Spontaneous emission from a three-level atom in two-band photonic crystals

Abstract

We investigate the spontaneous emission from a V three-level atom embedded in two-band isotropic photonic crystals. The dipoles of the two transitions from the two upper levels to the lower level are parallel. Due to the quantum interference between the two transitions and the existence of two bands, the populations in the upper levels display some novel properties, such as anti-trapping and continuous oscillation, which differ from that of a two-level atom (with two bands) and also differ from that if only one band (for three-level atom) is considered. The spontaneous emission field is composed of two parts: localized field and travelling field. The localized field is composed of one or two localized modes, and the travelling field is composed of no, one, two or three propagating modes depending on different conditions. The conditions for different combinations of localized modes and propagating modes are discussed.     

Position-dependent absorption-dispersion spectrum of a Λ-type three-level atom embedded in a defective photonic crystal

The position-dependent optical spectra of a Λ-type three-level atom embedded in a photonic crystal are studied by considering the double-band photonic band gap reservoir with defect modes in the band gap. It is shown that the number of absorption peaks, transparency windows and the slope of the dispersion curve can be modulated by adjusting the position of the embedded atom.     

Spontaneous emission of a driven five-level atom in a defective photonic crystal

Abstract

The free space spontaneous emission spectra of a driven five-level atom embedded in a defective double-band photonic band-gap material are investigated. The effect of quantum interference on the spontaneous emission spectra and its nature are discussed. It is shown that the nature of quantum interference in the presence of the driving field and defect mode may be destructive or constructive depending on the initial atomic coherency.     

Spontaneous emission from a four-level atom embedded in photonic crystals via quantum interference

The spontaneous emission of a four-level atom embedded in a one-dimensional photonic crystal is investigated. The atom has two upper levels coupled by the same vacuum modes to a common lower level and is driven by a coherent field to an auxiliary level. Spontaneous emission can be suppressed significantly due to the combinational influences of the interference effect and the band edge effect. The radiation field emitted by the atom is also studied. Spontaneous emission can be modified by controlling the Rabi frequency of the driving.     

Dispersion relation of surface plasmons near photonic band gaps: Influence of the interaction with light

Abstract

We present an experimental and theoretical study of the photonic band gap in the propagation of surface plasmons (SPs) on periodically corrugated surfaces. Our main purpose is to investigate the case where the band gap width is larger than the energy distance between the SP dispersion curve for a flat surface and the light line. We introduce a physical model of the interaction of light waves with SPs and derive an analytical expression for the SP wave vector near band gaps based on the coupled-mode approach involving three interacting modes (two of them are SP modes and one is a light mode). By using the interferometric measurement we have studied, for the first time, the SP propagation parameters in the vicinity of the photonic band gap (10 μm wavelength region). The predictions of our theory are in good agreement with the experimental data.     

Spontaneous emission from a three-level atom embedded in anisotropic photonic band gap structures

Abstract

We investigate spontaneous emissions from a three-level atom embedded in realistic anisotropic photonic band gap structures, where the band edge is assumed to be midway between the two upper levels of the atom. In the anisotropic model, the atom-field interaction is reduced to be smaller than that in the ideal isotropic model, which results in the reduction of suppression and oscillation effects in the spontaneous emission; however, we demonstrate that the suppression is strongly enhanced even in the anisotropic model by expanding the detuning between the upper level and the band edge, while the oscillation is greatly reduced. This demonstration is carried out by calculating the atomic state vector for a wide range of the detuning. Using the state vector, the atom-field interaction is studied for two field parts, a localized part and a propagating part, separately. For the localized part, the atom-field interaction is enhanced by expanding the detuning, in spite of the anisotropy, which leads to a strong suppression effect, while for the propagating part, the atom-field interaction is reduced, which leads to a weak oscillation effect. This result is relevant to strong memory effects with high-speed switching, which are attractive properties for a qubit.     

Engineering a light-emitting planar defect within three-dimensional photonic crystals

Abstract

Sandwich structures, constructed from a planar defect of rhodamine-B (RhB)-doped titania (TiO₂) and two photonic crystals, were synthesized via the self-assembly method combined with spin-coating. The modification of the spontaneous emission of RhB molecules in such structures was investigated experimentally. The spontaneous emission of RhB-doped TiO₂ film with photonic crystals was reduced by a factor of 5.5 over a large bandwidth of 13% of the first-order Bragg diffraction frequency when compared with that of RhB-doped TiO₂ film without photonic crystals. The angular dependence of the modification and the photoluminescence lifetime of RhB molecules demonstrate that the strong and wide suppression of the spontaneous emission of the RhB molecules is due to the presence of the photonic band gap.     

Structural and optical quality of binary photonic crystal heterostructures fabricated by the modified self-assembly method

Photonic crystal heterostructures constituting of two photonic crystals with different lattice constants are fabricated using the modified self-assembly method and their structural and optical properties are investigated. The results show that these photonic crystal heterostructures of high quality possess deep photonic band gaps and steep photonic band edges in their transmission spectra. Deep double photonic band gaps, steep photonic band edges and high transmittance in the pass band show good ordering of the heterostructure and may offer a probability for studying late-model ultra-fast all-optical switches.     

Properties of defect modes in geometrically chirped one-dimensional photonic crystals

The variation of the transmission coefficient with defect mode frequency in a geometrically chirped photonic crystal with central defect layer has been investigated theoretically using transfer matrix method and validated experimentally by fabricating and characterizing such photonic crystals. The defect mode frequency is extracted by modeling the defect layer as a Fabry-Perot resonant cavity with mirrors replaced by two geometrically chirped photonic crystals. It is shown that the structural asymmetry of the chirped photonic crystals with respect to the central defect layer affects the width of the photonic band gap and also induces coupling variation between the eigenmodes of the defect layer and those at the band edges of the constituent photonic crystals. This leads to variation in the defect mode transmittance across the photonic band gap and introduces notches at positions where the eigenmodes of the band edges have maximum transmission.     

Quasimode theory of quantum optical processes in photonic band gap materials

This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.     

Spontaneous emission and radiation properties of a driven four-level atom embedded in an anisotropic PBG

The spontaneous emission from a driven four-level tripod atom embedded in an anisotropic photonic crystal is investigated in this paper. We find that time-evolution properties and components of the emitted fields are dependent on the relative position of the upper level of the atom from the band edge and the space between two lower levels. The radiation field emitted by the atom is calculated more accurately. The energy is translated from one form to another with the increase of distance from the atom and the upper level's relative position. The evolution properties and the spontaneous spectrum are also studied. The results analyzed here are consistent with the distribution of emitted fields.     

Spontaneous emission from a three-level atom placed in three-dimensional photonic crystals in the long-time limit

The paper describes the spontaneous emission from a three-level atom placed in a periodic dielectric microstructure which exhibits a complete three-dimensional photonic band gap. By using the Euler approach, the upper level population of the atom is calculated for a wide range of relationships between the Rabi frequency and the detuning of the atomic transition frequency from the upper band edge. The results indicate that there are three cases of the relationship between Rabi frequency and detuning, which determine distinctive states of the atomic population in the long-time limit. When the detuning is greater than the Rabi frequency, the upper level has a zero steady-state atomic population, which leads to enhancement of spontaneous emission. When the magnitude of the detuning is less than the Rabi frequency, the upper level has a nonzero steady-state atomic population, which leads to suppression of spontaneous emission. When the negative detuning is greater than the Rabi frequency, the upper level has a nondecaying oscillatory-state atomic population due to long-time atomic splitting. These three properties of the spontaneous emission are relevant to several optical devices on an atomic scale, such as optical memories, switches and clocks.     

Localization of Light by a Set of Parallel Cylinders

Abstract

Using a rigorous theory of scattering, numerical evidence of the existence of localized modes in a one-dimensional or a two-dimensional set of circular dielectric rods is given. Particular attention is paid to the transition observed between the phenomena of propagation in periodic structures and localization phenomena in random structures. In particular, we show the strong connection between the phenomenon of a photonic band gap that appears in two-dimensional periodic sets of rods and the phenomenon of Anderson localization which is observed when the periodicity is broken     

The control of spontaneous emission from a three-level atom in an anisotropic photonic crystal with two asymmetric bands

We theoretically investigate the spontaneous emission light of an excited three-level atom embedded in an anisotropic photonic crystal with two asymmetric bands. The property of spontaneous emission relating to the atomic position in a unit cell of the crystal is described with a position-dependent phase difference. The atomic transition in free space can be manipulated by the other associated transition coupling to photonic crystal. The result shows that the spontaneous emission spectra are effectively shifted and tuned by the atomic position-dependent phase, which results in the asymmetric distribution of the photonic density of states between two bands, and the increasing band can push the emitted light towards the other band. The physical process can be further illuminated through analyzing the emitted field in photonic crystal. The result perhaps offers an interesting route towards tunable photonic devices.     

Two-dimensional penrose-tiled photonic quasicrystals: Diffraction of light and fractal density of modes

Abstract

We report measurements of the diffraction pattern of a two-dimensional photonic quasicrystal structure. Using a set of plane waves defined by the diffraction pattern we introduce a theoretical approach for the calculation of the band structure which captures the rotational and inflational properties of the quasicrystal. Based on this model we find that the density of modes of the quasicrystal displays a fractal character and a depleted region analogous to the band gap in a periodic system.     

光波在由左手材料和激活介质构成的光子晶体中的传输

用特征矩阵法计算了光波在包含左手材料和激活介质的一维光子晶体中的传播规律,当左手材料和激活介质厚度相等时,出现了超窄通带和透射率大于1的高增益现象,受激辐射的增强总是发生在带隙的边缘附近。进一步论证了受激辐射增强现象与光子带隙边缘群速度异常存在关联。随着频率的增加,光增益呈e指数增大。光频率不变时,光在光子晶体中的透射率随光子晶体周期数的增加呈线性增加。当左手材料和激活介质厚度不相等时,通带宽度增加,带边仍存在大于1的透射峰。     

The radiative characteristics and the decay properties of an excited Λ-type atom in anisotropic photonic crystals

The radiative characteristics and the decay properties of a Λ-type excited atom embedded in anisotropic photonic crystals are studied. It is found that the dynamic properties of the atom and the propagating characteristics of the emitted field are apparently influenced by the relative position of the upper level from the forbidden gap and the two lower levels. By Von Neumann measurement, the effects of measurements on the decaying atom are investigated. The frequent projection on the excited state can lead to decay suppression or an acceleration effect at rather low repetition rates, depending on the frequency of measurements and the relative position of the upper level from the photonic crystals band edge.     

一维杆状声子晶体的带隙特性

用有限元方法计算了一维杆状声子晶体的振动传输特性及其振动模态,从振形角度分析了一维杆状声子晶体相关参数(物理参数、尺寸参数)对带隙起始频率及带隙宽度的影响,发现带隙的形成与其模态振形密切相关,各参数对声子晶体带隙的影响主要是影响了个模态所在的频率,从而改变了其带隙的起始位置及宽度。     

Localized Modes in Metamaterial-Dielectric Photonic Crystals with a Dielectric-Superconductor Pair Defect

Transmission coefficient and dispersion relation are calculated for a one-dimensional photonic crystal of alternating dielectric-metamaterial slabs with a dielectric-superconductor pair defect. The presence of the superconductor slab in the pair defect layer leads to a strong depletion of the TM transmission coefficient in a frequency range close to the edges of the non-Bragg gap and around the characteristic resonance frequency of the superconductor and introduces TM electromagnetic modes inside such gap. The features of the arising modes depend on the relation between the thicknesses of the layers involved in the defect and a low-frequency mode can arise from the low-frequency continuum of the bulk metamaterial modes at a non-zero in-plane wave vector.     

Controllable preparation of the ordered pore arrays anodic alumina with high-quality photonic band gaps

High-quality photonic crystals (PCs) based on the ordered pore arrays anodic alumina are fabricated by the anodic oxidation method using the newly-designed periodic oxidation voltage wave. The obtained PCs own uniform narrow photonic band gaps (PBGs), steep photonic band edges, zero transmittances inside of the PBGs and high transmittances outside of the PBGs. Importantly, the high-quality PBGs of the anodic alumina PCs are tunable and controllable in the range from 350 nm to 1330 nm by modifying the anodizing voltage waveform. The benefit of newly-designed periodic oxidation voltage wave is to improve the optical properties of anodic alumina PCs.