Abstract

We present a novel design of two dimensional graded index medium that provides coupling of light with high coupling efficiency between two planar dielectric waveguides of different widths (15.46μm vs. 2.21μm). Poor light coupling performance of butt-coupler can be mitigated by implementing tapered coupler at the expense of long coupler section. In order to reduce coupling losses, a new coupling device approach based on graded index (GRIN) concept is proposed. The refractive index distribution is in the form of modified version of the Maxwell fish-eye lens. The inhomogeneous refractive index distribution is approximated by photonic crystals (PCs) such that the positions of each PC rods are appropriately arranged. Strong electric field focusing ability of the designed GRIN PC medium provides relatively high coupling efficiency that is around 90%. Spectral region corresponding to coupling efficiency over 75% has a bandwidth of Δω = 18.56% (284 nm). Finally, we discuss the durability of the proposed coupler against the lateral displacement and angular misalignment of output waveguides.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Saleh and M. C. Teich, Fundamental of Photonics (Wiley-Interscience, 1991).
  2. N. Tzoar and R. Pascone, “Radiation loss in tapered waveguides,” J. Opt. Soc. Am. A 71(9), 1107–1114 (1981).
    [CrossRef]
  3. D. W. Prather, J. Murakowski, S. Shi, S. Venkataraman, A. Sharkawy, C. Chen, and D. Pustai, “High-efficiency coupling structure for a single-line-defect photonic-crystal waveguide,” Opt. Lett. 27(18), 1601–1603 (2002).
    [CrossRef] [PubMed]
  4. A. Mekis and J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19(6), 861–865 (2001).
    [CrossRef]
  5. Ph. Lalanne and A. Talneau, “Modal conversion with artificial materials for photonic-crystal waveguides,” Opt. Express 10(8), 354–359 (2002).
    [PubMed]
  6. M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic mode conversion,” Appl. Phys. Lett. 78(11), 1466–1468 (2001).
    [CrossRef]
  7. T. D. Happ, M. Kamp, and A. Forchel, “Photonic crystal tapers for ultracompact mode conversion,” Opt. Lett. 26(14), 1102–1104 (2001).
    [CrossRef] [PubMed]
  8. E. Khoo, A. Liu, and J. Wu, “Nonuniform photonic crystal taper for high-efficiency mode coupling,” Opt. Express 13(20), 7748–7759 (2005).
    [CrossRef] [PubMed]
  9. L. H. Gabrielli and M. Lipson, “Integrated Luneburg lens via ultra-strong index gradient on silicon,” Opt. Express 19(21), 20122–20127 (2011).
    [CrossRef] [PubMed]
  10. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).
  11. H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett. 19(19), 1532–1534 (2007).
    [CrossRef]
  12. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105(10), 103708 (2009).
    [CrossRef]
  13. H. T. Chien, C. Lee, H. K. Chiu, K. C. Hsu, C. C. Chen, J. A. Ho, and C. Chou, “The comparison between the graded photonic crystal coupler and various coupler,” J. Lightwave Technol. 27(14), 2570–2574 (2009).
    [CrossRef]
  14. H. W. Wang and L. W. Chen, “High transmission efficiency of arbitrary waveguide bends formed by graded index photonic crystals,” J. Opt. Soc. Am. B 28(9), 2098–2104 (2011).
    [CrossRef]
  15. E. Centeno, D. Cassagne, and J.-P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
    [CrossRef]
  16. B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
    [CrossRef] [PubMed]
  17. B. Vasić and R. Gajić, “Self-focusing media using graded photonic crystals: focusing, fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110(5), 053103 (2011).
    [CrossRef]
  18. F. Gaufillet and É. Akmansoy, “Graded photonic crystals for graded index lens,” Opt. Commun. 285(10–11), 2638–2641 (2012).
    [CrossRef]
  19. E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
    [CrossRef]
  20. C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
    [CrossRef]
  21. E. Centeno, E. Akmansoy, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Light bending and quasi-transparency in metallic graded photonic crystals,” Photonics Nanostruct. Fundam. Appl. 8(2), 120–124 (2010).
    [CrossRef]
  22. H. T. Chien and C. C. Chen, “Focusing of electromagnetic waves by periodic arrays of air holes with gradually varying radii,” Opt. Express 14(22), 10759–10764 (2006).
    [CrossRef] [PubMed]
  23. M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108(10), 103505 (2010).
    [CrossRef]
  24. H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15(3), 1240–1253 (2007).
    [CrossRef] [PubMed]
  25. S. G. Lee, J. S. Choi, J. E. Kim, H. Y. Park, and C. S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16(6), 4270–4277 (2008).
    [CrossRef] [PubMed]
  26. C. R. Pollock and M. Lipson, Integrated Photonics (Kluwer Academic Publishers, 2003).
  27. P. Sanchis, J. Marti, J. Blasco, A. Martinez, and A. Garcia, “Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,” Opt. Express 10(24), 1391–1397 (2002).
    [PubMed]
  28. T. Alder, A. Stöhr, R. Heinzelmann, and D. Jäger, “High-efficiency fiber-to-chip coupling using low-loss tapered single-mode fiber,” IEEE Photon. Technol. Lett. 12(8), 1016–1018 (2000).
    [CrossRef]
  29. R. G. Hunsperger, A. Yariv, and A. Lee, “Parallel end-butt coupling for optical integrated circuits,” Appl. Opt. 16(4), 1026–1032 (1977).
    [CrossRef] [PubMed]
  30. P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, “Analysis of butt coupling in photonic crystals,” IEEE J. Quantum Electron. 40(5), 541–550 (2004).
    [CrossRef]
  31. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publisher, 2005).
  32. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
    [CrossRef]
  33. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
    [CrossRef]
  34. C. A. Swainson and A. J. C. Maxwell), “Problems,” Cambridge Dublin Math. J. 8, 188–189 (1854).
  35. A. D. Greenwood and J. M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antenn. Propag. Mag. 41(5), 9–18 (1999).
    [CrossRef]
  36. M. I. Kotlyar, Y. R. Triandaphilov, A. A. Kovalev, V. A. Soifer, M. V. Kotlyar, and L. O’Faolain, “Photonic crystal lens for coupling two waveguides,” Appl. Opt. 48(19), 3722–3730 (2009).
    [CrossRef] [PubMed]
  37. R. Orobtchouk, A. Layadi, H. Gualous, D. Pascal, A. Koster, and S. Laval, “High-efficiency light coupling in a submicrometric silicon-on-insulator waveguide,” Appl. Opt. 39(31), 5773–5777 (2000).
    [CrossRef] [PubMed]
  38. D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fiber and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
    [CrossRef]
  39. H. Kim, S. Lee, B. O. S. Park, and E. Lee, “High efficiency coupling technique for photonic crystal waveguides using a waveguide lens,” in Frontiers in Optics, OSA Technical Digest (Optical Society of America, 2003), paper MT68.
  40. E. Pshenay-Severin, C. C. Chen, T. Pertsch, M. Augustin, A. Chipoline, and A. Tunnermann, “Photonic crystal lens for photonic crystal waveguide coupling,” in Lasers and Electro-Optics Conference, Technical Digest (Optical Society of America, 2006), paper CthK3.

2012

F. Gaufillet and É. Akmansoy, “Graded photonic crystals for graded index lens,” Opt. Commun. 285(10–11), 2638–2641 (2012).
[CrossRef]

2011

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

B. Vasić and R. Gajić, “Self-focusing media using graded photonic crystals: focusing, fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110(5), 053103 (2011).
[CrossRef]

H. W. Wang and L. W. Chen, “High transmission efficiency of arbitrary waveguide bends formed by graded index photonic crystals,” J. Opt. Soc. Am. B 28(9), 2098–2104 (2011).
[CrossRef]

L. H. Gabrielli and M. Lipson, “Integrated Luneburg lens via ultra-strong index gradient on silicon,” Opt. Express 19(21), 20122–20127 (2011).
[CrossRef] [PubMed]

2010

B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
[CrossRef] [PubMed]

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

E. Centeno, E. Akmansoy, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Light bending and quasi-transparency in metallic graded photonic crystals,” Photonics Nanostruct. Fundam. Appl. 8(2), 120–124 (2010).
[CrossRef]

2009

2008

S. G. Lee, J. S. Choi, J. E. Kim, H. Y. Park, and C. S. Kee, “Reflection minimization at two-dimensional photonic crystal interfaces,” Opt. Express 16(6), 4270–4277 (2008).
[CrossRef] [PubMed]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

2007

H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett. 19(19), 1532–1534 (2007).
[CrossRef]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15(3), 1240–1253 (2007).
[CrossRef] [PubMed]

2006

H. T. Chien and C. C. Chen, “Focusing of electromagnetic waves by periodic arrays of air holes with gradually varying radii,” Opt. Express 14(22), 10759–10764 (2006).
[CrossRef] [PubMed]

E. Centeno, D. Cassagne, and J.-P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[CrossRef]

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fiber and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

2005

2004

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, “Analysis of butt coupling in photonic crystals,” IEEE J. Quantum Electron. 40(5), 541–550 (2004).
[CrossRef]

2002

2001

2000

T. Alder, A. Stöhr, R. Heinzelmann, and D. Jäger, “High-efficiency fiber-to-chip coupling using low-loss tapered single-mode fiber,” IEEE Photon. Technol. Lett. 12(8), 1016–1018 (2000).
[CrossRef]

R. Orobtchouk, A. Layadi, H. Gualous, D. Pascal, A. Koster, and S. Laval, “High-efficiency light coupling in a submicrometric silicon-on-insulator waveguide,” Appl. Opt. 39(31), 5773–5777 (2000).
[CrossRef] [PubMed]

1999

A. D. Greenwood and J. M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antenn. Propag. Mag. 41(5), 9–18 (1999).
[CrossRef]

1994

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

1981

N. Tzoar and R. Pascone, “Radiation loss in tapered waveguides,” J. Opt. Soc. Am. A 71(9), 1107–1114 (1981).
[CrossRef]

1977

1854

C. A. Swainson and A. J. C. Maxwell), “Problems,” Cambridge Dublin Math. J. 8, 188–189 (1854).

Akmansoy, E.

E. Centeno, E. Akmansoy, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Light bending and quasi-transparency in metallic graded photonic crystals,” Photonics Nanostruct. Fundam. Appl. 8(2), 120–124 (2010).
[CrossRef]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

Akmansoy, É.

F. Gaufillet and É. Akmansoy, “Graded photonic crystals for graded index lens,” Opt. Commun. 285(10–11), 2638–2641 (2012).
[CrossRef]

Albert, J.-P.

E. Centeno, D. Cassagne, and J.-P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[CrossRef]

Alder, T.

T. Alder, A. Stöhr, R. Heinzelmann, and D. Jäger, “High-efficiency fiber-to-chip coupling using low-loss tapered single-mode fiber,” IEEE Photon. Technol. Lett. 12(8), 1016–1018 (2000).
[CrossRef]

Ayre, M.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fiber and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

Baets, R.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fiber and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, “Analysis of butt coupling in photonic crystals,” IEEE J. Quantum Electron. 40(5), 541–550 (2004).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Bienstman, P.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fiber and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, “Analysis of butt coupling in photonic crystals,” IEEE J. Quantum Electron. 40(5), 541–550 (2004).
[CrossRef]

Blasco, J.

Bogaerts, W.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fiber and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

Caglayan, H.

O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[CrossRef]

Cakmak, O.

O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[CrossRef]

Cassagne, D.

E. Centeno, E. Akmansoy, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Light bending and quasi-transparency in metallic graded photonic crystals,” Photonics Nanostruct. Fundam. Appl. 8(2), 120–124 (2010).
[CrossRef]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

E. Centeno, D. Cassagne, and J.-P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[CrossRef]

Centeno, E.

E. Centeno, E. Akmansoy, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Light bending and quasi-transparency in metallic graded photonic crystals,” Photonics Nanostruct. Fundam. Appl. 8(2), 120–124 (2010).
[CrossRef]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

E. Centeno, D. Cassagne, and J.-P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[CrossRef]

Chen, C.

Chen, C. C.

Chen, L. W.

Chien, H. T.

Chiu, H. K.

Choi, J. S.

Chou, C.

Citrin, D. S.

H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett. 19(19), 1532–1534 (2007).
[CrossRef]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15(3), 1240–1253 (2007).
[CrossRef] [PubMed]

Colak, E.

O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[CrossRef]

Forchel, A.

Gabrielli, L. H.

Gajic, R.

B. Vasić and R. Gajić, “Self-focusing media using graded photonic crystals: focusing, fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110(5), 053103 (2011).
[CrossRef]

B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
[CrossRef] [PubMed]

Gao, T.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Garcia, A.

Gaufillet, F.

F. Gaufillet and É. Akmansoy, “Graded photonic crystals for graded index lens,” Opt. Commun. 285(10–11), 2638–2641 (2012).
[CrossRef]

Greenwood, A. D.

A. D. Greenwood and J. M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antenn. Propag. Mag. 41(5), 9–18 (1999).
[CrossRef]

Gualous, H.

Happ, T. D.

Heinzelmann, R.

T. Alder, A. Stöhr, R. Heinzelmann, and D. Jäger, “High-efficiency fiber-to-chip coupling using low-loss tapered single-mode fiber,” IEEE Photon. Technol. Lett. 12(8), 1016–1018 (2000).
[CrossRef]

Hingerl, K.

Ho, J. A.

Hsu, K. C.

Huang, T. J.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Hunsperger, R. G.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Isic, G.

Jäger, D.

T. Alder, A. Stöhr, R. Heinzelmann, and D. Jäger, “High-efficiency fiber-to-chip coupling using low-loss tapered single-mode fiber,” IEEE Photon. Technol. Lett. 12(8), 1016–1018 (2000).
[CrossRef]

Jin, J. M.

A. D. Greenwood and J. M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antenn. Propag. Mag. 41(5), 9–18 (1999).
[CrossRef]

Joannopoulos, J. D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

A. Mekis and J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19(6), 861–865 (2001).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Juluri, B. K.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Kamp, M.

Kee, C. S.

Khoo, E.

Kim, J. E.

Kiraly, B.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Koster, A.

Kotlyar, M. I.

Kotlyar, M. V.

Kovalev, A. A.

Kurt, H.

O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[CrossRef]

H. Kurt and D. S. Citrin, “Graded index photonic crystals,” Opt. Express 15(3), 1240–1253 (2007).
[CrossRef] [PubMed]

H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett. 19(19), 1532–1534 (2007).
[CrossRef]

Lalanne, Ph.

Ph. Lalanne and A. Talneau, “Modal conversion with artificial materials for photonic-crystal waveguides,” Opt. Express 10(8), 354–359 (2002).
[PubMed]

M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic mode conversion,” Appl. Phys. Lett. 78(11), 1466–1468 (2001).
[CrossRef]

Laval, S.

Layadi, A.

Lee, A.

Lee, C.

Lee, S. G.

Lin, S.-C. S.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Lipson, M.

Liu, A.

Lourtioz, J.-M.

E. Centeno, E. Akmansoy, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Light bending and quasi-transparency in metallic graded photonic crystals,” Photonics Nanostruct. Fundam. Appl. 8(2), 120–124 (2010).
[CrossRef]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

Lu, M.

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

Luyssaert, B.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, “Analysis of butt coupling in photonic crystals,” IEEE J. Quantum Electron. 40(5), 541–550 (2004).
[CrossRef]

Marti, J.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, “Analysis of butt coupling in photonic crystals,” IEEE J. Quantum Electron. 40(5), 541–550 (2004).
[CrossRef]

P. Sanchis, J. Marti, J. Blasco, A. Martinez, and A. Garcia, “Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,” Opt. Express 10(24), 1391–1397 (2002).
[PubMed]

Martinez, A.

Maxwell, A. J. C.

C. A. Swainson and A. J. C. Maxwell), “Problems,” Cambridge Dublin Math. J. 8, 188–189 (1854).

Mekis, A.

Murakowski, J.

Niemi, T.

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

O’Faolain, L.

Orobtchouk, R.

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Ozbay, E.

O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[CrossRef]

Palamaru, M.

M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic mode conversion,” Appl. Phys. Lett. 78(11), 1466–1468 (2001).
[CrossRef]

Park, H. Y.

Pascal, D.

Pascone, R.

N. Tzoar and R. Pascone, “Radiation loss in tapered waveguides,” J. Opt. Soc. Am. A 71(9), 1107–1114 (1981).
[CrossRef]

Peng, C.

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

Pessa, M.

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

Prather, D. W.

Pustai, D.

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

Sanchis, P.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, “Analysis of butt coupling in photonic crystals,” IEEE J. Quantum Electron. 40(5), 541–550 (2004).
[CrossRef]

P. Sanchis, J. Marti, J. Blasco, A. Martinez, and A. Garcia, “Mode matching technique for highly efficient coupling between dielectric waveguides and planar photonic crystal circuits,” Opt. Express 10(24), 1391–1397 (2002).
[PubMed]

Sharkawy, A.

Shi, S.

Soifer, V. A.

Stöhr, A.

T. Alder, A. Stöhr, R. Heinzelmann, and D. Jäger, “High-efficiency fiber-to-chip coupling using low-loss tapered single-mode fiber,” IEEE Photon. Technol. Lett. 12(8), 1016–1018 (2000).
[CrossRef]

Swainson, C. A.

C. A. Swainson and A. J. C. Maxwell), “Problems,” Cambridge Dublin Math. J. 8, 188–189 (1854).

Taillaert, D.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fiber and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

Talneau, A.

Tan, C.

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

Triandaphilov, Y. R.

Tzoar, N.

N. Tzoar and R. Pascone, “Radiation loss in tapered waveguides,” J. Opt. Soc. Am. A 71(9), 1107–1114 (1981).
[CrossRef]

Van Laere, F.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fiber and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

Van Thourhout, D.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fiber and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

Vasic, B.

B. Vasić and R. Gajić, “Self-focusing media using graded photonic crystals: focusing, fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110(5), 053103 (2011).
[CrossRef]

B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010).
[CrossRef] [PubMed]

Venkataraman, S.

Vynck, K.

E. Centeno, E. Akmansoy, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Light bending and quasi-transparency in metallic graded photonic crystals,” Photonics Nanostruct. Fundam. Appl. 8(2), 120–124 (2010).
[CrossRef]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

Wang, H. W.

Wu, J.

Yariv, A.

Appl. Opt.

Appl. Phys. Lett.

M. Palamaru and Ph. Lalanne, “Photonic crystal waveguides: out-of-plane losses and adiabatic mode conversion,” Appl. Phys. Lett. 78(11), 1466–1468 (2001).
[CrossRef]

E. Akmansoy, E. Centeno, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Graded photonic crystals curve the flow of light: an experimental demonstration by the mirage effect,” Appl. Phys. Lett. 92(13), 133501 (2008).
[CrossRef]

Cambridge Dublin Math. J.

C. A. Swainson and A. J. C. Maxwell), “Problems,” Cambridge Dublin Math. J. 8, 188–189 (1854).

Comput. Phys. Commun.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: a flexible free software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[CrossRef]

IEEE Antenn. Propag. Mag.

A. D. Greenwood and J. M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antenn. Propag. Mag. 41(5), 9–18 (1999).
[CrossRef]

IEEE J. Quantum Electron.

P. Sanchis, P. Bienstman, B. Luyssaert, R. Baets, and J. Marti, “Analysis of butt coupling in photonic crystals,” IEEE J. Quantum Electron. 40(5), 541–550 (2004).
[CrossRef]

IEEE Photon. Technol. Lett.

H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett. 19(19), 1532–1534 (2007).
[CrossRef]

T. Alder, A. Stöhr, R. Heinzelmann, and D. Jäger, “High-efficiency fiber-to-chip coupling using low-loss tapered single-mode fiber,” IEEE Photon. Technol. Lett. 12(8), 1016–1018 (2000).
[CrossRef]

J. Appl. Phys.

O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105(10), 103708 (2009).
[CrossRef]

B. Vasić and R. Gajić, “Self-focusing media using graded photonic crystals: focusing, fourier transforming and imaging, directive emission, and directional cloaking,” J. Appl. Phys. 110(5), 053103 (2011).
[CrossRef]

M. Lu, B. K. Juluri, S.-C. S. Lin, B. Kiraly, T. Gao, and T. J. Huang, “Beam aperture modifier and beam deflector using gradient-index photonic crystals,” J. Appl. Phys. 108(10), 103505 (2010).
[CrossRef]

J. Comput. Phys.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

N. Tzoar and R. Pascone, “Radiation loss in tapered waveguides,” J. Opt. Soc. Am. A 71(9), 1107–1114 (1981).
[CrossRef]

J. Opt. Soc. Am. B

Jpn. J. Appl. Phys.

D. Taillaert, F. Van Laere, M. Ayre, W. Bogaerts, D. Van Thourhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fiber and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45(8A), 6071–6077 (2006).
[CrossRef]

Opt. Commun.

F. Gaufillet and É. Akmansoy, “Graded photonic crystals for graded index lens,” Opt. Commun. 285(10–11), 2638–2641 (2012).
[CrossRef]

C. Tan, T. Niemi, C. Peng, and M. Pessa, “Focusing effect of a graded index photonic crystal lens,” Opt. Commun. 284(12), 3140–3143 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Photonics Nanostruct. Fundam. Appl.

E. Centeno, E. Akmansoy, K. Vynck, D. Cassagne, and J.-M. Lourtioz, “Light bending and quasi-transparency in metallic graded photonic crystals,” Photonics Nanostruct. Fundam. Appl. 8(2), 120–124 (2010).
[CrossRef]

Phys. Rev. B

E. Centeno, D. Cassagne, and J.-P. Albert, “Mirage and superbending effect in two-dimensional graded photonic crystals,” Phys. Rev. B 73(23), 235119 (2006).
[CrossRef]

Other

C. R. Pollock and M. Lipson, Integrated Photonics (Kluwer Academic Publishers, 2003).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House Publisher, 2005).

B. Saleh and M. C. Teich, Fundamental of Photonics (Wiley-Interscience, 1991).

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1964).

H. Kim, S. Lee, B. O. S. Park, and E. Lee, “High efficiency coupling technique for photonic crystal waveguides using a waveguide lens,” in Frontiers in Optics, OSA Technical Digest (Optical Society of America, 2003), paper MT68.

E. Pshenay-Severin, C. C. Chen, T. Pertsch, M. Augustin, A. Chipoline, and A. Tunnermann, “Photonic crystal lens for photonic crystal waveguide coupling,” in Lasers and Electro-Optics Conference, Technical Digest (Optical Society of America, 2006), paper CthK3.

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 (9)

Fig. 1
Fig. 1

Schematics of (a) butt-coupler and (b) tapered coupler are shown. Important structural parameters are denoted by Win, Wout and L. (c) Calculated transmission efficiencies of tapered coupler and butt-coupler. Shaded region represents the interested frequency interval.

Fig. 2
Fig. 2

(a) Schematic representation of coupling strategy used as a modified Maxwell fish-eye lens at the intermediate stage. The values of Win, Lc, and Wout are 21a, 16.5a and 3a, respectively (b) 2D refractive index distribution of the continuous MMF coupler.

Fig. 3
Fig. 3

(a) The dispersion curves corresponding to the first band are shown. (b) Group index dependency of each dispersion bands shown in (a). The three colored rectangles demonstrate different frequency regions where group index variations exhibit distinct characteristics.

Fig. 4
Fig. 4

(a) Schematic representation of the complete structure, i.e., input waveguide, coupler section, output waveguide. Intermediate region represents approximation of the MMFE lens by dielectric rods. (b) The index profiles of the specified eight regions are presented.

Fig. 5
Fig. 5

Calculated transmission efficiencies of the discrete graded-index (D-GRIN) and continuous graded-index (C-GRIN) modified Maxwell fish-eye lenses.

Fig. 6
Fig. 6

(a) Spatial intensity profile of the continuous MMFE coupling at ωa / 2πc=0.10 . (b) Cross-sectional intensity profiles at the input and output predefined locations (CSin and CSout). (c) Spatial intensity profile of the continuous MMFE coupling at ωa / 2πc=0.475 . (d) Corresponding cross-sectional intensity profiles for upper frequency band at the same locations.

Fig. 7
Fig. 7

(a) Spatial intensity profile of the GRIN PC MMFE coupling at ωa / 2πc=0.10 . (b) Cross-sectional intensity profiles at the input and output predefined locations. (c) Spatial intensity profile of the GRIN PC MMF coupling at ωa / 2πc=0.475 . (d) Cross-sectional intensity profiles at the input and output predefined locations.

Fig. 8
Fig. 8

Coupling efficiency variation curves of the designed discrete GRIN coupler under the misalignment occurring in lateral direction are presented. Lateral offset is schematically shown as an inset.

Fig. 9
Fig. 9

Coupling efficiency changes of the designed discrete GRIN coupler under the angularly misaligned cases. Angular misalignment is schematically shown as an inset.

Tables (1)

Tables Icon

Table 1 The values of the adjustable parameters at each distinct eight regions.

Equations (3)

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

n(r)= 2 1+ (r/R ) 2
n(x,y)= n 0 1 1+β (y/ (xα) ) 2
n( k i ,y)= n 0 α (α+ ( k i y) 2 ) ,

Metrics