Guided waves in a photonic bandgap structure with a line defect, SIAM J. Appl. Math, vol.64, issue.6, pp.2018-2033, 2004. ,
Quantum percolation and ballistic conductance on a lattice of wires, Physical Review B, vol.13, issue.3, p.1074, 1992. ,
DOI : 10.1080/00018736400101061
A gap in the spectrum of the Neumann???Laplacian on a periodic waveguide, Applicable Analysis, vol.32, issue.5, pp.1889-1915, 2013. ,
DOI : 10.1051/m2an/1998320505791
Introduction to quantum graphs, volume 186 of Mathematical Surveys and Monographs ,
Asymptotic analysis of an array of closely spaced absolutely conductive inclusions, Netw. Heterog. Media, vol.1, issue.3, pp.353-377, 2006. ,
Spectral theory of selfadjoint operators in Hilbert space Mathematics and its Applications (Soviet Series). D, 1987. ,
Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe: Bestimmung der Differentialgleichung durch die Eigenwerte, Acta Mathematica, vol.78, issue.0, pp.1-96, 1946. ,
DOI : 10.1007/BF02421600
Spectrum created by line defects in periodic structures, Mathematische Nachrichten, vol.33, issue.1, pp.17-181972, 2014. ,
DOI : 10.1007/BF02790171
On the spectrum of waveguides in planar photonic bandgap structures, Proc. A, p.47120140673, 2015. ,
DOI : 10.1137/100791798
Adjoint and self-adjoint differential operators on graphs, Electronic Journal of Differential Equations, vol.6, pp.1-10, 1998. ,
Trapped modes in thin and infinite ladder like domains: existence and asymptotic analysis, INRIA Research Report, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01287023
The spectral theory of periodic differential equations, 1973. ,
Lattice kronig-penney models. Physical review letters, p.3503, 1995. ,
Contact interactions on graph superlattices, Journal of Physics A: Mathematical and General, vol.29, issue.1, p.87, 1996. ,
DOI : 10.1088/0305-4470/29/1/011
Localized classical waves created by defects, Journal of Statistical Physics, vol.18, issue.6, pp.165-177, 1997. ,
DOI : 10.1007/BF02180202
Midgap defect modes in dielectric and acoustic media, SIAM J. Appl. Math, vol.58, issue.6, pp.1748-1773, 1998. ,
Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. I. Scalar Model, SIAM Journal on Applied Mathematics, vol.56, issue.1, pp.68-88, 1996. ,
DOI : 10.1137/S0036139994263859
Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. II. Two-Dimensional Photonic Crystals, SIAM Journal on Applied Mathematics, vol.56, issue.6, pp.1561-1620, 1996. ,
DOI : 10.1137/S0036139995285236
Second-order elliptic equation of divergence form having a compactly supported solution, Journal of Mathematical Sciences, vol.106, issue.3, pp.3078-3086, 2001. ,
DOI : 10.1023/A:1011379807662
Etude mathématique et numérique de la propagation des ondes dans des milieux périodiques localement perturbés, 2009. ,
A Dirichlet-to-Neumann Approach for The Exact Computation of Guided Modes in Photonic Crystal Waveguides, SIAM Journal on Scientific Computing, vol.35, issue.2, pp.438-461, 2013. ,
DOI : 10.1137/12086697X
URL : https://hal.archives-ouvertes.fr/hal-00937675
Absolute continuity of the spectra of periodic waveguides, Contemporary Mathematics, vol.339, pp.37-42, 2003. ,
DOI : 10.1090/conm/339/06098
Finite element methods for Navier-Stokes equations Theory and algo- rithms, of Springer Series in Computational Mathematics, 1986. ,
Spectra of graph neighborhoods and scattering, Proceedings of the London Mathematical Society, vol.97, issue.3, pp.718-752, 2008. ,
DOI : 10.1112/plms/pdn020
A computer-assisted proof for photonic band gaps, Zeitschrift f??r angewandte Mathematik und Physik, vol.60, issue.6, pp.1035-1052, 2009. ,
DOI : 10.1007/s00033-008-8021-2
Photonic Crystal -Molding the Flow of Light, 1995. ,
Photonic Crystal -The road from theory to practice, 2002. ,
Exact boundary conditions for periodic waveguides containing a local perturbation, Commun. Comput. Phys, vol.1, issue.6, pp.945-973, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00977852
Opening up and control of spectral gaps of the Laplacian in periodic domains, Journal of Mathematical Physics, vol.22, issue.4, p.121502, 2014. ,
DOI : 10.1090/S1061-0022-05-00878-2
Gaps in the spectrum of the Neumann Laplacian generated by a system of periodically distributed traps, Mathematical Methods in the Applied Sciences, vol.42, issue.6, pp.11-26, 2015. ,
DOI : 10.1070/RM1987v042n06ABEH001505
Abstract, Communications in Computational Physics, vol.4, issue.05, pp.1355-1388, 2014. ,
DOI : 10.1023/A:1013377415134
Floquet theory for partial differential equations, volume 60 of Operator Theory: Advances and Applications, 1993. ,
On guided waves in photonic crystal waveguides, Waves in periodic and random media, pp.105-115, 2002. ,
DOI : 10.1090/conm/339/06102
Quantum graphs. I. Some basic structures. Waves Random Media, pp.107-128, 2004. ,
Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs, Journal of Physics A: Mathematical and General, vol.38, issue.22, pp.4887-4900, 2005. ,
DOI : 10.1088/0305-4470/38/22/013
Quantum graphs, of Proc. Sympos. Pure Math, pp.291-312, 2008. ,
DOI : 10.1088/0959-7174/14/1/007
On guided electromagnetic waves in photonic crystal waveguides In Operator theory and its applications, volume 231 of Amer, Math. Soc. Transl. Ser, vol.2, pp.99-108, 2010. ,
Integral Representations and Liouville Theorems for Solutions of Periodic Elliptic Equations, Journal of Functional Analysis, vol.181, issue.2, pp.402-446, 2001. ,
DOI : 10.1006/jfan.2000.3727
Convergence of Spectra of Mesoscopic Systems Collapsing onto a Graph, Journal of Mathematical Analysis and Applications, vol.258, issue.2, pp.671-700, 2001. ,
DOI : 10.1006/jmaa.2000.7415
On the spectrum of the Laplace operator on the infinite Dirichlet ladder, St. Petersburg Mathematical Journal, vol.23, issue.6, pp.1023-1045, 2012. ,
DOI : 10.1090/S1061-0022-2012-01228-8
ELLIPTIC BOUNDARY VALUE PROBLEMS WITH PERIODIC COEFFICIENTS IN A CYLINDER, Mathematics of the USSR-Izvestiya, vol.18, issue.1, pp.101-112, 1981. ,
DOI : 10.1070/IM1982v018n01ABEH001384
An example of multiple gaps in the spectrum of a periodic waveguide, Sbornik: Mathematics, vol.201, issue.4, pp.99-124, 2010. ,
DOI : 10.1070/SM2010v201n04ABEH004082
Opening of a gap in the continuous spectrum of a periodically perturbed waveguide, Mathematical Notes, vol.87, issue.5-6, pp.764-786, 2010. ,
DOI : 10.1134/S0001434610050123
The asymptotic analysis of gaps in the spectrum of a waveguide perturbed with a periodic family of small voids, Journal of Mathematical Sciences, vol.22, issue.1, pp.247-301, 2012. ,
DOI : 10.1023/A:1011469822255
Bounded solutions in a T-shaped waveguide and the spectral properties of the Dirichlet ladder, Computational Mathematics and Mathematical Physics, vol.54, issue.8, pp.1261-1279, 2014. ,
DOI : 10.1134/S0965542514080090
Trapped modes in a T-shaped waveguide, Acoustical Physics, vol.56, issue.6, pp.1004-1015, 2010. ,
DOI : 10.1134/S1063771010060254
Elliptic problems in domains with piecewise smooth boundaries, 1994. ,
DOI : 10.1515/9783110848915
Asymptotic partial decomposition of domain for spectral problems in rod structures, Journal de Math??matiques Pures et Appliqu??es, vol.87, issue.1, pp.1-36, 2007. ,
DOI : 10.1016/j.matpur.2006.10.003
Bethe???Sommerfeld Conjecture, Annales Henri Poincar??, vol.9, issue.3, pp.457-508, 2008. ,
DOI : 10.1007/s00023-008-0364-x
Bethe-Sommerfeld conjecture for periodic operators with strong perturbations, Inventiones mathematicae, vol.2, issue.2, pp.467-540, 2010. ,
DOI : 10.12988/ijcms.2007.07003
Spectral Convergence of Quasi-One-Dimensional Spaces, Annales Henri Poincar??, vol.7, issue.5, pp.933-973, 2006. ,
DOI : 10.1007/s00023-006-0272-x
Spectral analysis on graph-like spaces, Lecture Notes in Mathematics, vol.2039 ,
DOI : 10.1007/978-3-642-23840-6
Methods of modern mathematical physics v. I-IV, pp.1972-1978 ,
Variational Problems??on Multiply Connected Thin Strips I:??Basic Estimates and Convergence??of the Laplacian Spectrum, Archive for Rational Mechanics and Analysis, vol.160, issue.4, pp.271-308, 2001. ,
DOI : 10.1007/s002050100164
The limiting equation for Neumann Laplacians on shrinking domains, Electron. J. Differential Equations, vol.25, issue.31, p.pp, 2000. ,
Absolute continuity in periodic waveguides, Proc. London Math. Soc, vol.85, issue.33, pp.717-741, 2002. ,
Absolute continuity of the spectrum of the magnetic schrödinger operator with a metric in a two-dimensional periodic waveguide, Algebra i Analiz, vol.14, pp.159-206, 2002. ,
On the Bethe???Sommerfeld conjecture for certain periodic Maxwell operators, Journal of Mathematical Analysis and Applications, vol.377, issue.1, pp.370-383, 2011. ,
DOI : 10.1016/j.jmaa.2010.10.067