Abstract

We present an algorithm for designing high efficiency (∼98%), small-footprint (1.5–4 square vacuum wavelengths) couplers between arbitrary nanophotonic waveguide modes in two dimensions. Our “objective-first” method is computationally fast (15 minutes on a single-core personal computer), requires no trial-and-error, and does not require guessing a good starting design. We demonstrate designs for various coupling problems which suggest that our method allows for the design of any single-mode, linear optical device.

© 2012 OSA

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  1. Y. Tang, Z. Wang, L. Wosinski, U. Westergren, S. He, “Highly efficient nonuniform grating coupler for silicon-on-insulator nanophotonic circuits,” Opt. Lett. 35, 1290–1292 (2010).
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    [PubMed]
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    [PubMed]
  8. G. Veronis, S. Fan, “Theoretical investigations of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides,” Opt. Express 15, 1211–1221 (2007).
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  9. R. Yang, R. A. Wahsheh, Z. Lu, M. A. G. Abushagur, “Efficient light coupling between dielectric slot waveguide and plasmonic slot waveguide,” Opt. Lett. 35, 649–651 (2010).
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  10. www.github.com/JesseLu/objective-first

2011

2010

2008

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. S. Ly-Gagnon, K. C. Saraswat, D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).

2007

2005

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[PubMed]

M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23, 4222–4238 (2005).

2001

Abushagur, M. A. G.

Baets, R.

Boyd, S.

Cerrina, F.

Di Cioccio, L.

Fan, S.

Fedeli, J.-M.

Hamann, H. F.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[PubMed]

He, S.

Kimerling, L.C.

Kocabas, S. E.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. S. Ly-Gagnon, K. C. Saraswat, D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).

Lagahe, C.

Latif, S.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. S. Ly-Gagnon, K. C. Saraswat, D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).

Lee, K. K.

Lim, D. R.

Lipson, M.

Lu, J.

Lu, Z.

Ly-Gagnon, D. S.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. S. Ly-Gagnon, K. C. Saraswat, D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).

McNab, S. J.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[PubMed]

Miller, D. A. B.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. S. Ly-Gagnon, K. C. Saraswat, D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).

O’Boyle, M.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[PubMed]

Okyay, A. K.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. S. Ly-Gagnon, K. C. Saraswat, D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).

Regreny, P.

Rojo Romeo, P.

Saraswat, K. C.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. S. Ly-Gagnon, K. C. Saraswat, D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).

Seassal, C.

Shin, J.

Tang, L.

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. S. Ly-Gagnon, K. C. Saraswat, D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).

Tang, Y.

Van Campenhout, J.

Van Thourhout, D.

Veronis, G.

Verstuyft, S.

Vlasov, Y. A.

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[PubMed]

Vuckovic, J.

Wahsheh, R. A.

Wang, Z.

Westergren, U.

Wosinski, L.

Yang, R.

J. Lightwave Technol.

Nat. Photonics

L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D. S. Ly-Gagnon, K. C. Saraswat, D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2, 226–229 (2008).

Nature

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[PubMed]

Opt. Express

Opt. Lett.

Other

www.github.com/JesseLu/objective-first

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Figures (22)

Fig. 1
Fig. 1

Boundary-value formulation of the design objective. The values of H z perfect , defined along the dashed box surrounding the design area (coupling structure), are shown in orange. The values of H z perfect along the top and bottom edges of the dashed box are set to zero. In this schematic, the fundamental and second-order waveguide modes have been chosen as the input and output modes respectively.

Fig. 2
Fig. 2

Coupler from a narrow, high-index (ε = 12.25) waveguide to a wide, low-index (ε = 2.25) waveguide. The H z perfect boundary values used as the design objective are shown in the upper-left plots, the generated structure is shown in the upper-right plot, and the simulated Hz fields of the device are shown in the bottom two plots. The computed efficiency of the coupler is high, 99.8%, and the device is also extremely compact, convering only 36 × 76 grid points, where the vacuum wavelength is 42 grid points (footprint of 1.55 square vacuum wavelengths). Computation time was 15 minutes on a personal computer.

Fig. 3
Fig. 3

Coupler that converts the fundamental waveguide mode to the second-order waveguide mode. This problem is quite difficult since the two modes are of opposite symmetry. For example, adiabatic approaches cannot be applied to this case. However, our method produces a device (which has the same dimensions and vacuum wavelength as Fig. 2) with a coupling efficiency of 98.0%. Computation time was 15 minutes on a personal computer.

Fig. 4
Fig. 4

Coupler between a dielectric slab waveguide to an air-core waveguide. Here, not only are the modes of opposite symmetry, but the output waveguide operates on a fundamentally different principle (distributed reflection) than the input waveguide (index guided). The device still achieves an efficiency of 98.9%, demonstrating the versatility of our method. The vacuum wavelength is 25 grid points, while the device footprint is still 36 × 76 grid points (footprint of 4.38 square vacuum wavelengths). Computation time was 15 minutes on a personal computer.

Fig. 5
Fig. 5

Coupler between a dielectric slab waveguide to a plasmonic metal-insulator-metal waveguide. The efficiency of the device is 97.5% and has the same wavelength and footprint as the device in Fig. 4. Computation time was 15 minutes on a personal computer.

Fig. 6
Fig. 6

Coupler between a dielectric slab waveguide to a plasmonic wire waveguide. The efficiency of the device is 99.1% and has the same wavelength and footprint as the device in Fig. 4. Computation time was 15 minutes on a personal computer.

Fig. 7
Fig. 7

Coupler from the first-order to the second-order mode of a wide dielectric waveguide. Efficiency: 99.3%, footprint: 1.55 square vacuum wavelengths.

Fig. 8
Fig. 8

Coupler from the first-order to the third-order mode of a wide dielectric waveguide. Efficiency: 98.3%, footprint: 1.55 square vacuum wavelengths.

Fig. 9
Fig. 9

Coupler from the first-order to the fourth-order mode of a wide dielectric waveguide. Efficiency: 90.6%, footprint: 1.55 square vacuum wavelengths.

Fig. 10
Fig. 10

Coupler from the second-order to the third-order mode of a wide dielectric waveguide. Efficiency: 96.8%, footprint: 1.55 square vacuum wavelengths.

Fig. 11
Fig. 11

Coupler from the second-order to the fourth-order mode of a wide dielectric waveguide. Efficiency: 86.3%, footprint: 1.55 square vacuum wavelengths.

Fig. 12
Fig. 12

Coupler from the third-order to the fourth-order mode of a wide dielectric waveguide. Efficiency: 80.1%, footprint: 1.55 square vacuum wavelengths.

Fig. 13
Fig. 13

Coupler from a wide, low-index waveguide to the second-order mode of a narrow, high-index waveguide. Efficiency: 96.9%, footprint: 1.55 square vacuum wavelengths.

Fig. 14
Fig. 14

Coupler from a wide, low-index waveguide to an “air-core” waveguide mode. Efficiency: 99.0%, footprint: 4.38 square vacuum wavelengths.

Fig. 15
Fig. 15

Coupler from a wide, low-index waveguide to a metal-insulator-metal plasmonic waveguide mode. Efficiency: 96.7%, footprint: 4.38 square vacuum wavelengths.

Fig. 16
Fig. 16

Coupler from a wide, low-index waveguide to a plasmonic wire waveguide mode. Efficiency: 99.7%, footprint: 4.38 square vacuum wavelengths.

Fig. 17
Fig. 17

Coupler from a dielectric waveguide to the lowest branch of a set of five plasmonic wire waveguides. Efficiency: 94.0%, footprint: 4.38 square vacuum wavelengths.

Fig. 18
Fig. 18

Coupler from a dielectric waveguide to the second branch of a set of five plasmonic wire waveguides. Efficiency: 97.3%, footprint: 4.38 square vacuum wavelengths.

Fig. 19
Fig. 19

Coupler from a dielectric waveguide to the middle branch of a set of five plasmonic wire waveguides. Efficiency: 98.5%, footprint: 4.38 square vacuum wavelengths.

Fig. 20
Fig. 20

Coupler from a dielectric waveguide to the middle branch of a set of five plasmonic metal-insulator-metal waveguides. Efficiency: 97.7%, footprint: 4.38 square vacuum wavelengths.

Fig. 21
Fig. 21

Coupler from a dielectric waveguide to the fourth branch of a set of five plasmonic metal-insulator-metal waveguides. Efficiency: 95.6%, footprint: 4.38 square vacuum wavelengths.

Fig. 22
Fig. 22

Coupler from a dielectric waveguide to the uppermost branch of a set of five plasmonic metal-insulator-metal waveguides. Efficiency: 87.5%, footprint: 4.38 square vacuum wavelengths.

Equations (7)

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decrease f ( x )
subject to g ( x , p ) = 0 ,
decrease g ( x , p ) 2
subject to f ( x ) = 0 ,
g ( x , p ) 2 = g ( H z , ε 1 ) 2 = × ε 1 × H z μ 0 ω 2 H z 2 ,
f ( x ) = f ( H z ) = [ H z H z perfect H z n H z perfect n ] boundary = 0 ,
ε 0 ε ε silicon .

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