From Poincaré sphere (Bloch sphere) to Projective space скачать в хорошем качестве

From Poincaré sphere (Bloch sphere) to Projective space

List of references Takenaka, Hiroshi. "A unified formalism for polarization optics by using group theory." Nouv. Rev. Opt., vol. 4, no. 1, 1 Jan. 1973, p. 37, doi:10.1088/0335-7368/4/1/304. H.K. Urbantke, The Hopf fibration—seven times in physics, Journal of Geometry and Physics 46 (2003) 125–150. https://arxiv.org/abs/1303.4496 -- del Castillo, G. F. Torres and I. Rubalcava-Garcia. "The Jones vector as a spinor and its representation on the Poincar´e sphere." https://arxiv.org/abs/2107.10810 -- Sugic, Danica, et al. "Particle-like topologies in light." Nat. Commun., vol. 12, no. 6785, 22 Nov. 2021, pp. 1-10, doi:10.1038/s41467-021-26171-5. https://arxiv.org/abs/1508.00920 Oblak, Blagoje. "From the Lorentz Group to the Celestial Sphere." Jones, G. A. and D. Singerman. Complex Functions. Cambridge UP, 1987. https://arxiv.org/abs/2303.17112 Saito, Shinichi. "Spin of Photons: Nature of Polarisation." arXiv, 30 Mar. 2023 (btw, it is better to use helicity or polarization for light, but not spin. Spin is not well defined for photons) 00:00:00 Intro. Poincare sphere 00:00:50 Each point --- polarization state of a plane wave 00:01:08 Why does it look like this 00:01:30 Spoiler! 00:01:45 Def. Equivalence relation 00:02:13 Def. Equivalence class 00:02:26 Def. Quotient set 00:02:50 Def. Real projective space 00:03:40 ℝℙ¹ (real projective line) Example 00:04:37 Stereographic projection 00:05:40 Be careful 00:05:50 ℝℙ² (real projective plane) Example 00:06:09 Boy's surface (immersion) 00:06:40 Complex projective space. (Complex projective line) 00:07:20 Stereographic projection in 2D 00:07:48 Finally optics!!! 00:08:47 Projecting polarization state to a sphere somehow 00:09:37 Is Riemann sphere indeed the same sphere? Proof 00:10:36 Stokes parameters map 2d complex space (and 3-sphere) to the 2-sphere