Preface to BIT 55:1

The normal mode helical antenna (NMHA) is widely used for RF communication applications and usually provides a potential front door path of coupling electromagnetic pulse (EMP). Many numerical methods are employed to analyze the transient response of antennas under EMP, such as time-domain finite difference (FDTD) and time domain integral equation (TDIF) methods. While the numerical methods give accurate results, they can be time-consuming and only provide snapshots of EMP response in very specific circumstances. In addition, the transient data obtained from numerical tools is often required to be handled for the subsequent EMP vulnerability assessment in the RF front end circuits of communication system. The analysis of transient response for communication systems in the presence of EMP was usually complicated in the traditional field-circuit method.

FDTD algorithms are being used as a numeric tool for the analysis of photonic crystals. The definition of the modes associated with them is of interest for the study of the capabilities of photonic crystal devices. The Principal Component Analysis (PCA) has been applied here to a sequence of images corresponding to the electromagnetic fields obtained from the FDTD simulations. PCA has revealed and quantified the importance of the modes appearing in the photonic crystals. The capability of PCA to produce spatial structures, or maps, associated with temporal evolutions has made possible the calculation of the modulus and phase of the modes existing in the photonic crystal. Some other modes, contributing with an almost negligible amount to the total variance of the original data, are also revealed by the method. Besides, PCA has been used to quantify the contribution of the numerical noise of the algorithm and to identify the effect of artifacts related with the matching of the computational grid and the inner geometry of the photonic crystal.

Despite their advantages in the analysis of transient electromagnetic scattering phenomena, the widespread implementation of time domain integral equation (TDIE) based methods was hampered by the fact that they tended to be unstable and computationally expensive. The recent rediscovery of TDIE based methods springs from two different sources: (i) fast methods ameliorate the computational complexity, (ii) implicit time stepping schemes make TDIE solutions stable enough for use in practical simulations (see Rao, S.M. and Wilton, D.R., 1991). Although these advances have made TDIE methods practical, the accuracy of TDIE methods remains largely unstudied. Though methods for improving the accuracy and convergence properties of the spatial discretization of TDIEs can be based on the well-known frequency domain method of moments (MoM) techniques, temporal discretization methods are still poorly understood. While exponentially convergent TDIE temporal discretization methods exist, they use basis functions that are noncausal and thus preclude the possibility of a time marching solution (see Weile, D.S. et al., 2000). We show how such methods can be modified to create a very accurate and stable time marching approach for the solution of TDIEs.

We investigate the optical coupling of excitons confined in site-controlled semiconductor quantum dots (QDs) with the modes of photonic crystal (PhC) cavities membrane cavities and waveguides. The structures are fabricated by organometallic vapor phase epitaxy of InGaAs/GaAs heterostructures on patterned (111)B GaAs substrates combined with electron-beam-based nanolithography. We elucidate the role of pure dephasing and phonon interaction on the weak exciton-cavity mode coupling, and demonstrate the simultaneous coupling of several QDs to the same optical mode of various PhC cavity configurations. In addition, coupling of QD systems to PhC waveguides for implementing single photon transport in the face of optical disorder is studied. Implications on the potential of constructing integrated quantum photonic circuits for on-chip manipulation of quantum light will be discussed.

In order to obtain tunable surface modes of photonic crystal, we add a magnetic material layer on the truncated surface of a two-dimensional photonic crystal. Through calculations of photonic band, we obtain the surface defect modes in the first and second gaps. Through the modulation of applied magnetic field, we can control the frequency, the group velocity and the exciting incidence direction of the surface defect mode. In particular, in the frequency range of surface defect modes, we can tune the group velocity to zero.

The effect of electromagnetically induced transparency on the spectrum of defect modes of one-dimensional photonic crystal is discussed theoretically. Narrowing of defect mode linewidth is predicted due to nonabsorbing highly dispersive medium in defect layer.

In this study, we have demonstrated a multi-layered structure to examine how the magneto-optical effects affect the behavior of the photonic spin Hall effect (PSHE). The Faraday and Voigt effects are taken into account. The multi-layered structure is one-dimensional (1D) photonic crystal (PC) with a defective plasma layer. The properties of the PSHE in both symmetric and asymmetric defective PCs are explored. The numerical results show that the applied magnetic field and the geometries of the structures have significantly changed the characteristics of the PSHE. The transverse displacements of the H-polarization can be easily enhanced by more than ten times, while the transverse displacement of the V-polarization can be easily suppressed by a few percent based the manipulating of the external magnetic field. Moreover, the magneto-optical effects can change the optimal incident angle for the assessment of the peak transverse displacements of the PSHE. In addition, the numerical results also show that the plasma frequency, defective plasma thickness, and the geometry of the structure have greatly influenced the behavior of the PSHE. The parameter dependencies of theses effects are also calculated and discussed.

The structure of one-dimensional photonic crystal (1DPC) containing indefinite metamaterials with a hyperbolic dispersion relation is proposed to realize the omnidirectional gap for the design of omnidirectional reflectors and filters. It is demonstrated that this 1DPC can result in a similar zero average index (zero-n¯) gap usually appearing in the 1DPC containing isotropic left-handed materials. The properties of zero-n¯ gap and defect modes of this photonic crystal are studied in detail. The edge of this zero-n¯ gap is insensitive to incident angle and polarization of light in contrast to the Bragg gap. When a defect layer is introduced into the 1DPC, a defect mode appears inside the omnidirectional gap. The spectral position of defect mode is found to be weakly dependent on the incident angle of light and nearly invariant to the scale length of photonic crystal.

Shock wave solutions of the Einstein equations have been constructed in coordinate systems in which the gravitational metric is only Lipschitz continuous, but the connection $Γ$ and curvature $Riem(Γ)$ are both in $L^{\infty}$. At this low level of regularity, the physical meaning of such gravitational metrics remains problematic. Here we address the mathematical problem as to whether the condition that $Riem(Γ)$ has the same regularity as $Γ$, is sufficient for the existence of a coordinate transformation which perfectly cancels out the jumps in the leading order derivatives of $δΓ$, thereby raising the regularity of the connection and the metric by one order--a subtle problem. We have now discovered, in a framework much more general than GR shock waves, that the regularization of non-optimal connections is determined by a nonlinear system of elliptic equations with matrix valued differential forms as unknowns, the Regularity Transformation equations, or RT-equations. In this paper we establish the first existence theory for the nonlinear RT-equations in the general case when $Γ, {\rm Riem}(Γ)\in W^{m,p}$, $m\geq1$, $n

We propose and optimize the horn waveguide couplers based on distributed Bragg reflector waveguide for coupling between two-dimensional dielectric cylinder photonic crystal waveguide and single mode planar dielectric waveguide and evaluate their transmission efficiency using the finite difference time domain method. The simulation results show that the power transmission efficiency is over 98% in a large part of the frequency range of the guided mode of photonic crystal waveguide. The highest transmission efficiency is 99.85%.

Electromagnetic field and potential computations on elements with curved contours in boundary element and volume integral methods require evaluation of a number of Jacobian complete and/or incomplete elliptic integrals of all three kinds for the same modulus but different angles, depending on the arc length and the angle coordinate of the field point. Up to now, they have been evaluated individually, repeating the same algorithms a number of times. To reduce such redundant computations, a compact algorithm based on a modified Landen transformation is developed for elliptic integrals with an extended integration range - pi <or= alpha /sub i/<or= pi . Computational accuracy and time saving are discussed.<<ETX>>

Get PDF Email Share Share with Facebook Share on X Post on reddit Share with LinkedIn Add to Mendeley Add to BibSonomy Share with WeChat Get Citation Copy Citation Text Andrey A. Sukhorukov, Yuri S. Kivshar, Ole Bang, Jordi Martorell, J. Trull, and R. Vilaseca, "Two-Color Nonlinear Localized Modes in Photonic Crystals," Optics & Photonics News 10(12), 34-35 (1999) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

The density of electromagnetic modes in photonic crystals based on the pyrochlore and kagomé lattices

We propose two principal schemes of all-optical adders and logical gates based on the dependence of electromagnetic spectra in photonic bandgap materials containing optically nonlinear layers on the light signal intensity. The photonic structure behavior with changing intensity is investigated for system consisting of periodical layered structure covered with optically nonlinear material. The theory of photonic band and local states dynamics is developed for linear 1D and 2D Si-SiO₂ and Ge-Se photonic crystals coated with the nonlinear doped glass. It is shown that the beam angular-frequency diagrams contain extremely sensitive areas inside the total reflection range, where the weak nonlinearity leads to dramatic change in light reflection and transmission. An overview of suitable nonlinear materials and PBG structures is made to evaluate logical device parameters for different frequencies of laser sources.

Exact modelling of generalised defect modes in photonic crystals