Spontaneous emission in one-dimensional photonic crystals

Spectral statistics of light in one-dimensional graphene-based photonic crystals

The optical properties and spectral statistics of light in one-dimensional photonic crystals in the representative classes of (AB)^{N} (composed of dielectric layers) and (AGBG)^{N} (composed of periodic stacking of graphene-dielectric layers) have been investigated using the transfer matrix method and random matrix theory. The proposed method provides new predictions to determine the chaos and regularity of the optical systems. In this analysis, the chaoticity parameter with q=0 for Poisson distribution and q→1 for Wigner distribution is determined based on the random matrix theory. It has been shown that two kinds of chaos and regularity modes can be found with Brody distribution. Also, as a part of this work, we found out the regular pattern in both classes of (AB)^{N} and (AGBG)^{N} when results were fit to a Brody distribution. Moreover, the effects of different parameters such as the number of unit cells, incident angle, state of polarization, and chemical potential of the graphene nanolayers on the structures' regularity are discussed. It is found that the regular patterns are seen in the band gaps. The results show that the structure (AGBG)^{N} has an extra photonic band gap compared to (AB)^{N}, which is tunable by changing the chemical potential of the graphene nanolayers. Therefore, the possibility of external control of the regularity using a gate voltage in the graphene-based photonic crystals is obtained. Finally, comparing of TE and TM waves based on the random matrix theory, which interpolates between regular and chaotic systems, indicates that the Poisson statistics well describes the TE waves.

Quantitative Analysis of Photon Density of States for One-Dimensional Photonic Crystals in a Rectangular Waveguide

Light propagation in one-dimensional (1D) photonic crystals (PCs) enclosed in a rectangular waveguide is investigated in order to achieve a complete photonic band gap (PBG) while avoiding the difficulty in fabricating 3D PCs. This work complements our two previous articles (Phys. Rev. E) that quantitatively analyzed omnidirectional light propagation in 1D and 2D PCs, respectively, both showing that a complete PBG cannot exist if an evanescent wave propagation is involved. Here, we present a quantitative analysis of the transmission functions, the band structures, and the photon density of states (PDOS) for both the transverse electric (TE) and transverse magnetic (TM) polarization modes of the periodic multilayer heterostructure confined in a rectangular waveguide. The PDOS of the quasi-1D photonic crystal for both the TE and TM modes are obtained, respectively. It is demonstrated that a “complete PBG” can be obtained for some frequency ranges and categorized into three types: (1) below the cutoff frequency of the fundamental TE mode, (2) within the PBG of the fundamental TE mode but below the cutoff frequency of the next higher order mode, and (3) within an overlap of the PBGs of either TE modes, TM modes, or both. These results are of general importance and relevance to the dipole radiation or spontaneous emission by an atom in quasi-1D periodic structures and may have applications in future photonic quantum technologies.

Direct Observation of Nanoscale Light Confinement without Metal

Manipulation of light below the diffraction limit forms the basis of nanophotonics. Metals can confine light at the subwavelength scale but suffer from high loss of energy. Recent reports have theoretically demonstrated the possibility of light confinement below the diffraction limit using transparent dielectric metamaterials. Here, nanoscale light confinement (<λ/20) in transparent dielectric materials is shown experimentally through a luminescent nanosystem with rationally designed dielectric claddings. Theoretically, green light with a wavelength of 540 nm has a transmission of 98.8% when passing through an ultrathin NaYF₄ /NaGdF₄ superlattice cladding (thickness: 6.9 nm). Unexpectedly, the complete confinement of green emission (540 nm) by such an ultrathin dielectric cladding is directly observed. FDTD calculations are used to confirm that the ultrathin dielectric cladding has negligible influence on the transmission of propagating light, but extraordinary confinement of evanescent waves. This will provide new opportunities for nanophotonics by completely averting the use of metals.

Quantitative analysis of photon density of states for a realistic superlattice with omnidirectional light propagation

Omnidirectional light propagation in a realistic superlattice is investigated. This work complements two previous articles [Phys. Rev. E 59, 3624 (1999); 61, 5802 (2000)] that analyzed the cases of transverse electric (TE) and transverse magnetic (TM) polarization modes, respectively, of the dielectric superlattice modeled by means of Dirac delta functions. We present a quantitative analysis of the transmission functions, the band structures, the equifrequency surfaces, and the photon density of states (PDOS) for both TE and TM modes of the real superlattice without any approximations on the given dielectric function profiles. One of the advantages is that the Brewster effect can be manifested via our approach. In addition, the modes corresponding to TM evanescent waves that are absent from the Dirac comb model can be predicted. Finally, the exact PDOS of the realistic superlattice for the TE and TM modes can be obtained, respectively. These results are relevant to the spontaneous emission by an atom or to dipole radiation in one-dimensional periodic structures.