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School CEA-EDF-Inria

School CEA EDF Inria - Waves in periodic media : mathematical and numerical aspects

  • Date : 15/04/2013 to 19/04/2013
  • Place : ENSTA ParisTech
  • Organiser(s) : Sonia Fliss

Objectives

The propagation of waves in periodic media has known a regain of interest for many important applications, particularly in optics for micro and nano-technology. Significative progress have been achieved in the past decades in the mathematical understanding and numerical solutions of related problems.
The aim of this course is to give a state of the art of the most important aspects of the subject.
The three main courses will give a general overview of the mathematical theory of wave(s) in periodic media, the development of adapted numerical methods and the links with the applications. Some more specific results will be adressed in complementary lectures.
This school is primarily dedicated to beginners or experienced researchers in the fields of applied mathematics or physics but also for engineers who want to deepen their fundamental knowledge on the subject.

Lectures

The school will be organized as follows :
3 main courses (each composed of 4 sessions of 1h30)  to introduce the basic aspects of the subject:

Peter Kuchment  - Texas A&M University (USA) :
(1) Floquet-Bloch thoery for periodic operators
(2) Structure of the spectrum
(3) Gad and edge Phenomena
(4) Miscellanea

Steven Johnson  - Massachussets Institute of Technology (USA) :
(1) Computing Bloch waves and Band structures
(2) Modeling microcavities and resonant devices
(3) Sources ans surface integral equations
(4) Optimization and inverse design in Photonics

Patrick Joly  - Inria Saclay-Île-de-France (France) :
(1) Introduction and generalities on DtN operators - the 1D periodic problem
(2) The periodic waveguide problem - application to the transmission between an homogeneous media and a photonic crystal
(3) The 2D time harmonic periodic problem - extension to multiple scattering
(4) Application of the DtN method to time dependentproblems

6 complementary courses (each composed of 1 session of 1h30) to tackle specific aspects given by specialists in the field:

  • "Bloch wave homogenization", Grégoire Allaire  - École Polytechnique (France)
  • "Trapped and guided modes in periodic structure" (2 sessions), Anne-Sophie Bonnet-Ben Dhia  - CNRS, Sonia Fliss  - ENSTA (France)
  • "An introduction to modal methods in nonaphotonics", Philippe Lalanne  - CNRS (France)
  • "Limiting amplitude and limiting absorption principle", Vu Hoang  - Karlsruhe Institue of Technology (Allemagne)
  • "Gap opening for 1D and quasi-1D periodic operators", Konstantin Pankrashkin  - Université Paris-Sud (France)

Program

Monday April 15

9:00-10:30 : Welcoming and introduction
10:30-11h : Coffee break
11h-12h30 : Lecture I - (1) : Peter Kuchment

Lunch

2:30-4:00 : Lecture II - (1) : Steven Johnson
4:00-4:30 : Coffee break
4:30 : 6:00 : Lecture III - (1) : Patrick Joly
From 6:00pm : Welcoming cocktail

Tuesday April 16

9:00-10:30 : Lecture III - (2) : Patrick Joly
10:30-11h : Coffee break
11h-12h30 : Lecture I - (2) : Steven Johnson

Lunch

2:30-4:00 : Lecture II - (2) : Peter Kuchment
4:00-4:30 : Coffee break
4:30 : 6:00 : Lecture IV : Philippe Lalanne

Wednesday April 17

9:00-10:30 : Lecture II - (3) : Peter Kuchment
10:30-11h : Coffee break
11h-12h30 : Lecture III - (3) : Patrick Joly

Lunch

2:30-4:00 : Lecture V : Vu Hoang
4:00-4:30 : Coffee break
4:30 : 6:00 : Lecture VI : Konstantin Pankrashkin
From 6:00pm : Dinner with the lecturers

Thursday April 18

9:00-10:30 : Lecture I - (3) : Steven Johnson
10:30-11h : Coffee break
11h-12h30 : Lecture II - (4) : Peter Kuchment

Lunch

2:30-4:00 : Lecture VII : Anne-Sophie Bonnet-Ben Dhia
4:00-4:30 : Coffee break
4:30 : 6:00 : Lecture VII : Sonia Fliss

Friday April 19

9:00-10:30 : Lecture I - (4) : Steven Johnson
10:30-11h : Coffee break
11h-12h30 : Lecture VIII : Grégoire Allaire

Lunch

2:30-4:00 : Lecture III - (4) : Patrick Joly
4:00-4:30 : Coffee break

Location

Keywords: Sonia Fliss Waves Saclay - Île-de-France School CEA-EDF-Inria

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