Conversion of waveguide modes in nonuniformly magnetized planar structures

An analysis is made of a planar structure with a nonuniform distribution of magnetization throughout the thickness of a waveguide layer that corresponds to the rotation of magnetic momentum in the plane of the layer. The results of the study show the feasibility of efficiently controlling the conversion of orthogonally polarized modes due to the change of thickness of the transition layer and the angle of magnetization rotation across the waveguide layer.     

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.     

TE0导模干涉刻写周期可调亚波长光栅理论研究

通过棱镜耦合激发非对称金属包覆介质波导结构中的TE₀导波模式, 利用两束TE₀模的干涉从理论上实现了周期可调的亚波长光栅刻写. 分析了TE₀模式的色散关系, 刻写亚波长光栅的周期与激发光源、棱镜折射率、光刻胶薄膜厚度及折射率之间的关系. 用有限元方法数值模拟了金属薄膜、光刻胶薄膜和空气多层结构中TE₀导模的干涉场分布. 研究发现, 激发光源波长越短, TE₀ 模干涉刻写的亚波长光栅周期越小; 光刻胶越厚, 刻写的亚波长光栅周期越小; 高折射率光刻胶有利于更小周期亚波长光栅的刻写. 相较于表面等离子体干涉光刻, 基于TE₀ 模的干涉可在厚光刻胶条件下通过改变激发光源、棱镜折射率、光刻胶材料折射率、特别是光刻胶薄膜的厚度等多种方式实现对亚波长光栅周期的有效调控.     

Guided-mode resonances in multimode planar periodic waveguides

<正>Using the effective medium theory and the waveguide eigenvalue equation,we design a multimode planar periodic waveguide.When a plane wave illuminates the grating at the designed angle and wavelength, more than one leaky modes are excited coincidentally.Then the reflection efficiency around this designed angle and wavelength is investigated using a rigorous coupled wave analysis formulation and a gap of reflection peaks is found.Electric field distributions reveal that this high reflectivity gap is due to the coupling between these two coincidentally excited leaky modes.     

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.     

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).     

Spectral phase induced by the reflection on a mirror-based waveguide grating in the neighborhood of modal resonance

A linearly polarized plane wave impinging on a mirror-based waveguide grating is shown to experience a 2pi phase shift of controllable slope in the reflection spectrum. Such a zeroth-order resonant grating effect is adequately confirmed by means of an ellipsometer. The close agreement between the analytical representation of grating coupled waveguide resonances with the experimental results confirms the relevance of the underlying phenomenological understanding of resonant gratings.     

Waveguide grating mirror for large-area semiconductor lasers

We have fabricated and tested a waveguide grating mirror that uses anomalous reflection of light associated with excitation of waveguide modes. Sharp features are observed in the reflection spectra in both the wavelength and the angular domains. We confirm experimentally that, when the waveguide grating mirror is placed a short distance in front of a large-area semiconductor laser, it can control the emission spectrum. This demonstration opens a new approach to the design of very compact semiconductor lasers operating in the single-frequency-single-mode regime.     

Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures

Basic steps in developing an original method of adiabatic modes that makes it possible to solve the direct and inverse problems of simulating and designing three-dimensional multilayered smoothly irregular open waveguide structures are described. A new element in the method is that an approximate solution of Maxwell’s equations is made to obey “inclined” boundary conditions at the interfaces between themedia being considered. These boundary conditions take into account the obliqueness of planes tangent to nonplanar boundaries between the media and lead to new equations for coupled vector quasiwaveguide hybrid adiabatic modes. Solutions of these equations describe the phenomenon of “entanglement” of two linear polarizations of an irregular multilayered waveguide, the appearance of a new mode in an entangled state, and the effect of rotation of the polarization plane of quasiwaveguide modes. The efficiency of the method is demonstrated by considering the example of numerically simulating a thin-film generalized waveguide Lüneburg lens.     

High-refractive-index measurement with an elastomeric grating coupler

An elastomeric grating coupler fabricated by the replica molding technique is used to measure the modal indices of a silicon-on-insulator (SOI) planar waveguide structure. Because of the van der Waals interaction between the grating mold and the waveguide, the elastomeric stamp makes conformal contact with the waveguide surface, inducing a periodic index perturbation at the contact region. The phase of the incident light is changed to match the guided modes of the waveguide. The modal and bulk indices are obtained by measuring the coupling angles. This technique serves to measure the high refractive index with a precision better than 10(-3) and allows the elastomeric stamp to be removed without damaging the surface of the waveguide.     

Peculiarities of spontaneous grating generation in light-sensitive waveguide layers during holographic grating formation

The generation of spontaneous (noise) gratings during the simultaneous formation of a holographic grating in thin (on the order of the cutoff thickness of the TE₀ waveguide mode) AgCl-Ag films by two laser beams with λ = 532 nm and polarization vectors that make an angle of 45° with the plane of incidence have been studied. The electron microscopy images and diffraction patterns have revealed a significant difference of the spontaneous-grating structure from the structure obtained under irradiation by one laser beam. The spontaneous gratings have a significant spread in the directions of their wave vector, and the diffraction pattern (recorded using a probe beam with λ = 337 nm) has the form of a bundle of diverging arcs that intersect at one point. This difference is caused by self-diffraction from the holographic grating, which is responsible for the main diffraction peaks with odd orders, the growth of spontaneous gratings because of the interference of the beams diffracted by the holographic grating with the waveguide TE₀ modes scattered in the film, and silver transport to the interference minima. The diffraction patterns are quantitatively analyzed and the period of the new (formed under two-beam irradiation) spontaneous gratings is calculated. The calculation results are in good agreement with the experimental data.     

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.     

Modelling of photonic crystal waveguides: a simple and accurate approach

We present an improved variational effective index method for reduction of 2-D Bragg grating problems to 1-D and show significant improvements particularly at smaller wavelengths. The method is based on the optimal variational (Vopt) method, which we have earlier used successfully for conventional waveguides. A 1-D transverse profile along with a longitudinal index variation are reduced to a 1-D longitudinal distribution, reflection and transmission spectra of which have been studied for both the TE and TM modes by transfer matrix methods. An accurate modeling for the out of plane scattering losses has been presented which occur when a guided wave propagating in a conventional waveguide impinges on a photonic crystal waveguide. Taking these losses into account brings the results pretty close to those of a rigorous 2-D Helmholtz solver QUEP, improving them remarkably over the variational EIM (vEIM) results.     

Study on guided-mode resonance characteristic of multilayer dielectric grating with broadband and wide using-angle

Guided-mode resonance in a diffraction band of multilayer dielectric gratings may lead to a catastrophic result in laser system, especially in the ultrashort pulse laser system, so the inhibition of guided-mode resonance is very important. In this paper the characteristics of guided-mode resonance in multilayer dielectric grating are studied with the aim of better understanding the physical process of guided-mode resonance and designing a broadband multilayer dielectric grating with no guided-mode resonance. By employing waveguide theory, all guided-wave modes appearing in multilayer dielectric grating are found, and the incident conditions, separately, corresponding to each guided-wave mode are also obtained. The electric field enhancement in multilayer dielectric grating is shown obviously. Furthermore, from the detailed analyses on the guided-mode resonance conditions, it is found that the reduction of grating period would effectively avoid the appearing of guided-mode resonance. And the expressions for calculating maximum periods, which ensure that no guided-mode resonance occurs in the requiring broad angle or wavelength range, are first reported. The above results calculated by waveguide theory and Fourier mode method are compared wit each other, and they are coincident completely. Moreover, the method that relies on waveguide theory is more helpful for understanding the guided-mode resonance excited process and analyzing how each parameter affects the characteristic of guided-mode resonance. Therefore, the effects of multilayer dielectric grating parameters, such as period, fill factor, thickness of grating layer, {\it et al.}, on the guided-mode resonance characteristic are discussed in detail based on waveguide theory, and some meaningful results are obtained.     

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.     

Micro-optical 3-dB mode converters

We present a detailed design of a 3-dB TE₀-TE₁ micro-optical mode converter using a chirped grating to phase-match the two propagation modes in an optical waveguide. Devices were fabricated in titanium in-diffused lithium niobate by ion-beam etching the tapered grating pattern into the waveguide surface. The power transfer between the two coupled modes was observed experimentally by varying the angle between the light beam and the normal grating wave-vector. Insertion loss of the TE₀-TE₁ mode converter due to spurious scattering was estimated at 1.5 dB.     

Derivative free method for computing modes of multilayer planar waveguide

A technique to solve generalized dispersion equation of multilayer planar waveguide has been demonstrated to obtain all the expected guided modes. The solution is based on the derivative free method for computing the zeros of an analytical function in complex plane. The derivative free method extracts the roots which are very close to actual zeros of the function. Roots are further refined using the robust iteration method to achieve the desired accuracy. Application of the proposed method has been verified by solving the modes of a variety of structures including lossless structure, leaky structure, quantum well waveguide, active waveguide, ARROW waveguide and metal clad waveguide. The method is efficient and computes all modes of planar waveguide with high accuracy.     

Polarization-independent grating couplers for silicon-on-insulator nanophotonic waveguides

We propose the use of subwavelength structures in a waveguide grating to achieve polarization-independent coupling of light between an optical fiber and a silicon-on-insulator (SOI) optical waveguide. The subwavelength structure allows the mode effective indices of the TE and TM modes in the grating section to be precisely engineered. We calculate that coupling efficiency of over 64% is possible using the proposed design for polarization-independent coupling between single-mode optical fibers and SOI nanophotonic waveguides.     

条形半导体激光器光束质量因子M2的理论计算

通过一个二维半矢量模型求得纯折射率导引脊形波导和掩埋波导这两种常见平面条形半导体激光器波导结构的模式光场分布，现通过描述光束传播的非傍轴矢量二阶矩，通过平面波谱的方法获得激光器出射光束在横向和侧向上的束腰、远场发散角和M^2因子。讨论了波导结构参量变化对M^2因子的影响，并对两种波导结构光束的性质与波导参量的关系进行了比较。