Photonic band gap enhancement in frequency-dependent dielectrics (original) (raw)
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Resonance-induced effects in photonic crystals
Journal of Physics: Condensed Matter, 1999
For the case of a simple face-centered-cubic photonic crystal of homogeneous dielectric spheres, we examine to what extent single-sphere Mie resonance frequencies are related to band gaps and whether the width of a gap can be enlarged due to nearby resonances. Contrary to some suggestions, no spectacular effects may be expected. When the dielectric constant of the spheres ε s is greater than the dielectric constant ε b of the background medium, then for any filling fraction f there exists a critical ε c above which the lowest lying Mie resonance frequency falls inside the lowest stop gap in the (111) crystal direction, close to its midgap frequency. If ε s < ε b , the correspondence between Mie resonances and both the (111) stop gap and a full gap does not follow such a regular pattern. If the Mie resonance frequency is close to a gap edge, one can observe a resonance-induced widening of a relative gap width by ≈ 5%.
Journal of The Optical Society of America B-optical Physics, 1993
The analogy between electromagnetic wave propagation in multidimensionally periodic structures and electronwave propagation in real crystals has proven to be a fruitful one. Initial efforts were motivated by the prospect of a photonic band gap, a frequency band in three-dimensional dielectric structures in which electromagnetic waves are forbidden irrespective of the propagation direction in space. Today many new ideas and applications are being pursued in two and three dimensions and in metallic, dielectric, and acoustic structures. We review the early motivations for this research, which were derived from the need for a photonic band gap in quantum optics. This need led to a series of experimental and theoretical searches for the elusive photonic band-gap structures, those three-dimensionally periodic dielectric structures that are to photon waves as semiconductor crystals are to electron waves. We describe how the photonic semiconductor can be doped, producing tiny electromagnetic cavities. Finally, we summarize some of the anticipated implications of photonic band structure for quantum electronics and for other areas of physics and electrical engineering.
Theoretical Foundations and Application of Photonic Crystals, 2018
Photonic crystals (PCs) are periodic systems that consist of dielectrics with different refractive indices. Photonic crystals have many potential technological applications. These applications are mainly based on the photonic bang gap effect. However the band gap is not only effect that follows from the periodic changing of the refractive index in the photonic crystal. The periodic change of the photon-matter interaction in photonic crystal medium gives rise to the fact that the mass of an electron in the photonic crystal must differ from its mass in vacuum. Anisotropy of a photonic crystal results in the dependence of the electromagnetic mass correction on the orientation of the electron momentum in a photonic crystal. This orientation dependence in turn gives rise to the significant correction to the transition frequencies in an atom placed in air voids of a photonic crystal. These corrections are shown to be comparable to the atomic optical frequencies. This effect allows one to control the structure of the atomic energy levels and hence to control resonance processes. It can serve as the basis for new line spectrum sources. The effect provides new ways of realization of quantum interference between decay channels that can be important for quantum information science.
Resonant Nonlinear Dielectric Response in a Photonic Band Gap Material
Physical Review Letters, 1996
We study the dielectric response of impurity two-level atoms in a photonic band gap (PBG) to an applied laser field. In this system, the atoms may exchange energy coherently by resonance dipoledipole interaction (RDDI) which is assumed to be strong compared to the spontaneous emission rate. When the applied Rabi frequency exceeds the RDDI energy scale, nonlinear saturation of the absorptive part of the susceptibility occurs while the real part of the nonlinear susceptibility remains large. This suggests that doped PBG materials may act as nearly lossless, but highly nonlinear dielectrics.
Photonic bandgaps in periodic dielectric structures
Progress in Quantum Electronics, 1994
Photonic bandgaps are defined as frequency intervals for which propagation of electromagnetic waves is forbidden in all 471 steradians within a dielectric structure with a periodic index of refraction. Such structures consist, for example, of dielectric spheres in suspension or air holes in a dielectric material, with a spatial period comparable to the electromagnetic wavelength. The principal feature of periodic structures is their ability to perturb the density of electromagnetic states within the structures. Since photonic bandgap materials can essentially suppress all states, the radiative dynamics within the materials can be strongly modified. By changing the atom-field radiative coupling, photonic bandgap materials could lead to the inhibition of spontaneous emission; if a local defect is introduced within the structure, it will behave like a high-Q microcavity. The existence of bandgaps can be predicted from a classical treatment of the vector wave equation. The use of the plane-wave expansion method can lead to accurate results but introduces two problems related to the dielectric discontinuities and the plane-wave cutoff. Experimental investigations at microwave frequencies have demonstrated many of the properties of photonic bandgap structures.
Phonon-polariton excitations in photonic crystals
Physical Review B, 2003
The incorporation of materials which exhibit transverse phonon-polariton excitations into a photonic crystal produces an intricate optical system possessing unique and varied photon phenomena. In particular, we demonstrate theoretically that such a system will exhibit both near-dispersionless bands with field localization in the polaritonic material and metalliclike bands with complete flux expulsion in an extremely small frequency interval around the characteristic phonon frequency. Moreover, when the fundamental resonances of the polaritonic rods overlap with the bands of a geometrically identical metallodielectric crystal, nearby states will couple to produce a band in which the localized field varies continuously between two distinct nodal patterns, in an exceedingly small frequency range. We also discuss the implications of losses on these phenomena and verify that our results can be realized experimentally.
Journal of Applied Physics, 2011
We discuss two points related to the simultaneous existence of phononic and photonic band gaps in a two-dimensional crystal constituted by a square array of holes drilled in a matrix. In a first part, using the case of a sapphire sample in the microwave range, we show that in addition to the phononic gap, an absolute photonic gap may be obtained making use of the high values as well as the anisotropy of the dielectric matrix elements in the microwave regime. In a second part, using the case of silicon in the telecom frequency range, we demonstrate that absolute photonic and phononic gaps may be obtained by making a combination of two crystals having slightly different filling factors. The calculations of the band structures and transmission coefficients were mainly computed using the finite difference time domain method.
Photonic bandgap of two-dimensional dielectric crystals
Solid-State Electronics, 1994
The existence of an absolute photonic bandgap in the near-infrared for two-dimensional periodic dielectric structures is discussed for photons propagating in the plane of such 2D crystals. A special emphasis is put on the influence of the shape and size of the filling pattern on the absolute bandgap formation. A very large absolute photonic bandgap is predicted for 2D crystals formed by etching into a semiconductor slab a periodic array of large vertical cylindric voids of circular cross-section arranged in a triangular lattice. The technological feasibility of such "optimum" air/GaAs 2D crystals by standard processing techniques (electron beam lithography and reactive ion etching) is demonstrated.