Local density of optical states in the three-dimensional band gap of a finite photonic crystal

Abstract

A three-dimensional (3D) photonic band gap crystal is an ideal tool to completely inhibit the local density of optical states (LDOS) at every position in the crystal throughout the band gap. This notion, however, pertains to ideal infinite crystals, whereas any real crystal device is necessarily finite. This raises the question as to how the LDOS in the gap depends on the position and orientation inside a finite-size crystal. Therefore, we employ rigorous numerical calculations using finite-difference time domain simulations of 3D silicon inverse woodpile crystals filled with air or with toluene, as previously studied in experiments. We find that the LDOS versus position decreases exponentially into the bulk of the crystal. From the dependence on dipole orientation, we infer that the characteristic LDOS decay length ρ is mostly related to far-field dipolar radiation effects, whereas the prefactor is mostly related to near-field dipolar effects. The LDOS decay length has a remarkably similar magnitude to the Bragg length for directional transport, which suggests that the LDOS in the crystal is dominated by vacuum states that tunnel from the closest interface toward the position of interest. Our work leads to design rules for applications of 3D photonic band gaps in emission control and lighting, quantum information processing, and in photovoltaics.

Targeted positioning of quantum dots inside 3D silicon photonic crystals revealed by synchrotron X-ray fluorescence tomography

“…In nanophotonics, for instance, fluorescing nanoparticles should reside at positions where the local density of optical states is either maximal, in case of cavities or antennae, [18][19][20] or minimal in case of a photonic band gap. 21,22 In biochemical detectors, antibodies should be positioned on the internal interfaces of the 3D substrate for maximum reactivity and selectivity. 23 In this representative study, we fabricate 3D photonic band gap crystals from silicon with the diamond-like inverse woodpile structure consisting of two perpendicular arrays of interpenetrating nanopores, 24 see figure 1(a).…”

“…In previous photonic band gap crystal studies, quantum dots were randomly positioned in the crystal, 3 whereas brushes will allow to selectively position the dots at places where they experience the maximal band gap effects. 22 Once the nanoparticles have been infiltrated, the challenge addressed here is to find back their final positions. Therefore, the first requirement is to find a probing method with the first requirement that it provides local information deep inside a 3D nanostructure with nanometer spatial resolution.…”

Controlled light propagation in random, periodic, and superperiodic silicon nanophotonic materials

“…From the outset, photonic band gaps have been pursued for their radical control over spontaneous emission [153,222], lasing [195], shielding of vacuum noise for qubits [78], and for ultimate 3D waveguiding [74,186]. Based on our observations and modeling, we project that studies with embedded emitters could resolve the density of states around the gap of the real crystal [80,223]. Furthermore, light can be reconfigurably steered to resonant and functional features, including Anderson localized states [9] or 'Cartesian' light states [97], that are otherwise hidden inside a complete 2D or 3D photonic band gap.…”

“…Due to the forbidden gap, if a light-emitting device such as a quantum emitter is placed inside a photonic crystal, its emission is prohibited. The band gap provides excellent shielding of such functional devices in photonic crystal cavities from vacuum fluctuations of the electromagnetic field [80]. However, this makes it difficult to address such devices from outside due to the band gap.…”

“…Such structures are called superperiodic, due to the presence of more than one periodicity within the same structure. As mentioned in the previous section, inverse woodpile crystals have a broad and robust 3D photonic band gap, which is optimal to confine embedded optical cavities and shield them from the surrounding vacuum [80,114].…”