FDTD study of subwavelength imaging by a photonic crystal slab

The problem of subwavelength imaging via a photonic crystal slab lens made of two-dimensional (2D) square arrays of parallel dielectric cylinders in air is studied and discussed theoretically. The finite-difference time-domain method is employed to investigate the unique features of imaging by such lens. We confirm earlier findings that a photonic crystal slab lens can provide the imaging of a point source. By analysing the transmission properties of the proposed structure, we demonstrate that inside the all-angle negative refraction, there are some favourable directions for waves to travel. We show that the surface termination of the photonic crystal is a key parameter to obtain a good quality image. The super-resolution of two sources separated by a distance less than the wavelength is also considered. It is shown that the achievable resolution is limited by the slab length.     

An efficient approach toward guided mode extraction in two-dimensional photonic crystals

A rigorous, fast and efficient method is proposed for analytical extraction of guided defect modes in two-dimensional photonic crystals, where each Bloch spatial harmonic is expanded in terms of Hermite-Gauss functions. This expansion, after being substituted in Maxwell’s equations, is analytically projected in the Hilbert space spanned by the Hermite-Gauss basis functions, and then a new set of first order coupled linear ordinary differential equations with non-constant coefficients is obtained. This set of equations is solved by employing successive differential transfer matrices, whereupon defect modes, i.e. the guided modes propagating in the straight line-defect photonic crystal waveguides and coupled resonator optical waveguides, are analytically derived. In this fashion, the governing differential equations are converted into an algebraic and easy to solve matrix eigenvalue problem. Thanks to the analyticity of the proposed approach, the eigenmodes of these structures can be extracted very quickly. The validity of the obtained results is however justified by comparing them to those derived by using the standard finite-difference time-domain method.     

Decay distribution of spontaneous emission from atoms in one-dimensional photonic crystal

Spontaneous emission behavior from atoms (or molecules) in one-dimensional photonic crystal with a defect is investigated. Taken all the TE and TM modes into account, the normalized spontaneous emission rate of the atom is calculated as a function of the position of the atom in the crystal. Results for both nonabsorbing dielectric structure and absorbing dielectric structure are presented. With the increase of the thickness of the defect in which the atoms are embedded, the oscillations of the spontaneous emission rate versus the position of the atom become dense and the lifetime distribution becomes narrow and sharp. The PC effect may lead to the coexistence of both accelerated and inhibited decay processes.     

Near-field optics and control of photonic crystals

We discuss recent progress and the exciting potential of scanning probe microscopy methods for the characterization and control of photonic crystals. We demonstrate that scanning near-field optical microscopy can be used to characterize the performance of photonic crystal device components on the sub-wavelength scale. In addition, we propose scanning probe techniques for realizing local, low-loss tuning of photonic crystal resonances, based on the frequency shifts that high-index nanoscopic probes can induce. Finally, we discuss prospects for on-demand spontaneous emission control. We demonstrate theoretically that photonic crystal membranes induce large variations in spontaneous emission rate over length scales of 50 nm that can be probed by single light sources, or nanoscopic ensembles of light sources attached to the end of a scanning probe.     

Ternary photonic crystal with left-handed material layer for refractometric application

A ternary photonic crystal with left-handed material (LHM) layer is examined for refractometric applications. One of the layers is assumed to be air and treated as an analyte. The transmittance from the ternary photonic crystal is studied in details and the wavelength shift due to the change in the refractive index of the analyte is investigated. The transmittance is investigated with the parameters of the LHM. It is found that the wavelength shift can be significantly enhanced with the decrease of both real part of the LHM permittivity and thickness.     

Spectral narrowing and lasing threshold in self-assembled active photonic crystal

Laser-induced emission from rhodamine-B dye embedded in pseudo band gap opaline photonic crystals is discussed. The photonic crystals are fabricated using rhodamine-B doped polystyrene colloids and show 65% reflectance at the stop band centered at 604 nm. The reflectance of the crystal is increased to 74% by coating with a thin layer of gold. Both spontaneous and stimulated emissions of the dye are observed in the photonic stop band environment by exciting the crystal with the second harmonic (532 nm) of a Q-switched Nd:YAG laser. The thin layer of gold functioned as a high reflecting end mirror to the dye-doped cavity when the crystal is pumped from the substrate side. Angle-dependent suppression at the stop band wavelength is observed in the spontaneous emission of the dye. Spectrally narrow stimulated emission and lasing is achieved in the gold coated dyed PhC at a threshold pump power of 60 mW in a selective direction of 22° from the direction of excitation. By studying emission from several photonic crystals with different number of layers, it is concluded that a sharp threshold for lasing is not observed in uncoated photonic crystals when they contained fewer than 30 ordered layers and lesser than 70% reflectance.     

Control of photonic band gaps in one-dimensional photonic crystals

The photonic band gaps in one-dimensional photonic crystals (PCs) are theoretically investigated. A new method to broaden the photonic band gaps is introduced. Based on the similar method, a kind of photonic crystals is constructed to generate photonic band gaps with proportioned central frequencies. This technology can be used for designing nonlinear PCs for harmonic generation.     

Directional coupler design based on coupled cavity waveguides in photonic crystals

We propose a directional coupler design based on coupled cavity waveguide in photonic crystals. The plane wave expansion is used to give the dispersion of the coupled cavity waveguides and two parallel such waveguides. The couple length is got from the dispersion curves. Based on the research of the dispersion, we present a directional coupler and the transmission property is given. This structure is potentially important for highly efficient directional coupler in integrate optical circuit.     

Modification of spontaneous emission from a five-level M-type atom in coupled cavity waveguide

We study the spontaneous emission spectrum of a five-level M-type atom driven by a microwave field, in which two upper levels are coupled by the same-coupled cavity waveguide reservoir to a lower level. The spectrum behavior presents a strong non-Lorentzian shape that originates from effective quantum interference in Markovian reservoir, in which the spectral line can be significantly enhanced and eliminated by adjusting the proper parameters of the system. However, for non-Markovian reservoir, it seems that the shape of emission spectrum is quite dependent on the geometry behavior of a coupled cavity waveguide.     

Broadband wave plates: Approach from one-dimensional photonic crystals containing metamaterials

Broadband wave plates working in subwavelength scale are realized by one-dimensional photonic crystals containing negative-index materials. It is demonstrated that the phase shift of reflected wave as a function of frequency changes smoothly within the stop band of the photonic crystal, while it changes sharply within the pass band. In the stop band, the difference between the phase of TE and that of TM reflected wave could remain constant in a rather wide frequency range. These properties are useful for designing compact wave plates or phase retarders which can be used in broad spectral bandwidth.     

Spontaneous emission spectra of a four-level atom in photonic crystals driven by two coherent fields

We investigate the spontaneous emission spectra of a four-level tripod-type atom embedded in a photonic crystal and driven by two coherent fields. It is found that due to the quantum interference caused by two driving fields, the spontaneous emission spectra have different features from the case of only one driving field. The spectra are sensitively dependent on the detuning of the driving fields. A dark line occurs for some particular initial states. By appropriately adjusting the external driving fields, the spectral-line can be narrowed, enhanced or suppressed.     

Entanglement of a two-level atom and its spontaneous emission near the edge of a photonic band gap

The entanglement of a two-level atom and its radiation field near the edge of a photonic band gap is studied by using the quantum entropy. Unlike the free space case, there is a steady-state entanglement between the atom and its spontaneous emission field even when the atomic transition frequency lies outside the band gap. Moreover, the degree of entanglement, which is due to the formation of atom–photon bound dressed state, depends on the detuning of the atomic transition frequency from the photonic band edge and can be controlled by a controllable photonic band gap crystal.     

A parametric study of the lensing properties of dodecagonal photonic quasicrystals

We present a study of the lensing properties of two-dimensional (2-D) photonic quasicrystal (PQC) slabs made of dielectric cylinders arranged according to a 12-fold-symmetric square-triangle aperiodic tiling. Our full-wave numerical analysis confirms the results recently emerged in the technical literature and, in particular, the possibility of achieving focusing effects within several frequency regions. However, contrary to the original interpretation, such focusing effects turn out to be critically associated to local symmetry points in the PQC slab, and strongly dependent on its thickness and termination. Nevertheless, our study reveals the presence of some peculiar properties, like the ability to focus the light even for slabs with a reduced lateral width, or beaming effects, which render PQC slabs potentially interesting and worth of deeper investigation.     

Blue light emission and amplification in left-handed isotropic Metallo-Semiconductor Photonic Crystal

A new left-handed isotropic design of semiconductor Photonic Crystal with plasmonic (Aluminum) nanorod inclusion is analyzed and proposed to demonstrate All-Angle Negative Refraction (AANR) with blue light amplification. It is shown that the proposed structure provides negative real values of both permeability (μ) and permittivity (?) with extremely low imaginary values for visible light. Phase slope and phase velocity is shown to be negative for blue light for proposed left-handed structure. Index matched to the incident medium and compensated losses due the gain assistance lead the light amplification in the designed structure. Finite Difference Time Domain (FDTD) method is applied to study left-handed transmission and reflection properties. Extremely high Left-Handed Transmission Efficiency is calculated which is found to be more than 99% for the proposed structure. Fabrication tolerance with effect of change in plasmonic nanorod radius by ±10% is also analyzed. Further, left-handed transmission for blue light is confirmed by analyzing the far-field spectrums of the proposed structure obtained by employing 3D FDTD method. Demonstration and study of near-field and far-field resonance reveals the nano-photonic application potential of the proposed structure as directional optical nano-antenna, polarizer and filter.     

Experimental analysis of true left-handed behaviour and transmission properties of composite metamaterials

We report the true left-handed transmission of a composite metamaterial (CMM) consisting of periodically stacked split-ring resonator (SRR) and wire elements. The negative permeability (μ < 0) gap is demonstrated explicitly by comparing SRR and closed-ring resonator structures. We confirm experimentally that the plasma cut-off frequency of the CMM is determined by the combined dielectric response of SRR and wire elements, and it is much lower than that of the wire-only medium. This is crucial to identify the left-handed transmission bands of the CMM. We further investigate the effect of intralayer and interlayer disorder on the transmission spectrum of CMM arising from misaligned fabrication and stacking of the SRR layers. We found that the intralayer disorder affects the μ < 0 gap of SRRs and the left-handed transmission band of CMM significantly, whereas the SRR transmission is rather immune to interlayer disorder.     

Study on optical switching effect of photonic crystals with negative effective index of refraction

Based on transmission spectra, optical switching effect of equivalent negative refractive photonic crystals (PCs) composed of a triangular array of air cylinders in a GaAs matrix is studied by the finite-difference time-domain (FDTD) method in this paper. The mechanism of wave resonance is probed and the propagation of optical waves in the PCs is described in terms of effective refraction index and Bloch waves. Our numerical results show that the probability of spontaneous radiation would be enhanced extremely under the influence of Bloch resonance waves, stimulated emission and photon tunnel effect, resulting in the optical waves being localized greatly in the PCs at particular frequencies. In addition, we found that the position of transmission peaks, with values much greater than unit, can be controlled by tuning the central frequency of the waveguide source. It means that photon current in the PCs can also be controlled to optimize transmission properties of PCs, so as to meet the requirements of novel optical devices based on PCs, such as all-optical switches.     

Reply to comment on “Negative refraction in 1D photonic crystals”

I refute the criticisms of Srivastava et al. (2008) [13] raised in Bénédicto et al. [14].     

Comparison of photonic bandgaps of two-dimensional periodic and quasi-periodic photonic crystals with different relative permittivity dielectric

Photonic bandgaps (PBGs) of two-dimensional (2D) triangular-lattice and square-lattice and decagonal quasi-periodic photonic crystals (PCs) have been analyzed, with a given scatterer radius and dielectric relative permittivity changing from 1 to 30 within air-cylinders-in-dielectric and dielectric-cylinders-in-air constructions. The results have shown that 2D quasi-periodic PC is more likely to generate PBG and complete PBG than 2D periodic PC. For the given scatterer radius and two constructions, PBG widths of the two types of 2D PCs vary little, whereas the corresponding center frequencies decrease in smooth “hyperbola-like” curves with dielectric relative permittivity increasing monotonically. The present results will guide the design of PBG-type microstructure photonic devices.     

Topological photonic states in gyromagnetic photonic crystals: Physics,properties, and applications

Topological photonic states (TPSs) as a new type of waveguide state with one-way transport property can resist backscattering and are impervious to defects, disorders and metallic obstacles. Gyromagnetic photonic crystal (GPC) is the first artificial microstructure to implement TPSs, and it is also one of the most important platforms for generating truly one-way TPSs and exploring their novel physical properties, transport phenomena, and advanced applications. Herein, we present a brief review of the fundamental physics, novel properties, and practical applications of TPSs based on GPCs. We first examine chiral one-way edge states existing in uniformly magnetized GPCs of ordered and disordered lattices, antichiral one-way edge states in cross magnetized GPCs, and robust one-way bulk states in heterogeneously magnetized GPCs. Then, we discuss the strongly coupling effect between two co-propagating (or counter-propagating) TPSs and the resulting physical phenomena and device applications. Finally, we analyze the key issues and prospect the future development trends for TPSs in GPCs. The purpose of this brief review is to provide an overview of the main features of TPSs in GPC systems and offer a useful guidance and motivation for interested scientists and engineers working in related scientific and technological areas.