Modified Maxwell fish-eye approach for efficient coupler design by graded photonic crystals

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

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]

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]

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]

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]

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. 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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

T. D. Happ, M. Kamp, and A. Forchel, “Photonic crystal tapers for ultracompact mode conversion,” Opt. Lett. 26(14), 1102–1104 (2001).
[Crossref] [PubMed]

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]

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]

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]

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

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

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]

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

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]

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

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]

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]

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]

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

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

T. D. Happ, M. Kamp, and A. Forchel, “Photonic crystal tapers for ultracompact mode conversion,” Opt. Lett. 26(14), 1102–1104 (2001).
[Crossref] [PubMed]

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]

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]

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]

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]

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

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]

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]

T. D. Happ, M. Kamp, and A. Forchel, “Photonic crystal tapers for ultracompact mode conversion,” Opt. Lett. 26(14), 1102–1104 (2001).
[Crossref] [PubMed]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

T. D. Happ, M. Kamp, and A. Forchel, “Photonic crystal tapers for ultracompact mode conversion,” Opt. Lett. 26(14), 1102–1104 (2001).
[Crossref] [PubMed]

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. Khoo, A. Liu, and J. Wu, “Nonuniform photonic crystal taper for high-efficiency mode coupling,” Opt. Express 13(20), 7748–7759 (2005).
[Crossref] [PubMed]

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]

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]

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]

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]

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]

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]

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, “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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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, 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]

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]

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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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[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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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

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]

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

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]

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]

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

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[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).
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[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]

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]

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]

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]

E. Khoo, A. Liu, and J. Wu, “Nonuniform photonic crystal taper for high-efficiency mode coupling,” Opt. Express 13(20), 7748–7759 (2005).
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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]

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]

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]

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]

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

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).
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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]

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]

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).
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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).
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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]

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).
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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]

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

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]

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]

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]

E. Khoo, A. Liu, and J. Wu, “Nonuniform photonic crystal taper for high-efficiency mode coupling,” Opt. Express 13(20), 7748–7759 (2005).
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