Syllabus and Lecture Notes

2025
OPTICS 3 :   CONTEMPORARY TOPICS IN  OPTICS

                           Birefringencia, Quantum Entanglement, Surface Plasmon Polaritons

LIGHT as a WAVE
PART-III    PROPAGATION of LIGHT in BIREFRINGENT MATERIAL                            

                               III-1   PROPAGATION OF GAUSSIAN BEAMS

                              III-2   Propagation of PLANE WAVES inside an anisotropic  (birefringent)  material                                                            

PART IV    QUANTUM MECHANICS EXPERIMENTS with LIGHT   
                                IV-1    THE HEISENBERG UNCERTAINTY PRINCIPLE                                                                                           .          .              (29-04-2025) 
                                             Understanding the Uncertainty Principle  through (the Fourier analysis of) universal property of waves
                                          Fourier spectral-decomposition of the wave-function  
                                          The wavefunction of a free-particle  (the non-relativistic and the relativistic cases)
                                          Appendix: Plane waves                                                 
                                IV-2    THE PRINCIPLE of COMPLEMENTARY:  Quantum Behavior of Photons, Electrons and Atoms              6/Mayo/2025       
                                              Complementary distinguishes the world of quantum phenomena from the realm of classical                                                     
                                              Two observables are ‘complimentary’ if precise knowledge of one of them implies that all
                                              possible outcomes of  measuring the  other one are equally probable.
                                IV-2   THE AMPLITUDE PROBABILITY         .                                                                                                                                               (6-Mayo-2025)                                        
                                              Amplitude probabilities in the two-slit experiment ( Attempts to watch electron’s "trajectories")
                                              When to add “probabilities” and not “amplitude-probabilities”
                                            Dirac's Bra and Ket notation
                               IV-3   QUANTUM ENTANGLEMENT                                                                                                                                                                (8-Mayo-2025)           
                                          Detailed illustration of entanglement process: Case of the Annihilation of the Positronium  
                                                          Disintegration of the spin-zero state of the positronium 

                                                          Polarization of the photons (Right and left circular polarization)

                                                          Conservation of parity in the positronium decay

                                                          The inversion operator

                                                          Conservation of parity

                                                          Joint and Conditional Probabilities
                                          (This lecture follows closely the Feynman's lecture    https://www.feynmanlectures.caltech.edu/III_18.html   )

                               IV-4   QUANTUM TELEPORTATION       .                                                                                                                                                                     

                                             Working principle of the quantum teleportation method proposed by Bennett
                                            Light propagation in birefringent materials

                                                          Spontaneous parametric down-conversion process  

                                                          Matching conditions: Type-I and Type-II  nonlinear crystals

                                             Classical and Quantum Bits (QUBITS

                                                          Generation of a Pair of Qubits  (A two-photon system)

                                                          How to generate entangled  two-qbit  states  (EBITS)

                                                          Bell States

                                             Analytical description of the proposed quantum teleportation
                                            Implementation of  Bell-states measurement

Surface Plasmon Polaritons at a Metal/Dielectric Interface    
PART-V     Electromagnetic Fields and Waves

                              V-1  THE MAXWELL EQUATIONS AND ELECTROMAGNETIC WAVES

                              V-2  LIGHT PROPAGATION IN NON-MAGNETIC MATERIALS                                                                        
                                           Complement: -   Summary about the Maxwell Equations                                                         
                                                                            -  Combining the ME to obtain the WAVE EQUATION: Case of no free charges nor free-current               

                              V-3   REFLECTION AND REFRACTION AT a DIELECTRIC / DIELECTRIC PLANE INTERFACE                                            

                              V-4   SURFACE PLASMON POLARITONS AT a METAL / DIELECTRIC INTERFACE                     
                                                             Transport of information via optical means (rather than via  electron particles) in nano-devices.
                                                              Data transmission via optical means imply much higher bandwidth operation.

THE QUANTUM CHARACTER  of LIGHT  
        PART- V   INTERACTION OF RADIATION with ATOMIC SYSTEMS

                              V-1  QUANTUM STATISTICS for PHOTONS AND FERMIONS

                               V-2  SEMICONDUCTOR MATERIALS Band - gap, chemical potential

                               V-3  CLASSICAL VIEW of LIGHT

                               V-4  EINSTEIN'S LAW OF RADIATION: THE QUANTUM VIEW OF LIGHT                                                                    (06-06-2024) 

                               V-5 OPTOELECTRONIC DEVICES: LASER DIODE