Optimal fiscal policy in a Schumpeterian model

Master'sMASTER OF SOCIAL SCIENCE

Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point

The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due to the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al. Nature 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors, i.e., encircling an EP in different directions results in different output states. Here, we propose a coupled ferromagnetic waveguide system that carries two EPs and design an experimental setup in which the trajectory of state evolution can be controlled in situ using a tunable external field, allowing us to dynamically encircle zero, one or even two EPs experimentally. The tunability allows us to control the trajectory of encircling in the parameter space, including the size of the encircling loop and the starting/end point. We discovered that whether or not the dynamics is chiral actually depends on the starting point of the loop. In particular, dynamically encircling an EP with a starting point in the parity-time-broken phase results in non-chiral behaviors such that the output state is the same no matter which direction the encircling takes. The proposed system is a useful platform to explore the topology of energy surfaces and the dynamics of state evolution in non-Hermitian systems and will likely find applications in mode switching controlled with external parameters.Comment: 15 pages, 11 figure

Acoustic circular dichroism in a three-dimensional chiral metamaterial

Circular dichroism (CD) is an intriguing chiroptical phenomenon associated with the interaction of chiral structures with circularly polarized lights. Although the CD effect has been extensively studied in optics, it has not yet been demonstrated in acoustic systems. Here, we demonstrate the acoustic CD effect in a three-dimensional chiral metamaterial supporting circularly polarized transverse sound. We find that the effect is negligible in the lossy metamaterial possessing $C_4$ rotational symmetry but can be strongly enhanced in the $C_2$-symmetric system with inhomogeneous loss. The phenomena can be understood based on the properties of the metamaterial's complex band structure and the quality factors of its eigenmodes. We show that the enhanced CD in the $C_2$-symmetric system is attributed to the polarization bandgaps and the non-Hermitian exceptional points appearing near the Brillouin-zone center and boundaries. The results contribute to the understanding of chiral sound-matter interactions and can find applications in acoustic sensing of chiral structures and sound manipulations based on its vector properties.Comment: 9 pages, 9 figure

Multiplexing spectral line shape of waveguide transmission by photonic spin-orbit interaction

Manipulating the spectral line shape exhibits great potential in realizing active optical circuits with switching, sensing, and modulation capabilities. Exploring unusual line shapes, such as Fano resonance and electromagnetically induced transparency (EIT), has attracted substantial interest. Conventional methods of engineering the spectral line shape have limited tunability and face challenges in multiplexing different spectral line shapes. Here, we propose and numerically demonstrate a new mechanism to tailor the transmission line shape almost at will by exploiting the interference of frequency-dependent chiral dipolar states in two helix particles sitting above a dielectric waveguide. We show that, by tuning the polarization of the chiral dipoles and exploiting transverse spin-orbit interaction, one can control the asymmetric Pancharatnam-Berry geometric phase for the excited guided waves propagating in opposite directions. The interference of the guided waves respectively excited by the two particles can give rise to transmissions with various line shapes, including Lorentzian-like, antiresonance-like, Fano-like, and EIT-like line shapes, which carry an intriguing property of line shape-momentum locking, i.e., the transmissions in opposite directions have different line shapes. Our findings open new possibilities for multiplexed and multifunctional nanophotonic designs with unprecedented capability of spectral-line shaping. The proposed structures can be conveniently integrated with optical circuits for on-chip applications.Comment: 9 pages, 5 figure