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InTech eBooks

Modification of the Electromagnetic Field in the Photonic Crystal Medium and New Ways of Applying the Photonic Band Gap Materials

R. Kh. Gainutdinov, Хамадеев Марат Актасович, A A Akhmadeev, Myakzyum Salakhov

Published Apr 4, 2018• 1 citation
Publisher

Abstract

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.

DOI
10.5772/intechopen.71367

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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.
Photonic crystals are periodic systems that consist of dielectrics with different refractive indices. They are designed to act on photons in contrast to semiconductor crystals whose periodicity affects the motion of electrons. Here we consider the interaction of an atomic electron with its own radiation field in the case when the atom is placed in air voids of a photonic crystal and is not in mechanical contact with the vibrational degrees of freedom of the dielectric host. A strong modification of this interaction from that in free space is shown to change the rest mass of the electron, and this has a significant effect on the shift of the atomic energy levels. This shift is investigated by using the example of atomic hydrogen in a high-index-contrast photonic crystal. The found effect may be of interest both from fundamental and practical points of view.
We study a recently predicted novel-type quantum electrodynamical effect that takes place in the photonic crystal medium. It consists in the fact that the modification of the interaction of a charged particle with its own radiation field in the photonic crystal medium results in the change in its mass. Consequences and possible applications of this effect are discussed. It is shown that, as a consequence of the effect, spectrum of the light emitted by atoms may be profoundly modified if, instead of being in free space, atoms are enclosed in air voids of a photonic crystal. Spectral lines of atoms in the photonic crystal medium are shifted in frequency, and this shift may be comparable to the atomic transition frequencies in free space.
Introduction The propagation of light in periodically ordered photonic crystals bears a strong analogy to the wave propagation of conduction electrons in atomic crystals. The development of Bloch modes and dispersion are determined by the interference of waves that are diffracted by lattice planes [19, 52]. The periodicity commensurate with the wavelength (a ≈ λ/2) gives rise to Bragg diffraction that is associated with frequency windows for which waves are forbidden to propagate in a particular direction. Such stop gaps have long been known to arise for electromagnetic waves, notably for X-rays in atomic crystals [214]. At optical frequencies, the stop gaps that occur in one-dimensional periodic structures, known as Bragg stacks, are widely used in optical laboratories as broadband highly reflecting dielectric mirrors [556]. The distinguishing feature of three-dimensional (3D) photonic crystals is that a common stop gap can be achieved for all directions and for all polarizations simultaneously: the widely pursued 3D photonic band gap . Historically a 3D band gap has never been considered for the propagation of X-rays in periodic media, since a gap requires a high refractive index contrast of order unity, whereas the refractive index varies by less then 10 −4 in the X-ray range. At frequencies inside the 3D photonic band gap, the density of optical states (DOS) completely vanishes. As the density of states can also be interpreted as the density of vacuum fluctuations [334], a 3D band gap thus serves as an effective shield to these fluctuations. The total absence of optical modes in a photonic band gap has implications beyond classical optics that break the analogy between the behavior of light in photonic crystals and the behavior of electrons in atomic crystals. 3D photonic band gap crystals play an important role in cavity quantum electrodynamics (cQED) [64, 549], where they offer at least five prospects for new physics. Firstly, probably the most eagerly pursued phenomenon is the complete inhibition of spontaneous emission: an excited quantum emitter – such as an atom, molecule, or quantum dot – embedded in a crystal with its transition frequency tuned to within the 3D band gap remains forever excited since it cannot decay to the ground state by emitting a photon.
Abstract The self-energy correction to the mass of an atomic electron placed into a void of the photonic crystal medium is investigated. In this study the one-dimensional photonic crystal made from gallium arsenide and vacuum layers is considered. We show that the electron mass change gives rise not only to the shifts of the atomic energies but also to the nonradiative transitions between atomic levels. These transitions add new channels to a decay of an atomic state that leads to a quantum interference between these channels.
If the electromagnetic waves are scattered by the periodic structure of media with different refractive indexes, a band gap in the transmitted spectrum can be generated. This is the photonic crystal whose band gap is usually uncontrollable as its structure parameters are fixed after the fabrication. Alternatively, based on the quantum theory in real space for single photons transporting along a one-dimensional waveguide embed by a series of two-level atoms, we propose here a quantum mechanical configuration to implement the photonic crystal with adjustable band gap. It is shown that if the scattering two-level atoms are arranged as a periodic array, the desirable band gap in the photonic transmission spectrum can be formed. This is the atomic-type photonic crystal, in which the center frequency of the gap can be controlled by adjusting the eigenfrequencies of the atoms. The possible physical implementations of our proposal with the voltage-biased superconducting qubits for the centimeter waves and the voltage-biased electrons on liquid helium for the millimeter waves are also discussed.