F. C. Moreira, V. V. Konotop, and B. A. Malomed, “Solitons in PT-symmetric periodic systems with the quadratic nonlinearity,” Phys. Rev. A 87, 013832 (2013).

[CrossRef]

S. Hu and W. Hu, “Defect solitons in parity-time symmetric optical lattices with self-defocusing nonlinearity,” Opt. Commun. 294, 311–324 (2013).

[CrossRef]

J. Zeng and Y. Lan, “Two-dimensional solitons in PT linear lattice potentials,” Phys. Rev. E 85, 047601 (2012).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Symmetric and asymmetric localized modes in linear lattices with an embedded pair of χ(2)-nonlinear sites,” Phys. Rev. A 86, 013829 (2012).

[CrossRef]

F. C. Moreira, F. K. Abdullaev, V. V. Konotop, and A. V. Yulin, “Localized modes in χ(2) media with PT—symmetric localized potential,” Phys. Rev. A 86, 053815 (2012).

[CrossRef]

J. Zeng and B. A. Malomed, “Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices,” Phys. Rev. A 85, 023824 (2012).

[CrossRef]

J. Zeng and B. A. Malomed, “Two-dimensional solitons and vortices in media with incommensurate linear and nonlinear lattice potentials,” Phys. Scr. T149, 014035 (2012).

[CrossRef]

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012).

[CrossRef]

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6, 178–218 (2012).

[CrossRef]

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. A. Vincenti, and A. Alú, “Transmission resonances in plasmonic metallic gratings,” J. Opt. Soc. Am. B 28, 253–264 (2011).

[CrossRef]

D. de Ceglia, M. A. Vincenti, M. Scalora, N. Akozbek, and M. J. Bloemer, “Plasmonic band edge effects on the transmission properties of metal gratings,” AIP Adv. 1, 032151 (2011).

[CrossRef]

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, “Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays,” Phys. Rev. Lett. 106, 093901 (2011).

[CrossRef]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).

[CrossRef]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).

[CrossRef]

E. Bulgakov, K. Pichugin, and A. Sadreev, “Symmetry breaking for transmission in a photonic waveguide coupled with two off-channel nonlinear defects,” Phys. Rev. B 83, 045109 (2011).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects,” Phys. Rev. E 83, 016604 (2011).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Dragging two-dimensional discrete solitons by moving linear defects,” Phys. Rev. E 84, 016608 (2011).

[CrossRef]

N. Dror and B. A. Malomed, “Solitons supported by localized nonlinearities in periodic media,” Phys. Rev. A 83, 033828 (2011).

[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and A. Reoksabutr, “Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials,” J. Mod. Opt. 58, 1977–1989 (2011).

[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).

[CrossRef]

S. Longhi, “Dynamic reflectionless defects in tight-binding lattices,” Phys. Rev. B 84, 193105 (2011).

[CrossRef]

A. Shapira, N. Voloch-Bloch, B. A. Malomed, and A. Arie, “Spatial quadratic solitons guided by narrow layers of a nonlinear material,” J. Opt. Soc. Am. B 28, 1481–1489 (2011).

[CrossRef]

L. Sanchez-Palencia and M. Lewenstein, “Disordered quantum gases under control,” Nat. Phys. 6, 87–95 (2010).

[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Dissipative defect modes in periodic structures,” Opt. Lett. 35, 1638–1640 (2010).

[CrossRef]

S. Longhi, “Bloch oscillations in tight-binding lattices with defects,” Phys. Rev. B 81, 195118 (2010).

[CrossRef]

J. Yang, “Fully localized two-dimensional embedded solitons,” Phys. Rev. A 82, 053828 (2010).

[CrossRef]

P. Genevet, J. P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).

[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progress in Optics 52, 63–148 (2009).

[CrossRef]

A. Abdelrahman, P. Hannaford, and K. Alameh, “Adiabatically induced coherent Josephson oscillations of ultracold atoms in an asymmetric two-dimensional magnetic lattice,” Opt. Express 17, 24358–24370 (2009).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Two-dimensional dissipative gap solitons,” Phys. Rev. E 80, 026606 (2009).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Gap solitons in Ginzburg-Landau media,” Phys. Rev. E 77, 056606 (2008).

[CrossRef]

R. Driben and B. A. Malomed, “Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials,” Eur. Phys. J. D 50, 317–323 (2008).

[CrossRef]

S. K. Adhikari and B. A. Malomed, “Symbiotic gap and semigap solitons in Bose-Einstein condensates,” Phys. Rev. A 77, 023607 (2008).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).

[CrossRef]

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16, 413–425 (2008).

[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).

[CrossRef]

S. A. Rinne, F. Garca-Santamara, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).

[CrossRef]

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).

[CrossRef]

A. Gubeskys and B. A. Malomed, “Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices,” Phys. Rev. A 76, 043623 (2007).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).

[CrossRef]

Z. Shi and J. Yang, “Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media,” Phys. Rev. E 75, 056602 (2007).

[CrossRef]

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A 76, 043826 (2007).

[CrossRef]

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, “Permanent magnetic lattices for ultracold atoms and quantum degenerate gases,” J. Phys. B 39, 847–860 (2006).

[CrossRef]

M. Storzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).

[CrossRef]

T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, “Self-trapped nonlinear matter waves in periodic potentials,” Phys. Rev. Lett. 96, 040401 (2006).

[CrossRef]

A. Boltasseva, S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, “Compact Bragg gratings for long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 912–918 (2006).

[CrossRef]

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78, 179–215 (2006).

[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).

[CrossRef]

I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. 96, 223903 (2006).

[CrossRef]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Pérez-Garca, “Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity,” Phys. Rev. A 74, 023614 (2006).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Pérez-Garca, “Driving defect modes of Bose-Einstein condensates in optical lattices,” Phys. Rev. Lett. 96, 060403 (2006).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).

[CrossRef]

T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).

[CrossRef]

U. Gavish and Y. Castin, “Matter-wave localization in disordered cold atom lattices,” Phys. Rev. Lett. 95, 020401 (2005).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice,” Europhys. Lett. 72, 698–704 (2005).

[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, “Photonic crystals for matter waves: Bose-Einstein condensates in optical lattices,” Opt. Express 12, 19–29 (2004).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B 37, 1443–1459 (2004).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Two-dimensional loosely and tightly bound solitons in optical lattices and inverted traps,” J. Phys. B 37, 2225–2239 (2004).

[CrossRef]

G. Van de Walle and J. Neugebauer, “First-principles calculations for defects and impurities: applications to III-nitrides,” J. Appl. Phys. 95, 3851–3879 (2004).

[CrossRef]

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B 18, 627–651 (2004).

[CrossRef]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).

[CrossRef]

J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sanchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett. 93, 256804 (2004).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Symmetric and asymmetric solitons in linearly coupled Bragg gratings,” Phys. Rev. E 69, 066610 (2004).

[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).

[CrossRef]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004).

[CrossRef]

J. Yang and T. R. Akylas, “Continuous families of embedded solitons in the third-order nonlinear Schrödinger equation,” Stud. Appl. Math. 111, 359–375 (2003).

[CrossRef]

J. Yang, “Stable embedded solitons,” Phys. Rev. Lett. 91, 143903 (2003).

[CrossRef]

A. Espinosa-Cerón, J. Fujioka, and A. Gómez-Rodrguez, “Embedded solitons: four-frequency radiation, front propagation and radiation inhibition,” Phys. Scr. 67, 314–324 (2003).

[CrossRef]

R. F. Rodrguez, J. A. Reyes, A. Espinosa-Cerón, J. Fujioka, and B. A. Malomed, “Standard and embedded solitons in nematic optical fibers,” Phys. Rev. E 68, 036606 (2003).

[CrossRef]

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).

[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90, 160407 (2003).

[CrossRef]

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).

[CrossRef]

A. Khelif, A. Choujaa, B. Djafari-Rouhani, M. Wilm, S. Ballandras, and V. Laude, “Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal,” Phys. Rev. B 68, 214301 (2003).

[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642–648 (2003).

[CrossRef]

J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28, 2094–2096 (2003).

[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).

[CrossRef]

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).

[CrossRef]

D. E. Pelinovsky and J. Yang, “A normal form for nonlinear resonance of embedded solitons,” Proc. R. Soc. A 458, 1469–1497 (2002).

[CrossRef]

J. Yang, “Dynamics of embedded solitons in the extended Korteweg–de Vries equations,” Stud. Appl. Math. 106, 337–365 (2001).

[CrossRef]

A. R. Champneys, B. A. Malomed, J. Yang, and D. J. Kaup, “Embedded solitons: solitary waves in resonance with the linear spectrum,” Physica D 152, 340–354 (2001).

[CrossRef]

J. Atai and B. A. Malomed, “Solitary waves in systems with separated Bragg grating and nonlinearity,” Phys. Rev. E 64, 066617 (2001).

[CrossRef]

V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).

[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001).

[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).

[CrossRef]

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).

[CrossRef]

H. Cao, J. Y. Xu, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997–2999 (2000).

[CrossRef]

G. Kaczmarczyk, A. Kaschner, A. Hoffmann, and C. Thomsen, “Impurity-induced modes of Mg, As, Si, and C in hexagonal and cubic GaN,” Phys. Rev. B 61, 5353–5357 (2000).

[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).

[CrossRef]

S. Noda, A. Chutinan, and M. Imada, “Trapping, and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).

[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).

[CrossRef]

J. Yang, B. A. Malomed, and D. J. Kaup, “Embedded solitons in second-harmonic-generating systems,” Phys. Rev. Lett. 83, 1958–1961 (1999).

[CrossRef]

A. R. Champneys and B. A. Malomed, “Moving embedded solitons,” J. Phys. A 32, L547–L553 (1999).

[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).

[CrossRef]

O. Painter, J. Vučković, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).

[CrossRef]

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).

[CrossRef]

Y. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).

[CrossRef]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).

[CrossRef]

S. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).

[CrossRef]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).

[CrossRef]

B. C. Gupta and K. Kundu, “Formation of stationary localized states due to nonlinear impurities using the discrete nonlinear Schrödinger equation,” Phys. Rev. B 55, 894–905 (1997).

[CrossRef]

B. C. Gupta and K. Kundu, “Stationary localized states due to a nonlinear dimeric impurity embedded in a perfect one-dimensional chain,” Phys. Rev. B 55, 11033–11036 (1997).

[CrossRef]

J. Fujioka and A. Espinosa, “Soliton-like solution of an extended NLS equation existing in resonance with linear dispersive waves,” J. Phys. Soc. Jpn. 66, 2601–2607 (1997).

[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).

[CrossRef]

M. I. Molina and G. Tsironis, “Nonlinear impurities in a linear chain,” Phys. Rev. B 47, 15330–15333 (1993).

[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).

[CrossRef]

S. R. Bickham and A. J. Sievers, “Intrinsic localized modes in a monatomic lattice with weakly anharmonic nearest-neighbor force constants,” Phys. Rev. B 43, 2339–2346 (1991).

[CrossRef]

H. R. Schober and B. B. Laird, “Localized low-frequency vibrational modes in glasses,” Phys. Rev. B 44, 6746–6754 (1991).

[CrossRef]

M. Vakhitov and A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16, 783–789 (1973).

[CrossRef]

F. C. Moreira, F. K. Abdullaev, V. V. Konotop, and A. V. Yulin, “Localized modes in χ(2) media with PT—symmetric localized potential,” Phys. Rev. A 86, 053815 (2012).

[CrossRef]

S. K. Adhikari and B. A. Malomed, “Symbiotic gap and semigap solitons in Bose-Einstein condensates,” Phys. Rev. A 77, 023607 (2008).

[CrossRef]

M. Storzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).

[CrossRef]

D. de Ceglia, M. A. Vincenti, M. Scalora, N. Akozbek, and M. J. Bloemer, “Plasmonic band edge effects on the transmission properties of metal gratings,” AIP Adv. 1, 032151 (2011).

[CrossRef]

J. Yang and T. R. Akylas, “Continuous families of embedded solitons in the third-order nonlinear Schrödinger equation,” Stud. Appl. Math. 111, 359–375 (2003).

[CrossRef]

T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).

[CrossRef]

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, “Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays,” Phys. Rev. Lett. 106, 093901 (2011).

[CrossRef]

T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, “Self-trapped nonlinear matter waves in periodic potentials,” Phys. Rev. Lett. 96, 040401 (2006).

[CrossRef]

T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).

[CrossRef]

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012).

[CrossRef]

A. Shapira, N. Voloch-Bloch, B. A. Malomed, and A. Arie, “Spatial quadratic solitons guided by narrow layers of a nonlinear material,” J. Opt. Soc. Am. B 28, 1481–1489 (2011).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

J. Atai and B. A. Malomed, “Solitary waves in systems with separated Bragg grating and nonlinearity,” Phys. Rev. E 64, 066617 (2001).

[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).

[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642–648 (2003).

[CrossRef]

A. Khelif, A. Choujaa, B. Djafari-Rouhani, M. Wilm, S. Ballandras, and V. Laude, “Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal,” Phys. Rev. B 68, 214301 (2003).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).

[CrossRef]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).

[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).

[CrossRef]

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, “Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays,” Phys. Rev. Lett. 106, 093901 (2011).

[CrossRef]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).

[CrossRef]

S. R. Bickham and A. J. Sievers, “Intrinsic localized modes in a monatomic lattice with weakly anharmonic nearest-neighbor force constants,” Phys. Rev. B 43, 2339–2346 (1991).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

P. Genevet, J. P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).

[CrossRef]

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. A. Vincenti, and A. Alú, “Transmission resonances in plasmonic metallic gratings,” J. Opt. Soc. Am. B 28, 253–264 (2011).

[CrossRef]

D. de Ceglia, M. A. Vincenti, M. Scalora, N. Akozbek, and M. J. Bloemer, “Plasmonic band edge effects on the transmission properties of metal gratings,” AIP Adv. 1, 032151 (2011).

[CrossRef]

J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sanchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett. 93, 256804 (2004).

[CrossRef]

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6, 178–218 (2012).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).

[CrossRef]

S. A. Rinne, F. Garca-Santamara, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Symmetric and asymmetric localized modes in linear lattices with an embedded pair of χ(2)-nonlinear sites,” Phys. Rev. A 86, 013829 (2012).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects,” Phys. Rev. E 83, 016604 (2011).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Dragging two-dimensional discrete solitons by moving linear defects,” Phys. Rev. E 84, 016608 (2011).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Pérez-Garca, “Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity,” Phys. Rev. A 74, 023614 (2006).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Pérez-Garca, “Driving defect modes of Bose-Einstein condensates in optical lattices,” Phys. Rev. Lett. 96, 060403 (2006).

[CrossRef]

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B 18, 627–651 (2004).

[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).

[CrossRef]

E. Bulgakov, K. Pichugin, and A. Sadreev, “Symmetry breaking for transmission in a photonic waveguide coupled with two off-channel nonlinear defects,” Phys. Rev. B 83, 045109 (2011).

[CrossRef]

H. Cao, J. Y. Xu, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997–2999 (2000).

[CrossRef]

P. Genevet, J. P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).

[CrossRef]

U. Gavish and Y. Castin, “Matter-wave localization in disordered cold atom lattices,” Phys. Rev. Lett. 95, 020401 (2005).

[CrossRef]

A. R. Champneys, B. A. Malomed, J. Yang, and D. J. Kaup, “Embedded solitons: solitary waves in resonance with the linear spectrum,” Physica D 152, 340–354 (2001).

[CrossRef]

A. R. Champneys and B. A. Malomed, “Moving embedded solitons,” J. Phys. A 32, L547–L553 (1999).

[CrossRef]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).

[CrossRef]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).

[CrossRef]

H. Cao, J. Y. Xu, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997–2999 (2000).

[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).

[CrossRef]

I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. 96, 223903 (2006).

[CrossRef]

A. Khelif, A. Choujaa, B. Djafari-Rouhani, M. Wilm, S. Ballandras, and V. Laude, “Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal,” Phys. Rev. B 68, 214301 (2003).

[CrossRef]

S. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).

[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).

[CrossRef]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Symmetric and asymmetric solitons in linearly coupled Bragg gratings,” Phys. Rev. E 69, 066610 (2004).

[CrossRef]

S. Noda, A. Chutinan, and M. Imada, “Trapping, and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6, 178–218 (2012).

[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).

[CrossRef]

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).

[CrossRef]

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. A. Vincenti, and A. Alú, “Transmission resonances in plasmonic metallic gratings,” J. Opt. Soc. Am. B 28, 253–264 (2011).

[CrossRef]

D. de Ceglia, M. A. Vincenti, M. Scalora, N. Akozbek, and M. J. Bloemer, “Plasmonic band edge effects on the transmission properties of metal gratings,” AIP Adv. 1, 032151 (2011).

[CrossRef]

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer, 2009).

A. Khelif, A. Choujaa, B. Djafari-Rouhani, M. Wilm, S. Ballandras, and V. Laude, “Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal,” Phys. Rev. B 68, 214301 (2003).

[CrossRef]

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012).

[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).

[CrossRef]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).

[CrossRef]

R. Driben and B. A. Malomed, “Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials,” Eur. Phys. J. D 50, 317–323 (2008).

[CrossRef]

N. Dror and B. A. Malomed, “Solitons supported by localized nonlinearities in periodic media,” Phys. Rev. A 83, 033828 (2011).

[CrossRef]

N. Dror and B. A. Malomed, “Stability of dipole gap solitons in two-dimensional lattice potentials,” in Spectral Analysis, Stability and Bifurcations in Nonlinear Physical Systems, O. Kirillov and D. E. Pelinovsky, eds. (Wiley, 2013).

T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).

[CrossRef]

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012).

[CrossRef]

J. Fujioka and A. Espinosa, “Soliton-like solution of an extended NLS equation existing in resonance with linear dispersive waves,” J. Phys. Soc. Jpn. 66, 2601–2607 (1997).

[CrossRef]

A. Espinosa-Cerón, J. Fujioka, and A. Gómez-Rodrguez, “Embedded solitons: four-frequency radiation, front propagation and radiation inhibition,” Phys. Scr. 67, 314–324 (2003).

[CrossRef]

R. F. Rodrguez, J. A. Reyes, A. Espinosa-Cerón, J. Fujioka, and B. A. Malomed, “Standard and embedded solitons in nematic optical fibers,” Phys. Rev. E 68, 036606 (2003).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).

[CrossRef]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).

[CrossRef]

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).

[CrossRef]

R. F. Rodrguez, J. A. Reyes, A. Espinosa-Cerón, J. Fujioka, and B. A. Malomed, “Standard and embedded solitons in nematic optical fibers,” Phys. Rev. E 68, 036606 (2003).

[CrossRef]

A. Espinosa-Cerón, J. Fujioka, and A. Gómez-Rodrguez, “Embedded solitons: four-frequency radiation, front propagation and radiation inhibition,” Phys. Scr. 67, 314–324 (2003).

[CrossRef]

J. Fujioka and A. Espinosa, “Soliton-like solution of an extended NLS equation existing in resonance with linear dispersive waves,” J. Phys. Soc. Jpn. 66, 2601–2607 (1997).

[CrossRef]

S. A. Rinne, F. Garca-Santamara, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).

[CrossRef]

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).

[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).

[CrossRef]

T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).

[CrossRef]

P. Genevet, J. P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).

[CrossRef]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).

[CrossRef]

U. Gavish and Y. Castin, “Matter-wave localization in disordered cold atom lattices,” Phys. Rev. Lett. 95, 020401 (2005).

[CrossRef]

P. Genevet, J. P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).

[CrossRef]

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, “Permanent magnetic lattices for ultracold atoms and quantum degenerate gases,” J. Phys. B 39, 847–860 (2006).

[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).

[CrossRef]

A. Espinosa-Cerón, J. Fujioka, and A. Gómez-Rodrguez, “Embedded solitons: four-frequency radiation, front propagation and radiation inhibition,” Phys. Scr. 67, 314–324 (2003).

[CrossRef]

M. Storzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).

[CrossRef]

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer, 2009).

A. Gubeskys and B. A. Malomed, “Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices,” Phys. Rev. A 76, 043623 (2007).

[CrossRef]

B. C. Gupta and K. Kundu, “Stationary localized states due to a nonlinear dimeric impurity embedded in a perfect one-dimensional chain,” Phys. Rev. B 55, 11033–11036 (1997).

[CrossRef]

B. C. Gupta and K. Kundu, “Formation of stationary localized states due to nonlinear impurities using the discrete nonlinear Schrödinger equation,” Phys. Rev. B 55, 894–905 (1997).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).

[CrossRef]

A. Abdelrahman, P. Hannaford, and K. Alameh, “Adiabatically induced coherent Josephson oscillations of ultracold atoms in an asymmetric two-dimensional magnetic lattice,” Opt. Express 17, 24358–24370 (2009).

[CrossRef]

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, “Permanent magnetic lattices for ultracold atoms and quantum degenerate gases,” J. Phys. B 39, 847–860 (2006).

[CrossRef]

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, “Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays,” Phys. Rev. Lett. 106, 093901 (2011).

[CrossRef]

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).

[CrossRef]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).

[CrossRef]

S. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).

[CrossRef]

G. Kaczmarczyk, A. Kaschner, A. Hoffmann, and C. Thomsen, “Impurity-induced modes of Mg, As, Si, and C in hexagonal and cubic GaN,” Phys. Rev. B 61, 5353–5357 (2000).

[CrossRef]

S. Hu and W. Hu, “Defect solitons in parity-time symmetric optical lattices with self-defocusing nonlinearity,” Opt. Commun. 294, 311–324 (2013).

[CrossRef]

S. Hu and W. Hu, “Defect solitons in parity-time symmetric optical lattices with self-defocusing nonlinearity,” Opt. Commun. 294, 311–324 (2013).

[CrossRef]

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).

[CrossRef]

T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).

[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).

[CrossRef]

S. Noda, A. Chutinan, and M. Imada, “Trapping, and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004).

[CrossRef]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004).

[CrossRef]

S. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).

[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).

[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).

[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004).

[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

G. Kaczmarczyk, A. Kaschner, A. Hoffmann, and C. Thomsen, “Impurity-induced modes of Mg, As, Si, and C in hexagonal and cubic GaN,” Phys. Rev. B 61, 5353–5357 (2000).

[CrossRef]

Y. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).

[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).

[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Dissipative defect modes in periodic structures,” Opt. Lett. 35, 1638–1640 (2010).

[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progress in Optics 52, 63–148 (2009).

[CrossRef]

G. Kaczmarczyk, A. Kaschner, A. Hoffmann, and C. Thomsen, “Impurity-induced modes of Mg, As, Si, and C in hexagonal and cubic GaN,” Phys. Rev. B 61, 5353–5357 (2000).

[CrossRef]

P. Genevet, J. P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).

[CrossRef]

A. R. Champneys, B. A. Malomed, J. Yang, and D. J. Kaup, “Embedded solitons: solitary waves in resonance with the linear spectrum,” Physica D 152, 340–354 (2001).

[CrossRef]

J. Yang, B. A. Malomed, and D. J. Kaup, “Embedded solitons in second-harmonic-generating systems,” Phys. Rev. Lett. 83, 1958–1961 (1999).

[CrossRef]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).

[CrossRef]

A. Khelif, A. Choujaa, B. Djafari-Rouhani, M. Wilm, S. Ballandras, and V. Laude, “Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal,” Phys. Rev. B 68, 214301 (2003).

[CrossRef]

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, “Permanent magnetic lattices for ultracold atoms and quantum degenerate gases,” J. Phys. B 39, 847–860 (2006).

[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).

[CrossRef]

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).

[CrossRef]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).

[CrossRef]

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, “Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays,” Phys. Rev. Lett. 106, 093901 (2011).

[CrossRef]

T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, “Self-trapped nonlinear matter waves in periodic potentials,” Phys. Rev. Lett. 96, 040401 (2006).

[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, “Photonic crystals for matter waves: Bose-Einstein condensates in optical lattices,” Opt. Express 12, 19–29 (2004).

[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90, 160407 (2003).

[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).

[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001).

[CrossRef]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).

[CrossRef]

M. Vakhitov and A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16, 783–789 (1973).

[CrossRef]

F. C. Moreira, V. V. Konotop, and B. A. Malomed, “Solitons in PT-symmetric periodic systems with the quadratic nonlinearity,” Phys. Rev. A 87, 013832 (2013).

[CrossRef]

F. C. Moreira, F. K. Abdullaev, V. V. Konotop, and A. V. Yulin, “Localized modes in χ(2) media with PT—symmetric localized potential,” Phys. Rev. A 86, 053815 (2012).

[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Dissipative defect modes in periodic structures,” Opt. Lett. 35, 1638–1640 (2010).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Pérez-Garca, “Driving defect modes of Bose-Einstein condensates in optical lattices,” Phys. Rev. Lett. 96, 060403 (2006).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Pérez-Garca, “Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity,” Phys. Rev. A 74, 023614 (2006).

[CrossRef]

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B 18, 627–651 (2004).

[CrossRef]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).

[CrossRef]

B. C. Gupta and K. Kundu, “Stationary localized states due to a nonlinear dimeric impurity embedded in a perfect one-dimensional chain,” Phys. Rev. B 55, 11033–11036 (1997).

[CrossRef]

B. C. Gupta and K. Kundu, “Formation of stationary localized states due to nonlinear impurities using the discrete nonlinear Schrödinger equation,” Phys. Rev. B 55, 894–905 (1997).

[CrossRef]

J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sanchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett. 93, 256804 (2004).

[CrossRef]

J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sanchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett. 93, 256804 (2004).

[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).

[CrossRef]

H. R. Schober and B. B. Laird, “Localized low-frequency vibrational modes in glasses,” Phys. Rev. B 44, 6746–6754 (1991).

[CrossRef]

J. Zeng and Y. Lan, “Two-dimensional solitons in PT linear lattice potentials,” Phys. Rev. E 85, 047601 (2012).

[CrossRef]

A. Khelif, A. Choujaa, B. Djafari-Rouhani, M. Wilm, S. Ballandras, and V. Laude, “Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal,” Phys. Rev. B 68, 214301 (2003).

[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).

[CrossRef]

L. Sanchez-Palencia and M. Lewenstein, “Disordered quantum gases under control,” Nat. Phys. 6, 87–95 (2010).

[CrossRef]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004).

[CrossRef]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).

[CrossRef]

S. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).

[CrossRef]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).

[CrossRef]

S. Longhi, “Dynamic reflectionless defects in tight-binding lattices,” Phys. Rev. B 84, 193105 (2011).

[CrossRef]

S. Longhi, “Bloch oscillations in tight-binding lattices with defects,” Phys. Rev. B 81, 195118 (2010).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Symmetric and asymmetric solitons in linearly coupled Bragg gratings,” Phys. Rev. E 69, 066610 (2004).

[CrossRef]

I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. 96, 223903 (2006).

[CrossRef]

F. C. Moreira, V. V. Konotop, and B. A. Malomed, “Solitons in PT-symmetric periodic systems with the quadratic nonlinearity,” Phys. Rev. A 87, 013832 (2013).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Symmetric and asymmetric localized modes in linear lattices with an embedded pair of χ(2)-nonlinear sites,” Phys. Rev. A 86, 013829 (2012).

[CrossRef]

J. Zeng and B. A. Malomed, “Two-dimensional solitons and vortices in media with incommensurate linear and nonlinear lattice potentials,” Phys. Scr. T149, 014035 (2012).

[CrossRef]

J. Zeng and B. A. Malomed, “Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices,” Phys. Rev. A 85, 023824 (2012).

[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).

[CrossRef]

A. Shapira, N. Voloch-Bloch, B. A. Malomed, and A. Arie, “Spatial quadratic solitons guided by narrow layers of a nonlinear material,” J. Opt. Soc. Am. B 28, 1481–1489 (2011).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Dragging two-dimensional discrete solitons by moving linear defects,” Phys. Rev. E 84, 016608 (2011).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects,” Phys. Rev. E 83, 016604 (2011).

[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and A. Reoksabutr, “Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials,” J. Mod. Opt. 58, 1977–1989 (2011).

[CrossRef]

N. Dror and B. A. Malomed, “Solitons supported by localized nonlinearities in periodic media,” Phys. Rev. A 83, 033828 (2011).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Two-dimensional dissipative gap solitons,” Phys. Rev. E 80, 026606 (2009).

[CrossRef]

R. Driben and B. A. Malomed, “Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials,” Eur. Phys. J. D 50, 317–323 (2008).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Gap solitons in Ginzburg-Landau media,” Phys. Rev. E 77, 056606 (2008).

[CrossRef]

S. K. Adhikari and B. A. Malomed, “Symbiotic gap and semigap solitons in Bose-Einstein condensates,” Phys. Rev. A 77, 023607 (2008).

[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).

[CrossRef]

A. Gubeskys and B. A. Malomed, “Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices,” Phys. Rev. A 76, 043623 (2007).

[CrossRef]

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A 76, 043826 (2007).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice,” Europhys. Lett. 72, 698–704 (2005).

[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Symmetric and asymmetric solitons in linearly coupled Bragg gratings,” Phys. Rev. E 69, 066610 (2004).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Two-dimensional loosely and tightly bound solitons in optical lattices and inverted traps,” J. Phys. B 37, 2225–2239 (2004).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B 37, 1443–1459 (2004).

[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642–648 (2003).

[CrossRef]

R. F. Rodrguez, J. A. Reyes, A. Espinosa-Cerón, J. Fujioka, and B. A. Malomed, “Standard and embedded solitons in nematic optical fibers,” Phys. Rev. E 68, 036606 (2003).

[CrossRef]

A. R. Champneys, B. A. Malomed, J. Yang, and D. J. Kaup, “Embedded solitons: solitary waves in resonance with the linear spectrum,” Physica D 152, 340–354 (2001).

[CrossRef]

J. Atai and B. A. Malomed, “Solitary waves in systems with separated Bragg grating and nonlinearity,” Phys. Rev. E 64, 066617 (2001).

[CrossRef]

A. R. Champneys and B. A. Malomed, “Moving embedded solitons,” J. Phys. A 32, L547–L553 (1999).

[CrossRef]

J. Yang, B. A. Malomed, and D. J. Kaup, “Embedded solitons in second-harmonic-generating systems,” Phys. Rev. Lett. 83, 1958–1961 (1999).

[CrossRef]

N. Dror and B. A. Malomed, “Stability of dipole gap solitons in two-dimensional lattice potentials,” in Spectral Analysis, Stability and Bifurcations in Nonlinear Physical Systems, O. Kirillov and D. E. Pelinovsky, eds. (Wiley, 2013).

M. Storzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).

[CrossRef]

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).

[CrossRef]

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A 76, 043826 (2007).

[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and A. Reoksabutr, “Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials,” J. Mod. Opt. 58, 1977–1989 (2011).

[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).

[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).

[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).

[CrossRef]

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, “Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays,” Phys. Rev. Lett. 106, 093901 (2011).

[CrossRef]

V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

M. I. Molina and G. Tsironis, “Nonlinear impurities in a linear chain,” Phys. Rev. B 47, 15330–15333 (1993).

[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).

[CrossRef]

F. C. Moreira, V. V. Konotop, and B. A. Malomed, “Solitons in PT-symmetric periodic systems with the quadratic nonlinearity,” Phys. Rev. A 87, 013832 (2013).

[CrossRef]

F. C. Moreira, F. K. Abdullaev, V. V. Konotop, and A. V. Yulin, “Localized modes in χ(2) media with PT—symmetric localized potential,” Phys. Rev. A 86, 053815 (2012).

[CrossRef]

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78, 179–215 (2006).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, “Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays,” Phys. Rev. Lett. 106, 093901 (2011).

[CrossRef]

G. Van de Walle and J. Neugebauer, “First-principles calculations for defects and impurities: applications to III-nitrides,” J. Appl. Phys. 95, 3851–3879 (2004).

[CrossRef]

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).

[CrossRef]

Y. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).

[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).

[CrossRef]

S. Noda, A. Chutinan, and M. Imada, “Trapping, and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).

[CrossRef]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).

[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).

[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).

[CrossRef]

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78, 179–215 (2006).

[CrossRef]

T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).

[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).

[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).

[CrossRef]

T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, “Self-trapped nonlinear matter waves in periodic potentials,” Phys. Rev. Lett. 96, 040401 (2006).

[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, “Photonic crystals for matter waves: Bose-Einstein condensates in optical lattices,” Opt. Express 12, 19–29 (2004).

[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90, 160407 (2003).

[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).

[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).

[CrossRef]

O. Painter, J. Vučković, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).

[CrossRef]

D. E. Pelinovsky and J. Yang, “A normal form for nonlinear resonance of embedded solitons,” Proc. R. Soc. A 458, 1469–1497 (2002).

[CrossRef]

D. E. Pelinovsky, Localization in Periodic Potential: From Schrödinger Operators to the Gross-Pitaevskii Equation (Cambridge University, 2011).

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Pérez-Garca, “Driving defect modes of Bose-Einstein condensates in optical lattices,” Phys. Rev. Lett. 96, 060403 (2006).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Pérez-Garca, “Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity,” Phys. Rev. A 74, 023614 (2006).

[CrossRef]

C. J. Pethick and H. Smith, Bose-Einstein Condensate in Dilute Gas (Cambridge University, 2008).

E. Bulgakov, K. Pichugin, and A. Sadreev, “Symmetry breaking for transmission in a photonic waveguide coupled with two off-channel nonlinear defects,” Phys. Rev. B 83, 045109 (2011).

[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).

[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).

[CrossRef]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004).

[CrossRef]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004).

[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).

[CrossRef]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).

[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and A. Reoksabutr, “Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials,” J. Mod. Opt. 58, 1977–1989 (2011).

[CrossRef]

R. F. Rodrguez, J. A. Reyes, A. Espinosa-Cerón, J. Fujioka, and B. A. Malomed, “Standard and embedded solitons in nematic optical fibers,” Phys. Rev. E 68, 036606 (2003).

[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

[CrossRef]

S. A. Rinne, F. Garca-Santamara, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).

[CrossRef]

J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sanchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett. 93, 256804 (2004).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).

[CrossRef]

R. F. Rodrguez, J. A. Reyes, A. Espinosa-Cerón, J. Fujioka, and B. A. Malomed, “Standard and embedded solitons in nematic optical fibers,” Phys. Rev. E 68, 036606 (2003).

[CrossRef]

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).

[CrossRef]

E. Bulgakov, K. Pichugin, and A. Sadreev, “Symmetry breaking for transmission in a photonic waveguide coupled with two off-channel nonlinear defects,” Phys. Rev. B 83, 045109 (2011).

[CrossRef]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Two-dimensional dissipative gap solitons,” Phys. Rev. E 80, 026606 (2009).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Gap solitons in Ginzburg-Landau media,” Phys. Rev. E 77, 056606 (2008).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice,” Europhys. Lett. 72, 698–704 (2005).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Two-dimensional loosely and tightly bound solitons in optical lattices and inverted traps,” J. Phys. B 37, 2225–2239 (2004).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B 37, 1443–1459 (2004).

[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642–648 (2003).

[CrossRef]

J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sanchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett. 93, 256804 (2004).

[CrossRef]

L. Sanchez-Palencia and M. Lewenstein, “Disordered quantum gases under control,” Nat. Phys. 6, 87–95 (2010).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

D. de Ceglia, M. A. Vincenti, M. Scalora, N. Akozbek, and M. J. Bloemer, “Plasmonic band edge effects on the transmission properties of metal gratings,” AIP Adv. 1, 032151 (2011).

[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).

[CrossRef]

O. Painter, J. Vučković, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).

[CrossRef]

H. R. Schober and B. B. Laird, “Localized low-frequency vibrational modes in glasses,” Phys. Rev. B 44, 6746–6754 (1991).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).

[CrossRef]

P. Genevet, J. P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).

[CrossRef]

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).

[CrossRef]

H. Cao, J. Y. Xu, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997–2999 (2000).

[CrossRef]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).

[CrossRef]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).

[CrossRef]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).

[CrossRef]

Z. Shi and J. Yang, “Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media,” Phys. Rev. E 75, 056602 (2007).

[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).

[CrossRef]

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, “Permanent magnetic lattices for ultracold atoms and quantum degenerate gases,” J. Phys. B 39, 847–860 (2006).

[CrossRef]

S. R. Bickham and A. J. Sievers, “Intrinsic localized modes in a monatomic lattice with weakly anharmonic nearest-neighbor force constants,” Phys. Rev. B 43, 2339–2346 (1991).

[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).

[CrossRef]

C. J. Pethick and H. Smith, Bose-Einstein Condensate in Dilute Gas (Cambridge University, 2008).

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).

[CrossRef]

V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).

[CrossRef]

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer, 2009).

M. Storzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).

[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).

[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001).

[CrossRef]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).

[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).

[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).

[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).

[CrossRef]

P. Genevet, J. P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).

[CrossRef]

G. Kaczmarczyk, A. Kaschner, A. Hoffmann, and C. Thomsen, “Impurity-induced modes of Mg, As, Si, and C in hexagonal and cubic GaN,” Phys. Rev. B 61, 5353–5357 (2000).

[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).

[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Dissipative defect modes in periodic structures,” Opt. Lett. 35, 1638–1640 (2010).

[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progress in Optics 52, 63–148 (2009).

[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).

[CrossRef]

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A 76, 043826 (2007).

[CrossRef]

T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).

[CrossRef]

M. I. Molina and G. Tsironis, “Nonlinear impurities in a linear chain,” Phys. Rev. B 47, 15330–15333 (1993).

[CrossRef]

M. Vakhitov and A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16, 783–789 (1973).

[CrossRef]

G. Van de Walle and J. Neugebauer, “First-principles calculations for defects and impurities: applications to III-nitrides,” J. Appl. Phys. 95, 3851–3879 (2004).

[CrossRef]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).

[CrossRef]

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).

[CrossRef]

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).

[CrossRef]

S. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).

[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).

[CrossRef]

D. de Ceglia, M. A. Vincenti, M. Scalora, N. Akozbek, and M. J. Bloemer, “Plasmonic band edge effects on the transmission properties of metal gratings,” AIP Adv. 1, 032151 (2011).

[CrossRef]

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. A. Vincenti, and A. Alú, “Transmission resonances in plasmonic metallic gratings,” J. Opt. Soc. Am. B 28, 253–264 (2011).

[CrossRef]

Y. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

O. Painter, J. Vučković, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).

[CrossRef]

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, “Dissipative defect modes in periodic structures,” Opt. Lett. 35, 1638–1640 (2010).

[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progress in Optics 52, 63–148 (2009).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

[CrossRef]

A. Khelif, A. Choujaa, B. Djafari-Rouhani, M. Wilm, S. Ballandras, and V. Laude, “Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal,” Phys. Rev. B 68, 214301 (2003).

[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).

[CrossRef]

H. Cao, J. Y. Xu, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997–2999 (2000).

[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).

[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

J. Yang, “Fully localized two-dimensional embedded solitons,” Phys. Rev. A 82, 053828 (2010).

[CrossRef]

Z. Shi and J. Yang, “Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media,” Phys. Rev. E 75, 056602 (2007).

[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).

[CrossRef]

I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. 96, 223903 (2006).

[CrossRef]

J. Yang and T. R. Akylas, “Continuous families of embedded solitons in the third-order nonlinear Schrödinger equation,” Stud. Appl. Math. 111, 359–375 (2003).

[CrossRef]

J. Yang, “Stable embedded solitons,” Phys. Rev. Lett. 91, 143903 (2003).

[CrossRef]

J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28, 2094–2096 (2003).

[CrossRef]

D. E. Pelinovsky and J. Yang, “A normal form for nonlinear resonance of embedded solitons,” Proc. R. Soc. A 458, 1469–1497 (2002).

[CrossRef]

A. R. Champneys, B. A. Malomed, J. Yang, and D. J. Kaup, “Embedded solitons: solitary waves in resonance with the linear spectrum,” Physica D 152, 340–354 (2001).

[CrossRef]

J. Yang, “Dynamics of embedded solitons in the extended Korteweg–de Vries equations,” Stud. Appl. Math. 106, 337–365 (2001).

[CrossRef]

J. Yang, B. A. Malomed, and D. J. Kaup, “Embedded solitons in second-harmonic-generating systems,” Phys. Rev. Lett. 83, 1958–1961 (1999).

[CrossRef]

V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).

[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).

[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).

[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).

[CrossRef]

F. C. Moreira, F. K. Abdullaev, V. V. Konotop, and A. V. Yulin, “Localized modes in χ(2) media with PT—symmetric localized potential,” Phys. Rev. A 86, 053815 (2012).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).

[CrossRef]

J. Zeng and B. A. Malomed, “Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices,” Phys. Rev. A 85, 023824 (2012).

[CrossRef]

J. Zeng and B. A. Malomed, “Two-dimensional solitons and vortices in media with incommensurate linear and nonlinear lattice potentials,” Phys. Scr. T149, 014035 (2012).

[CrossRef]

J. Zeng and Y. Lan, “Two-dimensional solitons in PT linear lattice potentials,” Phys. Rev. E 85, 047601 (2012).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

D. de Ceglia, M. A. Vincenti, M. Scalora, N. Akozbek, and M. J. Bloemer, “Plasmonic band edge effects on the transmission properties of metal gratings,” AIP Adv. 1, 032151 (2011).

[CrossRef]

H. Cao, J. Y. Xu, E. W. Seelig, and R. P. H. Chang, “Microlaser made of disordered media,” Appl. Phys. Lett. 76, 2997–2999 (2000).

[CrossRef]

R. Driben and B. A. Malomed, “Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials,” Eur. Phys. J. D 50, 317–323 (2008).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice,” Europhys. Lett. 72, 698–704 (2005).

[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642–648 (2003).

[CrossRef]

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal-insulator-metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).

[CrossRef]

G. Van de Walle and J. Neugebauer, “First-principles calculations for defects and impurities: applications to III-nitrides,” J. Appl. Phys. 95, 3851–3879 (2004).

[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and A. Reoksabutr, “Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials,” J. Mod. Opt. 58, 1977–1989 (2011).

[CrossRef]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B 7, R53–R72 (2005).

[CrossRef]

G. D’Aguanno, N. Mattiucci, M. J. Bloemer, D. de Ceglia, M. A. Vincenti, and A. Alú, “Transmission resonances in plasmonic metallic gratings,” J. Opt. Soc. Am. B 28, 253–264 (2011).

[CrossRef]

A. Shapira, N. Voloch-Bloch, B. A. Malomed, and A. Arie, “Spatial quadratic solitons guided by narrow layers of a nonlinear material,” J. Opt. Soc. Am. B 28, 1481–1489 (2011).

[CrossRef]

O. Painter, J. Vučković, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).

[CrossRef]

A. R. Champneys and B. A. Malomed, “Moving embedded solitons,” J. Phys. A 32, L547–L553 (1999).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps,” J. Phys. B 37, 1443–1459 (2004).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Two-dimensional loosely and tightly bound solitons in optical lattices and inverted traps,” J. Phys. B 37, 2225–2239 (2004).

[CrossRef]

S. Ghanbari, T. D. Kieu, A. Sidorov, and P. Hannaford, “Permanent magnetic lattices for ultracold atoms and quantum degenerate gases,” J. Phys. B 39, 847–860 (2006).

[CrossRef]

J. Hukriede, D. Runde, and D. Kip, “Fabrication and application of holographic Bragg gratings in lithium niobate channel waveguides,” J. Phys. D 36, R1–R16 (2003).

[CrossRef]

J. Fujioka and A. Espinosa, “Soliton-like solution of an extended NLS equation existing in resonance with linear dispersive waves,” J. Phys. Soc. Jpn. 66, 2601–2607 (1997).

[CrossRef]

L. Dal Negro and S. V. Boriskina, “Deterministic aperiodic nanostructures for photonics and plasmonics applications,” Laser Photon. Rev. 6, 178–218 (2012).

[CrossRef]

V. A. Brazhnyi and V. V. Konotop, “Theory of nonlinear matter waves in optical lattices,” Mod. Phys. Lett. B 18, 627–651 (2004).

[CrossRef]

P. Genevet, J. P. Tetienne, E. Gatzogiannis, R. Blanchard, M. A. Kats, M. O. Scully, and F. Capasso, “Large enhancement of nonlinear optical phenomena by plasmonic nanocavity gratings,” Nano Lett. 10, 4880–4883 (2010).

[CrossRef]

S. A. Rinne, F. Garca-Santamara, and P. V. Braun, “Embedded cavities and waveguides in three-dimensional silicon photonic crystals,” Nat. Photonics 2, 52–56 (2007).

[CrossRef]

L. Sanchez-Palencia and M. Lewenstein, “Disordered quantum gases under control,” Nat. Phys. 6, 87–95 (2010).

[CrossRef]

J. Billy, V. Josse, Z. C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).

[CrossRef]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose–Einstein condensate,” Nature 453, 895–898 (2008).

[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).

[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–673 (1997).

[CrossRef]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440, 1166–1169 (2006).

[CrossRef]

S. Noda, A. Chutinan, and M. Imada, “Trapping, and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).

[CrossRef]

M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen, and H. I. Smith, “A three-dimensional optical photonic crystal with designed point defects,” Nature 429, 538–542 (2004).

[CrossRef]

S. Hu and W. Hu, “Defect solitons in parity-time symmetric optical lattices with self-defocusing nonlinearity,” Opt. Commun. 294, 311–324 (2013).

[CrossRef]

A. Abdelrahman, P. Hannaford, and K. Alameh, “Adiabatically induced coherent Josephson oscillations of ultracold atoms in an asymmetric two-dimensional magnetic lattice,” Opt. Express 17, 24358–24370 (2009).

[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, “Photonic crystals for matter waves: Bose-Einstein condensates in optical lattices,” Opt. Express 12, 19–29 (2004).

[CrossRef]

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal-insulator-metal waveguide Bragg grating,” Opt. Express 16, 413–425 (2008).

[CrossRef]

M. Matuszewski, B. A. Malomed, and M. Trippenbach, “Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice,” Phys. Rev. A 76, 043826 (2007).

[CrossRef]

S. K. Adhikari and B. A. Malomed, “Symbiotic gap and semigap solitons in Bose-Einstein condensates,” Phys. Rev. A 77, 023607 (2008).

[CrossRef]

J. Zeng and B. A. Malomed, “Stabilization of one-dimensional solitons against the critical collapse by quintic nonlinear lattices,” Phys. Rev. A 85, 023824 (2012).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Symmetric and asymmetric localized modes in linear lattices with an embedded pair of χ(2)-nonlinear sites,” Phys. Rev. A 86, 013829 (2012).

[CrossRef]

F. C. Moreira, F. K. Abdullaev, V. V. Konotop, and A. V. Yulin, “Localized modes in χ(2) media with PT—symmetric localized potential,” Phys. Rev. A 86, 053815 (2012).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Pérez-Garca, “Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity,” Phys. Rev. A 74, 023614 (2006).

[CrossRef]

T. Mayteevarunyoo, B. A. Malomed, and G. Dong, “Spontaneous symmetry breaking in a nonlinear double-well structure,” Phys. Rev. A 78, 053601 (2008).

[CrossRef]

N. Dror and B. A. Malomed, “Solitons supported by localized nonlinearities in periodic media,” Phys. Rev. A 83, 033828 (2011).

[CrossRef]

F. C. Moreira, V. V. Konotop, and B. A. Malomed, “Solitons in PT-symmetric periodic systems with the quadratic nonlinearity,” Phys. Rev. A 87, 013832 (2013).

[CrossRef]

J. Yang, “Fully localized two-dimensional embedded solitons,” Phys. Rev. A 82, 053828 (2010).

[CrossRef]

A. Gubeskys and B. A. Malomed, “Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices,” Phys. Rev. A 76, 043623 (2007).

[CrossRef]

F. J. Garcia-Vidal and L. Martin-Moreno, “Transmission and focusing of light in one-dimensional periodically nanostructured metals,” Phys. Rev. B 66, 155412 (2002).

[CrossRef]

S. A. Darmanyan and A. V. Zayats, “Light tunneling via resonant surface plasmon polariton states and the enhanced transmission of periodically nanostructured metal films: an analytical study,” Phys. Rev. B 67, 035424 (2003).

[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency,” Phys. Rev. B 54, 7837–7842 (1996).

[CrossRef]

M. I. Molina and G. Tsironis, “Nonlinear impurities in a linear chain,” Phys. Rev. B 47, 15330–15333 (1993).

[CrossRef]

B. C. Gupta and K. Kundu, “Formation of stationary localized states due to nonlinear impurities using the discrete nonlinear Schrödinger equation,” Phys. Rev. B 55, 894–905 (1997).

[CrossRef]

B. C. Gupta and K. Kundu, “Stationary localized states due to a nonlinear dimeric impurity embedded in a perfect one-dimensional chain,” Phys. Rev. B 55, 11033–11036 (1997).

[CrossRef]

E. Bulgakov, K. Pichugin, and A. Sadreev, “Symmetry breaking for transmission in a photonic waveguide coupled with two off-channel nonlinear defects,” Phys. Rev. B 83, 045109 (2011).

[CrossRef]

S. Longhi, “Bloch oscillations in tight-binding lattices with defects,” Phys. Rev. B 81, 195118 (2010).

[CrossRef]

S. Longhi, “Dynamic reflectionless defects in tight-binding lattices,” Phys. Rev. B 84, 193105 (2011).

[CrossRef]

Y. A. Vlasov, M. A. Kaliteevski, and V. V. Nikolaev, “Different regimes of light localization in a disordered photonic crystal,” Phys. Rev. B 60, 1555–1562 (1999).

[CrossRef]

A. Khelif, A. Choujaa, B. Djafari-Rouhani, M. Wilm, S. Ballandras, and V. Laude, “Trapping and guiding of acoustic waves by defect modes in a full-band-gap ultrasonic crystal,” Phys. Rev. B 68, 214301 (2003).

[CrossRef]

S. R. Bickham and A. J. Sievers, “Intrinsic localized modes in a monatomic lattice with weakly anharmonic nearest-neighbor force constants,” Phys. Rev. B 43, 2339–2346 (1991).

[CrossRef]

H. R. Schober and B. B. Laird, “Localized low-frequency vibrational modes in glasses,” Phys. Rev. B 44, 6746–6754 (1991).

[CrossRef]

G. Kaczmarczyk, A. Kaschner, A. Hoffmann, and C. Thomsen, “Impurity-induced modes of Mg, As, Si, and C in hexagonal and cubic GaN,” Phys. Rev. B 61, 5353–5357 (2000).

[CrossRef]

Z. Shi and J. Yang, “Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media,” Phys. Rev. E 75, 056602 (2007).

[CrossRef]

W. C. K. Mak, B. A. Malomed, and P. L. Chu, “Symmetric and asymmetric solitons in linearly coupled Bragg gratings,” Phys. Rev. E 69, 066610 (2004).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Gap solitons in Ginzburg-Landau media,” Phys. Rev. E 77, 056606 (2008).

[CrossRef]

H. Sakaguchi and B. A. Malomed, “Two-dimensional dissipative gap solitons,” Phys. Rev. E 80, 026606 (2009).

[CrossRef]

J. Zeng and Y. Lan, “Two-dimensional solitons in PT linear lattice potentials,” Phys. Rev. E 85, 047601 (2012).

[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, “Spatial optical solitons in nonlinear photonic crystals,” Phys. Rev. E 65, 036609 (2002).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects,” Phys. Rev. E 83, 016604 (2011).

[CrossRef]

V. A. Brazhnyi and B. A. Malomed, “Dragging two-dimensional discrete solitons by moving linear defects,” Phys. Rev. E 84, 016608 (2011).

[CrossRef]

J. Yang and Z. Chen, “Defect solitons in photonic lattices,” Phys. Rev. E 73, 026609 (2006).

[CrossRef]

R. F. Rodrguez, J. A. Reyes, A. Espinosa-Cerón, J. Fujioka, and B. A. Malomed, “Standard and embedded solitons in nematic optical fibers,” Phys. Rev. E 68, 036606 (2003).

[CrossRef]

J. Atai and B. A. Malomed, “Solitary waves in systems with separated Bragg grating and nonlinearity,” Phys. Rev. E 64, 066617 (2001).

[CrossRef]

J. Yang, “Stable embedded solitons,” Phys. Rev. Lett. 91, 143903 (2003).

[CrossRef]

J. Yang, B. A. Malomed, and D. J. Kaup, “Embedded solitons in second-harmonic-generating systems,” Phys. Rev. Lett. 83, 1958–1961 (1999).

[CrossRef]

T. Anker, M. Albiez, R. Gati, S. Hunsmann, B. Eiermann, A. Trombettoni, and M. K. Oberthaler, “Nonlinear self-trapping of matter waves in periodic potentials,” Phys. Rev. Lett. 94, 020403 (2005).

[CrossRef]

T. J. Alexander, E. A. Ostrovskaya, and Y. S. Kivshar, “Self-trapped nonlinear matter waves in periodic potentials,” Phys. Rev. Lett. 96, 040401 (2006).

[CrossRef]

F. H. Bennet, T. J. Alexander, F. Haslinger, A. Mitchell, D. N. Neshev, and Y. S. Kivshar, “Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays,” Phys. Rev. Lett. 106, 093901 (2011).

[CrossRef]

K. J. K. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92, 183901 (2004).

[CrossRef]

J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sanchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett. 93, 256804 (2004).

[CrossRef]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, “Transmission resonances on metallic gratings with very narrow slits,” Phys. Rev. Lett. 83, 2845–2848 (1999).

[CrossRef]

I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. 109, 203903 (2012).

[CrossRef]

I. Makasyuk, Z. Chen, and J. Yang, “Band-gap guidance in optically induced photonic lattices with a negative defect,” Phys. Rev. Lett. 96, 223903 (2006).

[CrossRef]

M. Rechtsman, A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, and M. Segev, “Amorphous photonic lattices: band gaps, effective mass, and suppressed transport,” Phys. Rev. Lett. 106, 193904 (2011).

[CrossRef]

Y. S. Chan, C. T. Chan, and Z. Y. Liu, “Photonic band gaps in two dimensional photonic quasicrystals,” Phys. Rev. Lett. 80, 956–959 (1998).

[CrossRef]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).

[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143 (2000).

[CrossRef]

V. Yannopapas, N. Stefanou, and A. Modinos, “Effect of stacking faults on the optical properties of inverted opals,” Phys. Rev. Lett. 86, 4811–4814 (2001).

[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, “Nonlinear localized waves in a periodic medium,” Phys. Rev. Lett. 87, 083901 (2001).

[CrossRef]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).

[CrossRef]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).

[CrossRef]

E. Gavartin, R. Braive, I. Sagnes, O. Arcizet, A. Beveratos, T. J. Kippenberg, and I. Robert-Philip, “Optomechanical coupling in a two-dimensional photonic crystal defect cavity,” Phys. Rev. Lett. 106, 203902 (2011).

[CrossRef]

V. A. Brazhnyi, V. V. Konotop, and V. M. Pérez-Garca, “Driving defect modes of Bose-Einstein condensates in optical lattices,” Phys. Rev. Lett. 96, 060403 (2006).

[CrossRef]

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, “Anderson localization and nonlinearity in one-dimensional disordered photonic lattices,” Phys. Rev. Lett. 100, 013906 (2008).

[CrossRef]

U. Gavish and Y. Castin, “Matter-wave localization in disordered cold atom lattices,” Phys. Rev. Lett. 95, 020401 (2005).

[CrossRef]

C. Vanneste and P. Sebbah, “Selective excitation of localized modes in active random media,” Phys. Rev. Lett. 87, 183903 (2001).

[CrossRef]

M. Storzer, P. Gross, C. M. Aegerter, and G. Maret, “Observation of the critical regime near Anderson localization of light,” Phys. Rev. Lett. 96, 063904 (2006).

[CrossRef]

V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. 81, 4136–4139 (1998).

[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, “Matter-wave gap solitons in atomic band-gap structures,” Phys. Rev. Lett. 90, 160407 (2003).

[CrossRef]

J. Zeng and B. A. Malomed, “Two-dimensional solitons and vortices in media with incommensurate linear and nonlinear lattice potentials,” Phys. Scr. T149, 014035 (2012).

[CrossRef]

A. Espinosa-Cerón, J. Fujioka, and A. Gómez-Rodrguez, “Embedded solitons: four-frequency radiation, front propagation and radiation inhibition,” Phys. Scr. 67, 314–324 (2003).

[CrossRef]

A. R. Champneys, B. A. Malomed, J. Yang, and D. J. Kaup, “Embedded solitons: solitary waves in resonance with the linear spectrum,” Physica D 152, 340–354 (2001).

[CrossRef]

D. E. Pelinovsky and J. Yang, “A normal form for nonlinear resonance of embedded solitons,” Proc. R. Soc. A 458, 1469–1497 (2002).

[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton shape and mobility control in optical lattices,” Progress in Optics 52, 63–148 (2009).

[CrossRef]

M. Vakhitov and A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16, 783–789 (1973).

[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011).

[CrossRef]

M. C. W. van Rossum and T. M. Nieuwenhuizen, “Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion,” Rev. Mod. Phys. 71, 313–371 (1999).

[CrossRef]

O. Morsch and M. Oberthaler, “Dynamics of Bose-Einstein condensates in optical lattices,” Rev. Mod. Phys. 78, 179–215 (2006).

[CrossRef]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).

[CrossRef]

S. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).

[CrossRef]

S. Ogawa, M. Imada, S. Yoshimoto, M. Okano, and S. Noda, “Control of light emission by 3D photonic crystals,” Science 305, 227–229 (2004).

[CrossRef]

J. Yang, “Dynamics of embedded solitons in the extended Korteweg–de Vries equations,” Stud. Appl. Math. 106, 337–365 (2001).

[CrossRef]

J. Yang and T. R. Akylas, “Continuous families of embedded solitons in the third-order nonlinear Schrödinger equation,” Stud. Appl. Math. 111, 359–375 (2003).

[CrossRef]

D. E. Pelinovsky, Localization in Periodic Potential: From Schrödinger Operators to the Gross-Pitaevskii Equation (Cambridge University, 2011).

H. T. C. Stoof, K. B. Gubbels, and D. B. M. Dickerscheid, Ultracold Quantum Fields (Springer, 2009).

C. J. Pethick and H. Smith, Bose-Einstein Condensate in Dilute Gas (Cambridge University, 2008).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University, 2008).

N. Dror and B. A. Malomed, “Stability of dipole gap solitons in two-dimensional lattice potentials,” in Spectral Analysis, Stability and Bifurcations in Nonlinear Physical Systems, O. Kirillov and D. E. Pelinovsky, eds. (Wiley, 2013).