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We examine array of metal-mesh frameworks for their wide-band absorption. These take the form of quasi-crystal optical cages. An array of cages tends to focus the incoming radiation within each framework. An array of cage-within-cage funnels the radiation from the outer cage to its inner core even further.
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In pursuit of infrared (IR) radiation absorbers, we examine quasicrystal structures made of graphite wires. An array of graphitic cages and cage-within-cage, and whose overall dimensions is smaller than the radiation wavelength exhibit a flat absorption spectrum, A~0.83 between 10-30 microns and a quality loss factor of L~0.83 (L=A/Q, with Q, the quality factor). Simulations at microwave frequencies show multiple absorption lines. In the case of a cage within cage, energy is funneled towards the inner cage which result in a rather hot structure. Applications are envisioned as anti-fogging surfaces, EM shields and energy harvesting.
Recently, we developed a new family of 3D photonic hollow resonators which theoretically allow tight confinement of light in a fluid (gaz or liquid): the photon cages. These new resonators could be ideal for sensing applications since they not only localize the electromagnetic energy in a small mode volume but also enforce maximal overlap between this localized field and the environment (i.e. a potential volume of nano-particles). In this work, we will present numerical and experimental studies of the interaction of a photon cage optical mode with nano-emitters. For this, PbS quantum dot emitters in a PDMS host matrix have been introduced in photon cages designed to have optimal confinement properties when containing a PDMS-based active medium. Photoluminescence measurements have been performed and the presence of quantum dot emitters in the photon cages has been demonstrated.
We introduce the notion of a $[z, r; g]$-mixed cage. A $[z, r; g]$-mixed cage is a mixed graph $G$, $z$-regular by arcs, $r$-regular by edges, with girth $g$ and minimum order. In this paper we prove the existence of $[z, r ;g]$-mixed cages and exhibit families of mixed cages for some specific values. We also give lower and upper bounds for some choices of $z, r$ and $g$. In particular we present the first results on $[z,r;g]$- mixed cages for $z=1$ and any $rgeq 1$ and $ggeq 3$, and for any $zgeq 1$, $r=1$ and $g=4$.
Let $2 le r < m$ and $g$ be positive integers. An $({r,m};g)$--graph} (or biregular graph) is a graph with degree set ${r,m}$ and girth $g$, and an $({r,m};g)$-cage (or biregular cage) is an $({r,m};g)$-graph of minimum order $n({r,m};g)$. If $m=r+1$, an $({r,m};g)$-cage is said to be a semiregular cage. In this paper we generalize the reduction and graph amalgam operations from M. Abreu, G. Araujo-Pardo, C. Balbuena, D. Labbate (2011) on the incidence graphs of an affine and a biaffine plane obtaining two new infinite families of biregular cages and two new semiregular cages. The constructed new families are $({r,2r-3};5)$-cages for all $r=q+1$ with $q$ a prime power, and $({r,2r-5};5)$-cages for all $r=q+1$ with $q$ a prime. The new semiregular cages are constructed for r=5 and 6 with 31 and 43 vertices respectively.
The interplay of $pi$-flux and lattice geometry can yield full localization of quantum dynamics in lattice systems, a striking interference phenomenon known as Aharonov-Bohm caging. At the level of the single-particle energy spectrum, this full-localization effect is attributed to the collapse of Bloch bands into a set of perfectly flat (dispersionless) bands. In such lattice models, the effects of inter-particle interactions generally lead to a breaking of the cages, and hence, to the spreading of the wavefunction over the lattice. Motivated by recent experimental realizations of analog Aharonov-Bohm cages for light, using coupled-waveguide arrays, we hereby demonstrate that caging always occurs in the presence of local nonlinearities. As a central result, we focus on special caged solutions, which are accompanied by a breathing motion of the field intensity, that we describe in terms of an effective two-mode model reminiscent of a bosonic Josephson junction. Moreover, we explore the quantum regime using small particle ensembles, and we observe quasi-caged collapse-revival dynamics with negligible leakage. The results stemming from this work open an interesting route towards the characterization of nonlinear dynamics in interacting flat band systems.
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