Two-dimensional photonic crystals with a lattice defect: Spectrum of defect modes, localization of light, and formation of evanescent waves

Properties of an electromagnetic field localized in the defect modes of two-dimensional photonic crystals are studied. The defect-mode spectrum of these structures is calculated, electromagnetic field localization and channeling effects are analyzed, and the properties of the field inside and beyond a photonic crystal with a lattice defect are also studied. The calculations show that the electromagnetic field is localized in the defect mode of a photonic crystal in a region smaller than the wavelength. The dependence of the defect-mode spectrum on the parameters of the photonic crystal is investigated and possibilities for controlling the spectrum of defect modes are indicated. It is shown that the optical field leaving a photonic crystal possesses the properties of a evanescent wave, which means that spatial resolution substantially greater than the wavelength of the radiation can be achieved in the near field and opens up possibilities for using photonic crystals with a lattice defect in near-field optical microscopy. The possibility of externally controlling an optical field localized in the defect modes of a photonic crystals is demonstrated.     

Near-field probing of active photonic-crystal structures

We report a study of the optical near field of an active integrated component operating near the 1.55-mum telecommunications wavelength. The device is based on a two-dimensional photonic crystal etched in a suspended InP membrane. Topographic as well as optical information is collected by use of a scanning near-field optical microscope in collection mode, providing information about the local distribution of the losses.     

Near-field visualization of light confinement in a photonic crystal microresonator

By using scanning near-field optical microscopy, we directly map the subwavelength confinement of light around a point defect in a two-dimensional photonic crystal microresonator. Comparison of our results with the outcome of three-dimensional finite-difference time domain calculations allows us to identify small imperfections in the structure that result in the spatial modification of the intensity distribution.     

Proposal for a New Dense Wavelength Division Multiplexing Filter Based on Two-Dimensional Photonic Crystal Ring Resonator

Abstract

A new optical filter design based on a two-dimensional photonic crystal ring resonator structure with an N-channel model is proposed in this article. This study also shows that modifying the scatter radius and the waveguide width can significantly improve the performance of the original structure, which can solve the mode mismatch problem for output waveguide. Here, an example of a 16-channel photonic crystal ring resonator is provided; wavelength spacing of 1.6 nm and a high quality factor Q of 6,000 were achieved. The optical filter would be a potential key component in the application of dense wavelength division multiplexer devices.     

Near-field optics with photonic crystals

Finite-difference time-domain (FDTD) analysis of light propagation in a defect mode of a two-dimensional photonic band-gap (PBG) structure demonstrates that the light field is localized in such a structure within areas with subwavelength (λ/10) sizes. FDTD simulations reveal efficient formation of an evanescent wave at the output of such a PBG structure, permitting the subwavelength resolution to be achieved in the near field. A probe object with a size less than the wavelength of incident light is shown to perturb the near-field distribution behind the PBG structure and to change the signal detected in the far-field zone. The field intensity distribution inside a PBG structure is also sensitive to the presence of a probe object, offering a way to control the light field localized in defect modes of PBG structures. Received: 9 August 1999 / Accepted: 18 October 1999 / Published online: 10 November 1999     

Near-field probing of photonic crystals

Photonic crystals form an exciting new class of optical materials that can greatly affect optical propagation and light emission. As the relevant length scale is smaller than the wavelength of light, sub-wavelength detection forms an important ingredient to obtain full insight in the physical properties of photonic crystal structures. Spatially resolved near-field measurements allow the observation of phenomena that remain hidden to diffraction-limited far-field investigations. Here, we present near-field investigations in both collection and illumination modes that highlight the power of local studies. We show how propagation losses are unambiguously determined and that light detected in far-field transmission can actually contain contributions from different, sometimes unexpected, local scattering phenomena. Simulations are used to support our findings. Furthermore, it is shown that local coupling of light to a thick three-dimensional photonic crystal is position-dependent and that the spatial distribution of the coupling efficiency itself is frequency-dependent.     

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.     

光子晶体超窄带滤波器

本文利用光学传输矩阵法研究了一种类似于谐振腔结构的光子晶体.研究发现在这种光子晶体的光子带隙的中央存在一个极窄的透光窗口,窗口的宽度在红外波段1500nm附近可以做到0.0001nm以下,窗口内的透光率峰值可以接近100%,窗口以外的区域的透光率可以做到0.01%以下.通过改变所研究结构中的周期厚度、中间夹层厚度、两边光子晶体的周期重复数和波的入射角可以改变窄带透过窗口的位置和窄带的宽度.这种光子晶体可以用来制作超窄带滤波器,有望在光通信超密度波分复用技术和光学信息精密测量技术当中获得应用.     

Nonlinearities in the reflection and transmission spectra of the photonic bandgap heterostructures with n–i–p–i crystals

Nonlinear optical properties of photonic crystal heterostructures with embedded n–i–p–i superlattices are investigated. Self-consistent calculations of the transmission and reflection spectra near the defect mode are performed using the transfer-matrix method and taking into account the gain saturation. Analysis of features and output characteristics is carried out for one-dimensional photonic crystal heterostructure amplifiers in the GaAs–GaInP system having at the central part an active “defect” from doubled GaAs n–i–p–i crystal layers. The gain saturation in the active layers in the vicinity of the defect changes the index contrast of the photonic structure and makes worse the emission at the defect mode. Spectral bistability effect, which can be exhibited in photonic crystal heterostructure amplifiers, is predicted and the hysteresis loop and other attending phenomena are described. The bistability behavior and modulation response efficiency demonstrate the potential possibilities of the photonic crystal heterostructures with n–i–p–i layers as high-speed optical amplifiers and switches.      

实现全反射镜功能的光子晶体禁带特性

用传输矩阵法研究一维光子晶体G(AB)mC(AB)mH的能带特性及电场分布,结果发现:随着m的增大,在830—883nm波长范围内,光子晶体G(AB)mC(AB)mH禁带中的导带透射率逐渐趋于零,即光被禁止通过,实现全反射镜功能,且随着入射角的增大,光子晶体的禁带逐渐向短波方向移动。随着介质层G、H的折射率增大,光子晶体在833.6—879.1nm波长范围内出现大的禁带,亦实现全反射镜功能。光子晶体G(AB)5C(AB)5H内部存在很强的局域电场,即在光子晶体内传输的光,被强烈局域在禁带范围内,并在缺陷层C处达到极大值,而且随着m的增大,局域强度增强。这些光学传输特性,为研究、设计新型光学器件全反射镜、滤波器等提供指导。     

Tunable broadband isolator based on electro-optically induced linear gratings in a nonlinear photonic crystal

We theoretically propose a broadband optical isolator based on second-harmonic generation in a one-dimensional quadratic nonlinear photonic crystal (NPC) with an embedded defect. An external electric field along the z axis is applied to modulate the NPC refractive index periodically. Complete optical isolation always could be reached with the help of an external field. Influences of the defect position and thickness are discussed. The spectral and power tolerances of the isolator also have been investigated and show high contrast within a wide wavelength range at different power levels.     

一维缺陷光子晶体温度的测量

采用Si和SiO₂两种介质材料构造一维缺陷光子晶体,缺陷层介质为Si,利用传输矩阵法对带有缺陷的一维光子晶体的传光特性进行了理论分析,并得到其带隙特性.由于缺陷的存在,使得光子晶体的透射谱中产生缺陷峰.当被测温度变化时,根据两种介质的热光效应和热膨胀效应,光子晶体介质和缺陷层的光学厚度和折射率发生变化,透射谱缺陷峰产生漂移,由缺陷峰的中心波长漂移量得到被测温度的大小.构建了一维缺陷光子晶体测量温度的实验系统,实验结果表明缺陷峰中心波长与光子晶体所受的温度呈线性关系,测量灵敏度为0—2 关键词： 温度测量 一维光子晶体 传输矩阵法 缺陷峰     

Near-field observation of subwavelength confinement of photoluminescence by a photonic crystal microcavity

We present a direct, room-temperature near-field optical study of light confinement by a subwavelength defect microcavity in a photonic crystal slab containing quantum-well sources. The observations are compared with three-dimensional finite-difference time-domain calculations, and excellent agreement is found. Moreover, we use a subwavelength cavity to study the influence of a near-field probe on the imaging of localized optical modes.     

Design of photonic crystal superlens with improved image resolution

In this paper, we theoretically investigate the spatial resolution of a triangular two-dimensional photonic crystal superlens. We prove that this resolution can be improved by optimizing the air hole radius as well as the air hole shape. First, it is found that by decreasing the radius of the air holes, the spatial resolution is improved significantly. Next, we demonstrate that using elliptic air holes instead of circular air holes in a triangular two-dimensional photonic crystal can leads to good-quality images and focusing, with effective refractive index n_eff=−1 and enhanced image resolution. It is also shown that for the case of two sources, the resolution of such a photonic crystal lens can be made indeed better than the radiation wavelength.     

A novel proposal for all optical PhC-based demultiplexers suitable for DWDM applications

In this paper due to the crucial role of optical demultiplexers in wavelength division multiplexing and dense wavelength division multiplexing applications, we proposed a new mechanism for designing all optical photonic crystal based demultiplexers with 8, 16 and 32 output channels. Our proposed mechanism for wavelength selecting is a resonant defect structure which consists of one central defect and four defects around the central defect. It has been shown that the selected wavelength depends on the radius of the central defect and the distance between the central defect and other four defects. In all the three proposed demultiplexer the channels spacing is less than 1 nm. We used plane wave expansion method for extracting the band structure of the photonic crystal and employed finite difference time domain method for studying the optical properties of the designed devices.     

光控液晶光子晶体微腔全光开关

设计了一种缺陷模迁移光子晶体微腔全光开关. 两条二维三角晶格空气孔光子晶体波导由一个光子晶体微腔连接, 在微腔的点缺陷中填充掺有少量偶氮聚合物的苯乙炔类液晶. 通过调节控制光的偏振态, 使偶氮聚合物发生顺-反异构化反应, 带动液晶分子重新取向, 从而改变光子晶体微腔的谐振波长, 进而实现光的通过与截止. 运用时域有限差分法和平面波展开法分析 了二维光控液晶光子晶体微腔全光开关的光学特性. 数值计算结果表明: 对于1.55 μ通信波段通过外界偏振光控制所填充的向列相液晶 的折射率可以实现对光波的导通与截止. 分析结果显示, 此开关具有阈值低, 消光比较大, 体积小等优点. 关键词： 二维光子晶体微腔 波导 时域有限差分(FDTD) 液晶     

Sub-wavelength probing and modification of photonic crystal nano-cavities

In this work we present a sizeable and reversible spectral tuning of the resonances of a two-dimensional photonic crystal nano-cavity by exploiting the introduction of a sub-wavelength size glass tip. The comparison between experimental near-field data and results of numerical calculations shows that the spectral shift induced by the tip is proportional to the local electric field intensity of the cavity mode. This observation proves that the electromagnetic local density of states in a microcavity can be directly measured by mapping the tip-induced spectral shift with a scanning near-field optical microscope. Moreover, a non-linear control on the cavity resonance is obtained by exploiting the local heating induced by near-field laser excitation at different excitation powers. The temperature gradient due to the optical absorption results in an index of refraction gradient which modifies the dielectric surroundings of the cavity and shifts the optical modes.     

Photonic crystal waveguide directional couplers as wavelength selective optical filters

Waveguide directional couplers, formed by two closely spaced linear defect waveguides in a two-dimensional photonic crystal of air holes in a semiconductor matrix, are numerically studied using plane wave expansion and finite difference time domain methods. The coupling lengths are on a wavelength scale and show a strong wavelength dependence, allowing for the design of compact wavelength selective optical filters. Applications as a channel interleaver for the 1.55 μm wavelength range and as a micrometer sized 1.31/1.55 μm wavelength demultiplexer are presented.     

Nonlinear frequency conversion in 2D χ (2) photonic crystals and novel nonlinear double-circle construction

The analytic solution to the wave equation for small-signal sum-frequency process is derived in 2D χ ⁽²⁾ photonic crystals with use of the Green function method. It is predicted that the sum-frequency electrical field at quasi-phase matching (QPM) resonance is proportional to the angle-dependent effective crystal length. This implies that multiple wavelength QPM frequency conversion with controllable intensity output can be realized in a single 2D χ ⁽²⁾ photonic crystal. It is revealed that efficient frequency conversion requires both the QPM and the proper structure matching. A novel double-circle construction, different from the conventional Ewald construction, is presented to reflect important QPM processes. It is also shown that the QPM resonance tuning of second-harmonic generation can operate over the whole transparent wavelength range of crystals. Received 19 April 2001     

Light extraction from a light emitting diode with photonic structure in the surface layer investigated by NSOM

We present a light emitting diode with a two-dimensional photonic crystal structure prepared by interference lithography at the light emitting diode surface. The emission maximum is at 850 nm. The two-dimensional photonic crystal structure enhanced the light extraction efficiency by a factor of 1.39. The photonic crystal light emitting diode surface morphology was analyzed by atomic force microscopy. The enhanced extraction efficiency of the photonic crystal diode was documented from L(I) dependencies and was confirmed by near-field studies.