Geometry of best Approximations by Uri Shapira

DISCUSSION MEETING

STRUCTURED LIGHT AND SPIN-ORBIT PHOTONICS

ORGANIZERS:
Bimalendu Deb (IACS Kolkata, India), Tarak Nath Dey (IIT Guwahati, India), Subhasish Dutta Gupta (UOH, TIFR Hyderabad, India) and Nirmalya Ghosh (IISER Kolkata, India)

DATE: 29 November 2022 to 02 December 2022

VENUE: Ramanujan Lecture Hall, ICTS Bengaluru

Spin-orbit interaction (SOI) dealing with the coupling of spin and orbital degrees of freedom of massive and mass-less particles has led to several fundamental consequences in diverse fields of physics ranging from atomic, and condensed matter to classical and quantum optics. This phenomenon has led to a number of intriguing and nontrivial optical effects such as spin an orbital Hall effect of light, optical Rashba effect, photonic Aharonov-Bohm effect, rotational Doppler effect, transverse spin, Belinfante's spin momentum, and spin-momentum locking. It has opened up an emerging and fast-growing field, namely, 'Spin-orbit photonics', having a plethora of applications in both classical and quantum information processing. The intent of the discussion meeting is to summarize the current state of research in this promising field that is breaking new grounds. We aim to stimulate new ideas and encourage further research.

There will be a few pedagogical lectures on the first and second day of the meeting, followed by more advanced topics on recent developments in the remaining days.

Topics to be covered

Spin-orbit interaction (SOI) of light and geometrical phase
Transverse spin and momentum in structured light
Spin-controlled photonics using metasurfaces and structured light
Optical weak measurements
Interaction of structured light with atomic systems
ICTS is committed to building an environment that is inclusive, non-discriminatory, and welcoming of diverse individuals. We especially encourage the participation of women and other under-represented groups.

0:00:00 Geometry of best Approximations
0:01:51 Part 1: Introduction and results
0:06:13 Define inductively a sequence
0:10:49 Objects associated to best approximations
0:15:19 Directional lattice
0:23:45 Joint work with Barak weiss
0:25:32 Theorem
0:33:12 Aspects of best approximations
0:35:14 Theorem
0:41:08 Part 2: About the Proofs
0:42:47 Step 1: Change Coordinates
0:45:21 Step 2: Observation - How to detect best approximations
0:51:34 Main idea of the proof
0:54:45 Cross Sections