2016 Fiscal Year Research-status Report
Photonic Topological Insulators: Dynamical and Topological Effects
| Project/Area Number |
16K17761
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| Research Institution | Tohoku University |
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Principal Investigator |
LEIN MAXIMILIAN 東北大学, 原子分子材料科学高等研究機構, 助教 (50769891)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | topological insulators / photonic crystals / electromagnetic waves |
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| Outline of Annual Research Achievements |
During FY2016, I have collaborated with Giuseppe De Nittis on Projects 1 and 3 of the proposal. As a result we have finished one book (to appear as a SpringerBrief) and two publications are close to submission and will be finished during a visit at Pontificia Universidad de Chile in May 2017). Moreover, I have given two invited talks on project-related research at international conferences at CIRM (France) and the Center for Theoretical Physics of Complex Systems (Daejeon, South Korea); during a 3-week visit to Giuseppe De Nittis in Chile I gave two seminar talks; lastly, I have given an invited talk at a domestic conference (Tokyo Institute of Technology).
Kostya Bliokh (RIKEN) noticed that the equations we used in earlier publications to describe gyrotropic media were unphysical, and therefore I had to revisit some of my earlier publications. This resulted in two publications related to Project 3 that will be finalized in May 2017, one on the Schroedinger formalism of electromagnetic waves and a second paper on the topological classification of electromagnetic media. Furthermore, we have finished a book on a new framework for mathematically rigorous linear response theory. One of the motivations was to apply this new framework to Maxwell's equations in order to derive conductivity coefficients, which we conjecture to be topological quantities.
Throughout FY2016 I have met with Prof. Teruya Ishihara (Tohoku University) every other week in order to find a simple model that can explain the non-linear optical rectification effect in periodically structured surfaces (Project 2).
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Since all later work will depend on them, it was important to reconsider two earlier works, and I adapted the project schedule accordingly:
FY2016 Project 1: In view of the correct classification of topological photonic crystals, the development of a Weyl calculus with symmetries is no longer necessary.
FY2016 Project 2 has been postponed to FY2017.
FY2017 Project 3 and FY2018 Project 3 have started early, first contributions will be part of the Topological Classification paper.
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| Strategy for Future Research Activity |
The reshuffling of the schedule will have no long-term implications for the project. Moreover, thanks to interactions with people working on other classical waves such as surface plasmons, mechanical waves and spin waves, I plan to investigate which insights carry over from electromagnetic to other classical waves and vice versa. This should attract more attention to our results from other communities.
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| Causes of Carryover |
Unexpected restrictions on the usage of Wakate B funds made it impossible to pay for a trip of mine to Santiago de Chile as initially intended. The trip was paid for in full by my collaborator instead.
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| Expenditure Plan for Carryover Budget |
I will have added an additional trip to Santiago de Chile in May 2017 to work with Giuseppe De Nittis.
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