Light Propagation In Photonic Crystals Research Articles

Enhancement of Self-Collimation Effect in Photonic Crystal Membranes Using Hyperbolic Metamaterials.

Hyperbolic metamaterials (HMMs) exhibit high tunability in photonic devices. This study numerically investigates light propagation in photonic crystal (PhC) membranes containing HMMs. The proposed HMM PhC membranes contain square HMM rods, which comprise dielectric (Si) and metallic (Ag) layers. Owing to their property of subwavelength field localization, HMMs can be applied to PhCs to improve tunability and thus enhance the self-collimation (SC) effect of PhCs. The SC points were obtained in the second HMM PhC band, wherein the nearby dispersion curves change significantly. In addition, the effect of the HMM filling factor (i.e., the ratio of the metal-layer to unit-cell thicknesses) on the SC point frequency is studied. Finally, we demonstrate the efficient control of beam behaviors using HMM PhC membranes while considering the nonlinearity of Ag. The findings of this study confirm that high-performance HMM PhC membranes can be employed in nonlinear all-optical switches, filters, tunable lenses, and other integrated optical devices.

Optical control of light propagation in photonic crystal based on electromagnetically induced transparency**Project supported by the National Natural Science Foundation of China (Grant No. 11574188) and the Project for Excellent Research Team of the National Natural Science Foundation of China (Grant No. 61121064).

A kind of photonic crystal structure with modulation of the refractive index is investigated both experimentally and theoretically for exploiting electromagnetically induced transparency (EIT). The combination of EIT with periodically modulated refractive index medium gives rise to high efficiency reflection as well as forbidden transmission in a three-level atomic system coupled by standing wave. We show an accurate theoretical simulation via transfer-matrix theory, automatically accounting for multilayer reflections, thus fully demonstrate the existence of photonic crystal structure in atomic vapor.

Manipulation of light propagation in photonic crystal

The propagation of probe electromagnetic waves has been investigated in a heterostructure formed by layers having linear and nonlinear optical properties. The appearance of a forbidden bandgap for the probe electromagnetic field induced by another control electromagnetic field has been shown that leads to the trapping of the probe pulse inside the structure. Switching off the control field leads to resuming the propagation of the probe pulse. Implementation of nonlinear layer has been suggested.

Photonic eigenmodes and light propagation in periodic structures of chiral nanoparticles

We present a detailed analysis of the optical modes and light propagation in photonic crystals consisting of chiral spheres in a nonchiral isotropic medium, calculated by the full electrodynamic layer-multiple-scattering method. It is shown that resonant modes of the individual spheres give rise to narrow bands that hybridize with the extended bands of the appropriate symmetry associated with light propagation in an underlying effective chiral medium. The resulting photonic dispersion diagrams exhibit remarkable features, peculiar to a system that possesses time-reversal but not space-inversion symmetry, which are analyzed in terms of group theory. In particular, we reveal the occurrence of strong band bending away from the Bragg points with consequent negative-slope dispersion inside the first Brillouin zone, slow-photon bands, and frequency gaps. The calculated band structure is discussed in conjunction with relevant reflection diagrams, providing a consistent interpretation of the underlying physics.

Direct opal-like structures consisting of monodisperse polymer particles and synthesis of the related inverse structures

Three-dimensional periodic solid-state film structures with a face-centered cubic lattice and a high degree of perfection have been prepared from monodisperse particles of styrene copolymers with methacrylic acid. It has been shown that these structures can be successfully used not only as model objects for studying specific features of light propagation in photonic crystals but also as templates for synthesizing inverse opal-like structures. The influence of the degree of hydrophilization of the surface layer of polymer particles forming a polymer template and the template synthesis conditions on the quality of an inverse opal-like TiO2-based structure has been analyzed.

Light propagation in photonic crystal with gain: Applicability of the negative loss approximation

The applicability of the concept of permittivity with Im ɛ gain < 0 to describe the light propagation in a metamaterial system with gain is discussed using the example of a 1D photonic crystal containing gain layers. It is shown that this approach is in agreement with the principle of causality, unless lasing is present. Though the lasing process itself requires nonlinear analysis, the lasing threshold can be determined by linear (negative loss) approximation. Connecting the onset of lasing with the passage of the transfer function pole into the upper half-plane of the complex frequency, we show that (i) if the pump frequency lies in a pass band then an increase in the number N of elementary cells will sooner or later lead to lasing; (ii) if the frequency of the pump lies in the band gap, then lasing at band gap frequencies may occur in a sample with a low N before the band gap has been formed. Nevertheless, lasing will be necessarily suppressed by a further increase in N. In any case, for sufficiently large number of layers due to a finite line width of ɛ gain ( ω), lasing appears in the pass band even if the pump frequency is in the band gap.

Geometric optics of Bloch waves in a chiral and dissipative medium

We present a geometric optics theory for the transport of quantum particles (or classical waves) in a chiral and dissipative periodic crystal subject to slowly varying perturbations in space and time. Taking account of some properties of particles and media neglected in previous theory, we find important additional terms in the equations of motion of particles. The (energy) current density field, which traces the geometric optics rays, is not only governed by the Bloch band energy dispersion but also involves there additional fields. These are the angular momentum of the particle, the dissipation dipole density, and various geometric gauge fields in the extended phase space spanned by space-time and its reciprocal, momentum and frequency. For simplicity, the theory is presented using light propagation in photonic crystals.

Relationship between group velocity and symmetry of photonic crystals

Group velocity (GV) of eigenmode is a crucial parameter to explain the extraordinary phenomena about light propagation in photonic crystals (PhCs). To study relationships between group velocity and symmetry of PhCs, a new general expression of GV in PhCs made up of non-dispersive material is introduced. Based on this, the GVs of eigenmodes of PhCs, especially those of degenerate eigenmodes at highly symmetric points in the first Brillouin zone, are discussed. Some interesting results are obtained. For example, the summation of degenerate eigenmodes’ GVs is invariant under the operations of wave vector K-group MK. In addition, some numerical results are presented to verify them.

A hardware acceleration of the time domain boundary integral equation method for the wave equation in two dimensions

We aimed at reducing the runtime of the time domain boundary integral equation method (TDBIEM) for the two-dimensional scalar wave equation by the help of a special-purpose computer MDGRAPE-2, which is a high-performance vector-parallel computer dedicated to computing long-range forces in classical molecular dynamics simulations. To this end, we presented a formulation to make MDGRAPE-2 compute the layer potential that is the most time-consuming in a run of the TDBIEM, considering to minimise the amount of data-transfer between MDGRAPE-2 and the host computer. The newly implemented TDBIEM code using three MDGRAPE-2s boards was about 109 times faster than the conventional code in an analysis of 5400 boundary elements and 640 time steps. We also demonstrated that the present hardware acceleration helps to perform large-scale simulations such as light propagation in photonic crystals.

Quantitative analysis of subdiffractive light propagation in photonic crystals

We present a qualitative study of the subdiffractive light beam propagation in photonic crystals, based on the theoretical analysis of full Maxwell equation system beyond the slowly varying envelope and paraxial approximations. We calculate the zero diffraction curve in the parameter space, we calculate the weak asymptotical broadening (spreading in transverse direction), and we also analyze the dependence of subdiffractive propagation on the polarization orientation (both for TM and TE polarization).

Imaging Single Quantum Dots in Three-Dimensional Photonic Crystals

Performing fluorescence wide-field microscopy we have imaged single semiconductor quantum dots deep inside a 3-dimensional photonic crystal prepared from colloidal polymer beads. Exploring the emission diffraction patterns in defocused images of quantum dots we demonstrate that the direction-dependent photonic stop band imprints an anisotropy to the angular emission of a single quantum dot. Hence a single, quasi-point-like emitter is manipulated to radiate its photons only to certain well-defined directions by means of the anisotropic light propagation in photonic crystals. The experiments thus provide new routes to evaluate local, frequency selective optical properties in 3-dimensional photonic crystals employing single emitters.

Light propagation in finite and infinite photonic crystals: The recursive Green’s function technique

We report a computational method based on the recursive Green's function technique for calculation of light propagation in photonic crystal structures. The advantage of this method in comparison to the conventional finite-difference time domain (FDTD) technique is that it computes Green's function of the photonic structure recursively by adding slice by slice on the basis of Dyson's equation. This eliminates the need for storage of the wave function in the whole structure, which obviously strongly relaxes the memory requirements and enhances the computational speed. The second advantage of this method is that it can easily account for the infinite extension of the structure both into air and into the space occupied by the photonic crystal by making use of the so-called ``surface Green's functions.'' This eliminates the spurious solutions (often present in the conventional FDTD methods) related to, e.g., waves reflected from the boundaries defining the computational domain. The developed method has been applied to study scattering and propagation of the electromagnetic waves in the photonic band-gap structures including cavities and waveguides. Particular attention has been paid to surface modes residing on a termination of a semi-infinite photonic crystal. We demonstrate that coupling of the surface states with incoming radiation may result in enhanced intensity of an electromagnetic field on the surface and very high $Q$ factor of the surface state. This effect can be employed as an operational principle for surface-mode lasers and sensors.

Dual lattice photonic-crystal beam splitters

Light propagation in photonic crystals (PhC) is both sensitive to incident angle and wavelength. By combining two different PhC lattices, we utilize this effect to demonstrate a wavelength-dependent beam splitter with enhanced angular separation. The first lattice acts as a superprism that separates the incoming light according to wavelength, whereas the second lattice acts as an angular amplifier. We obtain 90° angular separation for two wavelengths separated by 70 nm (1300 nm regime) in a structure that is less than 10 μm long.

High Accuracy Finite-Difference Time-Domain Simulation of Light Propagation in Photonic Crystals.

We have introduced a high accuracy version of the Yee algorithm based on nonstandard finite differences for which the error is e∼(h/λ)2 compared with e∼(h/λ)6 for the ordinary one. This high accuracy allows the use of coarse numerical grids, which greatly reduces the computational cost. Realistic two-dimensional calculations can run on a personal computer, while three-dimensional ones can run on a fast workstation. Using this high accuracy algorithm, we developed computational models and methods to simulate optical propagation in photonic crystals, and to compute their transmission spectra, and bandgap structures. In addition, methodologies were developed to accurately represent arbitrary lattice structures on coarse grids.