Combining the two enhancement mechanisms of radiation-matter interaction, one in long wavelength regime (LWR) and the other via resonant Bragg reflection, we systematically studied the coupling strengths of various arrays of resonant units. As a general measure of the coupling strength, the radiative width of each resonance was calculated according to the first-principles theory of microscopic nonlocal response of matter. A numerical study was carried out for three resonant Bragg arrangements of (A) N atoms, (B) N chains of atoms, and (C) N planes of atoms. Different aspects of enhancement are clarified as the size-linear increase in LWR and its dimensionality dependence, the speed-up effect of decay, and the super-enhancement effect due to all these mechanisms in case (C) with its saturation behavior for large N.
A systematic study is made by means of a microscopic nonlocal response theory about the enhancement mechanisms of the optical signals of resonant matter units in various arrangements, where the lattice constant in one direction allows Bragg scattering. Considering that the radiative decay width is a general measure of the coupling strength, we study (a) its size-enhancement and saturation, (b) its speed-up effect due to Bragg scattering, and (c) a super-enhancement effect due to the combination of (a) and (b).
The subject of the review is the diffraction of an electromagnetic wave on a periodic condensed matter where the Bragg condition is satisfied at the frequency of resonance excited in this medium. The Bragg systems known as resonant photonic crystals in general have been considered, and the propagation, reflection, transmission, and diffraction of electromagnetic radiation in different objects—(I) periodic quantum-well structures near the exciton resonance, (II) optical lattices of atoms cooled in a laser field, and (III) bulk crystals and multilayers with gamma-ray resonance intranuclear transitions—have been described in a unified context. The main attention has been paid to the steady-state linear diffraction, including resonant reflection and transmission, which is the best studied and allows a comparison of the three aforementioned systems with the aim of revealing specific characteristics and common features. A characteristic common property of the considered systems is the suppression of non-radiative channels and an inhomogeneous broadening of the resonance frequency. The second fundamental property of resonant photonic crystals is that the interaction of light with resonant excitation can occur in two regimes depending on the thickness of the sample. In the superradiant regime realized for a small number of resonant layers N (fine structures), the height of the peak and half-width of the reflection spectrum monotonically increase with increasing value of N. With a further increase in N, there occurs a transition to a photonic-crystal regime where the half-width of the reflection spectrum is saturated, which manifests itself in the form of an optical stop band. The theoretical description is illustrated by experimental spectra measured for all three resonant Bragg systems.
We present a framework to investigate the collective properties of atomic lattices in one, two, and three dimensions. We analyze the single-photon band structure and associated atomic decay rates, revealing a fundamental dependence on dimensionality. One- and two-dimensional arrays are shown to be inherently radiative, exhibiting band gaps and decay rates that oscillate between superradiant and subradiant regimes, as a function of lattice spacing. In contrast, three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances. Furthermore, we demonstrate that this structural difference dictates the system dynamics, which crosses over from dissipative decay in lower dimensions to coherent transport in three dimensions. Our results provide insight into cooperative effects in atomic arrays at the single-photon level.
The influence of radiative coupling on the four-wave-mixing signals of multiple-quantum-well structures is investigated theoretically for excitation at the excitonic resonance. It is shown that amplitude and shape of the FWM signals depend strongly on the number of quantum wells N in the sample and on the periodicity of the structure. For a fixed delay time τ12, the signal amplitude of a Bragg structure increases quadratically with N due to constructive interference as long as the radiative decay rate Nγrad is small compared to the inverse delay time τ—112. For large N, if the enhanced radiative decay rate exceeds the inverse delay time, superradiant emission leads to a decrease of the observed signals with increasing N. The signals of anti-Bragg structures with an odd number of quantum wells decrease with increasing N due to destructive interference effects whereas anti-Bragg structures with an even number of quantum wells behave similarly to Bragg structures.
In nanostructures with a high excitonic coherence, the interplay between the spatial structure of the excitonic wavefunction and that of the radiation field plays an essential role, causing drastic size effects in the optical response, such as size-resonant enhancement of the radiative decay rate and the nonlinear response and the interchange of quantized levels. This article discusses such peculiar optical effects based on the theoretical treatment beyond the long-wavelength approximation and demonstrates the possibility of designing novel photofunctions with the explicit use of the spatial structures of the radiation field.
In view of the possibilities of laser spectroscopy with very short pulses and relatively high frequencies, we examine aspects of the theory of atom-field interactions that are related to violation of the condition of the long-wavelength approximation (LWA) according to which
kr⪡1, where
r is ``of the order of atomic dimensions'' and
k is the magnitude of the wave vector. On- and off-resonance transitions are considered, with
kr being larger than unity due to the large extent of the two wave functions involved in the coupling matrix element. The implementation of the analysis uses bound-free transition matrix elements with the
n=50 and 80 hydrogenic functions as initial states and values of
k up to
27eV, which is sufficient to produce
kr>1, thereby rendering the LWA inoperative. In spite of this, it is shown that, for on-resonance transitions, the results from the use of the well-known multipole operators resulting from the LWA [e.g., the electric dipole approximation (EDA)] agree with those from the exact expressions derived here from the application of the multipolar Hamiltonian. This numerical agreement is proven analytically. As a test of the kind of convergence of the multipole series expansion for small values of
k and large
r, it is shown that the lowest-order ratio of electric dipole to quadrupole matrix elements decreases rapidly within 1.0 atomic unit above threshold. Finally, it is shown that off-resonance couplings lead to differences between the full-interaction operator and the EDA which cannot be neglected. In the extreme case of intrashell couplings for the
n=50 shell, calculation shows that the
50p state is coupled to angular momentum states up to $\ensuremath{\ell}=21$, compared to the electric dipole coupling of $\ensuremath{\Delta}\ensuremath{\ell}=\ifmmode\pm\else\textpm\fi{}1$.