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IEEE Transactions on Dielectrics and Electrical Insulation

Dielectric materials as photonic crystal and formulation of lamb shift using anisotropic model

G.K. Johri, M. Johri, Akhilesh Tiwari, K. Yoshino

Published Feb 1, 2004• 6 citations
Publisher

Abstract

Dielectric studies with characteristics of a photonic crystal and a new expression of Lamb Shift including spatial average of dielectric constant for the material and its surrounding for odd parity of 2p/sub 1/2/ state of hydrogen for photon-atom interaction as a function of relative dispersion frequency, refractive index contrast and propagation vector using quadratic fluctuations and randomness in an anisotropic model of Brillouin Zone (BZ) for p-polarization are reported. The anomalous Lamb shift in 2p/sub 1/2/ level is significantly more than that obtained by using isotropic model which indicates that introducing anisotropic behaviour of BZ is important.

DOI
10.1109/tdei.2004.1266335

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•Jun 24, 2013•0 citations
Dielectric studies with characteristics of a photonic crystal and a new expression of Lamb Shift including spatial average of dielectric constant for the material and its surrounding for odd parity of 2p/sub 1/2/ state of hydrogen for photon-atom interaction as a function of relative dispersion frequency, refractive index contrast and propagation vector using quadratic fluctuations and randomness in an anisotropic model of Brillouin Zone (BZ) for p-polarization are reported. The anomalous Lamb shift in 2p/sub 1/2/ level is significantly more than that obtained by using isotropic model which indicates that introducing anisotropic behaviour of BZ is important.
Studies of anomalous Lamb shift in 2p/sub 1/2/ state of hydrogen for photon-atom interaction as a function of relative dispersion frequency, refractive index contrast and propagation vector using quadratic fluctuations and randomness in an anisotropic model of Brillouin Zone (BZ) for p polarization are reported. The anomalous Lamb shift in 2p/sub 1/2/ level is significantly more than that obtained by using isotropic model which indicates that odd parity 2p/sub 1/2/ state of hydrogen is significantly influenced by introducing anisotropic behaviour of BZ. This work is new and it is fruitful to provide information about optical properties in laser action within the photonic crystal.
Spontaneous emission in photonic crystals with anisotropic three-dimensional dispersion relation is studied. If the upper level is below a characteristic frequency omega(1), or above omega(2), or between omega(1) and omega(2), the radiation is a localized field with a frequency in the band gap, or a propagating field with a frquency in the band, or a diffusion field, respectively. An analytical expression for the Lamb shift is obtained. The Lamb shift for the current case is small compared to that in an ordinary vacuum or in one- or two-dimensional photonic crystals due to lower density of states.
We obtain a general result for the Lamb shift of excited states of multilevel atoms in inhomogeneous electromagnetic structures and apply it to study atomic hydrogen in inverse-opal photonic crystals. We find that the photonic-crystal environment can lead to very large values of the Lamb shift, as compared to the case of vacuum. We also suggest that the position-dependent Lamb shift should extend from a single level to a miniband for an assembly of atoms with random distribution in space, similar to the velocity-dependent Doppler effect in atomic/molecular gases.
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.
We describe the quantum electrodynamics of photons interacting with hydrogenic atoms and molecules in a class of strongly scattering dielectric materials. These dielectrics consist of an ordered or nearly ordered array of spherical scatterers with real positive refractive index and exhibit a complete photonic band gap or pseudogap for all directions of electromagnetic propagation. For hydrogenic atoms with a transition frequency in the forbidden optical gap, we demonstrate both the existence and stability of a photon-atom bound state. For a band gap to center frequency ratio \ensuremath{\Delta}\ensuremath{\omega}/${\mathrm{\ensuremath{\omega}}}_{0}$\ensuremath{\sim}5%, the photon localization length ${\ensuremath{\xi}}_{\mathrm{loc}}$\ensuremath{\ge}10L, where L is the lattice constant of dielectric array. This strong self-dressing of the atom by its own localized radiation field leads to anomalous Lamb shifts and a splitting of the excited atomic level into a doublet when the transition frequency lies near a photonic band edge. We estimate the magnitude of this splitting to be ${10}^{\mathrm{\ensuremath{-}}6}$ at the vacuum transition energies.The stability of this photon-bound state with respect to electromagnetic as well as vibrational decay mechanisms is examined. For an isolated molecule embedded in the solid fraction of the dielectric structure, the dominant mechanism for absorption and spontaneous emission is via optically driven electron-phonon interactions and the resulting phonon-absorption and -emission sidebands. Raman or Brillouin scattering of a localized photon into a propagating mode, or vice versa, directly by photon-phonon interaction is forbidden. For atoms not in contact with the solid fraction of the dielectric host, the electromagnetic two-photon spontaneous emission rate is on the scale of several days. For two identical atoms separated by a distance R within the photonic band gap, energy transfer from an excited atom to an unexcited atom occurs by a phase-shifted resonance dipole-dipole interaction which vanishes exponentially for R>${\ensuremath{\xi}}_{\mathrm{loc}}$. This leads to the formation of a narrow photonic impurity band within the gap when a finite density of atoms is present. This impurity band exhibits a different kind of nonlinear optical properties. When two neighboring atoms are both excited, single-photon spontaneous emission at \ensuremath{\sim}2\ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{0}$ occurs by a third-order electromagnetic process with rate \ensuremath{\Gamma}\ensuremath{\sim}${\mathrm{\ensuremath{\alpha}}}^{3}$${\mathrm{\ensuremath{\omega}}}_{0}$(a0{\mathit{a}}_{0}a0​/R)8{)}^{8})8, where a0{\mathit{a}}_{0}a0​ is the atomic Bohr radius and \ensuremath{\alpha} is the fine-structure constant.
Modern demands for high speed telecommunication and data processing have created the need for advanced materials that allow active manipulation of light waves. Subsequent research has shown that photonic crystals provide excellent candidates to accommodate these needs. Photonic crystals are a relatively new class of materials in which the refractive index is periodic in 1, 2 or 3 dimensions. This periodicity gives rise to a photonic band gap which in turn provides selective reflection of certain wavelengths of light. Another interesting property of photonic crystals is the anomalous dispersion that occurs close to the photonic band gap (i.e. at the band edge). The anomalous dispersion causes the group velocity of light to decrease considerably, allowing stronger interactions between the travelling light and the material of which the photonic crystal consists