Ivan Fernandez-Corbaton: Exact Multipolar Decompositions with Applications in Nanophotonics. Lecture

Materials: 1) I. Fernandez-Corbaton et al., "Exact dipolar moments of a localized electric current distribution", Opt. Express 23, 33044{33064 (2015) https://arxiv.org/abs/1507.00752 2) I. Fernandez-Corbaton et al., "On the dynamic toroidal multipoles from localized electric current distributions", Scientic Reports 7, 7527 (2017) https://www.nature.com/articles/s4159... 3) R. Alaee et al., "An electromagnetic multipole expansion beyond the long-wavelength approximation", Opt. Commun. 407, 17 {21 (2018) https://arxiv.org/pdf/1701.00755.pdf 4) R. Alaee et al., "Exact multipolar decompositions with applications in nanophotonics", Adv. Opt. Mater. 7, 1800783 (2019) https://onlinelibrary.wiley.com/doi/e... 5) Code https://github.com/RasoulAlaee/exact_... METANANO SCHOOL website: https://school.physics.itmo.ru/ 0:00 Intro 1:29 Start of the 1st lecture. Problem formulation 6:06 Current multipole moments and Electromagnetic field outside source 7:10 How the currents appear 9:00 Importance of multipole decomposition 11:42 Outline 14:05 A multipolar derivation in momentum (wavector) space 15:35 Parts of the source that do(do not) produce EM fields (|p|=w/c) 21:35 Question 1 27:00 Types of multipoles which produce EM fields (The longitudinal components do not radiate) 36:54 Question 2 40:54 Exact multipolar expressions and their approximations 47:05 Coefficients in fields and currents 50:35 Pretty expressions 53:55 On equivalence between different approaches 1:02:40 Exact vs approximate. Role of the bessel function. 1:07:00 Example. Current loop. 1:15:34 Question 3 1:23:40 Lecture 2 1:27:00 Outline 1:27:45 Toroidal multipoles and other splits 1:39:00 Let us insist on splitting 1:42:45 Changing basis 1:52:00 Helicity multipoles 2:00:17 Electromagnetic duality symmetry 2:18:00 Question 4 2:22:50 A different kind of electromagnetic source: Spin 2:34:00 Question 5 2:37:15 Multipoles as irreducible representations 2:41:50 Question 6 2:46:44 More about Cartesian vs. spherical 2:50:35 Transformations in the Poincar'e group