Maksim Skorobogatiy is Professor and Canada Research Chair in Photonic Crystals at the Department of Engineering Physics at École Polytechnique de Montréal, Canada. In 2005 he was awarded a fellowship from the Japanese Society for Promotion of Science, and he is a member of the Optical Society of America. Jianke Yang is Professor of Applied Mathematics at the University of Vermont, USA. He is a member of the Optical Society of America and the Society of Industrial and Applied Mathematics.

• 1. Introduction; 2. Hamiltonian formulation of Maxwell's equations (frequency consideration); 3. 1D Photonic crystals – multilayer stacks; 4. Bandgap guidance in the planar photonic crystal waveguides; 5. Hamiltonian formuation of Maxwell equations for waveguides (propagation constant consideration); 6. 2D photonic crystals; 7. Quasi-2D photonic crystals; 8. Nonlinear effects and gap-solution formation in periodic media; 9. Problem solution.

Maksim Skorobogatiy is Professor and Canada Research Chair in Photonic Crystals at the Department of Engineering Physics at École Polytechnique de Montréal, Canada. In 2005 he was awarded a fellowship from the Japanese Society for Promotion of Science, and he is a member of the Optical Society of America. Jianke Yang is Professor of Applied Mathematics at the University of Vermont, USA. He is a member of the Optical Society of America and the Society of Industrial and Applied Mathematics.

• 1. Introduction; 2. Hamiltonian formulation of Maxwell's equations (frequency consideration); 3. 1D Photonic crystals – multilayer stacks; 4. Bandgap guidance in the planar photonic crystal waveguides; 5. Hamiltonian formuation of Maxwell equations for waveguides (propagation constant consideration); 6. 2D photonic crystals; 7. Quasi-2D photonic crystals; 8. Nonlinear effects and gap-solution formation in periodic media; 9. Problem solution.

Maksim Skorobogatiy is Professor and Canada Research Chair in Photonic Crystals at the Department of Engineering Physics at École Polytechnique de Montréal, Canada. In 2005 he was awarded a fellowship from the Japanese Society for Promotion of Science, and he is a member of the Optical Society of America. Jianke Yang is Professor of Applied Mathematics at the University of Vermont, USA. He is a member of the Optical Society of America and the Society of Industrial and Applied Mathematics.

• 1. Introduction; 2. Hamiltonian formulation of Maxwell's equations (frequency consideration); 3. 1D Photonic crystals – multilayer stacks; 4. Bandgap guidance in the planar photonic crystal waveguides; 5. Hamiltonian formuation of Maxwell equations for waveguides (propagation constant consideration); 6. 2D photonic crystals; 7. Quasi-2D photonic crystals; 8. Nonlinear effects and gap-solution formation in periodic media; 9. Problem solution.