Abstract

Near the band edge of photonic crystal waveguides, localized modes appear due to disorder. We demonstrate a new method to elucidate spatial profile of the localized modes in such systems using precise local tuning. Using deconvolution with the known thermal profile, the spatial profile of a localized mode with quality factor (Q) > 105 is successfully reconstructed with a resolution of 2.5 μm.

© 2016 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]
  24. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69(11–12), 681 (1946).
  25. 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]
  26. M. Qiu, “Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,” Appl. Phys. Lett. 81(7), 1163 (2002).
    [Crossref]
  27. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31(20), 2972–2974 (2006).
    [Crossref] [PubMed]
  28. R. Sarma, A. Yamilov, P. Neupane, B. Shapiro, and H. Cao, “Probing long-range intensity correlations inside disordered photonic nanostructures,” Phys. Rev. B 90(1), 014203 (2014).
    [Crossref]
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    [PubMed]
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    [Crossref]

2016 (1)

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
[Crossref] [PubMed]

2015 (1)

S. Sokolov, J. Lian, E. Yüce, S. Combrié, G. Lehoucq, A. De Rossi, and A. P. Mosk, “Local thermal resonance control of GaInP photonic crystal membrane cavities using ambient gas cooling,” Appl. Phys. Lett. 106(17), 171113 (2015).
[Crossref]

2014 (3)

R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
[Crossref]

F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
[Crossref] [PubMed]

R. Sarma, A. Yamilov, P. Neupane, B. Shapiro, and H. Cao, “Probing long-range intensity correlations inside disordered photonic nanostructures,” Phys. Rev. B 90(1), 014203 (2014).
[Crossref]

2013 (1)

D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7(3), 188–196 (2013).
[Crossref]

2012 (5)

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012).
[PubMed]

H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-localized modes,” Phys. Rev. Lett. 108(11), 113901 (2012).
[Crossref] [PubMed]

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
[Crossref]

M. Spasenović, D. M. Beggs, P. Lalanne, T. F. Krauss, and L. Kuipers, “Measuring the spatial extent of individual localized photonic states,” Phys. Rev. B 86(15), 155153 (2012).
[Crossref]

S. R. Huisman, G. Ctistis, S. Stobbe, A. P. Mosk, J. L. Herek, A. Lagendijk, P. Lodahl, W. L. Vos, and P. W. H. Pinkse, “Measurement of a band-edge tail in the density of states of a photonic-crystal waveguide,” Phys. Rev. B 86(15), 155154 (2012).
[Crossref]

2011 (1)

V. Savona, “Electromagnetic modes of a disordered photonic crystal,” Phys. Rev. B. 83(8), 085301 (2011).
[Crossref]

2010 (3)

L. Sapienza, H. Thyrrestrup, S. R. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[Crossref] [PubMed]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (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]

2009 (4)

S. Combrié, Q. V. Tran, A. De Rossi, C. Husko, and P. Colman, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95(22), 221108 (2009).
[Crossref]

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-Induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[Crossref] [PubMed]

S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. 103(6), 063903 (2009).
[Crossref] [PubMed]

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62, 24–29 (2009).
[Crossref]

2006 (1)

2005 (2)

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72(15), 153102 (2005).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

2003 (1)

Y. Akahane, T. Asano, B-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

2002 (1)

M. Qiu, “Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,” Appl. Phys. Lett. 81(7), 1163 (2002).
[Crossref]

1984 (1)

S. John, “Electromagnetic Absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53(32), 2169–2172 (1984).
[Crossref]

1972 (1)

P. W. Anderson, “The size of localized States near the mobility edge,” Proc. Natl. Acad. Sci. 69(5), 1097–1099 (1972).
[Crossref] [PubMed]

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69(11–12), 681 (1946).

Akahane, Y.

Y. Akahane, T. Asano, B-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Anderson, P. W.

P. W. Anderson, “The size of localized States near the mobility edge,” Proc. Natl. Acad. Sci. 69(5), 1097–1099 (1972).
[Crossref] [PubMed]

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[Crossref]

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical methods for physicists, 3rd ed (Academic Press, 1985).

Asano, T.

Y. Akahane, T. Asano, B-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Balet, L.

F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
[Crossref] [PubMed]

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
[Crossref]

Baron, A.

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
[Crossref] [PubMed]

Barthelemy, P.

F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
[Crossref] [PubMed]

Beggs, D. M.

M. Spasenović, D. M. Beggs, P. Lalanne, T. F. Krauss, and L. Kuipers, “Measuring the spatial extent of individual localized photonic states,” Phys. Rev. B 86(15), 155153 (2012).
[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]

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31(20), 2972–2974 (2006).
[Crossref] [PubMed]

Bianchi, C.

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
[Crossref]

Bruck, R.

R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
[Crossref]

Burr, G.

Burresi, M.

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012).
[PubMed]

Cao, H.

R. Sarma, A. Yamilov, P. Neupane, B. Shapiro, and H. Cao, “Probing long-range intensity correlations inside disordered photonic nanostructures,” Phys. Rev. B 90(1), 014203 (2014).
[Crossref]

Caselli, N.

F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
[Crossref] [PubMed]

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
[Crossref]

Cluzel, B.

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
[Crossref] [PubMed]

Colman, P.

S. Combrié, Q. V. Tran, A. De Rossi, C. Husko, and P. Colman, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95(22), 221108 (2009).
[Crossref]

Combrié, S.

S. Sokolov, J. Lian, E. Yüce, S. Combrié, G. Lehoucq, A. De Rossi, and A. P. Mosk, “Local thermal resonance control of GaInP photonic crystal membrane cavities using ambient gas cooling,” Appl. Phys. Lett. 106(17), 171113 (2015).
[Crossref]

S. Combrié, Q. V. Tran, A. De Rossi, C. Husko, and P. Colman, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95(22), 221108 (2009).
[Crossref]

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-Induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[Crossref] [PubMed]

Ctistis, G.

S. R. Huisman, G. Ctistis, S. Stobbe, A. P. Mosk, J. L. Herek, A. Lagendijk, P. Lodahl, W. L. Vos, and P. W. H. Pinkse, “Measurement of a band-edge tail in the density of states of a photonic-crystal waveguide,” Phys. Rev. B 86(15), 155154 (2012).
[Crossref]

De Fornel, F.

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
[Crossref] [PubMed]

De Rossi, A.

S. Sokolov, J. Lian, E. Yüce, S. Combrié, G. Lehoucq, A. De Rossi, and A. P. Mosk, “Local thermal resonance control of GaInP photonic crystal membrane cavities using ambient gas cooling,” Appl. Phys. Lett. 106(17), 171113 (2015).
[Crossref]

S. Combrié, Q. V. Tran, A. De Rossi, C. Husko, and P. Colman, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95(22), 221108 (2009).
[Crossref]

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-Induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[Crossref] [PubMed]

Faggiani, R.

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
[Crossref] [PubMed]

Farjadpour, A.

Fiore, A.

F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
[Crossref] [PubMed]

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
[Crossref]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[Crossref]

Francardi, M.

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
[Crossref]

Gabet, R.

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-Induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[Crossref] [PubMed]

Garcia, P. D.

L. Sapienza, H. Thyrrestrup, S. R. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[Crossref] [PubMed]

Gardes, F. Y.

R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
[Crossref]

Gerardino, A.

F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
[Crossref] [PubMed]

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
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F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
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N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
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S. R. Huisman, G. Ctistis, S. Stobbe, A. P. Mosk, J. L. Herek, A. Lagendijk, P. Lodahl, W. L. Vos, and P. W. H. Pinkse, “Measurement of a band-edge tail in the density of states of a photonic-crystal waveguide,” Phys. Rev. B 86(15), 155154 (2012).
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R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
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M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-Induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
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E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
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S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. 103(6), 063903 (2009).
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S. R. Huisman, G. Ctistis, S. Stobbe, A. P. Mosk, J. L. Herek, A. Lagendijk, P. Lodahl, W. L. Vos, and P. W. H. Pinkse, “Measurement of a band-edge tail in the density of states of a photonic-crystal waveguide,” Phys. Rev. B 86(15), 155154 (2012).
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S. Combrié, Q. V. Tran, A. De Rossi, C. Husko, and P. Colman, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95(22), 221108 (2009).
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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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F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
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N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
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M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-Induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
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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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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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A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31(20), 2972–2974 (2006).
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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (Princeton University Press, 2008).

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A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72(15), 153102 (2005).
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R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
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M. Spasenović, D. M. Beggs, P. Lalanne, T. F. Krauss, and L. Kuipers, “Measuring the spatial extent of individual localized photonic states,” Phys. Rev. B 86(15), 155153 (2012).
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E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
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S. R. Huisman, G. Ctistis, S. Stobbe, A. P. Mosk, J. L. Herek, A. Lagendijk, P. Lodahl, W. L. Vos, and P. W. H. Pinkse, “Measurement of a band-edge tail in the density of states of a photonic-crystal waveguide,” Phys. Rev. B 86(15), 155154 (2012).
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R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
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M. Spasenović, D. M. Beggs, P. Lalanne, T. F. Krauss, and L. Kuipers, “Measuring the spatial extent of individual localized photonic states,” Phys. Rev. B 86(15), 155153 (2012).
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S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. 103(6), 063903 (2009).
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Lalouat, L.

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
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S. Sokolov, J. Lian, E. Yüce, S. Combrié, G. Lehoucq, A. De Rossi, and A. P. Mosk, “Local thermal resonance control of GaInP photonic crystal membrane cavities using ambient gas cooling,” Appl. Phys. Lett. 106(17), 171113 (2015).
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Li, L. H.

F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
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N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
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Lian, J.

S. Sokolov, J. Lian, E. Yüce, S. Combrié, G. Lehoucq, A. De Rossi, and A. P. Mosk, “Local thermal resonance control of GaInP photonic crystal membrane cavities using ambient gas cooling,” Appl. Phys. Lett. 106(17), 171113 (2015).
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H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-localized modes,” Phys. Rev. Lett. 108(11), 113901 (2012).
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S. R. Huisman, G. Ctistis, S. Stobbe, A. P. Mosk, J. L. Herek, A. Lagendijk, P. Lodahl, W. L. Vos, and P. W. H. Pinkse, “Measurement of a band-edge tail in the density of states of a photonic-crystal waveguide,” Phys. Rev. B 86(15), 155154 (2012).
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L. Sapienza, H. Thyrrestrup, S. R. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
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R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
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S. Mazoyer, J. P. Hugonin, and P. Lalanne, “Disorder-induced multiple scattering in photonic-crystal waveguides,” Phys. Rev. Lett. 103(6), 063903 (2009).
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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (Princeton University Press, 2008).

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R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
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A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
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Mosk, A. P.

S. Sokolov, J. Lian, E. Yüce, S. Combrié, G. Lehoucq, A. De Rossi, and A. P. Mosk, “Local thermal resonance control of GaInP photonic crystal membrane cavities using ambient gas cooling,” Appl. Phys. Lett. 106(17), 171113 (2015).
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S. R. Huisman, G. Ctistis, S. Stobbe, A. P. Mosk, J. L. Herek, A. Lagendijk, P. Lodahl, W. L. Vos, and P. W. H. Pinkse, “Measurement of a band-edge tail in the density of states of a photonic-crystal waveguide,” Phys. Rev. B 86(15), 155154 (2012).
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R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
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R. Sarma, A. Yamilov, P. Neupane, B. Shapiro, and H. Cao, “Probing long-range intensity correlations inside disordered photonic nanostructures,” Phys. Rev. B 90(1), 014203 (2014).
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Y. Akahane, T. Asano, B-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
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E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
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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).
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R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
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M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-Induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
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Pinkse, P. W. H.

S. R. Huisman, G. Ctistis, S. Stobbe, A. P. Mosk, J. L. Herek, A. Lagendijk, P. Lodahl, W. L. Vos, and P. W. H. Pinkse, “Measurement of a band-edge tail in the density of states of a photonic-crystal waveguide,” Phys. Rev. B 86(15), 155154 (2012).
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E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
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Reed, G. T.

R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
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R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
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F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
[Crossref] [PubMed]

N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
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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]

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. Burr, “Improving accuracy by subpixel smoothing in FDTD,” Opt. Lett. 31(20), 2972–2974 (2006).
[Crossref] [PubMed]

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H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-localized modes,” Phys. Rev. Lett. 108(11), 113901 (2012).
[Crossref] [PubMed]

L. Sapienza, H. Thyrrestrup, S. R. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[Crossref] [PubMed]

Sarma, R.

R. Sarma, A. Yamilov, P. Neupane, B. Shapiro, and H. Cao, “Probing long-range intensity correlations inside disordered photonic nanostructures,” Phys. Rev. B 90(1), 014203 (2014).
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R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
[Crossref] [PubMed]

Shapiro, B.

R. Sarma, A. Yamilov, P. Neupane, B. Shapiro, and H. Cao, “Probing long-range intensity correlations inside disordered photonic nanostructures,” Phys. Rev. B 90(1), 014203 (2014).
[Crossref]

Shinya, A.

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

Smolka, S.

H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-localized modes,” Phys. Rev. Lett. 108(11), 113901 (2012).
[Crossref] [PubMed]

L. Sapienza, H. Thyrrestrup, S. R. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[Crossref] [PubMed]

Sokolov, S.

S. Sokolov, J. Lian, E. Yüce, S. Combrié, G. Lehoucq, A. De Rossi, and A. P. Mosk, “Local thermal resonance control of GaInP photonic crystal membrane cavities using ambient gas cooling,” Appl. Phys. Lett. 106(17), 171113 (2015).
[Crossref]

Song, B-S.

Y. Akahane, T. Asano, B-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Spasenovic, M.

M. Spasenović, D. M. Beggs, P. Lalanne, T. F. Krauss, and L. Kuipers, “Measuring the spatial extent of individual localized photonic states,” Phys. Rev. B 86(15), 155153 (2012).
[Crossref]

Stobbe, S.

S. R. Huisman, G. Ctistis, S. Stobbe, A. P. Mosk, J. L. Herek, A. Lagendijk, P. Lodahl, W. L. Vos, and P. W. H. Pinkse, “Measurement of a band-edge tail in the density of states of a photonic-crystal waveguide,” Phys. Rev. B 86(15), 155154 (2012).
[Crossref]

Stobbe, S. R.

L. Sapienza, H. Thyrrestrup, S. R. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[Crossref] [PubMed]

Thomson, D. J.

R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
[Crossref]

Thyrrestrup, H.

H. Thyrrestrup, S. Smolka, L. Sapienza, and P. Lodahl, “Statistical theory of a quantum emitter strongly coupled to Anderson-localized modes,” Phys. Rev. Lett. 108(11), 113901 (2012).
[Crossref] [PubMed]

L. Sapienza, H. Thyrrestrup, S. R. Stobbe, P. D. Garcia, S. Smolka, and P. Lodahl, “Cavity quantum electrodynamics with Anderson-localized modes,” Science 327(5971), 1352–1355 (2010).
[Crossref] [PubMed]

Tran, N. V. Q.

M. Patterson, S. Hughes, S. Combrié, N. V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouën, “Disorder-Induced coherent scattering in slow-light photonic crystal waveguides,” Phys. Rev. Lett. 102(25), 253903 (2009).
[Crossref] [PubMed]

Tran, Q. V.

S. Combrié, Q. V. Tran, A. De Rossi, C. Husko, and P. Colman, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95(22), 221108 (2009).
[Crossref]

Troia, B.

R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
[Crossref]

van Tiggelen, B.

A. Lagendijk, B. van Tiggelen, and D. S. Wiersma, “Fifty years of Anderson localization,” Phys. Today 62, 24–29 (2009).
[Crossref]

Vignolini, S.

F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
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R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
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F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
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K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012).
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E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
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Wiersma, D. S.

F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
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K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012).
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R. Sarma, A. Yamilov, P. Neupane, B. Shapiro, and H. Cao, “Probing long-range intensity correlations inside disordered photonic nanostructures,” Phys. Rev. B 90(1), 014203 (2014).
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R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
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Appl. Phys. Lett. (4)

S. Sokolov, J. Lian, E. Yüce, S. Combrié, G. Lehoucq, A. De Rossi, and A. P. Mosk, “Local thermal resonance control of GaInP photonic crystal membrane cavities using ambient gas cooling,” Appl. Phys. Lett. 106(17), 171113 (2015).
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S. Combrié, Q. V. Tran, A. De Rossi, C. Husko, and P. Colman, “High quality GaInP nonlinear photonic crystals with minimized nonlinear absorption,” Appl. Phys. Lett. 95(22), 221108 (2009).
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N. Caselli, F. Intonti, C. Bianchi, F. Riboli, S. Vignolini, L. Balet, L. H. Li, M. Francardi, A. Gerardino, A. Fiore, and M. Gurioli, “Post-fabrication control of evanescent tunnelling in photonic crystal molecules,” Appl. Phys. Lett. 101(21), 211108 (2012).
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M. Qiu, “Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals,” Appl. Phys. Lett. 81(7), 1163 (2002).
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K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012).
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F. Riboli, N. Caselli, S. Vignolini, F. Intonti, K. Vynck, P. Barthelemy, A. Gerardino, L. Balet, L. H. Li, A. Fiore, M. Gurioli, and D. S. Wiersma, “Engineering of light confinement in strongly scattering disordered media,” Nat. Mater. 13(7), 720–725 (2014).
[Crossref] [PubMed]

Nat. Photonics (2)

R. Bruck, B. Mills, B. Troia, D. J. Thomson, F. Y. Gardes, Y. Hu, G. Z. Mashanovich, V. M. N. Passaro, G. T. Reed, and O. L. Muskens, “Device-level characterization of the flow of light in integrated photonic circuits using ultrafast photomodulation spectroscopy,” Nat. Photonics 9(1), 54–60 (2014).
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D. S. Wiersma, “Disordered photonics,” Nat. Photonics 7(3), 188–196 (2013).
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[Crossref]

S. R. Huisman, G. Ctistis, S. Stobbe, A. P. Mosk, J. L. Herek, A. Lagendijk, P. Lodahl, W. L. Vos, and P. W. H. Pinkse, “Measurement of a band-edge tail in the density of states of a photonic-crystal waveguide,” Phys. Rev. B 86(15), 155154 (2012).
[Crossref]

A. F. Koenderink, A. Lagendijk, and W. L. Vos, “Optical extinction due to intrinsic structural variations of photonic crystals,” Phys. Rev. B 72(15), 153102 (2005).
[Crossref]

E. Kuramochi, M. Notomi, S. Hughes, A. Shinya, T. Watanabe, and L. Ramunno, “Disorder-induced scattering loss of line-defect waveguides in photonic crystal slabs,” Phys. Rev. B 72(16), 161318 (2005).
[Crossref]

R. Sarma, A. Yamilov, P. Neupane, B. Shapiro, and H. Cao, “Probing long-range intensity correlations inside disordered photonic nanostructures,” Phys. Rev. B 90(1), 014203 (2014).
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R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, K. Vynck, B. O. Regan, B. Cluzel, F. De Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci Rep. 6, 27037 (2016).
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Science (1)

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J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: molding the flow of light (Princeton University Press, 2008).

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Figures (5)

Fig. 1
Fig. 1 (a) Visualization of the intensity of a typical disorder induced localized mode in a photonic crystal waveguide. (b) Zooming in of the center part of (a), the intensity is scaled down in order to show that the periodic oscillation of the intensity matches the period of the waveguide.
Fig. 2
Fig. 2 Experimental setup and schematic representation of the sample. A Photodiode (PD) is used to detect the transmission signal. Polarization maintaining lensed fibers (PMF) are used to couple light from the CW IR laser to the sample and couple light out of sample to the PD.
Fig. 3
Fig. 3 (a) Transmission spectrum of the sample. (b) Zoomed in reference (black) and pumped (red) transmission spectra of the sample. The system transmission here is defined as the ratio between the power we send into the input fiber and the power we detect on the PD.
Fig. 4
Fig. 4 (a) Black circles: mean value of wavelength shift versus pump spot position of 5 independent measurements. The standard deviation is approximately equal to the symbol size. Red curve: temperature distribution along the waveguide direction. (b) Black curve: reconstructed mode profile along the waveguide direction. Pink bar: 3σE confidence interval.
Fig. 5
Fig. 5 Numerical validation of the mode reconstruction method. (a) Amplitude of the y component of the electric field |Ey| of a simulated mode. (b) Black circles: wavelength shift versus pump spot position. The effect of the pump is simulated by the relative change of the dielectric constant distribution as shown in the top left. (c) Green curve: directly simulated intensity projected along the x axis. Black curve: reconstructed profile from simulated measurement.

Equations (3)

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Δ λ ( r 0 ) λ 0 δ ( r 0 r ) | E ( r ) | 2 d r ( r ) | E ( r ) | 2 d r .
Δ λ ( x 0 ) α ( T ( x 0 x ) T 0 ) | E X ( x ) | 2 d x .
I ( f x ) = S ( f x ) H ( f x ) G ( f x ) ,

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