Abstract

We report on the design and characterization of focusing-curved subwavelength grating couplers for ultra-broadband silicon photonics optical interfaces. With implementation of waveguide dispersion engineered subwavelength structures, an ultra-wide 1-dB bandwidth of over 100 nm (largest reported to date) near 1550 nm is experimentally achieved for transverse-electric polarized light. By tapering the subwavelength structures, back reflection is effectively suppressed and grating coupling efficiency is increased to −4.7 dB. A compact device footprint of 40 µm × 20 µm is realized by curving the gratings in a focusing scheme.

© 2014 Optical Society of America

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2014 (1)

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Quantum Electron. 20(4), 8201313 (2014).

2013 (3)

2012 (5)

2011 (2)

M. Asghari and A. V. Krishnamoorthy, “Silicon photonics: Energy-efficient communication,” Nat. Photon. 5(5), 268–270 (2011).
[CrossRef]

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Quantum Electron. 17(3), 597–608 (2011).
[CrossRef]

2010 (5)

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photon. 4(8), 492–494 (2010).
[CrossRef]

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[CrossRef]

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22(15), 1156–1158 (2010).
[CrossRef]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, D. X. Xu, S. Janz, A. Densmore, and T. J. Hall, “Subwavelength grating crossings for silicon wire waveguides,” Opt. Express 18(15), 16146–16155 (2010).
[CrossRef] [PubMed]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and Í. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[CrossRef] [PubMed]

2007 (2)

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, and D. X. Xu, “Gradient-index antireflective subwavelength structures for planar waveguide facets,” Opt. Lett. 32(13), 1794–1796 (2007).
[CrossRef] [PubMed]

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

2003 (1)

1997 (1)

Almeida, V. R.

Alonso-Ramos, C.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Quantum Electron. 20(4), 8201313 (2014).

Asghari, M.

M. Asghari and A. V. Krishnamoorthy, “Silicon photonics: Energy-efficient communication,” Nat. Photon. 5(5), 268–270 (2011).
[CrossRef]

Baehr-Jones, T.

Baets, R.

Y. Li, D. Vermeulen, Y. De Koninck, G. Yurtsever, G. Roelkens, and R. Baets, “Compact grating couplers on silicon-on-insulator with reduced backreflection,” Opt. Lett. 37(21), 4356–4358 (2012).
[CrossRef] [PubMed]

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

Bedard, D.

Bock, P. J.

Bogaerts, W.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

Bräuer, A.

Cheben, P.

Chen, R. T.

Chen, X.

Chen, Y. M.

Cheng, Z.

Chrostowski, L.

Y. Wang, W. Shi, X. Wang, J. Flueckiger, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Fully-etched grating coupler with low back reflection,” in Proc. SPIE Photonics North (2013).
[CrossRef]

Claes, T.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

Covey, J.

Dannberg, P.

De Dobbelaere, P.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Quantum Electron. 17(3), 597–608 (2011).
[CrossRef]

De Koninck, Y.

Delâge, A.

Densmore, A.

Flueckiger, J.

Y. Wang, W. Shi, X. Wang, J. Flueckiger, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Fully-etched grating coupler with low back reflection,” in Proc. SPIE Photonics North (2013).
[CrossRef]

Fung, C. K.

Fung, C. K. Y.

X. Chen, K. Xu, Z. Cheng, C. K. Y. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett. 37(17), 3483–3485 (2012).
[CrossRef] [PubMed]

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22(15), 1156–1158 (2010).
[CrossRef]

Galland, C.

Gloeckner, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Quantum Electron. 17(3), 597–608 (2011).
[CrossRef]

Halir, R.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Quantum Electron. 20(4), 8201313 (2014).

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and Í. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[CrossRef] [PubMed]

Hall, T. J.

Hochberg, M.

Hosseini, A.

Hvam, J. M.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[CrossRef]

Jaeger, N. A. F.

Y. Wang, W. Shi, X. Wang, J. Flueckiger, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Fully-etched grating coupler with low back reflection,” in Proc. SPIE Photonics North (2013).
[CrossRef]

Janz, S.

Karthe, W.

Kley, E.-B.

Krishnamoorthy, A. V.

M. Asghari and A. V. Krishnamoorthy, “Silicon photonics: Energy-efficient communication,” Nat. Photon. 5(5), 268–270 (2011).
[CrossRef]

Kwong, D.

Lapointe, J.

Li, C.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22(15), 1156–1158 (2010).
[CrossRef]

Li, Y.

Lim, A. E.-J.

Liow, T. Y.

Lipson, M.

Liu, L.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[CrossRef]

Lo, G.-Q.

Lo, S. M. G.

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22(15), 1156–1158 (2010).
[CrossRef]

Luan, F.

Ma, R.

Masini, G.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Quantum Electron. 17(3), 597–608 (2011).
[CrossRef]

Mekis, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Quantum Electron. 17(3), 597–608 (2011).
[CrossRef]

Molina-Fernandez, I.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Quantum Electron. 20(4), 8201313 (2014).

Molina-Fernández, Í.

Narasimha, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Quantum Electron. 17(3), 597–608 (2011).
[CrossRef]

O’Faolain, L.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

Ortega-Monux, A.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Quantum Electron. 20(4), 8201313 (2014).

Ou, H.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[CrossRef]

Panepucci, R. R.

Pinguet, T.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Quantum Electron. 17(3), 597–608 (2011).
[CrossRef]

Post, E.

Pu, M.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[CrossRef]

Roelkens, G.

Sahni, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Quantum Electron. 17(3), 597–608 (2011).
[CrossRef]

Scheerlinck, S.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

Schmid, J. H.

Schnabel, B.

Schrauwen, J.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

Shi, W.

Y. Wang, W. Shi, X. Wang, J. Flueckiger, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Fully-etched grating coupler with low back reflection,” in Proc. SPIE Photonics North (2013).
[CrossRef]

Shum, P.

Subbaraman, H.

Taillaert, D.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

Tsang, H. K.

Van Laere, F.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

Van Thourhout, D.

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

Vermeulen, D.

Waldhäusl, R.

Wang, X.

Y. Wang, W. Shi, X. Wang, J. Flueckiger, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Fully-etched grating coupler with low back reflection,” in Proc. SPIE Photonics North (2013).
[CrossRef]

Wang, Y.

Y. Wang, W. Shi, X. Wang, J. Flueckiger, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Fully-etched grating coupler with low back reflection,” in Proc. SPIE Photonics North (2013).
[CrossRef]

Wanguemert-Perez, J. G.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Quantum Electron. 20(4), 8201313 (2014).

Wong, C. Y.

Xiao, Z.

Xu, D. X.

Xu, D.-X.

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Quantum Electron. 20(4), 8201313 (2014).

Xu, K.

Xu, X.

Yang, S.

Yun, H.

Y. Wang, W. Shi, X. Wang, J. Flueckiger, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Fully-etched grating coupler with low back reflection,” in Proc. SPIE Photonics North (2013).
[CrossRef]

Yurtsever, G.

Yvind, K.

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[CrossRef]

Zhang, J.

Zhang, Y.

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Quantum Electron. 17(3), 597–608 (2011).
[CrossRef]

R. Halir, A. Ortega-Monux, J. H. Schmid, C. Alonso-Ramos, J. Lapointe, D.-X. Xu, J. G. Wanguemert-Perez, I. Molina-Fernandez, and S. Janz, “Recent advances in silicon waveguide devices using sub-wavelength gratings,” IEEE J. Quantum Electron. 20(4), 8201313 (2014).

IEEE Photon. Technol. Lett. (2)

F. Van Laere, T. Claes, J. Schrauwen, S. Scheerlinck, W. Bogaerts, D. Taillaert, L. O’Faolain, D. Van Thourhout, and R. Baets, “Compact focusing grating couplers for silicon-on-insulator integrated circuits,” IEEE Photon. Technol. Lett. 19(23), 1919–1921 (2007).
[CrossRef]

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22(15), 1156–1158 (2010).
[CrossRef]

Nat. Photon. (2)

M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics,” Nat. Photon. 4(8), 492–494 (2010).
[CrossRef]

M. Asghari and A. V. Krishnamoorthy, “Silicon photonics: Energy-efficient communication,” Nat. Photon. 5(5), 268–270 (2011).
[CrossRef]

Opt. Commun. (1)

M. Pu, L. Liu, H. Ou, K. Yvind, and J. M. Hvam, “Ultra-low-loss inverted taper coupler for silicon-on-insulator ridge waveguide,” Opt. Commun. 283(19), 3678–3682 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (9)

X. Xu, H. Subbaraman, J. Covey, D. Kwong, A. Hosseini, and R. T. Chen, “Colorless grating couplers realized by interleaving dispersion engineered subwavelength structures,” Opt. Lett. 38(18), 3588–3591 (2013).
[CrossRef] [PubMed]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D. X. Xu, A. Densmore, J. Lapointe, and Í. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[CrossRef] [PubMed]

Z. Xiao, F. Luan, T. Y. Liow, J. Zhang, and P. Shum, “Design for broadband high-efficiency grating couplers,” Opt. Lett. 37(4), 530–532 (2012).
[CrossRef] [PubMed]

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, C. K. Fung, Y. M. Chen, and H. K. Tsang, “Focusing subwavelength grating coupler for mid-infrared suspended membrane waveguide,” Opt. Lett. 37(7), 1217–1219 (2012).
[CrossRef] [PubMed]

X. Chen, K. Xu, Z. Cheng, C. K. Y. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett. 37(17), 3483–3485 (2012).
[CrossRef] [PubMed]

Y. Li, D. Vermeulen, Y. De Koninck, G. Yurtsever, G. Roelkens, and R. Baets, “Compact grating couplers on silicon-on-insulator with reduced backreflection,” Opt. Lett. 37(21), 4356–4358 (2012).
[CrossRef] [PubMed]

Z. Cheng, X. Chen, C. Y. Wong, K. Xu, and H. K. Tsang, “Broadband focusing grating couplers for suspended-membrane waveguides,” Opt. Lett. 37(24), 5181–5183 (2012).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, and D. X. Xu, “Gradient-index antireflective subwavelength structures for planar waveguide facets,” Opt. Lett. 32(13), 1794–1796 (2007).
[CrossRef] [PubMed]

Other (5)

Y. Wang, W. Shi, X. Wang, J. Flueckiger, H. Yun, N. A. F. Jaeger, and L. Chrostowski, “Fully-etched grating coupler with low back reflection,” in Proc. SPIE Photonics North (2013).
[CrossRef]

Q. Zhong, W. Shi, Y. Wang, L. Chrostowski, and D. V. Plant, “An ultra-broadband fiber grating coupler with focusing curved subwavelength structures,” in Proc. Optical Fiber Communications (OFC) Conference (2014), paper Th2A.15.
[CrossRef]

V. I. Kopp, J. Park, M. Wlodawski, E. Hubner, J. Singer, D. Neugroschl, A. Z. Genack, P. Dumon, J. Van Campenhout, and P. Absil, “Two-dimensional, 37-channel, high-bandwidth, ultra -dense silicon photonics optical interface,” in Proc. Optical Fiber Communications (OFC) Conference (2014), paper Th5C.4.
[CrossRef]

https://www.lumerical.com/tcad-products/fdtd/ .

Y. Wang, “Grating coupler design based on silicon-on-insulator,” Master thesis, University of British Columbia (2013).

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Figures (7)

Fig. 1
Fig. 1

(a) 3-D schematic illustration of the periodic subwavelength gratings with interleaved high and low RI regions. (b) Top-view of the periodic subwavelength gratings. Λ G and f f G are the grating period and filling factor, Λ S is the subwavelength grating period, f f S H and f f S L are the subwavelength filling factors of the high and low RI regions, respectively. (c) Cross-section showing the material system of the subwavelength gratings. The drawings are not to scale.

Fig. 2
Fig. 2

Simulated transmission spectrum of the SWGC with optimized grating parameters.

Fig. 3
Fig. 3

SEM images of a fabricated focusing-curved SWGC. The lower-right grating region of (a) is zoomed and shown in (b).

Fig. 4
Fig. 4

Measured transmission spectrum of the focusing-curved SWGC. Inset shows the Fabry-Perot ripples near the spectrum peak.

Fig. 5
Fig. 5

Simulated peak coupling efficiency versus the air gap between the fiber and the grating surface.

Fig. 6
Fig. 6

SEM images of a fabricated focusing-curved SWGC with tapered grating design. The lower-right grating region of (a) is magnified and shown in (b).

Fig. 7
Fig. 7

Measured transmission spectrum of the focusing-curved SWGC tapered grating design. Inset shows the Fabry-Perot ripples near the spectrum peak.

Tables (1)

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Table 1 Comparison of the broadband SWGCs realized to date

Equations (4)

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k o n e f f k o n c sin θ = 2 π Λ G ,
B W = η n c cos θ | n e f f ( λ o ) n c sin θ λ o d n e f f ( λ ) d λ | ,
x 2 + y 2 k o n eff y k o n c sinθ=2πN,
( y N λ o n c sinθ n eff 2 n c 2 sin 2 θ ) 2 ( N λ o n eff n eff 2 n c 2 sin 2 θ ) 2 + x 2 ( N λ o ( n eff 2 n c 2 sin 2 θ ) ) 2 =1.

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