Ultrashort 2-D photonic crystal directional couplers

A novel approach to reduce the coupling length and to increase the coupling coefficient in waveguide directional couplers implemented on two-dimensional (2-D) photonic crystals (PhC) is proposed. To increase the coupling coefficient of a 2-D PhC directional coupler, which is composed of two parallel PhC waveguides separated by one or several rows of rods, the radius of the rods between both waveguides is reduced. The application of this feature to ultrasmall channel interleavers and wavelength demultiplexers is addressed.     

Relation between normal-mode and coupled-mode analyses of parallel waveguides

The analysis of parallel waveguides can be performed either by expressing the coupling of energy between individual, primary guides (coupled-mode approach) or by directly analyzing a structure consisting of all the guides and their surrounding media (normal-mode approach). A comparison of these two approaches, as well as the derivation of relations enabling the conversion of data, when possible, from one approach to the other, are presented in this paper. Finally, the results are used to investigate the dependence of the coupling coefficient on the spacing between the guides. Although the derivations are performed for 2-D (slab) configurations, the results pertain to 3-D guides as well, by applying an effective refractive-index method. It is also shown that normal-mode analysis predicts incomplete transfer of energy for strongly coupled guides, even for perfectly symmetric configurations.     

Fabrication and characterization of polymer optical waveguides with integrated micromirrors for three-dimensional board-level optical interconnects

This paper describes the fabrication and characterization of optical/electrical printed circuit boards (O/E-PCB) with embedded multimodal step index (MM-SI) waveguides and integrated out-of-plane micromirrors (IMMs) for three-dimensional (3-D) optical interconnects. Optical circuitry is built up on PCBs using UV lithography; 45/spl deg/ input/output (I/O) couplers are fabricated by inclined exposure. Commercial polymers are used as optical core and cladding materials. Critical mirror properties of angle, surface quality, reflectivity, and coupling efficiency are characterized experimentally and theoretically. Optical and scanning electron microscopy, white light interferometry, and fiber scanning method are used in the investigations. Sloping profiles measured as a function of the incident light showed the attainment of mirror angles of /spl alpha/=36/spl deg/-45/spl deg/ with /spl plusmn/2/spl deg/ consistency. Near-field optical imaging with a white light source showed that out-of-plane beam turning was achieved. Topography investigations revealed a rectilinear negative tapering shape regardless of the incoming beam angle or type of substrate. However, higher substrate reflectancy was observed to lower the mirror angle. The average propagation loss measured for 10-cm-long waveguides at /spl lambda/=850 nm by the cut-back method was 0.60 dB/cm; the excess loss calculated for the mirror coupling was 1.8-2.3 dB. The results showed that the IMMs can be incorporated in O/E-PCBs to couple light in and out of planar waveguides. Furthermore, the presented results indicate that optical waveguides with integrated micromirrors for optical 3-D wiring can be produced compatible with volume manufacturing techniques.     

Design of Taper Structure for Highly Efficient Coupling Between 1-D Photonic Crystal Coupled Resonator Optical Waveguide and Straight Waveguide

This paper presents a design method of a taper structure for highly efficient coupling between 1-D photonic crystal coupled resonator optical waveguides (1-D PC-CROWs) and input straight waveguides. We propose a new taper structure where not only air hole radius but also waveguide width are varied linearly in order to adjust the dispersion curves shift. By using the proposed tapered structure, we can connect each waveguide with high transmission over wide bandwidth. Our numerical simulation results show that a transmission of 98% around 1550 nm wavelength in a 6.6 $mu$m long taper can be obtained with a 42 nm bandwidth.      

Resonant coupling of near-infrared radiation to photonic bandstructure waveguides

Sharp resonance features are observed in the polarized reflectivity spectra of semiconductor photonic crystals fabricated by deep periodic patterning of AlGaAs surface waveguides. Both one- (1-D) and two-dimensional (2-D) lattices are studied by angular dependent reflectivity. By comparison with theory we show that the sharp features in reflectivity arise from resonant coupling of the external radiation to the folded band structure of the photonic crystal waveguides. Wavevector selective coupling to “heavy photon” states at the edge of the photonic Brillouin zone is demonstrated for the 1-D lattices. In the case of the 2-D lattices we observe polarization mixing of the photonic hands. Theoretical reflectivity spectra were obtained from a numerical solution of Maxwells equations for the patterned waveguide and were found to be in very good agreement with experiment     

Three-dimensional propagation analysis of coupling efficiency using segmentation and local normal mode expansion for vertically coupled microring resonator filter

A novel three-dimensional (3-D) propagation analysis of coupled waveguides using local normal modes and the segmentation along the propagation axis was developed. The coupling efficiency of vertically coupled microring resonators was optimally designed using this analysis. The computation time is much faster and the required memory capacity is much smaller than those of the 3-D finite-difference time-domain (FDTD) method.     

Characteristics of coupling between parallel-plate waveguides with and without dielectric plugs

An analysis is presented of the coupling between parallel-plate waveguides excited in TE modes. Integro-differential equations are formulated for finite arrays of such waveguides with arbitrary widths and spacings. The waveguides, moreover, may be loaded with dielectric plugs having different dielectric constants and thicknesses. Solutions to these equations are effected by the method of moments. Extensive numerical data are obtained for the coupling between two waveguides, and their characteristics are examined in detail. The results show that in unloaded situations the coupling diminishes monotonically with increasings/lambda, wheresis the separation between the waveguides andlambdais the wavelength. At a given frequency, moreover, the coupling for largesdecreases asymptotically ass^{-3/2}. By contrast, an asymptotic dependence ofs^{-3/2}was uncovered earlier for TM-mode coupling. It is found that substantially different coupling behavior may result when the waveguides are loaded by dielectric plugs because of the excitation by the aperture discontinuity of higher order modes, which propagate inside the dielectric but are attenuated in the unloaded waveguide region. Of particular interest is the observation, under suitable conditions, of resonance characteristics in the coupling as functions of both the frequency and the thickness of the dielectric plug. These resonances are found to occur when the impedances of a certain higher order mode satisfy the transverse resonance condition, and thus are the manifestation of the resonances of such modes inside the cavity formed by the dielectric plug.     

Full-vector finite-element beam propagation method for anisotropicoptical device analysis

A finite-element full-vectorial beam-propagation method is presented, for the first time, for the analysis of 3-D anisotropic optical waveguides. Full 3×3 permittivity and permeability tensors are considered. The formulation takes into account the polarization dependence and the component coupling due to the waveguide geometry and the medium anisotropy without any analytical approximations. The perfectly matched anisotropic absorber is introduced to eliminate the influence of the computational border on the numerical solutions. The correctness of the proposed approach is verified by analyzing several kinds of anisotropies. For the first time, a full vectorial finite-element propagation analysis is presented for diffuse waveguides and magnetooptic devices     

基于厄米-高斯函数法研究1维光子晶体波导

为了对折射率型1维光子晶体缺陷波导中的光传输进行有效数值模拟,采用此类型波导的厄米-高斯函数展开方法进行了研究。首先给出了计算方法的详细理论推导,然后利用该方法计算了偏振态不同、结构参量不同的情况下波导本征模式的色散关系、模场空间分布、能量控制因子及等效折射率。结果表明,1维光子晶体缺陷波导与阶跃平面光波导主要差别在于高阶模式,且可通过调节1维光子晶体的结构参量来有效调控高阶模式的传输。     

Three-Dimensional Tapered Spot-Size Converter Based on (111) Silicon-on-Insulator

A novel method is presented to realize a three- dimensional (3-D) spot-size converter (SSC) by standard silicon micromachining techniques, for efficient coupling from single-mode fiber to silicon photonic chip. The SSC is comprised of input–output waveguides and a 3-D tapered coupler on silicon-on-insulator (SOI) substrate. The dimensions are decreased linearly in both vertical and horizontal directions from input facet to output facet. The slope in the vertical direction is originated from the angle between the surface of (111) SOI wafer and the real (111) crystal plane. Fabrication of the device has large process tolerance and its effectiveness was conformed by optical loss measurement.      

Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes

Two-dimensional (2-D) photonic crystal (PC) directional couplers (DCs) that have a triangular lattice pattern of air holes in a planar dielectric slab are theoretically and experimentally analyzed. Unlike the 2-D PC DC structure with a dielectric rod in air, which is frequently used in theoretical studies, more practical PC DCs tend to be multimode in nature and exhibit a large group velocity dispersion, thus creating decoupling points in the dispersion relation without any additional modifications to the structure. The multimode nature and large dispersion lead to interference which degrades the coupling properties. By inserting three rows of air holes between neighboring line-defect waveguides in order to separate them, we have successfully reduced the multimode region and obtained a single-mode region. In this case, the large dispersion allows the creation of a PC DC with wavelength selectivity and a coupling length as short as 30 a,/spl sim/10 /spl mu/m for a=345 nm, where a is the lattice constant. The transmission spectra obtained experimentally showed good agreement with the theory whereas their transmission ranges were restricted to those of bent waveguides. These results are encouraging for practical application to optical communications.     

基于二维光子晶体的多频段太赫兹波滤波器研究

基于二维光子晶体,提出一种多频段 太赫兹(THz)波滤波器。在光子晶体中引入3条平行的横向波导,通过改变介质柱的半 径或插入半径较小的介质柱在 相邻波导之间构成耦合区域,使特定频率的THz波从中部波导耦合至上、下侧光子晶体波 导并分别从端口2和1输出, 其余的THz波经中部波导从端口3输出,最终达到多频段滤波的效果。利用时域有限差 分法和平面波展开法对所提出 的器件计算和仿真结果显示,频率为f=3.24和3.75THz的THz波分 别从端口1、2和3输出中,传输效率分 别达到95%和99% ,表明本文结构能很好实现多频段滤波效果。     

Waveguide Interconnection in Silica-Based Planar Lightwave Circuit Using Femtosecond Laser

The interconnection of waveguides inside a silica- based planar lightwave circuit (PLC) is demonstrated both two- and three-dimensionally by using a femtosecond laser. The waveguides written with a femtosecond laser can be successfully connected to waveguides inside a PLC with low loss. Unlike previous work on the direct writing of 2-D and 3-D waveguides in bulk glass, the waveguide must be written a few tens of micrometers beneath the surface of a PLC composed of multilayers of different glasses. To realize a low-loss waveguide, we studied the sensitivity difference for femtosecond pulses in each layer in detail and developed a multiple-scanning technique with a femtosecond laser for writing waveguides. In addition, we investigated a mode-field (MF) diameter control technique to allow us to achieve the low-loss interconnection of PLC and written waveguides. We also studied particular problems caused by nonlinear optical effects, such as the positional displacement of written waveguides from the focal point. As a result, we achieved a low-loss waveguide with almost the same MF diameter as a PLC waveguide and performed the first demonstration of interconnection between PLC waveguides. The excess losses at 1550 nm were 1.4 and 2.3 dB for 2-D and 3-D interconnection, respectively.      

AWG中阵列波导耦合系数的计算

针对阵列波导光栅（AWG）中阵列波导耦合系数的计算问题，提出了基于光束传播方法（BPM）的叠加积分方法的修正方法。将修正前、后的结果与简单叠加积分方法的结果作了分析比较，从而验证了修正方法的正确性。分析了阵列波导之间的耦合对耦合系数的影响，阵列波导间距越小，影响越大。     

An analysis of intersecting diffused channel waveguides

The coupling characteristics of intersecting diffused channel waveguides are computed for realistic three-dimensional diffusion profiles by means of the propagating beam method (PBM). Both TE and TM polarizations are treated for waveguides formed onz-cut LiNbO3. Good agreement between computed and previously reported measured results is found for the TE polarization. Agreement between computed and measured results is not as good for the TM polarization. This is explained by the fact that the applicable2Deltan-waveguide supports four modes, which should make coupling characteristics very sensitive to input conditions.     

Study and design of step-index channel waveguide bends withlarge-angle and low-loss characteristics

By using micro-prisms, improved three-dimensional (3-D) bends of the embedded and buried waveguides of step-index profile are proposed. A simple phase compensation rule for the optimal design of the micro-prism is also presented. Through the simulation of 3-D semivectorial finite-difference beam propagation method, the transmission characteristics of the improved bends are shown to have been enhanced dramatically as compared with those of the conventional ones. Even for a bend angle of as large as 10°, the normalized transmitted power can still be greater than 95%. These results of 3-D bends are then compared with those of the two-dimensional (2-D) ones which are simplified from 3-D structures by the effective index method, and physical explanation of the discrepancy between the 3-D and 2-D results is introduced. The influences of waveguide structures and prism parameters on the transmission characteristics are discussed in detail. Some criteria for the design of large-angle low-loss 3-D improved bends are also accessed     

High $Q$ -Factor Microrings Using Slightly Etched Rib Waveguides

The paper reports the design, fabrication and characterization of silicon-on-insulator (SOI) microring resonators using shallow etched rib waveguides. The variation of the $Q$-factor of microring resonators as a function of the ring diameter and coupling gap between the input waveguide and the ring is studied. Such structures are fabricated using e-beam lithography and reactive ion etching steps. Propagation loss of shallow etching rib waveguide has been evaluated to 0.8 dB/cm for wavelengths around 1550 nm. With a ring diameter of 100 $mu{rm m}$ and a coupling gap of 450 nm, the measured $Q$ -factor is 35300. These results are matched by 3-D numerical optical modeling.      

An analytic solution for mode coupling in optical waveguide branches

Mode coupling between local normal modes in branching and separating optical waveguides is treated. An analytic solution for power transfer is provided for structures whose shape has a particular functional form. Analytic results are compared to numerical calculations for linear branches. Numerical examples for the design of shaped structures fabricated with Ti:LiNbO3channel waveguides are given.     

Enhancement of power transfer in periodic array of optical waveguides via intermediate Bloch states

A directional coupling mechanism between different waveguides in a periodic array of waveguides is suggested. The optical power transfer between two different waveguides is mediated by the coupling between zero-order modes of two of the waveguides and the second band of the periodic structure. Analytical solutions for the no-detuning (narrow band) and far-from-resonance cases are presented. The far-from-resonance case is shown to resemble a simple two-mode system with complete optical power transfer between the two waveguides, coupled by localized gratings. The transfer is mediated by the second band of the periodic structure. The transition length depends strongly on the shape of the perturbation, and depends exponentially on the distance between the waveguides, yet it allows us to transfer power from one waveguide to another at such distances, for which the transition via conventional directional tunneling mechanism is impossible. Our analytical results are supported by numerical calculations carried out for a model problem with realistic parameters.     

Electromagnetic modeling of waveguides involving finite-sizedielectric regions

A moment method for handling arbitrarily shaped 2-D and 3-D waveguides that involve either conductors, finite-size dielectric regions, or both is presented. A procedure for modeling the dielectric allows 2-D rooftop functions to represent both the 3-D polarization current in the dielectric and the surface current on the conductors, and precludes the presence of fictitious charge within the dielectric. Examples include coaxial, microstrip, and dielectric waveguides. Numerical convergence, consistency with physical principles, and agreement with the literature are demonstrated