 (1992).
[Crossref]

Kimerling, L. C.

Kitao, M.

Kokubun, Y.

H. Haeiwa, T. Naganawa, and Y. Kokubun, “Wide range center wavelength trimming of vertically coupled microring resonator filter by direct UV irradiation to SiN ring core,” IEEE Photonics Technol. Lett. 16(1), 135–137 (2004).
[Crossref]

Kolomiets, B. T.

B. T. Kolomiets, “Vitreous semiconductors I,” Phys. Status Solidi 7(2), 359–372 (1964).
[Crossref]

Koshiba, M.

T. Yasuda, Y. Tsuji, and M. Koshiba, “Tunable light propagation in photonic crystal coupler filled with liquid crystal,” IEEE Photonics Technol. Lett. 17(1), 55–57 (2005).
[Crossref]

Krishnamoorthy, A. V.

Lambert, S.

Li, G.

Liang, H.

Lipson, M.

Lira, H. L.

Lopez, C.

Lucas, J.

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

Luo, L. W.

Maeda, S.

Manipatruni, S.

Mao, S. S. H.

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

Marti-Carrera, F. I.

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

Maxwell, G. D.

G. D. Maxwell, R. Kashyap, B. J. Ainslie, D. L. Williams, and J. R. Armitage, “UV written 1.5 µm reflection filters in single mode planar silica guides,” Electron. Lett. 28(22), 2106–2107 (1992).
[Crossref]

Melloni, A.

Minakata, M.

Morichetti, F.

Munk, D.

Naganawa, T.

H. Haeiwa, T. Naganawa, and Y. Kokubun, “Wide range center wavelength trimming of vertically coupled microring resonator filter by direct UV irradiation to SiN ring core,” IEEE Photonics Technol. Lett. 16(1), 135–137 (2004).
[Crossref]

Neyts, K.

Ogusu, K.

Okamoto, K.

Ollivier, S.

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

Owen, A. E.

A. E. Owen, A. P. Firth, and P. J. S. Ewen, “Photo-induced structural and physico-chemical changes in amorphous chalcogenide semiconductors,” Philosoph. Mag. Part B 52(3), 347–362 (1985).
[Crossref]

Pain, T.

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

Poitras, C.

Pomerene, A. T.

Poon, A. W.

Qian, W.

Ra, Y.

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

Richardson, K.

Richardson, M.

Rivero, C.

Rosenbluh, M.

Schrauwen, J.

Schulte, A.

Scott, R. P.

Seaford, L. L.

Shafiiha, R.

Shi, Y.

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

Singh, V.

Soref, R.

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

Sorel, M.

Steier, W. H.

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

Su, T.

Trotter, D. C.

Tsuji, Y.

T. Yasuda, Y. Tsuji, and M. Koshiba, “Tunable light propagation in photonic crystal coupler filled with liquid crystal,” IEEE Photonics Technol. Lett. 17(1), 55–57 (2005).
[Crossref]

Vallée, R.

Van Thourhout, D.

Velha, P.

Watts, M. R.

Wiederhecker, G. S.

Williams, D. L.

G. D. Maxwell, R. Kashyap, B. J. Ainslie, D. L. Williams, and J. R. Armitage, “UV written 1.5 µm reflection filters in single mode planar silica guides,” Electron. Lett. 28(22), 2106–2107 (1992).
[Crossref]

Yamasaki, J.

Yasuda, T.

T. Yasuda, Y. Tsuji, and M. Koshiba, “Tunable light propagation in photonic crystal coupler filled with liquid crystal,” IEEE Photonics Technol. Lett. 17(1), 55–57 (2005).
[Crossref]

Yoo, S. J. B.

Zadok, A.

Zhang, X.

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

Zhou, L.

L. Zhou, K. Okamoto, and S. J. B. Yoo, “Athermalizing and trimming of slotted silicon microring resonators with UV-sensitive PMMA upper-cladding,” IEEE Photonics Technol. Lett. 21(17), 1175–1177 (2009).
[Crossref]

L. Zhou and A. W. Poon, “Fano resonance-based electrically reconfigurable add-drop filters in silicon microring resonator-coupled Mach-Zehnder interferometers,” Opt. Lett. 32(7), 781–783 (2007).
[Crossref] [PubMed]

Zortman, W. A.

Zoubir, A.

Electron. Lett. (1)

G. D. Maxwell, R. Kashyap, B. J. Ainslie, D. L. Williams, and J. R. Armitage, “UV written 1.5 µm reflection filters in single mode planar silica guides,” Electron. Lett. 28(22), 2106–2107 (1992).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1678–1687 (2006).
[Crossref]

IEEE Photonics Technol. Lett. (4)

T. Yasuda, Y. Tsuji, and M. Koshiba, “Tunable light propagation in photonic crystal coupler filled with liquid crystal,” IEEE Photonics Technol. Lett. 17(1), 55–57 (2005).
[Crossref]

H. Haeiwa, T. Naganawa, and Y. Kokubun, “Wide range center wavelength trimming of vertically coupled microring resonator filter by direct UV irradiation to SiN ring core,” IEEE Photonics Technol. Lett. 16(1), 135–137 (2004).
[Crossref]

L. Zhou, K. Okamoto, and S. J. B. Yoo, “Athermalizing and trimming of slotted silicon microring resonators with UV-sensitive PMMA upper-cladding,” IEEE Photonics Technol. Lett. 21(17), 1175–1177 (2009).
[Crossref]

A. Chen, V. Chuyanov, F. I. Marti-Carrera, S. Garner, W. H. Steier, S. S. H. Mao, Y. Ra, L. R. Dalton, and Y. Shi, “Trimming of polymer waveguide Y-junction by rapid photobleaching for tuning the power splitting ratio,” IEEE Photonics Technol. Lett. 9(11), 1499–1501 (1997).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Express (8)

L. W. Luo, G. S. Wiederhecker, J. Cardenas, C. Poitras, and M. Lipson, “High quality factor etchless silicon photonic ring resonators,” Opt. Express 19(7), 6284–6289 (2011).
[Crossref] [PubMed]

J. Schrauwen, D. Van Thourhout, and R. Baets, “Trimming of silicon ring resonator by electron beam induced compaction and strain,” Opt. Express 16(6), 3738–3743 (2008).
[Crossref] [PubMed]

A. Canciamilla, F. Morichetti, S. Grillanda, P. Velha, M. Sorel, V. Singh, A. Agarwal, L. C. Kimerling, and A. Melloni, “Photo-induced trimming of chalcogenide-assisted silicon waveguides,” Opt. Express 20(14), 15807–15817 (2012).
[Crossref] [PubMed]

A. H. Atabaki, A. A. Eftekhar, M. Askari, and A. Adibi, “Accurate post-fabrication trimming of ultra-compact resonators on silicon,” Opt. Express 21(12), 14139–14145 (2013).
[Crossref] [PubMed]

S. Ibrahim, N. K. Fontaine, S. S. Djordjevic, B. Guan, T. Su, S. Cheung, R. P. Scott, A. T. Pomerene, L. L. Seaford, C. M. Hill, S. Danziger, Z. Ding, K. Okamoto, and S. J. B. Yoo, “Demonstration of a fast-reconfigurable silicon CMOS optical lattice filter,” Opt. Express 19(14), 13245–13256 (2011).
[Crossref] [PubMed]

H. L. Lira, S. Manipatruni, and M. Lipson, “Broadband hitless silicon electro-optic switch for on-chip optical networks,” Opt. Express 17(25), 22271–22280 (2009).
[Crossref] [PubMed]

W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18(23), 23598–23607 (2010).
[Crossref] [PubMed]

P. Dong, W. Qian, H. Liang, R. Shafiiha, D. Feng, G. Li, J. E. Cunningham, A. V. Krishnamoorthy, and M. Asghari, “Thermally tunable silicon racetrack resonators with ultralow tuning power,” Opt. Express 18(19), 20298–20304 (2010).
[Crossref] [PubMed]

Opt. Lett. (5)

Opt. Mater. (1)

E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier, and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31(11), 1688–1692 (2009).
[Crossref]

Philosoph. Mag. Part B (1)

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[Crossref]

Phys. Status Solidi (1)

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[Crossref]

Other (8)

R. Califa, H. Genish, D. Munk, Y. Kaganovskii, I. Bakish, M. Rosenbluh, and A. Zadok, “Photo-induced tuning of chalcogenide on silicon photonic integrated circuits,” Proceedings of Conference on Lasers and Electro-Optics (CLEO), San Jose, CA (2015), paper STh1G3.
[Crossref]

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications, 6th ed. (Oxford University, 2007).

K. Shemesh, Y. Kaganovskii, and M. Rosenbluh, “Fabrication of channel waveguides in chalcogenide glass films by a focused laser beam,” Chapter 5 in: Planar Waveguides and other Confined Geometries: Theory, Technology, Production, and Novel Applications, G. Marowsky, ed., (Springer, 2014).

Y. Shen, I. Divliansky, D. Basov, and S. Mookherjea, “Perfect set-and-forget alignment of silicon photonic resonators and interferometers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper PDPC3.

F. Gan, T. Barwicz, M. A. Popovic, M. S. Dahlem, C. W. Holzwarth, P. T. Rakich, H. I. Smith, E. P. Ippen, and F. X. Kartner, “Maximizing the thermo-optic tuning range of silicon photonic structures,” in Photonics in Switching, (Institute of Electrical and Electronics Engineers, 2007), pp.67–68.

E. Chandross, A. Hale, V. Kuck, E. Laskowski, C. Madsen, R. Scotti, and J. Shmulovich, “Tunable directional optical waveguide couplers,” US Patent US6002823 A (Aug. 5, 1998).

G. T. Reed and A. P. Knights, Silicon Photonics: an Introduction (Wiley, 2004).

C. K. Madsen and J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, 1999).

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Figures (8)

Fig. 1
Fig. 1 Illustration of the cross-section of a directional coupler comprised of two silicon-on-insulator partially-etched ridge waveguides. The upper cladding chalcogenide layer of the left panel is removed from above the two cores in the right panel.

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Fig. 2
Fig. 2 Calculated power coupling ratios of a 300 μm-long directional coupler, formed between two partially-etched, 700 nm-wide silicon-photonic ridge waveguides. The transverse separation between the waveguides cores is 300 nm. Different curves correspond to different lengths x of sections not covered by chalcogenide upper cladding (see legend). The dashed blue line denotes the value of critical coupling into the race-track resonators fabricated in this work, r = 0.69 (section 3).

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Fig. 3
Fig. 3 Calculated power coupling ratios of a 50 μm-long directional coupler formed between two 500-nm wide, fully-etched silicon-photonic rib waveguides. The transverse separation between the waveguides cores is 200 nm. Different curves correspond to different length x of sections not covered by chalcogenide upper cladding (see legend).

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Fig. 4
Fig. 4 Top-view, optical microscope image of a fabricated race-track resonator in silicon-on-insulator. An upper cladding layer of chalcogenide glass covers the lighter-colored region. This upper layer was subsequently removed from above a small section of the coupler region, using focused laser beam illumination. A magnified view is shown in the inset.

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Fig. 5
Fig. 5 SEM image of a FIB cross section of the coupler, following the photo-removal of the chalcogenide cladding. A magnified view of the two waveguides is shown in the inset.

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Fig. 6
Fig. 6 Left - Measured spectral transfer functions of a silicon-on-insulator race-track resonator. Different curves correspond to different lengths x of sections within the directional coupler that are not covered by chalcogenide upper cladding (see legend). Right – corresponding simulations

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Fig. 7
Fig. 7 Measured spectral transfer functions of a silicon-on-insulator race-track resonator, following several steps of photo-removal of the upper cladding layer from above the directional coupler. The lengths x of the directional coupler section not covered by the upper cladding are noted in the legend. Tuning of the coupler is evident.

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Fig. 8
Fig. 8 Measured spectral transfer functions of a silicon-on-insulator race-track resonator, before (red) and after (blue) the photo-removal of the upper cladding from a 35 μm-long section of the directional coupler. Additional measurements were taken over 95 days following the tuning of the coupler (see legend). All measurements were taken at 25 ± 0.1 °C.

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Equations (3)

Equations on this page are rendered with MathJax. Learn more.

κ( λ )=π ( n even − n odd ) /λ ,
r( λ )= cos 2 [ ∫ 0 L κ'( x' )dx' ]= cos 2 ( κL−Δκ⋅x ).
r=exp( − π n g Qλ C )=0.69.

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