Abstract

A novel concept for an all-dielectric unidirectional output double-grating coupler is proposed and rigorously analyzed. In addition to a superstrate side grating, a second grating is placed on the substrate side. The periodicities of the gratings are chosen such that no propagating diffracted orders are present outside the structure in the superstrate region and only a single order is present outside the structure in the substrate region. The concept provides a robust output coupler requiring neither phase-matching between gratings nor any resonances in the structure, and is very tolerant to potential fabrication errors. Up to 96% coupling efficiency from the substrate-side grating is obtained over a wide range of grating properties.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Tamir, ed., Integrated Optics (Springer-Verlag, New York, 1975).
  2. V. R. Almeida, R. R. Panepucci, and M. Lipson, "Nanotaper for compact mode conversion," Opt. Lett. 28, 1302-1304 (2003).
    [CrossRef] [PubMed]
  3. T. P. Felici, and D. F. G. Gallagher, "Improved waveguide structures derived from new rapid optimization techniques," in Physics and Simulation of Optoelectronic Devices XI, M. Osinski, H. Amano, P. Blood, eds., Proc. SPIE 4986, 375-385 (2003).
    [CrossRef]
  4. B. Luyssaert, P. Bienstman, P. Vandersteegen, P. Dumon, and R. Baets, "Efficient nonadiabatic planar waveguide tapers," J. Lightwave Technol. 23, 2462-2468 (2005).
    [CrossRef]
  5. L. Vaissie, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
    [CrossRef]
  6. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
    [CrossRef]
  7. E. G. Johnson, O. V. Smolski, J. K. O'Daniel, A. Mehta, K. Shavitranuruk, P. Srinivasan, and M. G. Moharam, "Micro- and Nano-Optics in Surface Emitting Lasers," in Nanophotonics (OSA, Uncasville, CT, USA, 2006).
  8. J. K. O'Daniel, O. V. Smolski, M. G. Moharam, and E. G. Johnson, "Integrated wavelength stabilization of in-plane semiconductor lasers by use of a dual-grating reflector," Opt. Lett. 31, 211-213 (2006).
    [CrossRef] [PubMed]
  9. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995).
    [CrossRef]
  10. E. Silberstein, P. Lalanne, J. P. Hugonin, and Q. Cao, "Use of grating theories in integrated optics," J. Opt. Soc. Am. A 18, 2865-2875 (2001).
    [CrossRef]
  11. L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 16, 17 (1996).
  12. M. G. Moharam, and A. B. Greenwell, "Efficient rigorous calculations of power flow in grating coupled surface-emitting devices," in Photon Management, F. Wyrowski; ed., Proc. SPIE 5456, 57 (2004).
    [CrossRef]
  13. P. Dong, and A. G. Kirk, "Compact double-grating coupler between vertically stacked silicon-on-insulator waveguides," Appl. Opt. 44, 7540-7547 (2005).
    [CrossRef] [PubMed]
  14. Q. Cao, P. Lalanne, and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A 19, 335-338 (2002).
    [CrossRef]
  15. P. Lalanne, and J. P. Hugonin, "Bloch-wave engineering for high-Q, small-V microcavities," IEEE J. Quantum Electron., 39, 1430-1438 (2003).
    [CrossRef]

2006 (1)

2005 (3)

2004 (1)

M. G. Moharam, and A. B. Greenwell, "Efficient rigorous calculations of power flow in grating coupled surface-emitting devices," in Photon Management, F. Wyrowski; ed., Proc. SPIE 5456, 57 (2004).
[CrossRef]

2003 (2)

V. R. Almeida, R. R. Panepucci, and M. Lipson, "Nanotaper for compact mode conversion," Opt. Lett. 28, 1302-1304 (2003).
[CrossRef] [PubMed]

P. Lalanne, and J. P. Hugonin, "Bloch-wave engineering for high-Q, small-V microcavities," IEEE J. Quantum Electron., 39, 1430-1438 (2003).
[CrossRef]

2002 (2)

Q. Cao, P. Lalanne, and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A 19, 335-338 (2002).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

2001 (1)

1996 (1)

1995 (1)

Almeida, V. R.

Baets, R.

B. Luyssaert, P. Bienstman, P. Vandersteegen, P. Dumon, and R. Baets, "Efficient nonadiabatic planar waveguide tapers," J. Lightwave Technol. 23, 2462-2468 (2005).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Bienstman, P.

B. Luyssaert, P. Bienstman, P. Vandersteegen, P. Dumon, and R. Baets, "Efficient nonadiabatic planar waveguide tapers," J. Lightwave Technol. 23, 2462-2468 (2005).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Bogaerts, W.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Cao, Q.

De Mesel, K.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Dong, P.

Dumon, P.

Gaylord, T. K.

Grann, E. B.

Greenwell, A. B.

M. G. Moharam, and A. B. Greenwell, "Efficient rigorous calculations of power flow in grating coupled surface-emitting devices," in Photon Management, F. Wyrowski; ed., Proc. SPIE 5456, 57 (2004).
[CrossRef]

Hugonin, J. P.

Johnson, E. G.

J. K. O'Daniel, O. V. Smolski, M. G. Moharam, and E. G. Johnson, "Integrated wavelength stabilization of in-plane semiconductor lasers by use of a dual-grating reflector," Opt. Lett. 31, 211-213 (2006).
[CrossRef] [PubMed]

L. Vaissie, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

Kirk, A. G.

Krauss, T. F.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Lalanne, P.

Li, L.

Lipson, M.

Luyssaert, B.

Mehta, A.

L. Vaissie, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

Moerman, I.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Moharam, M. G.

O'Daniel, J. K.

Panepucci, R. R.

Pommet, D. A.

Silberstein, E.

Smolski, O. V.

J. K. O'Daniel, O. V. Smolski, M. G. Moharam, and E. G. Johnson, "Integrated wavelength stabilization of in-plane semiconductor lasers by use of a dual-grating reflector," Opt. Lett. 31, 211-213 (2006).
[CrossRef] [PubMed]

L. Vaissie, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

Taillaert, D.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Vaissie, L.

L. Vaissie, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

Van Daele, P.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Vandersteegen, P.

Verstuyft, S.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

P. Lalanne, and J. P. Hugonin, "Bloch-wave engineering for high-Q, small-V microcavities," IEEE J. Quantum Electron., 39, 1430-1438 (2003).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling betweencompact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

L. Vaissie, O. V. Smolski, A. Mehta, and E. G. Johnson, "High efficiency surface-emitting laser with subwavelength antireflection structure," IEEE Photon. Technol. Lett. 17, 732-734 (2005).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (4)

Opt. Lett. (2)

Proc. SPIE (1)

M. G. Moharam, and A. B. Greenwell, "Efficient rigorous calculations of power flow in grating coupled surface-emitting devices," in Photon Management, F. Wyrowski; ed., Proc. SPIE 5456, 57 (2004).
[CrossRef]

Other (3)

E. G. Johnson, O. V. Smolski, J. K. O'Daniel, A. Mehta, K. Shavitranuruk, P. Srinivasan, and M. G. Moharam, "Micro- and Nano-Optics in Surface Emitting Lasers," in Nanophotonics (OSA, Uncasville, CT, USA, 2006).

T. P. Felici, and D. F. G. Gallagher, "Improved waveguide structures derived from new rapid optimization techniques," in Physics and Simulation of Optoelectronic Devices XI, M. Osinski, H. Amano, P. Blood, eds., Proc. SPIE 4986, 375-385 (2003).
[CrossRef]

T. Tamir, ed., Integrated Optics (Springer-Verlag, New York, 1975).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1.
Fig. 1.

Power flow in a single surface grating with a 275 nm period, 250 nm depth, and 50% fill factor, which shows the splitting of diffracted energy between a substrate region (70%) and a superstrate region (30%). (a). Transverse power flow over the entire computational window. (b). Transverse power flow near the initial grating interface. (c).-(d). 3D view of transverse and normal power flow showing the power magnitude.

Fig. 2.
Fig. 2.

A simple drawing of the dual grating output coupler device considered in this study, as well as the principal directions of energy flow in the structure.

Fig. 3.
Fig. 3.

The normalized longitudinal Poynting vector component and refractive index distribution of the single mode waveguide showing both location and size of the graded index section relative to the substrate and the power distribution within the graded index section.

Fig. 4.
Fig. 4.

The output diffracted angle in air vs. the substrate grating period, for substrate index of nsub = 3.24, and a superstrate grating period of (a) 225 nm. and (b) 148 nm.

Fig. 5.
Fig. 5.

A sketch showing the computational and power collection windows for both a single surface grating with an “infinite” substrate and a dual grating coupler. Dotted lines represent interfaces used to define layer scattering matrices.

Fig. 6.
Fig. 6.

(a). Real part and (b). imaginary part of the Bloch mode index of the fundamental mode in the superstrate grating vs. superstrate grating period for various grating thicknesses.

Fig. 7.
Fig. 7.

Power flow in a single surface grating (a) Transverse power flow over the length of the coupler (b) Transverse power flow near the initial grating interface. (c)-(d) 3D view of transverse and normal power flow showing the power magnitude.

Fig. 8.
Fig. 8.

Contour plot showing the effects of varying grating period and grating depth on the 1st order Transmission efficiency for an infinite binary grating with an input refractive index, ninput = 3.24, an output refractive index, noutput = 1, a grating tooth refractive index of nridge = 3.24, a grating groove refractive index, ngroove = 1, an input angle, θinput = −19.83°, and a grating fill factor of 30%.

Fig. 9.
Fig. 9.

Contour plot showing the effects of varying the half-height grating fill factor and grating tooth sidewall angle on the 1st order Transmission efficiency for an infinite binary grating with an input refractive index, ninput = 3.24, an output refractive index, noutput = 1, a grating tooth refractive index of nridge = 3.24, a grating groove refractive index, ngroove = 1, an input angle, θinput = −19.83°, a grating period of 586.66 nm, and a grating depth of 260 nm. Sloped sidewalls are approximated by an 8 level staircase profile. White background regions with a fill factor less than 67% represent gratings with triangular teeth which were not considered.

Fig. 10.
Fig. 10.

(a). Relationship between substrate thickness/grating separation and fractional substrate output coupling. Resonances indicate coupling to higher order super-modes of the entire waveguide stack. (b). Sum of the reflection into all individual modes at the computational window’s input interface.

Fig. 11.
Fig. 11.

Substrate output power coupling vs. (a) the superstrate grating thickness and (b) the substrate grating thickness.

Fig. 12.
Fig. 12.

Map showing the effects of varying the half-height grating fill factor and grating tooth sidewall angle on the substrate output power coupling for the dual grating coupler. As in Fig. 9, the white background regions with a fill factor less than 67% represent gratings with triangular teeth which were not considered.

Fig. 13.
Fig. 13.

Power flow in a dual grating coupler with a superstrate grating having a 220 nm period, 250 nm depth, and 50% fill factor, and a substrate grating having a 586.67 nm period, a 260 nm depth, and a 30% fill factor, which show the splitting of diffracted energy between the substrate region (96%) and superstrate region (~2%). (a) Transverse power flow over the entire computational window. (b) Transverse power flow near the initial superstrate grating interface. (c)-(d) 3D view of transverse and normal power flow showing the power magnitude.

Fig. 14.
Fig. 14.

(a). Transverse power flow in air at 2 μm from the surface of the substrate grating. (b) Angular spectrum of the transverse power in air, and an inset showing the shape of the angular spectrum at ± 3° of its maximum value.

Fig. 15.
Fig. 15.

(a). Transverse power flow in air at 100 μm from the surface of the substrate grating, calculated by propagating the angular spectrum using an Inverse Discrete Fourier Transform. (b) Transverse power flow in air at 100 μm from the surface of the substrate grating spatially filtered at ± 3° of the maximum angular spectrum component.

Equations (6)

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

k tangential , diffracted = k tangential , mode p K sup
n sin θ dif = n mode p λ 0 Λ sup
Λ sup < λ 0 ( n mode + 1 )
Λ sup > λ 0 ( n mode + n sub )
sin θ dif , out = sin θ air = ( n mode + λ 0 Λ sup ) p λ 0 Λ sub
λ 0 ( n mod e sin θ air + λ 0 Λ sup ) < Λ sub < 2 λ 0 ( n mode sin θ air + λ 0 Λ sup )

Metrics