Abstract

We propose, design and analyze a novel mode converter in silicon waveguide based on a graded index co-directional grating coupler. The device has a periodic variation in its refractive index along the propagation direction and a graded index profile along the transverse direction. The graded index profile is realized by the implementation of nanoscale dielectric metamaterial consisting of silicon features that are etched into the waveguide based on the concept of effective medium. Design considerations are discussed and analyzed in details in the framework of the coupled mode theory (CMT) and the effective medium theory (EMT). Using 3D finite difference time domain (FDTD) simulations we show that the mode converter can couple between different symmetric and asymmetric modes which are propagating along a single bus multimode waveguide. Mode purity on the order of 96%, crosstalk with the input mode of better than −23dB, and transmission of more than 96% can be obtained, with device length as short as 20µm, and over ~25nm spectral bandwidth around the design wavelength of 1550nm.

© 2014 Optical Society of America

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2014 (3)

2013 (5)

2012 (8)

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-Division Multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012).
[Crossref]

M. Salsi, C. Koebele, D. Sperti, P. Tran, H. Mardoyan, P. Brindel, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, and G. Charlet, “Mode-Division Multiplexing of 2 × 100 Gb/s channels using an LCOS-based spatial modulator,” J. Lightwave Technol. 30(4), 618–623 (2012).
[Crossref]

J. Sakaguchi, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi, and M. Watanabe, “Space Division Multiplexed transmission of 109-Tb/s data signals using homogeneous seven-core fiber,” J. Lightwave Technol. 30(4), 658–665 (2012).
[Crossref]

J. Lu and J. Vučković, “Objective-first design of high-efficiency, small-footprint couplers between arbitrary nanophotonic waveguide modes,” Opt. Express 20(7), 7221–7236 (2012).
[Crossref] [PubMed]

D. Dai, Y. Tang, and J. E. Bowers, “Mode conversion in tapered submicron silicon ridge optical waveguides,” Opt. Express 20(12), 13425–13439 (2012).
[Crossref] [PubMed]

V. Liu, D. A. B. Miller, and S. Fan, “Ultra-compact photonic crystal waveguide spatial mode converter and its connection to the optical diode effect,” Opt. Express 20(27), 28388–28397 (2012).
[Crossref] [PubMed]

M. Blau and D. M. Marom, “Optimization of spatial aperture-sampled mode multiplexer for a three-mode fiber,” IEEE Photon. Technol. Lett. 24(23), 2101–2104 (2012).
[Crossref]

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

2011 (3)

M. J. Paniccia, “A perfect marriage: optics and silicon,” Optik & Photonik 6(2), 34–38 (2011).
[Crossref]

F.-C. H. M.-C. Wu, “Adiabatic mode conversion in multimode waveguides using chirped computer-generated planar holograms,” IEEE Photon. Technol. Lett. 23, 807–809 (2011).

D. Dai and J. E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires,” Opt. Express 19(11), 10940–10949 (2011).
[Crossref] [PubMed]

2010 (1)

S.-Y. Tseng and M.-C. Wu, “Adiabatic mode conversion in multimode waveguides using computer-generated planar holograms,” IEEE Photon. Technol. Lett. 22(16), 1211–1213 (2010).
[Crossref]

2009 (2)

B. Desiatov, I. Goykhman, and U. Levy, “Nanoscale mode selector in silicon waveguide for on chip nanofocusing applications,” Nano Lett. 9(10), 3381–3386 (2009).
[Crossref] [PubMed]

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

2008 (3)

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic Networks-on-Chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57(9), 1246–1260 (2008).
[Crossref]

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

I. Gasulla and J. Capmany, “1 Tb/s x km Multimode fiber link combining WDM transmission and low-linewidth lasers,” Opt. Express 16(11), 8033–8038 (2008).
[Crossref] [PubMed]

2007 (1)

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref] [PubMed]

2006 (4)

2005 (3)

2003 (1)

1998 (1)

1982 (1)

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Abashin, M.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref] [PubMed]

Ahn, J.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Astruc, M.

Aubry, A.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

Awaji, Y.

Beausoleil, R. G.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Berdagué, S.

Bergman, K.

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic Networks-on-Chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57(9), 1246–1260 (2008).
[Crossref]

Bergmen, K.

L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref] [PubMed]

Besse, P.-A.

Bigo, S.

Binkert, N.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Blau, M.

M. Blau and D. M. Marom, “Optimization of spatial aperture-sampled mode multiplexer for a three-mode fiber,” IEEE Photon. Technol. Lett. 24(23), 2101–2104 (2012).
[Crossref]

Bolle, C.

Boutin, A.

Bowers, J. E.

Brindel, P.

Burrows, E. C.

Capmany, J.

Carloni, L. P.

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic Networks-on-Chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57(9), 1246–1260 (2008).
[Crossref]

Castro, J.

Charlet, G.

Cheben, P.

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
[Crossref] [PubMed]

Chen, C. P.

L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref] [PubMed]

Chen, G.

Cunningham, J.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref] [PubMed]

Da Ros, F.

Dai, D.

Davis, A.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Densmore, A.

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
[Crossref] [PubMed]

Desiatov, B.

M. Grajower, G. M. Lerman, I. Goykhman, B. Desiatov, A. Yanai, D. R. Smith, and U. Levy, “Subwavelength plasmonics for graded-index optics on a chip,” Opt. Lett. 38(18), 3492–3495 (2013).
[Crossref] [PubMed]

B. Desiatov, I. Goykhman, and U. Levy, “Nanoscale mode selector in silicon waveguide for on chip nanofocusing applications,” Nano Lett. 9(10), 3381–3386 (2009).
[Crossref] [PubMed]

Ding, Y.

Eckner, J.

Elesin, Y.

Esmaeelpour, M.

Essiambre, R.-J.

Facq, P.

Fainman, Y.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref] [PubMed]

U. Levy, M. Nezhad, H.-C. Kim, C.-H. Tsai, L. Pang, and Y. Fainman, “Implementation of a graded-index medium by use of subwavelength structures with graded fill factor,” J. Opt. Soc. Am. A 22(4), 724–733 (2005).
[Crossref] [PubMed]

Fan, S.

Fattal, D.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Fiorentino, M.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Frandsen, L. H.

Frellsen, L. F.

Gabrielli, L. H.

L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref] [PubMed]

Gamper, E.

Gasulla, I.

Ge, A.

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

Geraghty, D. F.

Giden, I. H.

Gnauck, A. H.

Goldhar, J.

Goykhman, I.

M. Grajower, G. M. Lerman, I. Goykhman, B. Desiatov, A. Yanai, D. R. Smith, and U. Levy, “Subwavelength plasmonics for graded-index optics on a chip,” Opt. Lett. 38(18), 3492–3495 (2013).
[Crossref] [PubMed]

B. Desiatov, I. Goykhman, and U. Levy, “Nanoscale mode selector in silicon waveguide for on chip nanofocusing applications,” Nano Lett. 9(10), 3381–3386 (2009).
[Crossref] [PubMed]

Grajower, M.

Greiner, C. M.

Hayashi, T.

Ho, S.-T.

Y. Huang, G. Xu, and S.-T. Ho, “An ultracompact optical mode order converter,” IEEE Photon. Technol. Lett. 18(21), 2281–2283 (2006).
[Crossref]

Honkanen, S.

Hu, T.

Huang, B.

Huang, Y.

Y. Huang, G. Xu, and S.-T. Ho, “An ultracompact optical mode order converter,” IEEE Photon. Technol. Lett. 18(21), 2281–2283 (2006).
[Crossref]

Huang, Y.-Z.

Iazikov, D.

Ikeda, K.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref] [PubMed]

Janz, S.

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
[Crossref] [PubMed]

Jiang, G.

Jiang, X.

Jouppi, N. P.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Kang, J. U.

Kanno, A.

Kawanishi, T.

Kim, H.-C.

Kim, Y.

Kobayashi, T.

Koebele, C.

Krishnamoorthy, A.

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref] [PubMed]

Kurt, H.

Lamontagne, B.

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

Lapointe, J.

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

Lau, W. T.

Lee, B.-T.

Lerman, G. M.

Leuthold, J.

Levy, U.

M. Grajower, G. M. Lerman, I. Goykhman, B. Desiatov, A. Yanai, D. R. Smith, and U. Levy, “Subwavelength plasmonics for graded-index optics on a chip,” Opt. Lett. 38(18), 3492–3495 (2013).
[Crossref] [PubMed]

B. Desiatov, I. Goykhman, and U. Levy, “Nanoscale mode selector in silicon waveguide for on chip nanofocusing applications,” Nano Lett. 9(10), 3381–3386 (2009).
[Crossref] [PubMed]

U. Levy, M. Abashin, K. Ikeda, A. Krishnamoorthy, J. Cunningham, and Y. Fainman, “Inhomogenous dielectric metamaterials with space-variant polarizability,” Phys. Rev. Lett. 98(24), 243901 (2007).
[Crossref] [PubMed]

U. Levy, M. Nezhad, H.-C. Kim, C.-H. Tsai, L. Pang, and Y. Fainman, “Implementation of a graded-index medium by use of subwavelength structures with graded fill factor,” J. Opt. Soc. Am. A 22(4), 724–733 (2005).
[Crossref] [PubMed]

Li, Y.

Lingle, R.

Lipson, M.

L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref] [PubMed]

Liu, V.

Lu, J.

Luo, L.-W.

L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref] [PubMed]

Maier, S. A.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

Mardoyan, H.

Marom, D. M.

M. Blau and D. M. Marom, “Optimization of spatial aperture-sampled mode multiplexer for a three-mode fiber,” IEEE Photon. Technol. Lett. 24(23), 2101–2104 (2012).
[Crossref]

McCurdy, A. H.

McLaren, M.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Melchior, H.

Miller, D. A. B.

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Mossberg, T. W.

Mumtaz, S.

Nezhad, M.

Oner, B. B.

Ophir, N.

L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref] [PubMed]

Ou, H.

Pang, L.

Paniccia, M. J.

M. J. Paniccia, “A perfect marriage: optics and silicon,” Optik & Photonik 6(2), 34–38 (2011).
[Crossref]

Peckham, D. W.

Pendry, J. B.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012).
[Crossref] [PubMed]

Peucheret, C.

Poitras, C. B.

L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref] [PubMed]

Poon, A. W.

Post, E.

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

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S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

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Santori, C. M.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Schmid, J. H.

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

Schreiber, R. S.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Shacham, A.

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic Networks-on-Chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57(9), 1246–1260 (2008).
[Crossref]

Shao, H.

Shi, Y.

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M. Grajower, G. M. Lerman, I. Goykhman, B. Desiatov, A. Yanai, D. R. Smith, and U. Levy, “Subwavelength plasmonics for graded-index optics on a chip,” Opt. Lett. 38(18), 3492–3495 (2013).
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[Crossref] [PubMed]

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Spillane, S. M.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

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J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Verluise, F.

Vuckovic, J.

Wada, N.

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J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

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F.-C. H. M.-C. Wu, “Adiabatic mode conversion in multimode waveguides using chirped computer-generated planar holograms,” IEEE Photon. Technol. Lett. 23, 807–809 (2011).

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S.-Y. Tseng and M.-C. Wu, “Adiabatic mode conversion in multimode waveguides using computer-generated planar holograms,” IEEE Photon. Technol. Lett. 22(16), 1211–1213 (2010).
[Crossref]

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J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
[Crossref] [PubMed]

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Y. Huang, G. Xu, and S.-T. Ho, “An ultracompact optical mode order converter,” IEEE Photon. Technol. Lett. 18(21), 2281–2283 (2006).
[Crossref]

Xu, J.

Xu, Q.

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

Yanai, A.

Yang, J.

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Yu, H.

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Adv. Opt. Technol. (1)

J. H. Schmid, P. Cheben, S. Janz, J. Lapointe, E. Post, A. Ge, A. Densmore, B. Lamontagne, P. Waldron, and D.-X. Xu, “Subwavelength grating structures in silicon-on-insulator waveguides,” Adv. Opt. Technol. 2008, e685489 (2008).

Appl. Opt. (2)

Appl. Phys., A Mater. Sci. Process. (1)

J. Ahn, M. Fiorentino, R. G. Beausoleil, N. Binkert, A. Davis, D. Fattal, N. P. Jouppi, M. McLaren, C. M. Santori, R. S. Schreiber, S. M. Spillane, D. Vantrease, and Q. Xu, “Devices and architectures for photonic chip-scale integration,” Appl. Phys., A Mater. Sci. Process. 95(4), 989–997 (2009).
[Crossref]

IEEE Photon. Technol. Lett. (4)

M. Blau and D. M. Marom, “Optimization of spatial aperture-sampled mode multiplexer for a three-mode fiber,” IEEE Photon. Technol. Lett. 24(23), 2101–2104 (2012).
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F.-C. H. M.-C. Wu, “Adiabatic mode conversion in multimode waveguides using chirped computer-generated planar holograms,” IEEE Photon. Technol. Lett. 23, 807–809 (2011).

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Y. Huang, G. Xu, and S.-T. Ho, “An ultracompact optical mode order converter,” IEEE Photon. Technol. Lett. 18(21), 2281–2283 (2006).
[Crossref]

IEEE Trans. Comput. (1)

A. Shacham, K. Bergman, and L. P. Carloni, “Photonic Networks-on-Chip for future generations of chip multiprocessors,” IEEE Trans. Comput. 57(9), 1246–1260 (2008).
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J. Lightwave Technol. (4)

J. Opt. Soc. Am. A (1)

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B. Desiatov, I. Goykhman, and U. Levy, “Nanoscale mode selector in silicon waveguide for on chip nanofocusing applications,” Nano Lett. 9(10), 3381–3386 (2009).
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Nat. Commun. (1)

L.-W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
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Science (1)

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Figures (10)

Fig. 1
Fig. 1 (a) Schematic representation of the refractive index in the proposed device. Input and output waveguides have a constant refractive index of Si (3.46), while the converter section consists of a periodic variation in the propagation direction (z-axis) and has a graded index profile in the transverse direction (x-axis). The simulated modes are super imposed on the physical structure. (b) 3D conceptual model of the proposed mode converter. Si fraction relative to air varies across the x-axis and creates the required graded index profile along that direction. (c) Schematic representation of a waveguide with a graded index profile. Light propagates along the z axis while being confined in the core layer n1. The duty cycle of the alternating layers n1 and n2 varies along the x axis in order to spatially control the effective index in that direction.

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Fig. 2
Fig. 2 (a) Waveguide cross section, (b-c) normalized Eŷ field amplitude of the modes to be coupled.

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Fig. 3
Fig. 3 TM0 to TM3 mode conversion with a graded index sinusoidal grating - (a) Refractive index profile of the device. The right and left uniform sections represent the input and output waveguides, and the intermediate segment between them is the converter section; (b) Analytic calculation of the power exchange between the two modes; (c) 3D FDTD simulation showing the Ey field (out of plane) propagation in the device.

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Fig. 4
Fig. 4 TM0 to TM3 mode conversion with graded index sinusoidal grating - (a) Refractive index profile of the device. The right and left uniform sections represent the input and output waveguides, and the intermediate segment between them is the converter section; (b) 3D FDTD simulation showing the Ey field propagation in the device. Simulation parameters are the same as in Fig. 3 except for the converter length which is now restricted to 6μm (corresponding to the first complete power exchange location in Fig. 3). Dashed lines mark the converter section.

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Fig. 5
Fig. 5 TM0 to TM3 mode conversion with graded index rectangular grating - (a) Refractive index profile of the device. The right and left uniform sections are the input and output waveguides, and the intermediate segment between them is the converter section; (b) Analytic calculation of the power exchange between the two modes; (c) 3D FDTD simulation of the Ey field (out of plane) propagation in the device.

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Fig. 6
Fig. 6 Mapping between the EMT based graded index profile and the physical structure. (a) the desired refractive index profile (identical to Fig. 5(a); (b) the physical binary grating structure; (c) the obtained discrete refractive index profile.

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Fig. 7
Fig. 7 3D conceptual model of the proposed device.

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Fig. 8
Fig. 8 TM0 to TM3 mode conversion with EMT based graded index rectangular grating - (a) Refractive index profile of the device. The right and left uniform sections represent the input and output waveguides, and the intermediate segment between them is the converter section; (b) 3D FDTD simulation of the Ey field (out of plane) propagation in the device; (c) Analytic calculation of the power exchange between the two modes.

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Fig. 9
Fig. 9 Mode purity, transmission and crosstalk vs. wavelength for the TM0 to TM3 mode converter.

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Fig. 10
Fig. 10 TM0 to TM1 and TM2 mode conversion with EMT based graded index rectangular grating - (a) 3D FDTD simulation of the Ey field (out of plane) propogation in a TM0 to TM1 mode converter. Simulation parameters are: n0 = 3.35, Δnmax = 0.055, Λ = 100nm, etching depth of 50nm, δ = 5.3μm, DC = 50%, and converter length of 20μm. (b) 3D FDTD simulation showing the Ey field (out of plane) propogation in a TM0 to TM2 mode converter. Simulation parameters are: n0 = 3.35, Δnmax = 0.055, Λ = 200nm, etching depth of 50nm, δ = 7μm, DC = 50%, and converter length of 19μm.

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Tables (1)

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Table 1 Comparison between the ‘ideal’ structures and the real device

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Equations (16)

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n TE ( 0 ) = f n 1 2 +( 1−f ) n 2 2
n TE ( 2 ) = [ n TE ( 0 ) ] 2 + 1 3 [ Λ λ πf( 1−f )( n 1 2 − n 2 2 ) ] 2
n TM ( 0 ) = n 1 2 ⋅ n 2 2 f n 2 2 +( 1−f ) n 1 2
n TM ( 2 ) = [ n TM ( 0 ) ] 2 + 1 3 [ Λ λ πf( 1−f )( 1 n 1 2 − 1 n 2 2 )⋅[ n TE ( 0 ) ]⋅ [ n TM ( 0 ) ] 3 ] 2
n( x,y,z )= n 0 +Δn( x,y,z )= n 0 +Δn( x,y )⋅exp[ i( β m − β j )z ]+c.c.
Δ n ˜ sin ( q=0 ) =0     ;     Δ n ˜ sin ( q=1 ) =Δn( x,y )
Δn( x,y )=Δ n max ⋅ [ E y TM0 ( x,y=0 ) ] * ⋅ E y TM3 ( x,y=0 )
Δ n ˜ rect ( q=0 ) =( 2⋅DC−1 )⋅Δn( x,y )      ;      Δ n ˜ rect ( q=1 ) =2Δn( x,y )⋅DC⋅sinc ( π⋅DC )
ε( x,y,z )= ε 0 ( x,y,z )+Δε( x,y,z )
E( x,y,z,t )= ∑ 1 M A m ( z ) E m ( x,y ) e i( ωt− β m z )
d dz A m =−i ∑ j ∑ q κ mj ( q ) A j e i( β m − β j − q2π δ )z
κ mj ( q ) = ω 4 ∫ −∞ ∞ ∫ −∞ ∞ E m * ( x,y )⋅Δ ε ˜ ( q ) ( x,y )⋅ E j ( x,y )  dxdy
κ mj ( q ) = ω ∈ 0 n 0 2 ∫ −∞ ∞ ∫ −∞ ∞ E m * ( x,y )⋅Δ n ˜ ( q ) ( x,y )⋅ E j ( x,y )  dxdy
κ mj ( q=1 ) = ω ∈ 0 n 0 2 ∫ −∞ ∞ ∫ −∞ ∞ Δ n max ⋅ | E m ( x,y ) | 2 ⋅ | E j ( x,y ) | 2   dxdy
A 1 ( z )=cos( sz )⋅ A 1 ( 0 )−i κ 12 ( q ) s sin( sz )⋅ A 2 ( 0 )
A 2 ( z )=−i κ 12 ( q )* s sin( sz )⋅ A 1 ( 0 )+cos( sz )⋅ A 2 ( 0 )

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