Photonic Density Of States Research Articles

Excitation Mechanisms of Green Emission from Terbium Ions Embedded Inside the Sol-Gel Films Deposited onto Nanoporous Substrates

In this work we investigate the excitation mechanism of Tb3+ ions in different inorganic sol-gel matrices (composite film of YAlO3 and Al2O3; Ba0,6Sr0,3Ca0,1:TiO3) in porous anodic alumina films. The interest in synthesis of light-emitting materials in porous anodic alumina arises from its unique tailor-made honey-comb structure, strongly enhanced Tb luminescence and great photonic density of states at direction along the channels of the anisotropic light scattering. All discussed sol-gel films were synthesized by spin-on deposition on porous anodic alumina grown on a silicon wafer and annealed at different temperatures. An influence of the annealing temperature on the terbium PL was studied using XRD, 2D photoluminescence excitation and time-resolved spectroscopy. Further, the comparison of thermal quenching data for the most intensive 5D4 →7F5 luminescence band and excitation band of Tb 3+ ions was performed for the temperature range of 10 - 300 K. From the resultant data, mechanisms of Tb excitation and its dependence on the annealing conditions are proposed and discussed.

Spontaneous emission from a two-level atom in anisotropic one-band photonic crystals: A fractional calculus approach

Spontaneous emission (SE) from a two-level atom in a photonic crystal (PC) with anisotropic one-band model is investigated using the fractional calculus. Analytically solving the kinetic equation in terms of the fractional exponential function, the dynamical discrepancy of SE between the anisotropic and isotropic systems is discussed on the basis of different photon density of states (DOS) and the existence of incoherent diffusion field that becomes even more clearly as the atomic transition frequency lies close to the band edge. With the same atom-field coupling strength and detuning in the forbidden gap, the photon-atom bound states in the isotropic system turn into the unbound ones in the anisotropic system that is consistent with the experimental observation in $Phys.$ $Rev.$ $Lett.$ \textbf{96}, 243902 (2006). Dynamics along different wavevectors with various curvatures of dispersion is also addressed with the changes of the photon DOS and the appearance of the diffusion fields.

Optical properties of 1D photonic crystals with correlated and uncorrelated disorder

We introduce both correlated disorder and uncorrelated disorder to one-dimensionaldielectric periodic structures and investigate their effects on light transmission, localizationlength, density of photonic states and decay rate of resonant modes. The photonicbandgaps are more robust against uncorrelated disorder due to the preservation oflong-range structural order. While correlated disorder enhances light localization near theband edges, uncorrelated disorder causes a divergence of localization length near the gapedges. The correlated disorder induces a larger fluctuation of decay rates for the bandgapmodes than the pass band modes. In contrast, the resonant modes near the pass bandcenter experience the strongest fluctuation of decay rates in the presence of uncorrelateddisorder.

Nonclassical properties of atomic radiation field in a nonlinear photonic crystal

We study spectral properties and photon statistical characteristics of a strongly driven two-level atom produced within a nonlinear photonic crystal. This study reveals that when a large discontinuity in the local photon density of states and the cavity field mode is resonant with the central component of the Mollow spectrum of atomic resonance fluorescence, there is squeezing of the cavity field below the quantum shot noise limit and the peak of the cavity field spectrum that is achieved in the nonlinear photonic crystal is higher than that in the linear photonic crystal. Furthermore, we can see the statistics of the photons emitted by the atom into the microcavity is sub-Poissonian and close to Poissonian when the frequency of the driving field is high.

Reflectivity comb in coherently dressed three-level media

The photonic density of states of a light beam propagating through ultracold atoms may be easily modified by modulating the atomic susceptibility with a light grating. This was predicted and observed in a resonantly absorbing atomic sample supporting electromagnetically induced transparency where a probe nearly resonant with a standing wave coupling beam experiences a fully developed stop-band. In the present work, a probe that is resonant with higher harmonics of the standing wave frequency in a highly asymmetric three-level Λ-configuration or a ladder configuration, is predicted to exhibit a peculiar multipeak all-optically tunable reflection pattern. Such an unusual reflectivity spectrum is shown to be related to a suppression of the absorption akin to the Borrmann effect in the dynamical X-ray diffraction in crystals. This novel effect can actually be observed in atomic hydrogen but also in a variety of atoms, such as, for example, strontium, provided the optical lattice has been angle-tuned.

Characteristics of spontaneous emission in confined one-dimensional photonic crystals

We present a type of confined one-dimensional photonic crystal (1D PC) that is composed of a 1D PC confined by perfect conductor boundaries in the lateral directions of the 1D PC. The dispersion relations are derived using the classical electromagnetic approach, and the photonic density of states and local photonic density of states are calculated numerically. It is found that the combined action of the periodic modulation and the quantization of wave vectors in the lateral directions may give rise to photonic bandgaps and sharp peaks in the photonic density of states, which provides us with an effective way to control the spontaneous emission (SE). Based on this, the SE is investigated by the lifetime distribution function. The numerical results show that there is a wide lifetime distribution with the coexistence of accelerated and inhibited decay processes of the SE.

Emission modification of CdSe quantum dots by titanium dioxide visible logpile photonic crystal

Air band modes of three-dimensional photonic crystals (3DPCs) have a higher photonic density of states, potentially enabling greater emission enhancement. However, it is challenging to introduce emitters into the “air” region without significantly disturbing the photonic band structure of the PC. Here, we overcome this difficulty by introducing a low refractive index aerogel matrix containing CdSe quantum dots (625 nm peak emission) into a titanium dioxide logpile PC. We observe that the aerogel infiltration indeed preserves the bandstructure. We measure an emission suppression of ∼0.25 times inside and an enhancement of approximately three times outside the bandgap with only one vertical unit cell.

Structures and physiological functions of silica bodies in the epidermis of rice plants

We characterized silica structures in the epidermis of rice plant leaves and investigated their physiological functions from optical and mechanical viewpoints. By treating the distribution of silica bodies as a triangular lattice in the xy plane, and performing a theoretical optical analysis on this lattice, we discovered that a reduction in the photonic density of states may inhibit leaves of rice plant from being heated markedly higher than 20 °C. Ladderlike structures in the epidermis were mechanically investigated. These structures are conjectured to inhibit flat leaves from undergoing twisting torsions, which may assist the leaf to absorb sunlight more effectively for photosynthesis.

Photoluminescence of ZnO infiltrated into a three-dimensional photonic crystal

The effect of the photonic band gap (stopband) of the photonic crystal, the synthesized SiO2 opal with embedded zinc oxide, on its luminescence in the violet spectral region is studied. It is shown that the position of the photonic band gap in the luminescence and reflectance spectra of the infiltrated opal depends on the diameter of the constituent nanoglobules, the volume fraction of zinc oxide, and on the signal’s acceptance angle. It is found that, for the ZnO-opal nanocomposites, the emission intensity is decreased and the luminescence decay time is increased in the spatial directions, in which the photonic band gap coincides in spectral position with the luminescence peak of zinc oxide. The change in the decay time can be attributed to the change in the local density of photonic states in the photonic band gap.

Possible rationale for ultimate enhancement factor in single molecule Raman spectroscopy

The Purcell’s original idea [E.M. Purcell, Phys. Rev. 69 (1946) 682] on modification of photon spontaneous emission rate is extended to modification of photon spontaneous scattering rate. Simultaneous account for local incident field and local density of photon states enhancements in close proximity to a silver spheroid is found to provide up to 10 14-fold Raman scattering cross-section rise up. A model of the so-called ‘hot spots’ in surface enhanced spectroscopy is elaborated as local areas with high Q-factor at incident and scattered (emitted) light frequencies. Transient Raman experiments are proposed towards verification of the model.

Photonic density of states in the vicinity of a single-wall finite-length carbon nanotube

Photonic density of states in the vicinity of a single-wall finite-length carbon nanotube (CNT) is investigated theoretically in this paper. The analysis is based on the fluctuation-dissipative theorem in the Callen–Welton form. The Dyson equation for the Green dyadic of the electromagnetic field in the presence of CNT is formulated and a method for its numerical solution is elaborated. We show that the photonic density of states spectrum has a nontrivial resonant structure in the terahertz range in the vicinity of the metallic single-wall CNT. The origin of these resonances is the surface plasmon resonances on the CNT's edges.

Optical properties of chiral photonic crystals with linear profiles of modulation parameters

The oblique propagation of light through a layer of chiral photonic crystal (PC) with linear profiles of modulation parameters is considered. The problem is solved by the method of Ambartsumyan layer addition. The wavelength dependences of the amplitude characteristics have been studied at different angles of incidence in two cases, i.e., in a chiral PC with a linear profile of modulation period and a chiral PC with a linear profile of modulation depth. It is shown that the photonic band gap is broadened in both cases and that omnidirectional reflection occurs under certain conditions. The nonreciprocity features are investigated for these two cases and it is shown that a chiral PC with a linear profile of modulation period can operate as an ideal optical diode in a certain frequency range. The features of the effect of change in the modulation parameters on the photon density of states, group velocity, and group velocity dispersion are analyzed. It is shown that, when the modulation parameters change in space, the photon density of states at the photonic band gap edges significantly decreases. It is proposed to use PCs with a spatially changing modulation period can be used to compress (expand) light pulses.

Manipulation of the local density of photonic states to elucidate fluorescent protein emission rates

We present experiments to determine the quantum efficiency and emission oscillator strength of exclusively the emitting states of the widely used enhanced green fluorescent protein (EGFP). We positioned the emitters at precisely defined distances from a mirror to control the local density of optical states, resulting in characteristic changes in the fluorescence decay rate that we monitored by fluorescence lifetime microscopy. To the best of our knowledge, this is the first emission lifetime control of a biological emitter. From the oscillation of the observed emission lifetimes as a function of the emitter to mirror distance, we determined the radiative and nonradiative decay rates of the fluorophore. Since only the emitting species contribute to the change in emission lifetimes, the rates determined characterize specifically the quantum efficiency and oscillator strength of the on-states of the emitter, in contrast to other methods that do not differentiate between emitting and dark states. The method reported is especially interesting for photophysically complex systems like fluorescent proteins, where a range of emitting and dark forms has been observed. We have validated the analysis method using Rhodamine 6G dye, obtaining results in very good agreement with the literature. For EGFP we determine the quantum efficiency of the on-states to be 72%. As expected for this complex system, our value is higher than that determined by methods that average over on- and off-states.

Specific features of the emission of chiral photonic crystals with an anisotropic defect: I. Thickness effects

The specific features of defect modes of chiral photonic crystals with an anisotropic defect have been investigated. Peculiarities of the spectra of polarization observables of the system under consideration are analyzed at different thicknesses of the defect layer. It is shown that single refraction occurs in a defect mode, even though the system is anisotropic and inhomogeneous. We also investigated the specific features of the spectra of the photon density of states, light intensity at the defect center, and the Q factor of defect modes at different thicknesses of the defect layer and chiral photonic crystals. It is shown that the lasing wavelength of chiral photonic crystals with an anisotropic defect enriched in laser dyes (resonant atoms) can be controlled in a different way: by varying the defect layer thickness. It is shown that this system can operate as a narrow-band filter (mirror) with a controlled frequency width and location of the total transmission (reflection) range on the frequency scale.

Spontaneous emission near the band edge of a three-dimensional photonic crystal: afractional calculus approach

We suggest a better mathematical method, fractional calculus, for studying the behavior ofthe atom–field interaction in photonic crystals. By studying the spontaneous emission of anatom in a photonic crystal with a one-band isotropic model, we found that the long-timeinducing memory of the spontaneous emission is a fractional phenomenon. This behaviorcould be well described by fractional calculus. The results show no steady photon–atombound state for the atomic resonant transition frequency lying in the proximity of theallowed band edge which was encountered in a previous study (Woldeyohannes and John2003 J. Opt. B: Quantum Semiclass. Opt. 5 R43). The correctness of this result is validatedby the ‘cut-off smoothing’ density of photon states (DOS) with fractional calculus. Byobtaining a rigorous solution without the multiple-valued problem for the system,we show that the method of fractional calculus has a logically concise property.

Optically excited secondary emission spectra of photonic crystals based on synthetic opals

The photonic dispersion, the group-velocity dispersion, the effective mass, refractive index, and the spectral distribution of the density of photonic states near the edge of the photonic stop band are numerically calculated in the one-dimensional model for photonic crystals based on synthetic opals. The fluorescence spectra of rhodamine 6G and 2,5-bis(2-benzoxazolyl)hydroquinone molecules infiltrated into a synthetic opal are measured. For both substances, it is observed that the spontaneous emission intensity in the range of the photonic stop band is appreciably suppressed. A blue shift of the fluorescence spectrum of rhodamine 6G molecules is revealed. Secondary emission of synthetic opals infiltrated with colloidal silver is observed in the Stokes range under excitation of opals by radiation at λ = 400 nm. The spectrum of the secondary emission is located in the range 450–590 nm, which contains the stop band and intervals near its edges.

Nonlinear Verdet law in magnetophotonic crystals: Interrelation between Faraday and Borrmann effects

The magneto-optical Faraday effect is studied in one-dimensional magnetophotonic crystals !MPCs. Mechanisms of a strong enhancement of the Faraday rotation at the edges of the photonic band gap are considered. High difference of refractive indexes of bismuth-substituted yttrium iron garnet !Bi:YIG and SiO2 layers provides a strong spatial localization of the optical field in Bi:YIG layers, which leads to manifold Faraday rotation enhancement at the photonic band edges. The Faraday rotation angle in the finite MPCs appears to be a nonlinear function of the total thickness of magnetic material in the stack that can be interpreted as the nonlinear Verdet law. Relation between the enhancement of the Faraday rotation and localization of optical field in magnetic layers is treated as a Borrmann-type effect. This relation shows that the Faraday rotation can be considered as a measure of the density of photonic states trapped within Bi:YIG layers.

THz Thermal Radiation Enhancement Using an Electromagnetic Crystal

Thermal radiation in the terahertz (THz) range only occupies a tiny portion of the whole blackbody power spectrum at room temperature. We demonstrate that a thermal radiator, which is constructed from an electromagnetic (EM) crystal, can be designed so that its photon density of states (DOS) is enhanced in the THz frequency range. We also demonstrate, as a consequence, that this source may lead to large enhancements of the radiated power over the values associated with normal blackbody radiation at those frequencies. The THz thermal radiation enhancement effects of various EM crystals, including both silicon and tungsten woodpile structures and a cubic photonic cavity (CPC) array, are explored. The DOS of the woodpile structures and the CPC array are calculated, and their thermal radiation intensities are predicted numerically. These simulations show that the radiated power can be enhanced by a factor of 11.8 around 364 GHz and 2.6 around 406 GHz, respectively, for the silicon and tungsten woodpile structures in comparison to the normal blackbody radiation values at those frequencies. It is also shown that an enhancement factor of more than 100 may be obtained by using the CPC array. A silicon woodpile EM crystal with a band gap around 200 GHz was designed and fabricated. The transmission property of this woodpile structure was verified using the THz time-domain spectroscopy (TDS). Thermal emissions from the fabricated silicon woodpile and a control blackbody sample were measured. Enhancements of the woodpile source radiation over the blackbody were observed at several frequencies which are consistent with the theoretical predictions.

Nonclassical light generation by a photonic-crystal one-atom laser

We investigate the effects of sub-Poissonian photon statistics and photon antibunching in the light generation by a photonic-crystal one-atom laser. The physical system consists of a two-level light emitter strongly coupled to a high-quality microcavity engineered within a photonic crystal and coherently driven by a strong external laser field. This study reveals that the electromagnetic environment provided by the photonic crystal facilitates light generation characterized by pronounced sub-Poissonian photon statistics and photon antibunching, and strongly enhanced relative to that from a one-atom laser in a conventional optical cavity. The characteristics of the cavity photon statistics are fundamentally distinct from those of a corresponding microcavity in ordinary vacuum. For large discontinuities in the photon density of states between Mollow spectral components of atomic resonance fluorescence, in the good cavity regime, the photon statistics is sub-Poissonian, in contrast to the case of a conventional cavity where sub-Poissonian photon statistics is present only for a bad cavity. These results suggest the possibility of using a photonic-crystal one-atom laser as an efficient source of nonclassical light.

Fractional Dynamics of the Spontaneous Emission of an Atom in Photonic Crystals

We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with one-band isotropic model, we found that the long-time inducing memory of the spontaneous emission is a fractional phenomenon. This behavior could be well described by the fractional calculus. And the results show no steady photon-atom bound state for the atomic resonant transition frequency lying in the proximity of allowed band edge which is encountered in the previous study [J. Opt. B: Quantum Semiclass. Opt. {\bf 5}, R43 (2003)]. The correctness of this result is validated by the ``cut-off smoothing'' density of photon states (DOS) with fractional calculus. By obtaining a rigorous solution without the multiple-valued problem for the system, we show the method of fractional calculus has logically concise property.