Applications of the expanded basis method to study the behavior of light in polaritonic photonic crystal slab with losses

We apply the expanded basis method (EBM) to investigate the behavior of light in polaritonic photonic crystal (PC) slabs with losses. The influence of losses on transmissivity is studied. It is found that the transmissivity is significantly lowered with the increase of losses, in particular, it is abruptly decreased in the vicinity of transverse-optical-phonon frequency. The electromagnetic (EM) dissipation is mainly dominated by the imaginary part of dielectric constant of PC. The larger the imaginary part of the dielectric constant, the more the EM energy depletion is. The variation of EM dissipation with the number of period layers in the PC slab is approximately linear or oscillatory increase with the number of period layers.     

A new anti-reflection surface structure for photonic crystal slab lens

An optimized surface modification structure for suppressing the reflections at the surfaces of photonic crystal slab lens is reported in this paper. The total reflection of the slab lens with proposed anti-reflection surface structure is reduced to below 0.3% for the incident angle of light less than 48 degrees. The image efficiency of the slab lens for the normal incident Gaussian beam with waist width equal to the wavelength is near 99%.     

Near-field effect in two-atom system

The self-consistent problem is solved for the interaction of two dipole atoms situated at arbitrary distance from one another with the field of quasiresonant light wave. Atoms are considered to be linear Lorenz oscillators. Polarizing fields inside the system include both Coulomb and retarding parts. The solutions obtained are investigated for the case when atoms have the same polarizabilities and interatomic distance is much less than external light wavelength. Formulas for electric fields inside and outside of small object are obtained. It is shown that longitudinal and transverse optical oscillations are possible to exist inside small two-atom object. Dispersion laws of these oscillations depend upon interatomic distance and upon angle between axis of the system and the direction of propagation of external wave. The field outside the small object in wave zone is linearly polarized with the choice of linear polarization of external field. However, the directions of polarization of these waves are different and depend essentially upon frequency. The amplitude of field outside small object in wave zone is shown to depend essentially on the frequency of external field and interatomic distance. The results obtained are treated as near-field effect in the optics of small objects making it possible to investigate the structure of small objects with optical radiation. Received 26 October 1998 and Received in final form 26 January 2000     

Angular tuning of defect modes spectrum in the one-dimensional photonic crystal with liquid-crystal layer

A one-dimensional ZrO₂/SiO₂ photonic crystal with a 4-n -pentyl-4' -cyanobiphenyl (5CB) nematic defect layer was used to investigate the transmission spectra of light polarized parallel and perpendicular to the liquid-crystal director at different angles of incidence. The spectra of the photonic crystal were shown to split into four polarized components T_ij at oblique incidence. When the incident angle increased, the bandgap edges and the defect modes shifted towards short wavelengths, while the amplitudes of the defect modes increased for the transverse magnetic polarization and decreased for the transverse electric polarization. The observed discrepancy between the defect mode amplitudes in the center and near the edges of the photonic bandgap was found to be related to the radiation losses inside the defect layer of a non-ideal photonic crystal. The simulated transmission spectra obtained using recurrence relations and taking into account the decay of defect modes are in good agreement with the experimental data.     

Demonstration of a new transport regime of photon in two-dimensional photonic crystal

A new transport regime of photon in two-dimensional photonic crystal near the Dirac point has been demonstrated by exact numerical simulation. In this regime, the conductance of photon is inversely proportional to the thickness of sample, which can be described by Dirac equation very well. Both of bulk and surface disorders always reduce the transmission, which is in contrast to the previous theoretical prediction that they increase the conductance of electron at the Dirac point of graphene. However, regular tuning of interface structures can cause the improvement of photon conductance. Furthermore, large conductance fluctuations of photon have also been observed, which is similar to the case of electron in graphene.     

Study on composite photonic crystal patch antenna

The paper investigated a composite photonic crystal patch antenna by using the method of finite difference time domain (FDTD). The results show that there exists a wave resonance state at 2.635 GHz, where the real part of the permittivity and permeability are all negative; its refraction index is –1. The effect has largely enhanced the electromagnetic wave’s resonance intensity, and has improved the localized extent of electromagnetic energy obviously in such photonic crystal structure (PBG), resulting in a higher antenna gain, a lower return loss, and a better improvement of the antenna’s characteristics. Due to such the advantages, the use of patch antennas can be extended to such fields as mobile communication, satellite communication, aviation, etc.     

Zonal model of nonstationary self-focusing of femtosecond laser radiation in air: effective beam characteristics evolution

The generic scenario of intense femtosecond laser pulse propagation in the air from the viewpoint of evolution of its integral effective parameters (energy transfer coefficient, effective radius, effective duration, limiting angular divergence) is considered. The analysis of variation of the effective parameters along the propagation path in the single and multiply filamentation scenarios based on numerical calculations is presented. It is shown that the process of self-action of the ultrashort radiation is characterized by the formation in a medium of the nonlinearity layer, after which optical pulse propagates quasi-linearly with the limiting angular divergence that depends mainly on initial pulse power. The effective pulse temporal duration and the effective beam radius increase after the passage through the nonlinearity layer, and their values are mostly determined by the initial beam power also. The coefficient of energy transmission of femtosecond laser radiation is lower than in the linear medium and has a tendency to decrease with the increase of the pulse power.     

Light scattering from mesoscopic objects in diffusive media

No direct imaging is possible in turbid media, where light propagates diffusively over length scales larger than the mean free path .The diffuse intensity is, however, sensitive to the presence of any kind of object embedded in the medium, e.g. obstacles or defects. The long-ranged effects of isolated objects in an otherwise homogeneous, non-absorbing medium can be described by a stationary diffusion equation. In analogy with electrostatics, the influence of a single embedded object on the intensity field is parametrized in terms of a multipole expansion. An absorbing object is chiefly characterized by a negative charge, while the leading effect of a non-absorbing object is due to its dipole moment. The associated intrinsic characteristics of the object are its capacitance Q or its effective radius ,and its polarizability P. These quantities can be evaluated within the diffusion approximation for large enough objects. The situation of mesoscopic objects, with a size comparable to the mean free path, requires a more careful treatment, for which the appropriate framework is provided by radiative transfer theory. This formalism is worked out in detail, in the case of spherical and cylindrical objects of radius R, of the following kinds: (i) totally absorbing (black), (ii) transparent, (iii) totally reflecting. The capacitance, effective radius, and polarizability of these objects differ from the predictions of the diffusion approximation by a size factor, which only depends on the ratio .The analytic form of the size factors is derived for small and large objects, while accurate numerical results are obtained for objects of intermediate size .For cases (i) and (ii) the size factor is smaller than one and monotonically increasing with ,while for case (iii) it is larger than one and decreasing with . Received: 7 August 1998 / Accepted: 3 September 1998     

Dynamics of atomic decay in a special one dimensional photonic crystal

Recently, Liu et al. [Phys. Rev. B 74, 075314 (2006)] pointed out that the atomic instant decay rate in one dimensional photonic crystal (1DPC) showed a series of pulse-like peaks with time. In this paper, we continue their work, and adopt a special 1DPC, in which the refractive indexes of both constitution layers in a period are the same, to perform the analysis in detail. Our results show that the pulse-like peak of instant decay rate originates from the interaction between the atom and the sub-reservoir, the latter of which corresponds to the group of reflected fields having the same optical distance. The atom interacts with such a sub-reservoir mainly after the time needed for propagation. However, near the arrival time of the reflected field, the atomic level is broadened and couples to all frequency components of the sub-reservoir, and the pulse-like peak of instant decay rate appears. Although our conclusion is deduced with the special 1DPC, it is also valid for more general cases and might be useful to measure the quantum Zeno and anti-Zeno effect, since the interval of repeated measurements may be expanded to several optical cycles in 1DPC, which will facilitate the observation of the quantum Zeno or anti-Zeno effect.     

The influence on atomic decay by inserting a LHM layer into an ordinary one dimensional multi-layer structure

Inserting left-handed material (LHM) layers into a one dimensional structure can influence the spontaneous emission (SpE) of a two-level atom. This has been investigated, starting from the simplest case of a three-layer system, where we find the reflected field (atom can “see”) passing through LHM layer is stronger than that through the corresponding normal layer. Indeed the induced decay is more strongly influenced by reflected field passing through LHM layer. Based on this and after further analysis of reflectivity, we find that, a quarter photonic crystal (PC) composed of alternately LHM and RHM can inhibit the atomic spontaneous emission more intensely compared to an ordinary PC.     

Analysis of photonic band gaps in a two-dimensional photonic crystal with centrifugal core-shell rods

The absolute photonic band gap (PBG) in two-dimensional (2D) photonic crystal with excentric core-shell rods is studied in this paper. The core rod shifts away from the core-shell rod center, and its position is decided by two new introduced parameters — the shift angle θ and the offset ρ. We use the FDTD algorithm to calculate the photonic bands of the photonic crystal, and analyze how the offset and shift angle affect the photonic bang gap of excentric core-shell photonic crystal for different core rod size. It has been shown that the variation of the photonic band gap is quite peculiar.     

A matrix study of the transfer of polarized radiation in plasmas. Application to neon-like germanium lasers

In order to solve the radiative-transfer equation for polarized beams propagating in plasmas a matrix approach is applied. The solution is the four-components Stokes vector, and the effect of the medium on the state of the radiation is represented by an amplification operator. Our approach is applied to the neon-like germanium 23.6 nm line, when a right-circularly polarized beam is injected into an amplifying plasma. The conditions governing the recovery of the initial polarization state are investigated over the entire spectrum of the output. Received: 10 October 1997 / Revised: 12 January 1998 / Accepted: 27 January 1998     

Lateral shifts of an optical beam in an anisotropic metamaterial slab

The lateral shift of a light beam at the surface of an anisotropic metamaterial slab is investigated. Analytical expressions of the lateral shifts are derived using the stationary-phase method, in the case that total reflection does and does not occur at the first interface. The sign of the lateral shift in two situations is discussed, and the necessary conditions for the lateral shift to be positive or negative are given. It is shown that the thickness and physical parameters of the anisotropic metamaterial slab, as well as the incident angle of the light beam, strongly affect the properties of the lateral shift, and numerical results validate these conclusions. The effect of a lossy metamaterial on the lateral shift is also investigated. A restriction on the thickness of the slab is obtained, which is necessary for the stationary-phase method to remain valid.     

Properties of the peaks of second harmonic light through Fibonacci-class ferroelectric domains

After establishing the method of constructing a class of one-dimensional (1D) Fibonacci-class quasiperiodic (FC(n)) ferroelectric domains system, we have studied the properties of the electric field of the second harmonic generation (SHG) by means of the small-signal approximation in the case of the vertically transmission. It was found that only the second harmonic light (SHL) peaks which were indexed by two special integers q and p would be the brightest and the spectra whose positions were decided by successive FC(n) integers and were perfect self-similar without considering the dispersive effect of the refractive index on SHL. The effect of the vacancies for some special spectral lines was also studied generally. The analytic results were confirmed by the numerical simulations. Received 26 October 1999 and Received in final form 6 January 2000     

Frequency dependence of the photonic noise spectrum in an absorbing or amplifying diffusive medium

A theory is presented for the frequency dependence of the power spectrum of photon current fluctuations originating from a disordered medium. Both the cases of an absorbing medium (“grey body”) and of an amplifying medium (“random laser”) are considered in a waveguide geometry. The semiclassical approach (based on a Boltzmann-Langevin equation) is shown to be in complete agreement with a fully quantum mechanical theory, provided that the effects of wave localization can be neglected. The width of the peak in the power spectrum around zero frequency is much smaller than the inverse coherence time, characteristic for black-body radiation. Simple expressions for the shape of this peak are obtained, in the absorbing case, for waveguide lengths large compared to the absorption length, and, in the amplifying case, close to the laser threshold. Received 8 August 2000     

Propagation of light-pulses at a negative group-velocity

This paper deals with the apparent superluminal propagation of electromagnetic pulses in a linear dispersive medium. One specifically examines the possibility that the pulse leaving the medium may be nearly identical to the incident one (low distortion) and in significant advance of it (strongly negative group-delays). Favourable conditions are obtained in a dilute medium where the required anomalous dispersion originates in an ensemble of narrow absorption or gain lines. Analytical expressions of the advancement of the pulse centre-of-gravity and of the lowest order distortion are established from the transfer-function of the medium. The experiments already achieved with arrangements involving a single absorption-line or a gain-doublet are analysed in detail and compared. The considerable difficulties to overcome in order to attain advancements comparable to the pulse width without important distortion are pointed out. New and promising schemes involving a narrow dip in a gain profile or absorption-doublets are proposed. Received 4 July 2002 / Received in final form 8 November 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: bruno.macke@univ-lille1.fr RID="b" ID="b"Unité Mixte de Recherche de l'Université et du CNRS (UMR 8523)     

Long-range perturbations produced by a localized packet of ion-acoustic waves in a collisionless plasma

We demonstrate the in situ detection of cold ⁸⁷Rb atoms near a dielectric surface using the absorption of a weak, resonant evanescent wave. We have used this technique in time of flight experiments determining the density of atoms falling on the surface. A quantitative understanding of the measured curve was obtained using a detailed calculation of the evanescent intensity distribution. We have also used it to detect atoms trapped near the surface in a standing-wave optical dipole potential. This trap was loaded by inelastic bouncing on a strong, repulsive evanescent potential. We estimate that we trap 1.5×10⁴ atoms at a density 100 times higher than the falling atoms. Received 14 May 2002 Published online 8 October 2002 RID="a" ID="a"e-mail: spreeuw@science.uva.nl     

Spontaneous emission from a three-level atom embedded in an anisotropic photonic crystal

We study the spontaneous emission properties of a V-type three-level atom embedded in a photonic crystal with the anisotropic dispersion relation. We show that the localized field can disappear and the diffusion field can become intense in some regions. This originates from no singularity of the density of states. The quantum interference leads to oscillatory, quasi-oscillatory or complete decay behavior of population. The complete decay can also be realized in certain condition without depending on the initial state. Received 9 April 2000 and Received in final form 1st August 2000     

Anomalous lateral beam shift and total absorption due to excitation of surface waves in materials with negative refraction

We studied electromagnetic beam reflection from layered structures that include materials with negative refraction. Excitation of leaky surface waves leads to the formation of anomalous lateral shifts in the reflected beams with single or double peak structures. The presence of reasonable losses within material with negative refraction, besides significant influence on manifestation of the giant lateral shifts, can lead to their total suppression and anomalously high absorption of the incident radiation. If, in addition to the resonant excitation of leaky surface waves, radiation inflow exactly compensates their irreversible damping, total absorption of the incoming radiation can be achieved for moderately wide beams.