Optimized coupling of a Gaussian beam into an optical waveguide with a grating coupler: comparison of experimental and theoretical results

The coupling efficiency of grating couplers is derived for a Gaussian incident beam. Its optimum value depends on the beam waist and on the position of a light spot with respect to the coupler edge for given grating parameters. The characteristic coupling length has been experimentally determined for the grating coupler studied. Relative measurements of the coupling efficiency as a function of incident beam characteristics are in good agreement with the numerical results.     

Compact double-grating coupler between vertically stacked silicon-on-insulator waveguides

We analyze a compact double-grating coupler that provides coupling through radiation modes between two vertically stacked silicon-on-insulator waveguides. The grating is sufficiently strong to be considered a one-dimensional photonic bandgap structure that facilitates a short coupling length. Simulations suggest that a 29% coupling efficiency is achievable in coupling light from one waveguide to another with 12.9 microm long binary gratings. We found that the coupling efficiency is enhanced by Fabry-Perot resonance between two gratings. The coupling efficiency can be increased by use of a blazed grating. We use the eigenmode expansion method to design and optimize the binary grating coupler, and the results are verified by use of the finite-difference time-domain method.     

Grating coupler dispersion compensation with a surface-relief reflection grating

Experimental results are presented that show that diffraction off a surface-relief reflection grating can be used to extend the FWHM input coupling efficiency versus the coupled-light wavelength of a grating coupler from 0.7 to 17 nm. Use of a surface-relief reflection grating allows high diffraction efficiency over a wide wavelength range. Dispersion-matching calculations are included that illustrate that for certain output coupling applications the FWHM can be extended to 33 am. Analysis shows that for inputcoupling applications the lateral beam shift resulting from angular dispersion may be the limiting factor for wavelength compensation.     

High-Efficiency Light Coupling in a Submicrometric Silicon-on-Insulator Waveguide

Light coupling into a sub-micrometer-thick waveguide is usually done through a grating coupler. Coupling efficiency is strongly enhanced by addition of a mirror above the grating. This new kind of coupler can be designed to achieve efficiencies as great as 80%. Numerical calculations for a high-angular-spread Gaussian incident beam are compared with experimental results obtained for a standard silicon-on-insulator waveguide.     

Amplitude modulation and beam-steering properties of active binary phase gratings with reconfigurable absorption areas

By combining a binary phase grating and materials with a controllable absorption, it is shown theoretically that it is possible to modulate the light in a zero-order diffraction beam and that a high contrast level for the beam modulation can be obtained. The intensity of higher diffraction orders also changes, but it is calculated that high contrasts cannot be achieved for these higher-order beams with the active gratings that we examine. This specific modulator design that we use can be applied both for transmitted and for reflected light. Using the same ideas, one may build a beam-deflection device by varying the period of the grating by selectively changing the absorption levels in the grating. The deflection efficiency of the device can be improved compared with other designs by use of a grating with a reduced intensity of the nondeflected zero-order beam.     

Analysis of input-grating couplers having finite lengths

Planar waveguide-grating couplers are analyzed to determine the effects of grating length, the incident beam size, and the coupling length of the grating on the input-coupling efficiency. The emphasis is to examine the effects of these finite lengths on the range of angles over which input coupling occurs and the shape of the efficiency curve. A general formula for normalized input-coupling efficiency is given to relate these lengths. When any one of these characteristic lengths is much smaller than the other two, both the angular width and angular dependence of the coupling efficiency for a scan of the incident beam angle will be mainly determined by that characteristic length. This is demonstrated experimentally for two cases: one has a relatively short grating length, and the other has a short coupling length.     

扩束光纤与宽波导光栅的光耦合特性

为了研究光纤与宽波导光栅的有效耦合,基于高斯光束与波导光栅的光耦合理论,以30μm宽波导光栅为研究对象,利用矩阵光学和高斯光束理论分析和设计了一种扩束光纤,并通过分析其耦合损耗,建立了扩束光纤与波导光栅耦合模型.优化所设计扩束光纤的结构参数后,得到束腰半径为10.8μm的输出光束.最后分析了扩束光纤的结构容差,并讨论了所设计扩束光纤的输出光束、单模光纤的输出光束以及束腰半径为16 μm的自由空间高斯光束各自在光栅表面的位置变化对光栅耦合效率的影响.可知扩束光纤输出的光束与单模光纤输出的光束相比具有较大的位置容差,与束腰半径为16 μm的自由空间高斯光束相比,光耦合效率基本相同.     

Highly efficient Y-junctions with arc-bend branch structures of sunlight guiding systems for indoor illumination

This paper proposes both symmetrical and asymmetric Y-junctions with arc-bend branch structures for auxiliary indoor-illumination applications. These arc-bend branch structures can be used as a concave-mirror-like light guide, to change the direction of beam propagation and also to converge the beam spread angle. Optical simulation results show that the proposed arc-bend Y-junctions can achieve an inner coupling efficiency, not including plastic/air interfaces, above 90% in both usages: beam combiner and splitter. Particularly, when the applied branch opening angle becomes large, this high optical efficiency becomes more significant than those of linear straight Y-junctions. Moreover, it is also confirmed that the coupling efficiency of the symmetric arc-bend junction can be as high as 90.0%, and the asymmetric coupling efficiency is 93.4%, even if the branch opening angle is quite large.     

Light coupling into an optical microcantilever by an embedded diffraction grating

By measuring the excitation efficiency of an optical waveguide on a diffraction grating one can accurately register the changes in the incidence angle of the exciting light beam. This phenomenon was applied to detect ultrasmall deflections of silicon dioxide cantilevers of submicrometer thickness that were fabricated with corrugation on top to act as diffraction grating couplers. The power of light coupled into the cantilevers was monitored with a conventional photodetector and modulated using mechanical vibration of the cantilever, thus changing the spatial orientation of the coupler with respect to the incident light beam. The technique can be considered as an alternative to the methods known for detection of cantilever deflection.     

Effect of reconstruction beam polarization on the kinetics of anisotropic gratings in bacteriorhodopsin

Anisotropic gratings are recorded on bacteriorhodopsin films by two parallelly polarized beams, and the effect of the polarization orientation of the reconstructing beam on the diffraction efficiency kinetics is studied. A theoretical model for the diffraction efficiency kinetics of the anisotropic grating is developed by combining Jones-matrix and photochromic two-state theory. It is found that the polarization azimuth of the reconstructing beam produces a cosine modulation on the kinetics of the diffraction efficiency, being positive at the peak efficiency and negative for steady state. By adding auxiliary violet light during grating formation, the saturation of the grating can be restrained. As a result, the negative cosine modulation for the steady-state diffraction efficiency changes to a positive one. In addition, the steady-state diffraction efficiency is increased appreciably for all reconstructing polarization orientations.     

Wideband two-port beam splitter of a binary fused-silica phase grating

The usual beam splitter of multilayer-coated film with a wideband spectrum is not easy to achieve. We describe the realization of a wideband transmission two-port beam splitter based on a binary fused-silica phase grating. To achieve high efficiency and equality in the diffracted 0th and -1st orders, the grating profile parameters are optimized using rigorous coupled-wave analysis at a wavelength of 1550 nm. Holographic recording and the inductively coupled plasma dry etching technique are used to fabricate the fused-silica beam splitter grating. The measured efficiency of (45% x 2) = 90% diffracted into the both orders can be obtained with the fabricated grating under Littrow mounting. The physical mechanism of such a wideband two-port beam splitter grating can be well explained by the modal method based on two-beam interference of the modes excited by the incident wave. With the high damage threshold, low coefficient of thermal expansion, and wideband high efficiency, the presented beam splitter etched in fused silica should be a useful optical element for a variety of practical applications.     

Polarization-dependent diffraction efficiency of a photorefractive volume grating and suppression of this efficiency

In terms of refractive-index ellipsoid of a uniaxial crystal, the relationship between the diffraction efficiency of a volume grating and the polarization state of a readout beam is theoretically analyzed. The direction of a refractive light beam and the corresponding refractive-index modulation will both be changed by a variation of the polarization state. In the polarization state of the readout beam, which may lead to a strong variation in the diffraction efficiency of the volume grating. This kind of polarization-dependent diffraction efficiency of a volume grating in an anisotropic crystal is extremely disadvantageous for some applications. A method to suppress the polarization-dependent diffraction efficiency by use of double volume gratings is presented, and experiments with LiNbO3:Fe crystal are also demonstrated. The experimental results indicate that this method can well suppress the polarization-dependent diffraction efficiency of a volume grating. Furthermore, the diffraction properties of the double volume gratings are almost independent of the polarization state of the readout beam. The relative values of the diffraction peaks are calculated on the basis of the relationship between index modulation and the state of polarization. The experimental values are in good agreement with the theoretical analyses.     

Design, fabrication, and performance of preferential-order volume grating waveguide couplers

Both a nonfocusing and a focusing preferential-order volume grating waveguide coupler were designed, fabricated, and tested. These volume grating couplers are designed to outcouple a 633-nm wave guided in an adjacent polyimide waveguide film. The slanted-fringe volume gratings are recorded holographically by the interference of two 364-nm waves. The dynamics of the holographic photopolymer HRF600X001 are investigated in relation to the interaction with the guided wave. The fabricated couplers exhibited a preferential coupling of 98%, a spatial coupling rate of 3.6 mm(-1), and a coupling efficiency of 95%. The focusing grating coupler focused the outcoupled beam to a focal line with a full width at half-maximum of 10.49 mum located 25 mm above the grating.     

Volume grating couplers: polarization and loss effects

We analyze the polarization-dependent performance and the loss performance of volume grating couplers using a leaky-mode approach in conjunction with rigorous coupled-wave analysis for two configurations: the volume grating in the cover layer and the volume grating in the waveguide. The angular dependence of TE and TM polarization coupling efficiency is studied, and designs for polarization-dependent and polarization-independent couplers are presented for both configurations. Polarization-dependent couplers are obtained with an outcoupling angle close to normal. Polarization-independent couplers are obtained with outcoupling angles away from normal, 46.7 deg in the case of a volume grating in the cover layer and 54.4 deg in the case of a volume grating in the waveguide. The effect of loss on coupler performance is also analyzed. It is found that, for cases of practical importance, the effect of lossy coupler materials is small. The estimated loss for a commercially available material is 5 dB/cm. For TE-polarized light and the volume grating in the waveguide, a loss of this magnitude reduces the coupling efficiency by less than 3%, whereas in the case of the volume grating in the cover layer, it reduces the coupling efficiency by less than 0.3%.     

反射型阶梯光栅的特性分析

衍射效率是评价二元光学器件质量性能的重要指标之一.针对反射性阶梯光栅,利用几何方法计算出斜入射情况下光束在台阶边缘的光程差的分布情况,根据多缝夫琅和费衍射推导出反射型阶梯光栅的衍射光强表达式.并在此基础上,讨论了台阶数N取2和N趋向于无穷两种极限情况下阶梯光栅光强公式的变化情况,得到区别于一般文献所表达的衍射效率公式.初步试验表明,反射型阶梯光栅的衍射效率与台阶数、蚀刻深度与入射波长的比值均有密切相关.     

Coupled-wave Analysis of the Bragg Effect Waveguide Coupler

Abstract

A coupled-wave analysis is presented for the Bragg effect waveguide coupler. This device consists of a slanted volume phase grating which is integrated inside the lightguiding layer of an optical waveguide. The wave propagation is described by a set of leaky wave modes. Self-consistency relations are derived to determine the angular mode spectrum and the corresponding radiation loss coefficients. A maximum input coupling efficiency of 80% is predicted for an incident Gaussian beam. The power of a waveguide mode should be emitted into a single output beam reaching an efficiency of almost 100%.     

Holographic Bragg grating input-output couplers for polymer waveguides at an 850-nm wavelength

Bragg gratings used as input-output couplers in polymeric waveguides have been demonstrated at infrared wavelengths. These Bragg grating couplers were holographically formed volume phase gratings with a near-45 degrees fringe slant angle embedded directly into a waveguide layer. A photopolymer was used for both producing a planar waveguide and constructing the embedded Bragg grating coupler. A coupling efficiency of 23% for input and 5% for output has been achieved at 850 nm. The output-coupling beam profiles are also discussed.     

Design of a high-efficiency grating coupler based on a silicon nitride overlay for silicon-on-insulator waveguides

A waveguide grating coupler based on a silicon nitride overlay at 1.55 μm for TE polarization is designed with no experimental demonstration. Its coupling efficiency for a fiber is 76%, the 1 dB bandwidth is 75 nm, and the coupling angle is 10°. The effects of different device parameters on the coupling performance for the grating coupler are discussed. The coupling efficiency of our grating coupler is almost equal, yet the 1 dB spectral bandwidth is around 25 nm broader, as compared with the grating coupler design based on a poly-silicon overlay. The coupling performance of our coupling device could still be further improved. The grating coupler presented in this paper is applicable to the optical coupling in nanophotonic integrated circuits.     

Grating Couplers Fabricated by Electron-Beam Lithography for Coupling Free-Space Light Into Nanophotonic Devices

Grating couplers with nanoscale periodicity have been fabricated on silicon-on-insulator (SOI) substrates by electron beam lithography and reactive ion etching. A versatile experimental apparatus has been implemented to measure the efficiency of these gratings in coupling free-space radiation into planar waveguides. This coupling efficiency has been measured as a function of grating depth and the angle and wavelength of incident radiation. Coupling efficiencies of at least 5% and as high as 20% are demonstrated for wavelengths in the vicinity of 1550 nm and incident angles around 45deg.