Metallic graded photonic crystals for graded index lens

We have designed a flat graded index lens made from a metallic graded 2D photonic crystal. The gradient of index has been obtained by varying the filling factor of a flat slab of photonic crystal in the direction perpendicular to that of the propagation of the electromagnetic field. This gradient has been designed in such a way that the flat slab focuses a plane wave. With applications in the microwave range in view, we considered a photonic crystal which consists of copper strips.     

Superbending effect in two-dimensional graded photonic crystals

We study the superbending effect in a two-dimensional graded photonic crystal (GPC) for both TE and TM modes. We show that the lateral beam shift is extremely sensitive to the wavelength for the TM mode but not TE mode, indicating the potential in designing some special superbending devices, for example, TE/TM splitter and polarization-indifference waveguide at prescribed wavelengths.     

Reflection properties of metallic photonic crystals

Received: 10 November 1997/Accepted: 16 November 1997     

Light frequency conversion in photonic crystals

Light frequency conversion when light interacts with a shock wave propagating through a photonic crystal is investigated. Two new phenomena are found, the first is that frequency increases by integral multiple of a certain amount in the process of frequency conversion. The second phenomenon is frequency conversion that still occurs when the shock wave front is replaced by a vacuum area. Through FDTD simulations and analytical theory, photon-phonon interaction and surface decaying mode interpretations for the mechanism of frequency conversion are found.     

Graded photonic crystals for graded index lens

A graded index lens made from graded 2D photonic crystal has been designed by the means of the Finite Difference Time Domain (FDTD) method. The gradient of index has been obtained by varying the filling factor of a flat slab of photonic crystal in the direction perpendicular to that of the propagation of the electromagnetic field. This gradient has been designed in such a way that the flat slab focuses a plane wave. As only a few layers are necessary, graded photonic crystals show their ability to efficiently control the propagation of light and may apply to various photonic devices, from the microwave range to the optical domain.     

Tunable photonic band-gaps in one-dimensional photonic crystals containing linear graded index material

We have demonstrated control of the photonic band gaps (PBGs) in 1-D photonic crystals using linear graded index material. The analysis of PBG has been done in THz region by considering photonic crystals in the form of ten periods of second, third and fourth generation of the Fibonacci sequence as unit cell. The unit cells are constituted of two kinds of layers; one is taken of linear graded index material and other of normal dielectric material. For this investigation, we used a theoretical model based on transfer matrix method. We have obtained a large number of PBGs and their bandwidths can be tuned by changing the grading profile and thicknesses of linear graded index layers. The number of PBGs increases with increase in the thicknesses of layers and their bandwidths can be controlled by the contrast of initial and final refractive index of the graded layers. In this way, we provide more design freedom for photonic devices such as reflectors, filters, optical sensors, couplers, etc.     

Conductivity and permittivity of two-dimensional metallic photonic crystals

Two-dimensional metallic photonic crystals with different filling factors were manufactured and investigated by broadband terahertz spectroscopy. This technique allowed an independent determination of conductivity and dielectric permittivity in an extremely large dynamic range. Nearly ideal plasmonic behavior is observed for all compositions. Transmittance maxima are observed close to the plasma frequency and attributed to the longitudinal resonance. The plasmon frequencies agree well with existing calculations, while damping effects are underestimated by almost 1 order of magnitude.     

Electrophysical properties of metallic wire photonic crystals

Simple nonintersecting thin metallic wire photonic crystals are studied using the integral equation method based on the Green’s function for periodically arranged sources. A wavenumber- and wavevector-dependent effective permittivity tensor is derived upon homogenization, and the band diagram and the per-mittivity for the lower dispersion branch are calculated.     

Light propagation and oscillations in two-dimensional graded square photonic lattices

We have studied the optical oscillations and transitions in two-dimensional graded square photonic lattices (GSPL) formed by evanescently coupled optical waveguide arrays with parabolic confinements in all transverse directions. When we retain only the orthogonal couplings, decoupled one-dimensional models can be used to obtain the various normal modes, which correspond to a variety of optical oscillations. Six different combinations of Bloch oscillation (BO), dipole oscillation (DO), and reflections from the boundaries of finite lattice are classified on the phase diagram. If we include the diagonal couplings, transitions among various oscillations are obtained with the Hamiltonian optics approach and confirmed by the field-evolution analysis. We studied in detail a typical example in which a switching occurs from the constituent BO and DO to both DOs in the two orthogonal directions. The method to analyze the complex field evolution in GSPL can be extended to similar systems with different types of lattices and/or confinements.     

Optical properties of one-dimensional photonic crystals containing graded materials

The optical properties of an one-dimensional photonic crystal containing graded materials are studied theoretically. The graded layers have space dispersive permittivity and magnetic permeability which vary along the direction perpendicular to the surface of the layer. The gradation profiles of permittivity are studied in detail. We show that the structure possesses forbidden band gaps in its transmission spectra and the gradation profiles of permittivity affect the band gaps significantly. For the exponential gradation profile ε₁(x) = α e^βx, the number of the band gaps increases and the total frequency region corresponding to the gaps becomes large with increasing parameter β. On the other hand, the position of band gaps can be changed by the adjustment of the gradation profiles even if possessing same volume-average permittivity in the graded layers. Therefore, we can achieve suitable photonic band gaps by choosing gradation profiles of permittivity.     

Decay of a quantum dot in two-dimensional metallic photonic crystals

In this paper we have developed a theory for the decay of a quantum dot doped in a two-dimensional metallic photonic crystal consisting of two different metallic pillars in an air background medium. This crystal structure forms a full two-dimensional photonic band gap when the appropriate pillar sizes are chosen. The advantage of using two metals is that one can easily control the density of states and optical properties of these photonic crystals by changing the plasma energies of two metals rather than one. Using the Schrödinger equation method and the photonic density of states, we calculated the linewidth broadening and the spectral function of radiation due to spontaneous emission for two-level quantum dots doped in the system. Our results show that by changing the plasma energies one can control spontaneous emission of quantum dots doped in the metallic photonic crystal.     

Tailoring the ultrafast dephasing of quasiparticles in metallic photonic crystals

The ultrafast dephasing of waveguide-plasmon polaritons in metallic photonic crystal slabs is investigated in the femtosecond regime by second-order nonlinear autocorrelation. We find a drastic modification of the dephasing rates due to interaction between localized particle plasmons and optical waveguide modes and subsequent modification of the photonic density of states. In the strong coupling regime our measurements give clear evidence for the appearance of ultrafast polaritonic beat phenomena. All experimental results agree well with theoretical simulations based on a coupled damped harmonic oscillator model.     

Tailoring self-assembled metallic photonic crystals for modified thermal emission

We predict that modified thermal emission can result from three-dimensional, self-assembled photonic crystals. In previous tungsten structures, known as inverse opals, strong absorption prevented any influence of the periodicity. We consider the origin of this effect and show how to tailor both absorption and surface coupling in experimentally realizable metallic inverse opals. Calculations for tungsten, molybdenum, and tantalum crystals show that their optical properties can be similar to or even better than the tungsten woodpile, where modified thermal emission has already been seen.     

Theoretical study on the photonic band gap in one-dimensional photonic crystals with graded multilayer structure

We theoretically investigate the photonic band gap in one-dimensional photonic crystals with a graded multilayer structure. The proposed structure constitutes an alternating composite layer (metallic nanoparticles embedded in TiO2 film) and an air layer. Regarding the multilayer as a series of capacitance, effective optical properties are derived. The dispersion relation is obtained with the solution of the transfer matrix equation. With a graded structure in the composite layer, numerical results show that the position and width of the photonic band gap can be effectively modulated by varying the number of the graded composite layers, the volume fraction of nanoparticles and the external stimuli.     

Optical properties of chiral photonic crystals with graded modulation parameters

The oblique transmission of light through a layer of a chiral photonic crystal with graded modulated parameters is considered. The problem is solved by the Ambartsumian’s layer addition method. Dependences of amplitude characteristics on the wavelength at different incident angels are presented for two cases: namely, for the case of a chiral photonic crystal with a linearly varied spatial period of modulation and in the case of a chiral photonic crystal with a linearly varied spatial depth of modulation. The case of a minimal influence of dielectric boundaries is considered. It is shown that in both cases a broadening of the photonic forbidden band gap takes place.     

Light propagation in 1D photonic crystals with dissipation

Light propagation in one-dimensional (1D) photonic crystals with dissipation (including metal layers) is studied analytically. The proper effective refractive indices and extinctions of dissipative layers in case of oblique incidence are introduced. Then, the formalism available for nondissipative photonic crystals is modified by replacing the conventional refractive indices with effective ones. Propagation in a bilayer dielectric-metallic crystal is computed as an example.     

Diamagnetic response of metallic photonic crystals at infrared and visible frequencies

We show analytically and numerically that diamagnetic response (effective magnetic permeability mue<1) at infrared and visible frequencies can be achieved in photonic crystals composed of metallic nanowires or nanospheres when the wavelength is much larger than the lattice constant a (lambda approximately 2000a). When lambda approximately100a, the metallic photonic crystals will exhibit strong diamagnetic response (mue<0.8), leading to many interesting phenomena such as the unusual Brewster angle for s waves and incident-angle-and-polarization-independent reflection and transmission.     

Electrodynamics of metallic photonic crystals and the problem of left-handed materials

An analytical theory of low frequency electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. The evidence for such waves has been obtained recently by experiments and computations. The cutoff frequency of these waves, omega(0), is studied. An analytical expression for the permittivity epsilon is obtained and shown to be negative below omega(0). If the crystal is embedded into a medium with a negative mu, there are no propagating modes at any frequency. Thus, such a compound system is not a left-handed material (LHM). The recent experimental results on the LHM are discussed.     

Opals with a thin-film metallic defect-hybrid colloidal plasmonic photonic crystals

Hybrid photonic crystals consisting of a thin-film opal and a thin profiled gold film situated on the surface or inside the opal have been prepared. The optical transmittance spectra of hybrid crystals have been studied. It has been found that the spectra exhibit minima due to diffraction resonances in the photonic crystal and bands of enhanced transmission due to transfer of radiation through the metal film surface by plasmon polaritons. It has been shown that the transmittance spectra of hybrid crystals with a metal film on the surface are subjected to a stronger modification than the hybrids having a metal film inside the crystal.     

Modified solution-processible fabrication of metallic photonic crystals with template removal

High-temperature annealing and pre-annealing lift-off procedures are employed to improve the solutionproeessible technique for the fabrication of one- （1D） and two-dimensional （2D） metallic photonic crystals （MPCs） based on colloidal gold nanoparticles. This enables the successful fabrication of gold nanowires or nanocylinder array structures with the photoresist template removed completely, which is crucial for the application of MPCs in biosensors and optoelectronic devices. Microscopic measurements show homogeneous 1D and 2D photonic structures with an area as large as 100 mm2. Plasmonic resonance of the gold nanostructures and its coupling with the resonance mode of the planar waveguide underneath the photonic structures are observed, implying the excellent optical properties of this kind of MPCs based on the improved fabrication technique.