Localization and channeling of light in defect modes of two-dimensional photonic crystals

The spatial distribution of the electromagnetic field in a two-dimensional photonic crystal with a lattice defect is investigated. It is shown that in such a structure the field can be localized in a region smaller than one wavelength in size. The dependence of the spectrum of defect modes on the parameters of a two-dimensional photonic crystal is investigated. The light field at the exit of the photonic crystal possesses properties of a nonradiative mode, making it possible to achieve spatial resolution in the near-field much higher than the radiation wavelength. The possibilities of using this phenomenon in optical near-field microscopy to produce optical memory devices and to increase the efficiency of nonlinear optical interactions are discussed. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 323–328 (10 September 1999)     

Magneto-optical defects in two-dimensional photonic crystals

We analyze the properties of magneto-optical defect states in two-dimensional photonic crystals. With out-of-plane magnetization, the magneto-optical coupling splits doubly-degenerate TE states into two counter-rotating modes at different frequencies. The strength of magneto-optical coupling strongly depends on the spatial overlap of the cavity domain structures and the cross product of the modal fields. The transport property of the resultant nonreciprocal states is demonstrated in a junction circulator structure with a magneto-optical cavity coupled to three waveguides. By a proper matching of the magneto-optical frequency splitting with the cavity decay rate into the waveguide, ideal three-port circulator characteristics with complete isolation and transmission can be achieved, with an operational bandwidth proportional to the magneto-optical constant. The proposed optical circulator in a bismuth-iron-garnet/air photonic crystal is demonstrated with finite-difference time-domain calculations and is compared to an alternative implementation of silicon/air crystal infiltrated with a single bismuth-iron-garnet domain.     

Diffraction inhibition in two-dimensional photonic crystals

We show the existence of flat equal-frequency contour across the entire first Brillouin zone in two-dimensional photonic crystals. Under this condition, light diffraction can be inhibited. Moreover, the beam can be highly localized between two neighboring rows of the defect-free photonic crystal. Such a finding may have novel applications in light beam manipulations and on-chip integrated photonic devices.     

Negative refraction in two-dimensional photonic crystals

We present some of our recent results for negative refraction in photonic crystals. The concept of negative refraction in photonic crystals is firstly introduced. Then, the propagation of electromagnetic waves in photonic crystals is systematically studied. By the layer Korringa–Kohn–Rostoker method, the coupling efficiency between external plane waves and the Bloch waves in photonic crystals is investigated. It is found that the coupling coefficient is highly angular dependent even for an interface between air with n=1 and a photonic crystal with effective index n_eff=-1. It is also shown that, for point imaging by a photonic crystal slab, owing to the negative refraction, the influence of the surface termination on the transmission and the imaging quality is significant. Finally, we present results experimentally demonstrating negative refraction in a two-dimensional photonic crystal at optical communication wavelengths. PACS 42.70.Qs; 41.85.Ct; 42.30.Va     

Slow light in photonic crystals

The problem of slowing down light by orders of magnitude has been extensively discussed in the literature. Such a possibility can be useful in a variety of optical and microwave applications. Many qualitatively different approaches have been explored. Here we discuss how this goal can be achieved in linear dispersive media, such as photonic crystals. The existence of slowly propagating electromagnetic waves in photonic crystals is quite obvious and well known. The main problem, though, has been how to convert the input radiation into the slow mode without losing a significant portion of the incident light energy to absorption, reflection, etc. We show that the so-called frozen mode regime offers a unique solution to the above problem. Under the frozen mode regime, the incident light enters the photonic crystal with little reflection and, subsequently, is completely converted into the frozen mode with huge amplitude and almost zero group velocity. The linearity of the above effect allows the slowing of light regardless of its intensity. An additional advantage of photonic crystals over other methods of slowing down light is that photonic crystals can preserve both time and space coherence of the input electromagnetic wave.     

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.     

Optical circulators in two-dimensional magneto-optical photonic crystals

We propose an optical circulator formed of a magneto-optical cavity in a 2D photonic crystal. With spatially engineered magnetic domain structures, the cavity can be designed to support a pair of counterrotating states at different frequencies. By coupling the cavity to three waveguides, and by proper matching of the frequency split of the cavity modes with the coupling strength between the cavity and the waveguide, ideal three-port circulators with complete isolation and transmission can be created. We present a guideline for domain design needed to maximize the modal coupling and the operational bandwidth for any given magneto-optical constant.     

Band-edge-induced Bragg diffraction in two-dimensional photonic crystals

Two-dimensional photonic crystals composed of two orthogonal volume diffraction gratings have been photogenerated in photopolymers. When the read beam is set at the Bragg angle, the diffraction efficiency of the transmission grating is strongly enhanced at the band edge of the reflection grating recorded in the material. Such a device provides Bragg operation and enhancement of the diffraction efficiency of the thin diffraction grating together with good wavelength selectivity. Such advantages could be interesting for optical signal processing.     

Wave-vector diagrams for two-dimensional photonic crystals

Photonic crystals exhibit band gaps, meaning that electromagnetic fields cannot propagate in them for specific ranges of wavelengths and directions. The calculation of band structure diagrams has been intensively studied and is now well understood. In contrast to that, so-called wave-vector diagrams (i.e. dispersion surfaces, depicting the loci of all relevant wave vectors at a fixed wavelength) are less known and used. In principle, they show how the effective index of the structure depends on the direction of propagation. A method to calculate explicitly wave-vector diagrams for two-dimensional photonic crystals is derived which leads finally to quadratic eigenvalue problems. Results for square and triangular lattices are presented and some applications are discussed.     

Wave-vector diagrams for two-dimensional photonic crystals

Photonic crystals exhibit band gaps, meaning that electromagnetic fields cannot propagate in them for specific ranges of wavelengths and directions. The calculation of band structure diagrams has been intensively studied and is now well understood. In contrast to that, so-called wave-vector diagrams (i.e. dispersion surfaces, depicting the loci of all relevant wave vectors at a fixed wavelength) are less known and used. In principle, they show how the effective index of the structure depends on the direction of propagation. A method to calculate explicitly wave-vector diagrams for two-dimensional photonic crystals is derived which leads finally to quadratic eigenvalue problems. Results for square and triangular lattices are presented and some applications are discussed.     

Band-gap properties of two-dimensional low-index photonic crystals

We study the band-gap properties of two-dimensional photonic crystals created by a lattice of rods or holes conformed in a symmetric or asymmetric triangular structure. Using numerical plane-wave method, we calculate a minimum value of the refractive-index contrast for opening both partial and full two-dimensional spectral gaps for both TM- and TE-polarized waves. We also analyze the effect of ellipticity of rods and holes and their orientation on the threshold value and the relative size of the band gaps.     

Refraction of light in protection windows of uniaxial crystals

Specific features of light refraction on the surface of plates of uniaxial crystals are considered. A method of calculating birefringence in the protection crystalline windows under oblique incidence is developed. The possibility of refracting on the surface of the plate for oblique incidence of the ray without further splitting into ordinary and extraordinary rays is shown.     

Magnetic surface plasmon-induced tunable photonic bandgaps in two-dimensional magnetic photonic crystals

We experimentally studied magnetically controllable photonic band gaps (PBGs) in two-dimensional magnetic photonic crystals consisting of ferrite rods. Besides the conventional PBG that relates to Bragg scattering, two other types of PBG, resulting from magnetic surface plasmon (MSP) resonance and spin-wave resonance, respectively, are observed. The PBG due to MSP resonance is particularly interesting because of its analogy to surface plasmon in metal; furthermore, it is shown to be completely tunable by an external static magnetic field from both an experimental and a theoretical point of view.     

Compact triplexer in two-dimensional hexagonal lattice photonic crystals

We design a compact triplexer based on two-dimensional (2D) hexagonal lattice photonic crystals (PCs).A folded directional coupler (FDC) is introduced in the triplexer beside the point-defect micro-cavities and line-defect waveguides.Because of the reflection feedback of the FDC,high channel drop efficiency can be realized and a compact size with the order of micrometers can be maintained.The proposed device is analyzed using the plane wave expansion method,and its transmission characteristics are calculated using the finite-difference time-domain method.The footprint of the triplexer is about 12× 9 μm,and its extinction ratios are less than –20 dB for 1310 nm,approximately –20 dB for 1490 nm,and under –40 dB for 1550 nm,making it a potentially essential device in future fiber-to-the-home networks.     

Arbitrary angle waveguide bends in two-dimensional photonic crystals

Arbitrary angle waveguide bends in two-dimensional photonic crystals are studied with modeling and calculation. The lattice orientation restriction to bending angles can be avoided by incorporating an annular air groove into the bending corner. Theoretical analysis shows that the sharp bends transmit guided lightwaves with a very slight difference of propagation properties between straight waveguides and bend sections. A transmission of larger than 90% with a bandwidth of wider than 52 nm is obtained in the vicinity of 1.55 μm for the sharp bends with bending angles from 0° to 165°.     

Quasi phase matching in two-dimensional nonlinear photonic crystals

We analyze quasi-phase-matched (QPM) conversion efficiency of the five possible types of periodic two-dimensional nonlinear structures: Hexagonal, square, rectangular, centered-rectangular, and oblique. The frequency conversion efficiency, as a function of the two-dimensional quasi-phase-matching order, is determined for the general case. Furthermore, it is demonstrated for two basic feasible motifs, a circular motif and a rectangular motif. This enables to determine the optimal motif dimensions for achieving the highest conversion efficiency. We find that a rectangular motif is more efficient than a circular motif for quasi-phase-matched processes that rely on a single reciprocal lattice vector (RLV), and that under optimal choice of motif dimensions, it converges into a one-dimensional periodic structure. In addition, in a few specific cases we found that higher order QPM can be significantly more efficient than lower order QPM.     

Selective stop-band switching in two-dimensional multicomponent photonic crystals

A comprehensive theoretical investigation of the stop-band switching in two-dimensional multicomponent photonic crystals is carried out. The calculations are performed within the analytical model based on analysis of the scattering form-factor. Earlier, this approach was used to describe experimental data obtained in a study of synthetic opals representing three-dimensional photonic crystals. We report here on the development of a new version of this model applicable to the class of two-dimensional photonic crystals. The existence of resonant (non-switchable) stop-bands and the possibility of selectively controlling light flows propagating at different wavelengths is predicted. These effects draw up new guidelines for the design of two-dimensional photonic crystals possessing desired optical qualities.     

Modelling and design of complete photonic band gaps in two-dimensional photonic crystals

In this paper, we investigate the existence and variation of complete photonic band gap size with the introduction of asymmetry in the constituent dielectric rods with honeycomb lattices in two-dimensional photonic crystals (PhC) using the plane-wave expansion (PWE) method. Two examples, one consisting of elliptical rods and the other comprising of rectangular rods in honeycomb lattices are considered with a view to estimate the design parameters for maximizing the complete photonic band gap. Further, it has been shown that complete photonic band gap size changes with the variation in the orientation angle of the constituent dielectric rods.      

a-Si:H based two-dimensional photonic crystals

We describe the fabrication processes of silicon-based two-dimensional photonic crystals (2D-PCs) with a photonic band gap in the near-IR range. The procedures involve electron beam lithography followed by an anisotropic etching step of hydrogenated amorphous silicon thin films deposited by plasma enhanced chemical vapor deposition. Micrometric and submicrometric arrays of cylindrical holes are transferred using a poly-methylmethacrylate resist layer as a mask. A careful comparison between standard parallel plate reactive ion etching and inductively coupled plasma etching techniques is performed, aimed at obtaining periodic structures with high aspect ratio and good profile sharpness.     

2维光子晶体中的掺杂效应数值研究

 把平面波展开方法(PWM)用于2维光子晶体掺杂情况下透射特性的研究,计算得到了粗细不同的空气柱掺杂、相同半径不同介质柱掺杂、不同柱体形状掺杂情况下2维光子晶体的透射系数与入射光频率的关系曲线。结果表明2维光子晶体的禁带的宽度、位置、透过率与掺杂体半径、掺杂体介电常数、掺杂体柱体几何形状等因素有关,掺杂因素相差越大透射曲线变化越明显,特别是损耗介质的掺入更使得禁带可调要素增加。