Modelling of finite-size grating waveguide filters on the basis of a free-space diffraction approach

The field reflection coefficientR of a high strength and short length waveguide grating section is obtained by resorting to a free-space diffraction approach whereby the waveguide grating is excited by means of a virtual high index prism. The effective index of the guided mode, the coupling coefficient between contradirectionally propagating modes of the grating waveguide as well as the modal field are first obtained in the case of an infinite grating by interpreting the results given by an exact diffraction solution by means of a three-wave coupled mode formalism. These results are then introduced in the coupled wave analysis of the structure of finite extent to provide the field at the entrance of the waveguide grating section where the usual overlap integral with the incident field delivers the reflection coefficient. We neglect only the result of radiation mode propagation. This assumption can be made when the grating section is longer than the propagating length of all the leaky modes.     

Modelling of finite-size grating waveguide filters on the basis of a free-space diffraction approach

The field reflection coefficient R of a high strength and short length waveguide grating section is obtained by resorting to a free-space diffraction approach whereby the waveguide grating is excited by means of a virtual high index prism. The effective index of the guided mode, the coupling coefficient between contradirectionally propagating modes of the grating waveguide as well as the modal field are first obtained in the case of an infinite grating by interpreting the results given by an exact diffraction solution by means of a three-wave coupled mode formalism. These results are then introduced in the coupled wave analysis of the structure of finite extent to provide the field at the entrance of the waveguide grating section where the usual overlap integral with the incident field delivers the reflection coefficient. We neglect only the result of radiation mode propagation. This assumption can be made when the grating section is longer than the propagating length of all the leaky modes.     

Coupling efficiency in grating tuned carbon dioxide waveguide lasers

The coupling efficiency in typical CO₂ waveguide lasers when the feedback element is a diffraction grating is investigated theoretically. A scalar diffraction integral approach is adopted, and the laser is assumed to operate on its lowest loss waveguide mode.     

阵列波导光栅波分复用/解复用器光谱响应效率的理论模型

基于单模光波导的本征模场分布,瑞利－索末菲衍射积分公式和天线原理的互易定理,给出耦合器中两个非接触平面光波导耦合特性的描述.基此,根据等光程差不等振幅多光束干涉的光场叠加原理,推导出新颖的阵列波导光栅波分复用/解复用器的光谱响应效率的解析函数表达式,这些表达式可为快速精确分析阵列波导光栅波分复用/解复用器的特性提供理论基础.同时,介绍了一个计算阵列波导光栅波分复用/解复用器特性的例子,给出其光谱响应度和信号通道串扰.     

Phase shift upon resonant coupling into a thin corrugated optical waveguide

The coupling of light into a waveguide by a surface grating leads to the attenuation of the transmitted beam when the resonant modes of the waveguide are excited. These can be tuned by changing the incident angle or the wavelength. Upon excitation of a mode, the transmitted beam experiences a significant phase shift that can be measured and compared with that predicted by the Kramers-Kronig relations.     

Optimization of optical waveguide grating couplers

The conditions for the optimal coupling between an incident beam of finite cross section and a waveguide mode by means of a finite-size grating have been established in the general case of noncollinear excitation.     

Analytical model of a corrugated optical waveguide

An analytical model of the diffraction energy exchange between the radiative and the waveguide modes in a planar optical waveguide corrugated by a waveguide grating with an arbitrary form of teeth is developed on the basis of the coupled-wave method. It is shown that the mechanism of the energy exchange between the modes is determined by the partial interaction of all components of the spatial frequency spectrum of the waveguide modes with the corresponding components of the spatial frequency spectrum of the grating. It is established that gratings with an asymmetric tooth profile providing a shift of the peak of the spatial frequency spectrum toward matching are characterized by a higher diffraction efficiency α; however, at small thicknesses δ of the waveguide grating, the efficiency is almost independent of the tooth profile. It is shown that gratings with a symmetric profile give on average a decreasing dependence α(δ), while gratings with an optimized asymmetric profile yield a monotonically increasing saturating dependence α(δ).     

Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits

It is generally admitted that the extraordinary transmission of metallic grating with very narrow slits is mainly due to the excitation of surface plasmons on the upper and lower interfaces of the grating. We show that the surface plasmon contribution is not the prime effect and that waveguide mode resonance and diffraction are responsible for the extraordinary transmission. Additionally and surprisingly, we reveal that the transmittance of subwavelength metallic gratings is always nearly zero for frequencies corresponding to surface plasmon excitation. This finding implies that surface plasmons play a negative role in the transmission.     

薄膜光栅耦合器的研究

在玻璃衬底上制备了周期为0.56μm的薄膜光栅耦合器,用复制法把光栅做在玻璃衬底上。实验中,我们观察到,激光束既可以从光栅的上面(空气区)或下面(衬底区)耦合于波导薄膜内,又可以通过光栅由波导薄膜中耦合出来。调节激光束入射角可以激发不同阶的波导模式。由实验测得的输入耦合效率达66.0±0.5％。 关键词：     

Perfect absorption in a monolayer graphene at the near-infrared using a compound waveguide grating by robust critical coupling

We present a perfect graphene absorber with a compound waveguide grating at the near-infrared. The analytical approach is mainly based on the coupled leaky mode theory, which turns the design of the absorber to finding out the required leaky modes supported by the grating structure. Perfect absorption occurs only when the radiative loss of the leaky mode matches the intrinsic absorption loss, which is also named the critical coupling condition.Furthermore, we also demonstrate that the critical coupling of the system can be robustly controlled, and the perfect absorption wavelength can be easily tuned by adjusting the parameters of the compound waveguide grating.     

Hybrid waveguide-surface plasmon polariton modes in a guided-mode resonance grating

We analyze the coupling between surface plasmon polaritons in a metal grating and the guided modes of a dielectric waveguide. Our model structure is a gold wire grating on a slab waveguide made of silicon nitride on silica wafer. The excitation of guided-mode resonances, surface plasmon polariton modes and hybrid waveguide-plasmon modes are observed in numerical simulations. Our experiments verify the existence of the predicted modes. These hybrid modes add significant degrees of freedom in designing structures for plasmonic applications.     

Two-dimensional coupled mode equation for grating waveguide excitation by a focused beam

The problem of grating coupling of a focused incident beam under non-normal incidence into a slab waveguide is given a complete three-dimensional (3D) solution. The diffracted field is expressed as the Fourier integral of a regular part and of a singular part resulting from the existence of the coupled guided mode. A suitable expression of the field in the neighborhood of the pole and a rigorous definition of the modal field lead to a generalized coupled mode equation relating the incident field and the two-dimensional (2D) modal field propagating in the plane of the slab waveguide. The phenomenological parameters involved in the coupled wave equation: the propagation constant, the radiation coefficient as well as the modal field shape are derived from the exact treatment of plane wave diffraction in the same structure. The solution of the complete coupling problem is given in the particular case of a Gaussian incident beam, and of a high index step-index waveguide.     

波导耦合纳米光栅结构的光学滤波和角分辨调谐特性

利用干涉光刻技术制备了波导耦合纳米光栅结构,系统研究了其波导共振模式的角分辨调谐特性及其对光栅参数、入射光偏振特性的依赖关系,并作了相应的理论模拟.特别研究了光栅周期和厚度对波导共振模式角分辨调谐速率的影响.实验结果对于器件进一步应用于滤波、生物传感技术具有重要的指导意义. 关键词： 波导耦合光栅 干涉光刻 角分辨 调谐速率     

Design for broadband high-efficiency grating couplers

In this Letter, we propose general optimization methods to design broadband high-efficiency grating couplers for planar waveguides. We attribute the coupling bandwidth to the mismatch of effective indices between the diffracted beam and the actual grating structure around the operation wavelength for fiber to waveguide excitation. The coupling bandwidth formula is deduced. A simple parameter-separate optimization procedure is proposed for general layered grating couplers for high coupling efficiency. Using our principle, we optimized a grating coupler for a horizontal slot waveguide operating at wavelength 1.55 μm for TM polarization. The grating coupler has 1 dB bandwidth of 60 nm and coupling efficiency of 65% with incident light from single-mode optical fiber (SMF) at 8°.     

Long period grating in/on planar and channel waveguides: A theory description

A comprehensive, complete theory suitable for a long period grating (LPG) on/in a planar or channel waveguide is described on the basis of coupled mode theory. The theory aims at key characteristic parameters with respect to the effect of the LPG, including resonance wavelength, transmission power of the guided mode in the waveguide, full-width at half-maximum (FWHM) of the power attenuation band in transmission spectrum of the guided mode, and coupling coefficient between a guided and a coupled mode. The type of the grating including relief and index modulation, different polarization state combinations of the guided mode and the resonant mode, and slanted grating structure are considered in this theory. The influences of the coupling between two guided modes and between a guided mode and a substrate mode are discussed. The role of cladding layer in a long period waveguide grating is demonstrated in particular. Finally, the expressions for the sensitivity of resonance wavelength as a function of external temperature, pressure and surrounding refractive index are derived.     

Design of an augmented reality display based on polarization grating

A new optical system for an augmented reality(AR) display is proposed in this paper.The optical system mainly includes a ray deflector, coupling input grating, optical waveguide, and coupling output grating.Both the ray deflector and the coupling input grating are designed based on the diffraction characteristics of the polarization grating, and the coupling output grating is the Bragg reflection grating.Compared with other AR schemes, this AR optical system not only reduces the number of projections from two to one, but also improves the efficiency of light coupling into the optical waveguides.The energy loss is reduced by utilizing the single-order diffraction characteristics of the polarization grating in its coupling input structure.The light deflector uses the polarization selectivity of the polarization grating and the characteristics of the rotating light of the twisted nematic liquid crystal layer to realize beam deflection.The working principle of the optical system is experimentally and theoretically demonstrated.     

All-Optical Bistability in Grating Coupling to Nonlinear Waveguide

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刻蚀光纤布拉格反射器特性的理论分析

从理论上研究了波导耦合型刻蚀光纤布拉格反射器的特性。采用正交模式耦合理论描述其中的光栅辅助正反向模式耦合，用非正交模式耦合理论描述输入输出接口的模式激发，给出了分析耦合波导布格瓣反射器的角析表达式，分析表明刻光张布拉格反应器中存在三种布拉格反应，在频谱中表现为六个分立的反射峰，与实验结果相符，其反射率不仅决定事系数，还与其结构参数，尤其是Ａｌ２Ｏ３层的厚度，Ａｌ２Ｏ３层与光纤芯的距离以及匹配层折射     

Autocollimation reflection of light from the surface of corrugated waveguides with leaky modes

The diffraction of light at the corrugated surface of a layer structure was studied. We show that the excitation of the waveguide modes in a layer structure causes a significant change in the diffraction efficiency of the corrugated structure. It is found that the diffraction efficiency of a grating in the autocollimation regime may be as much as 100% with reasonable depths of the grating. The efficiency of a waveguide-grating mirror in dye lasers is experimentally demonstrated.