Abstract

We have designed and for the first time experimentally verified a topology optimized mode converter with a footprint of ~6.3 μm × ~3.6 μm which converts the fundamental even mode to the higher order odd mode of a dispersion engineered photonic crystal waveguide. 2D and 3D topology optimization is utilized and both schemes result in designs theoretically showing an extinction ratio larger than 21 dB. The 3D optimized design has an experimentally estimated insertion loss lower than ~2 dB in an ~43 nm bandwidth. The mode conversion is experimentally confirmed in this wavelength range by recording mode profiles using vertical grating couplers and an infrared camera. The experimentally determined extinction ratio is > 12 dB and is believed to be limited by the spatial resolution of our setup.

© 2014 Optical Society of America

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2014 (2)

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Time domain topology optimization of 3D nanophotonic devices,” Photon. Nanostruct. Fund. Appl. 12(1), 23–33 (2014).
[CrossRef]

B. Wohlfeil, S. Burger, C. Stamatiadis, J. Pomplun, F. Schmidt, L. Zimmermann, K. Petermann, “Numerical simulation of grating couplers for mode multiplexed systems,” Proc. SPIE 8988, 89880K (2014).
[CrossRef]

2013 (1)

2012 (3)

2011 (1)

J. S. Jensen, O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5(2), 308–321 (2011), doi:.
[CrossRef]

2010 (1)

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

2008 (1)

2006 (2)

2005 (1)

2004 (1)

2003 (1)

2001 (1)

1988 (1)

M. P. Bendsøe, N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods Appl. Mech. Eng. 71(2), 197–224 (1988).
[CrossRef]

Bendsøe, M. P.

M. P. Bendsøe, N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods Appl. Mech. Eng. 71(2), 197–224 (1988).
[CrossRef]

Borel, P. I.

Burger, S.

B. Wohlfeil, S. Burger, C. Stamatiadis, J. Pomplun, F. Schmidt, L. Zimmermann, K. Petermann, “Numerical simulation of grating couplers for mode multiplexed systems,” Proc. SPIE 8988, 89880K (2014).
[CrossRef]

Chen, G.

Da Ros, F.

Ding, Y.

Elesin, Y.

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Time domain topology optimization of 3D nanophotonic devices,” Photon. Nanostruct. Fund. Appl. 12(1), 23–33 (2014).
[CrossRef]

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[CrossRef]

Fage-Pedersen, J.

Fan, S.

Frandsen, L. H.

Gomez-Iglesias, A.

Harpøth, A.

Ho, S.-T.

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

Huang, B.

Huang, Y.

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

Hvam, J. M.

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

Jensen, J. S.

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Time domain topology optimization of 3D nanophotonic devices,” Photon. Nanostruct. Fund. Appl. 12(1), 23–33 (2014).
[CrossRef]

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[CrossRef]

J. S. Jensen, O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5(2), 308–321 (2011), doi:.
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12(9), 1996–2001 (2004).
[CrossRef] [PubMed]

Joannopoulos, J.

Johnson, S.

Kang, J. U.

Kikuchi, N.

M. P. Bendsøe, N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods Appl. Mech. Eng. 71(2), 197–224 (1988).
[CrossRef]

Krauss, T. F.

Kristensen, M.

Lavrinenko, A. V.

Lazarov, B. S.

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Time domain topology optimization of 3D nanophotonic devices,” Photon. Nanostruct. Fund. Appl. 12(1), 23–33 (2014).
[CrossRef]

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[CrossRef]

Lee, B. T.

Li, J.

Liu, L.

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

Liu, V.

Lu, J.

Miller, D. A. B.

O’Faolain, L.

Ou, H.

Y. Ding, J. Xu, F. Da Ros, B. Huang, H. Ou, C. Peucheret, “On-chip two-mode division multiplexing using tapered directional coupler-based mode multiplexer and demultiplexer,” Opt. Express 21(8), 10376–10382 (2013).
[CrossRef] [PubMed]

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

Petermann, K.

B. Wohlfeil, S. Burger, C. Stamatiadis, J. Pomplun, F. Schmidt, L. Zimmermann, K. Petermann, “Numerical simulation of grating couplers for mode multiplexed systems,” Proc. SPIE 8988, 89880K (2014).
[CrossRef]

Peucheret, C.

Pomplun, J.

B. Wohlfeil, S. Burger, C. Stamatiadis, J. Pomplun, F. Schmidt, L. Zimmermann, K. Petermann, “Numerical simulation of grating couplers for mode multiplexed systems,” Proc. SPIE 8988, 89880K (2014).
[CrossRef]

Pu, M.

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

Schmidt, F.

B. Wohlfeil, S. Burger, C. Stamatiadis, J. Pomplun, F. Schmidt, L. Zimmermann, K. Petermann, “Numerical simulation of grating couplers for mode multiplexed systems,” Proc. SPIE 8988, 89880K (2014).
[CrossRef]

Shi, P.

Shin, S. Y.

Sigmund, O.

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Time domain topology optimization of 3D nanophotonic devices,” Photon. Nanostruct. Fund. Appl. 12(1), 23–33 (2014).
[CrossRef]

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[CrossRef]

J. S. Jensen, O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5(2), 308–321 (2011), doi:.
[CrossRef]

P. I. Borel, A. Harpøth, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, O. Sigmund, “Topology optimization and fabrication of photonic crystal structures,” Opt. Express 12(9), 1996–2001 (2004).
[CrossRef] [PubMed]

Stamatiadis, C.

B. Wohlfeil, S. Burger, C. Stamatiadis, J. Pomplun, F. Schmidt, L. Zimmermann, K. Petermann, “Numerical simulation of grating couplers for mode multiplexed systems,” Proc. SPIE 8988, 89880K (2014).
[CrossRef]

Vuckovic, J.

White, T. P.

Wohlfeil, B.

B. Wohlfeil, S. Burger, C. Stamatiadis, J. Pomplun, F. Schmidt, L. Zimmermann, K. Petermann, “Numerical simulation of grating couplers for mode multiplexed systems,” Proc. SPIE 8988, 89880K (2014).
[CrossRef]

Xu, G.

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

Xu, J.

Yvind, K.

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

Zimmermann, L.

B. Wohlfeil, S. Burger, C. Stamatiadis, J. Pomplun, F. Schmidt, L. Zimmermann, K. Petermann, “Numerical simulation of grating couplers for mode multiplexed systems,” Proc. SPIE 8988, 89880K (2014).
[CrossRef]

Comput. Methods Appl. Mech. Eng. (1)

M. P. Bendsøe, N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method,” Comput. Methods Appl. Mech. Eng. 71(2), 197–224 (1988).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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

Laser Photon. Rev. (1)

J. S. Jensen, O. Sigmund, “Topology optimization for nano-photonics,” Laser Photon. Rev. 5(2), 308–321 (2011), doi:.
[CrossRef]

Opt. Commun. (1)

M. Pu, L. Liu, H. Ou, K. Yvind, 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 (7)

Opt. Lett. (2)

Photon. Nanostruct. Fund. Appl. (2)

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Design of robust and efficient photonic switches using topology optimization,” Photon. Nanostruct. Fund. Appl. 10(1), 153–165 (2012).
[CrossRef]

Y. Elesin, B. S. Lazarov, J. S. Jensen, O. Sigmund, “Time domain topology optimization of 3D nanophotonic devices,” Photon. Nanostruct. Fund. Appl. 12(1), 23–33 (2014).
[CrossRef]

Proc. SPIE (1)

B. Wohlfeil, S. Burger, C. Stamatiadis, J. Pomplun, F. Schmidt, L. Zimmermann, K. Petermann, “Numerical simulation of grating couplers for mode multiplexed systems,” Proc. SPIE 8988, 89880K (2014).
[CrossRef]

Other (2)

L. Luo, L. H. Gabrielli, and M. Lipson, “On-chip mode-division multiplexer,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper CTh1C.6.

Y. Ding, H. Ou, J. Xu, M. Xiong, and C. Peucheret, “On-chip mode multiplexer based on a single grating coupler,” in Proceedings of IEEE Photonics Conference (Institute of Electrical and Electronics Engineers, 2012), pp. 707–708.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Sketch of the PhCW design. (b) The 2D banddiagram showing that with D2>D, the TE1 mode (cyan cross) can be made monotonic (blue circle) in an ~45 nm bandwidth (grey) while the fundamental TE0 (pink cross and red circle) is left unchanged. For the calculation of the 2D banddiagram we used an equivalent slab waveguide index of 2.983. (c) Mode profiles for the TE0 (red) and TE1 (blue) mode.

Fig. 2
Fig. 2

(a) PhCW with arbitrarily chosen design domain (green) used in the TO. (b) PhCW with standard butt coupling interfaces and design domain (green) for optimizing the output coupling of the TE1 mode to the PhW. (c, d) PhCW TE0-TE1 mode converter with optimized output couplers obtained utilizing (c) 2D and (d) 3D TO.

Fig. 3
Fig. 3

(a) 3D FDTD-calculated transmission spectra for the 2D TopOpt (red square) and 3D TopOpt (blue circle) mode converter with TopOpt output coupling interfaces. Also shown is the spectrum for the 3D TopOpt converter having a butt coupling output interface (orange triangle). All spectra are normalized to TE0 transmission in a PhW. The inset shows the power flux recorded in the output PhW for the 3D TopOpt mode converter as a function of the relative position across the PhW with 0 nm being the center. (b) 3D FDTD-calculated propagation of the Hz-field through the 3D TopOpt mode converter from Fig. 2(d) calculated near maximum transmission at 1545 nm.

Fig. 4
Fig. 4

SEM image of the fabricated PhCW 3D TopOpt (a) TE0-TE1 mode converter and the (b) TE0-TE1-TE0 mode converter. The latter has been overlaid with the 3D FDTD-calculated Hz-field at 1530 nm for the fabricated structure.

Fig. 5
Fig. 5

Measured transmission spectrum for the 3D TopOpt X2 mode converter (black) normalized to TE0 transmission through a PhW. The corresponding 3D-FDTD calculated spectrum (blue-circle) is also shown.

Fig. 6
Fig. 6

(a) Configuration for measuring mode profiles of the X1 and X2 mode converters. (b) Mode profiles recorded for the 3D TopOpt mode converter at different wavelengths. The top row is for the X1 converter and the bottom row is for the X2 converter. (c) Line scans across the mode profiles for the 3D TopOpt X1 mode converter as a function of the relative position in the grating with 0 μm being the center of the grating.

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