Phonon polaritonics in two-dimensional materials

Extreme confinement of electromagnetic energy by phonon polaritons holds the promise of strong and new forms of control over the dynamics of matter. To bring such control to the atomic-scale limit, it is important to consider phonon polaritons in two-dimensional (2D) systems. Recent studies have pointed out that in 2D, splitting between longitudinal and transverse optical (LO and TO) phonons is absent at the $\Gamma$ point, even for polar materials. Does this lack of LO--TO splitting imply the absence of a phonon polariton in polar monolayers? Here, we derive a first-principles expression for the conductivity of a polar monolayer specified by the wavevector-dependent LO and TO phonon dispersions. In the long-wavelength (local) limit, we find a universal form for the conductivity in terms of the LO phonon frequency at the $\Gamma$ point, its lifetime, and the group velocity of the LO phonon. Our analysis reveals that the phonon polariton of 2D is simply the LO phonon of the 2D system. For the specific example of hexagonal boron nitride (hBN), we estimate the confinement and propagation losses of the LO phonons, finding that high confinement and reasonable propagation quality factors coincide in regions which may be difficult to detect with current near-field optical microscopy techniques. Finally, we study the interaction of external emitters with two-dimensional hBN nanostructures, finding extreme enhancement of spontaneous emission due to coupling with localized 2D phonon polaritons, and the possibility of multi-mode strong and ultra-strong coupling between an external emitter and hBN phonons. This may lead to the design of new hybrid states of electrons and phonons based on strong coupling.Comment: 8 pages, 3 figure

COMPENSATING VARIATION FOR RECREATIONAL POLICY: A RANDOM UTILITY APPROACH TO BOATING IN FLORIDA

A nested logit random utility travel cost model is developed for recreational boating in southwest Florida. Using data from a survey of recreational boaters, the model estimates site choice probabilities and compensating variation for changes in boating speed limits. Behavior is modeled as a two-step, discrete-choice process, where boaters first select a launch point for their trailered boats, then select a boating destination based on site characteristics. The results of this particular model are currently being used in policy applications in Florida.Resource /Energy Economics and Policy,

The UK recession in context — what do three centuries of data tell us?

The Quarterly Bulletin has a long tradition of using historical data to help analyse the latest developments in the UK economy. To mark the Bulletin’s 50th anniversary, this article places the recent UK recession in a long-run historical context. It draws on the extensive literature on UK economic history and analyses a wide range of macroeconomic and financial data going back to the 18th century. The UK economy has undergone major structural change over this period but such historical comparisons can provide lessons for the current economic situation.