Amphoteric-like refraction in a two-dimensional photonic crystal

High-index contrast photonic crystals possess an intricate photonic band structure that is responsible for surprising phenomena as the surperprism effect, self-collimation, power splitting or negative refraction. Recently, it was reported that at the interface between an isotropic medium and a uniaxial crystal (or between two uniaxial crystals) a phenomenon known as amphoteric refraction, that is, positive as well as negative refraction, can take place. By means of a equifrequency contours analysis and finite-difference time-domain simulations, we show that a two dimensional photonic crystal can also present amphoteric refraction by properly choosing the lattice orientation and the termination. However, total transmission is difficult to achieve because a Bloch mode is excited inside the photonic crystal and the coupling efficiency from this mode to an external plane wave is lower than one.     

Polaritonic and photonic gap interactions in a two-dimensional photonic crystal

If an ionic material is used in a photonic crystal, the lattice resonance creates a polaritonic gap in the infrared range. The interaction between a polaritonic gap and the structure gap in a 2D square photonic crystal is studied by transfer matrix photonic band structure calculations. The polaritonic gap appears for a surprisingly low volume density of the ionic material. The TM gaps are larger than the TE gaps, as in the dielectric case. By varying the lattice constant, the structure gaps can be shifted across the polaritonic gap, and the effects of merging the two gaps can be studied.     

Supercontinuum generation in a two-dimensional photonic kagome crystal

We demonstrate the generation of ultrabroad spectra in a photonic crystal fiber with a kagome-lattice transverse structure. This two-dimensional periodic photonic lattice allows for strong confinement of light without employing defect states nor using photonic bandgap guiding. Light guiding is mediated by total internal reflection in the intersections of the lattice structure, similar to tapered or micro-structured fibers. The kagome lattice structure is manufactured from a soft glass with a high nonlinearity. Using a Ti:sapphire oscillator as a pump source, we observe for the first time impressive supercontinuum generation in the guided modes of a 2D photonic lattice. Supercontinuum generation is caused by fission and radiation of higher-order solitons in the anomalous dispersion range. Our spectrum encompasses the spectral range from 200 to 1750 nm. The dependence of the continuum on coupling spot location, fiber length, and pump wavelength and power as well as on pulse duration and polarization state is investigated. Using a numerical simulation for the lattice structure, pulse propagation through this structure is theoretically studied. Our model reveals the mechanism of supercontinuuum generation in the 2D photonic structure and explains the essential experimental findings.Electronic supplementary material to this article is avaiable at and accessible for authorized users.     

Fast thermo-optical excitability in a two-dimensional photonic crystal

We experimentally demonstrate excitability in a semiconductor two-dimensional photonic crystal. Excitability is a nonlinear dynamical mechanism underlying pulselike responses to small perturbations in systems possessing one stable state. We show that a band-edge photonic crystal resonator exhibits class II excitability, resulting from the nonlinear coupling between the high-Q optical mode, the charge-carrier density, and the fast (sub-micros) thermal dynamics. In this context, the critical slowing down of the electro-optical dynamics close to the excitable threshold can delay the optical response by an amount comparable to the duration of the output pulse (5 ns). The latter results from a short thermal dynamical excursion along a high local intensity manifold of the phase space.     

Silicon-based two-dimensional photonic crystal waveguides

A review of the properties of silicon-based two-dimensional (2D) photonic crystals is given, essentially infinite 2D photonic crystals made from macroporous silicon and photonic crystal slabs based on silicon-on-insulator basis. We discuss the bulk photonic crystal properties with particular attention to the light cone and its impact on the band structure. The application for wave guiding is discussed for both material systems, and compared to classical waveguides based on index-guiding. Losses of resonant waveguide modes above the light line are discussed in detail.     

The two-dimensional superconducting photonic crystal

The band structure of a two-dimensional superconducting photonic crystal is studied. The temperature dependence of the photonic band structure in a wide temperature region below the superconducting transition is analyzed. It is found that the photonic crystal has two full band gaps and two incomplete band gaps, which are shifted to the high frequency region with decreasing temperature.     

Larger complete photonic bandgaps in two-dimensional photonic crystal heterostructure

A two-dimensional photonic crystal heterostructure with a large complete photonic bandgap is presented. It consists of two photonic crystals, whose dielectric configurations are reverse, with triangular lattice of circular columns. The structure retains the ease of fabrication while increasing the maximum quality factor of the gap 2–3 times after optimization. Photonic bandgap properties are calculated using a plane-wave method and the transmission spectra are obtained.     

非截面二维光子晶体排列矩形波导的全模式分析

在对周期性结构进行谐波分析的基础上，导出了非截面二维光子晶体排列矩形波导的本征值方程. 基于此方程，可以对该类光子晶体波导的所有可能模式进行分析. 分析认为，非截面二维光子晶体排列矩形波导内能存在的模式包括E_(y)，TE_y，H_(y)和TM_y模式；改变波导高度，可以实现E_(y)模式和H_(y)模式与其他模式通带的完全分离. 然而改变任一结构参数，都不能使E_(y)和H_(y)的各个模式通带，以及E_(y)1模式和H_(y)1模式的通带完全隔离. 波导单模工作的带宽由E_(y)1和E_(y)2模式的低端截止频率决定. 关键词： 波导 光子晶体 本征值方程 模式     

Optomechanical coupling in a two-dimensional photonic crystal defect cavity

Periodically structured materials can sustain both optical and mechanical modes. Here we investigate and observe experimentally the optomechanical properties of a conventional two-dimensional suspended photonic crystal defect cavity with a mode volume of ~3(λ/n)3. Two families of mechanical modes are observed: flexural modes, associated to the motion of the whole suspended membrane, and localized modes with frequencies in the GHz regime corresponding to localized phonons in the optical defect cavity of diffraction-limited size. We demonstrate direct measurements of the optomechanical vacuum coupling rate using a frequency calibration technique. The highest measured values exceed 80 kHz, demonstrating high coupling of optical and mechanical modes in such structures.     

Propagation loss in a two-dimensional triangular photonic crystal waveguide

By means of a plane-wave-based transfer-matrix method, we present an extensive study of propagation loss in two-dimensional (2D) photonic crystal waveguides with limited cladding wall thickness. We examine the dependence of propagation loss on both the propagation direction and the waveguide wall thickness. It is shown that the propagation loss is a function of excitation frequency, wall thickness and waveguide outermost surface morphology. The conclusion that the propagation loss essentially decays exponentially with respect to the cladding wall thickness of a waveguide is valid only to a certain degree. In addition, we find that the propagation loss exhibit very complex behavior with respect to the excitation frequency.     

Band structure of a two-dimensional resonant photonic crystal

The band structure of two-dimensional resonant photonic crystals of two types has been calculated using the expansion of eigenfunctions in plane waves. Crystals of one type consist of infinite dielectric cylinders forming a square lattice filled with a resonant gas, and crystals of the other type consist of infinite cylindrical holes filled with a resonant gas and forming a square lattice in a dielectric matrix. It has been shown that, in both cases, the dispersion of a resonant gas in combination with the dispersion of a two-dimensional structure with a photonic band gap leads to the appearance of an additional narrow transmission band near the edge of the band gap or an additional band gap in the continuous spectrum of the photonic crystal. The calculations performed have demonstrated that new dispersion properties substantially depend on the density of the resonant gas, the position of the resonant frequency with respect to the edge of the band gap, and the direction of propagation of electromagnetic waves.     

High quality factor in a two-dimensional photonic crystal cavity on silicon-on-insulator

We propose a design for high quality factor two-dimensional (2D) photonic crystal cavities on silicon-on-insulator (SOI). A quality factor of up to 1.2×10(7) with a modal volume of 2.35(λ/n)(3) is simulated. A very high quality factor of 200,000 is experimentally demonstrated for a 2D cavity fabricated on SOI.     

Lasing mechanism in two-dimensional photonic crystal lasers

We conduct a comprehensive investigation of the lasing mechanism in a photonic crystal slab laser with a refractive index that is periodic in two dimensions. Experimental spectra of laser structures fabricated with organic gain media are presented. It is found that lasing frequencies can be explained in terms of Van Hove singularities in the density of modes. We also observe lasing spectra that cannot be obtained from structures with one-dimensional periodicity, such as traditional distributed feedback lasers. Lasing frequencies are computed using numerical techniques. Received: 7 April 1999 / Accepted: 12 April 1999 / Published online: 19 May 1999     

Absolute photonic band gaps in a two-dimensional photonic crystal with hollow anisotropic rods

The plane-wave expansion method is used to calculate photonic band gaps for two structures with hollow anisotropic tellurium (Te) rods. Both structures are found to have absolute band gaps at the low- and high-frequency regions. Compared with the photonic crystal with solid Te rods, the photonic crystal with hollow Te rods has a large absolute band gap at the high-frequency region: for the triangular lattice of oval hollow Te rods, there is an absolute band gap of 0.058w_e (w_e=2πc/a), and for the square lattice of square hollow Te rods, there is an absolute band gap of 0.056w_e.     

Switchable nonlinear two-dimensional ferroelectric photonic crystal

A two-dimensional photonic crystal with a system of electrodes providing interaction of the incident and transmitted light waves has been developed on the basis of an epitaxial ferroelectric BaSrTiO₃ film. Investigation of the spectral characteristics has revealed the presence of a photonic band gap near 1.5 eV. A possibility of spatial frequency reconstruction of the second-harmonic wave generated by the photonic crystal is shown. The switching efficiency is as high as 6000%.     

Asymmetry reversal in the reflection from a two-dimensional photonic crystal

The measured, angle-dependent, reflection spectra of a two-dimensional GaAs photonic crystal consist of an asymmetric peak on top of an oscillating background. At large angles of incidence (>70 degrees), the asymmetry of the peak is observed to flip for p-polarized light. We explain the observed spectra with a Fano model that includes loss and interference between a resonant waveguide component and direct Fresnel reflection of the layered structure. We show that the reversal of the asymmetry of the line is due to a change in sign of the direct reflection at Brewster's angle.     

Faraday rotation in a two-dimensional photonic crystal with a magneto-optic defect

We study the magneto-optic (MO) Faraday rotation in a two-dimensional square-lattice photonic crystal with a central MO defect layer in the optical wavelength range. We show that when a TM plane wave is incident upon a photonic crystal, an enhancement of Faraday rotation takes place in a region where a resonance peak appears in the photonic bandgap. In this region the mode conversion is high.     

Negative refraction at infrared wavelengths in a two-dimensional photonic crystal

We report on the first experimental evidence of negative refraction at telecommunication wavelengths by a two-dimensional photonic crystal field. Samples were fabricated by chemically assisted ion beam etching in the InP-based low-index constrast system. Experiments of beam imaging and light collection show light focusing by the photonic crystal field. Finite-difference time-domain simulations confirm that the observed focusing is due to negative refraction in the photonic crystal area.     

Spectral properties of a two-dimensional resonant metal-dielectric photonic crystal

We have studied the transmission spectra of resonant two-dimensional photonic crystals of two types, one of which consists of nanocomposite cylinders that form a square lattice in vacuum and the other of which consists of cylindrical holes that form a square lattice in nanocomposite matrix. The nanocomposite consists of metallic nanospheres that are dispersed in a transparent matrix and is characterized by an effective resonant dielectric permittivity. We show that, depending on the position of the resonant frequency of the nanocomposite with respect to the boundaries of the band gap, there arises either an additional transmission band in the transmission spectrum in the band gap or an additional band gap in the continuous spectrum of the photonic crystal. As the structural and geometric parameters of the system change, both the additional transmission band and the additional band gap are considerably modified. We analyze particular features of the spatial distribution of the electromagnetic field intensity in crystals. The considered effects can be used to extend the possibilities of creating new photonic crystals with specified properties.     

Analysis of photonic band gaps in a two-dimensional photonic crystal with centrifugal core-shell rods

The absolute photonic band gap (PBG) in two-dimensional (2D) photonic crystal with excentric core-shell rods is studied in this paper. The core rod shifts away from the core-shell rod center, and its position is decided by two new introduced parameters — the shift angle θ and the offset ρ. We use the FDTD algorithm to calculate the photonic bands of the photonic crystal, and analyze how the offset and shift angle affect the photonic bang gap of excentric core-shell photonic crystal for different core rod size. It has been shown that the variation of the photonic band gap is quite peculiar.