基于亚波长光栅的VCSEL偏振控制研究

为了确定亚波长光栅在微电机械系统(MEMS)波长可调谐VCSEL不同位置(上DBR上表面、上DBR下表面以及内腔)中实现TE和TM偏振控制的光栅参数范围以及光栅在哪个位置时实现偏振控制最稳定,通过MATLAB建立MEMS波长可调VCSEL的模型,然后计算光栅在3种位置时上反射镜(包括空气隙和光栅)随光栅参数变化的反射率,以此来确定它们实现TE/TM稳定偏振的光栅参数范围(即高反射范围内的参数)。将各自的高反射所对应反射率减去相同光栅参数范围内TM/TE低反射对应的反射率,通过反射率差值确定光栅在哪种位置时MEMS波长可调谐VCSEL实现偏振是最稳定的。最后得出的结论是光栅在上DBR下表面几乎无法控制TM偏振,而将光栅放置于内腔中,无论是在TE偏振控制上还是TM偏振上都是最稳定的。在实现TE偏振稳定的参数范围内,TE的阈值增益比TM最小少10 cm~(-1);而在实现TM偏振稳定时,在TE偏振稳定的参数范围内,TE的阈值增益比TM最小少5 cm~(-1)。     

Apodized fully-etched surface grating coupler using subwavelength structure for standard silicon-on-insulator waveguide

We design and demonstrate the fully-etched apodized grating couplers based on the silicon-on-insulator (SOI) platform using subwavelength structure for both transverse electric (TE) and transverse magnetic (TM) modes operation. The subwavelength grating (SWG) is used to engineer the refractive index using second-order effective medium theory (EMT). The whole designing procedure is given in details, especially a feasible and programmable method is developed to precisely manipulate the coupling strength of each grating cycle. A perfect Gaussian output beam can be synthesized for the TE mode operation, achieving a field overlap up to 98.3% with the Gaussian fiber mode. The simulated peak coupling losses are ?4.63 and ?2.99 dB for the TE mode and the TM mode, respectively, which are comparable with conventional shallowly etched grating couplers, realizing a fabrication simplification without performance penalty. The measured peak coupling loss is ?7.6 dB for the TE mode coupler with a 1 dB bandwidth of 45 nm, and ?6.1 dB for the TM mode coupler with a 1 dB bandwidth of 34 nm.     

一维增透亚波长光栅的研究

将具有高透射性的亚波长光栅置于微机械波长可调谐垂直腔面发射激光器(VCSEL)的内腔当中可以提高波长的调谐范围,为了使波长调谐范围达到最优则必须优化高透射性的亚波长光栅使其透射率达到最大。利用严格耦合波法分析了亚波长光栅的占空比、周期、厚度和入射角对其透射率的影响并找出最优的光栅参数。通过计算分析可得,对于TE和TM偏振存在最佳的占空比使其透射率达到99.5%。在文中条件下,它们对应的占空比分别为0.23和0.80。而光栅厚度对于TE和TM偏振透射率的影响是周期性的,在一个周期内存在一个最佳值使其透射率达到最高。在文中条件下,TE偏振的厚度周期是150 nm,TM偏振的厚度周期是300 nm。当光栅参数不变时,无论是TE还是TM偏振光,它们的透射率只有在垂直入射光栅时(入射角为0°)才能达到最大。而通过等效介质原理可以得出,周期对透射率没有影响。最后计算了透射率在光栅厚度和占空比同时变化时的变化趋势,并从中得出最优的光栅参数。     

Design of a 50/50 splitting ratio non-polarizing beam splitter based on the modal method with fused-silica transmission gratings

The optical design of a beam splitter that has a 50/50 splitting ratio regardless of the polarization is presented. The non-polarizing beam splitter (NPBS) is based on the fused-silica rectangular transmission gratings with high intensity tolerance. The modal method has been used to estimate the effective index of the modes excited in the grating region for TE and TM polarizations. If a phase difference equals an odd multiples of π/2 for the first two modes (i.e. modes 0 and 1), the incident light will be diffracted into the 0 and ?1 orders with about 50% and 50% diffraction efficiency for TM and TE polarizations, respectively.     

Refractive indices of E.G.M. grown Li(Nb,Ta)O3 solid-solution optical waveguide

A solid-solution Li(Nb,Ta)O₃ thin film optical waveguide was fabricated onto a y-plate LiTaO₃ substrate by the epitaxial-growth-by-melting (E.G.M.) technique, in which single-crystal powder of Li(Nb_0.75Ta_0.25)O₃ was used. The waveguide supported eight TM and six TE modes. Studies on optical waveguiding mode indices indicated that the refractive index distribution obeys well the Fermi function. The parameters of the Fermi function were determined, and their values are discussed on the basis of the LiNbO₃-LiTaO₃ pseudo-binary phase diagram.     

Subwavelength gratings fabricated on semiconductor substrates via E-beam lithography and lift-off method

We present results of the fabrication and measurements on reflective polarizers consisting of stacked bi-layer subwavelength metal gratings prepared on GaAs (100) substrates. These linear gratings were fabricated using electron-beam direct-writing lithography and the lift-off method with periods less than the wavelength of light used for measurements. At normal incidence, the polarizer reflects the light polarized perpendicular to the grating lines (transverse magnetic polarization, TM polarized) but absorbs parallel-polarized light (transverse electric polarization, TE polarized). By optimizing structural parameters, the polarization extinction ratio close to 20 has been experimentally achieved at wavelength of 650 nm.     

Permeability tensor versus permittivity one in theory of nonreciprocal optical components

We discuss symmetry properties of the combined systems: electromagnetic field (TE and TM modes) + medium (nondiagonal permeability tensor [μ] and nondiagonal permittivity one [?]) in 2D photonic crystals with transverse magnetization. We show that the origin of orthogonality of the pairs (TE mode + [?]) and (TM mode + [μ]) is different parities of the corresponding fields with respect to the horizontal plane of symmetry of the crystal. As a result of this symmetry, a common use only of the permittivity tensor [?] in the electromagnetic theory of nonreciprocal optical components, ignoring the permeability tensor [μ], leads to loss of a significant part of possible solutions related to TE modes.     

Bragg反射齿型平面凹面衍射光栅性能研究

本文基于Bragg反射光栅是一维光子晶体的一种特例结构, 提出利用一维光子晶体理论进行Bragg衍射光栅的设计并对其性能进行研究分析. 根据一维光子晶体理论, 建立了罗兰圆结构的凹面椭圆Bragg蚀刻衍射光栅, 研究了TE/TM模式下器件的分光特性以及入射角度改变对器件角色散造成的影响; 同时, 文中对比了空气介质型和金属铝线型椭圆Bragg蚀刻衍射光栅的光学性能. 研究结果表明: 选择合适的器件参数, 可以实现TE/TM模式下1.465-1.615 μm范围内波长衍射效率在95% 以上, 且空气介质型结构光栅的通道均匀性要优于金属铝线型结构光栅; 入射角在30°-60°范围内变化时, 相同入射角度下, TM模式下器件角色散大于TE模式. 基于Bragg衍射光栅设计的波分复用器是一种尺寸小、衍射效率高的新型EDG 波分复用器, 为未来密集型EDG波分复用器发展提供了一种新的设计思路.     

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.     

Electromagnetic wave modulation in hollow vanadium dioxide microcrystals

The optical properties of vanadium dioxide (VO₂) single crystals with a hollow rectangular inner channel are numerically simulated. In such microstructures, electromagnetic waves are shown to propagate in the form of waveguide modes, and the semiconductor-metal phase transition in VO₂ results in substantial modulation of the mode propagation constant. The propagation constants are calculated for TE, TM, and EH modes in the spectral range 0.8–1.3 μm.     

Fill factor controlled nanoimprinted ZnO nanowires based on atomic layer deposition

Enhanced diffraction by sub-wavelength nanostructures to convert incident electromagnetic radiation into waveguide modes has applications in anti-reflective coatings for optoelectronic devices. We propose a metal oxide (ZnO) nanowire grid polarizer as such a nanostructure, fabricated by ultraviolet nanoimprint lithography and whose fill factor (FF) is controlled by atomic layer deposition. Using finite difference time domain simulations, we investigated the polarization-dependent optical transmittance of the structures and calculated the polarizing efficiency. Optical profiles such as electric and magnetic field intensity and current density distributions of specific FF nanopatterns were determined for the transverse magnetic and transverse electric modes. The effects of geometrical parameters including the wire-grid period, fill ratio, and spacing between the wire-grid layers on diffraction wavelength were characterized. Respective FF-controlled ZnO nanowire structures were fabricated and their experimental optical transmittances were measured for nanowire grid polarizer applications.     

Optical properties of metamaterial-based devices modulated by a liquid crystal

Due to the fact that it is possible to manipulate light with photonic crystals (PCs), PCs hold a great potential for designing new optical devices. There has been an increase in research on tuning the optical properties of PCs to design devices. We presented a numerical study of optical properties of metamaterial-based devices by liquid crystal infiltration. The plane wave expansion method and finite-difference time-domain method for both TE and TM modes revealed optical properties in photonic crystal structures in an air background for a square lattice. E7 type has been used as a nematic liquid crystal and SrTiO₃ as a ferroelectric material. We showed the possibility of the metamaterials for a two-dimensional photonic crystal cavity on a ferroelectric base infiltrated with a nematic liquid crystal.     

Amorphous Si waveguides with high-quality stacked gratings for multi-layer Si optical circuits

To realize a stacked multi-layer silicon-based photonic device, a waveguide with a stacked grating was fabricated by using amorphous Si (a-Si) material, which is suitable for constructing layered structures. The fabrication method was based on forming a flat a-Si layer on a non-flat structure by using only spin-on-glass (SOG) coating technique. The a-Si grating was precisely constructed on the a-Si waveguide with gold alignment marks for electron beam lithography. Transmitted and reflected light power dependence on the grating period, wavelength, and polarization was systematically measured and compared with the designed dependence. As a result, the reflected light power exhibited a characteristic peak structure at a particular wavelength. Remarkable transverse electric/transverse magnetic (TE/TM) mode dependence was also observed. Furthermore, the measured and the designed properties were in excellent agreement with each other. Consequently, the designed structure was well reproduced in the actual stacked structure based on the a-Si material. These results pave the way for novel a-Si based integrated photonic devices such as polarization selectors and wavelength filters, indicating that a-Si is an excellent material for implementing Si-based multi-layer optical circuits.     

Thermal tuning of surface plasmon resonance: Ag gratings on barium strontium titanate thin films

Surface plasmon tuning via thermally induced refractive index changes in ferroelectrics is investigated. Epitaxial (Ba_0.7Sr_0.3)TiO₃ (BST) thin films were deposited on MgO (001) substrates by pulsed laser deposition. The refractive index of BST thin films measured by the prism-coupling technique was found to increase from 2.3932 (TE)/1.9945 (TM) at room temperature to 2.3949 (TE)/1.9965 (TM) at 66°C. Then 30-nm-Ag gratings with periodicity 750 nm and width 300 nm were fabricated on BST by soft ultraviolet nanoimprint lithography and subsequent lift-off process. The reflection spectra from 500 to 1000 nm with incident angle from 5° to 60° were measured at room temperature and 66°C, with a collimated and p-polarized light incident perpendicularly to the grating direction. Several modes were observed from the spectra. At 66°C, a red shift of a dip at about 850 nm by 2 nm was obtained at an incident angle of 15°. Calculations confirmed that the observed modes belong to the (−1), (2), (−2) and (3) surface plasmon modes from the Ag and BST interfaces and localized mode; the red shift by thermal tuning is also confirmed. The results indicate the feasibility of active modulation in surface plasmon resonance in solid-state structures.     

A detailed study of metallic surface-relief grating

This paper presents a more detailed interaction of an electromagnetics light with a metallic surface-relief subwavelength grating utilizing the rigorous coupled-wave analysis. The focus of this work is the accurate modeling of undetermined aspects of diffraction patterns produced by binary metallic grating structures, specially gold grating. First-order diffraction efficiency for rectangular-groove gold grating with equal groove and ridge widths are presented for various wavelengths as a function of period, groove depth, polarization and angle of incidence. We also studied diffraction efficiency of both of TE and TM polarization modes against increasing of incident angle as well as TE polarization against increment of grating period. As a result, very low reflectivity at zero-order was found out for TE and TM polarizations at the pitch of Λ = 2λ. Having been studied diffraction efficiency of metallic surface-relief gratings, we also examined polarization-dependent efficiency of diffraction orders, for different groove depths. Simulation results have been completely presented.     

Corrugated neat thin-film conjugated polymer distributed-feedback lasers

Wave-guided thin-film distributed-feedback (DFB) polymer lasers are fabricated by spin coating a PPV-derived semiconducting polymer, thianthrene-DOO-PPV, onto oxidised silicon wafers with corrugated second-order periodic gratings. The gratings are written by reactive ion beam etching. Laser action is achieved by transverse pumping with picosecond laser pulses (wavelength 347.15 nm, duration 35 ps). The DFB-laser surface emission and edge emission are analysed. Outside the grating region the polymer film is used for comparative wave-guided travelling wave laser (amplified spontaneous emission (ASE)) studies. The pump pulse threshold energy density for wave-guided DFB-laser action (4–9 μJ cm^-2) is found to be approximately a factor of two lower than the threshold for wave-guided travelling wave laser action. The spectral width of the DFB laser (down to Δλ_DFB≈0.07 nm) is considerably narrower than that of the travelling wave laser (Δλ_TWL≈14 nm). The DFB-laser emission is highly linearly polarised transverse to the grating axis (TE mode). Only at high pump pulse energy densities does an additional weak TM mode build up. The surface-emitted DFB-laser radiation has a low divergence along the grating direction. For both the DFB lasers and the travelling wave lasers, gain saturation occurs at high excitation energy densities. Received: 7 January 2002 / Revised version: 15 February 2002 / Published online: 14 March 2002     

Wave propagation in uniaxial graded-index optical waveguides

Propagation of guided-modes in uniaxial optical waveguides is investigated. When the optical axis lies in the plane of the waveguide, a coupling between TE and TM modes takes place. Based on the coupled-mode theory, the propagating constants of the hybrid modes, the coupling coefficient and the interaction length are determined. A simple model is proposed to describe the guided mode behaviour. The results are illustrated for the case of Ti-diffused LiNbO₃ waveguide.     

Electromagnetic plane-wave scattering from a sectorial groove in a perfectly conducting plane

Scattering characteristics of plane waves by a sectorial groove in a perfectly conducting plane are investigated. Both the transverse magnetic (TM) and transverse electric (TE) polarizations of the incident wave are considered. Judicious use of the region-matching technique provides a rigorous series solution to the problem. The analyzed region is separated into two sub-regions by choosing a semi-circular auxiliary boundary. Thefield in each sub-region is expanded as a summationof proper wave functions with unknown coefficients. Enforcing the matching of conditions on the auxiliary boundary and of boundary condition on the circular-arc surface of the groove leads to a linear set of equations and the unknown coefficients are then determined. Numerical results demonstrate the influence of central angles of the sectorial groove on echo width, far-field pattern and near-field distribution. The presented geometry is easily applicable to the design and fabrication of a grating structure for optical switches and tunable filters.      

Ultracompact and fabrication-tolerant integrated polarization splitter

Design and fabrication of a 2×2 two-mode interference (TMI) coupler based on-chip polarization splitter is presented. By changing the angle between the access waveguides, one can tune the effective TMI length for the mode with less optical confinement (transverse magnetic, TM) to coincide with the target TMI length for a desired transmission of the mode with higher optical confinement (transverse electric, TE). The fabricated 0.94?μm long 2×2 TMI splits the input power into TM (bar) and TE (cross) outputs with splitting ratio over 15?dB over 50?nm bandwidth. Fabrication tolerance analysis shows that the device is tolerant to fabrication errors as large as 60?nm.     

对称单负介质包层平面波导的模式特征

系统研究了负μ材料(MNG)作为包层的对称三层平板波导的传输特性. 研究发现,这种波导既支持快波的传播,又支持TE₀,TE₁模式的慢波传输. 其模式特性不同于左手介质波导和传统介质波导,导模存在的模折射率范围要比它们的大. MNG波导的TE₀快波模缺失,且TE_m模(m>1)的传播常数大于TM_m模的传播常数. TE_m模具有双模特征,且与波导的结构参数密切相关,导致波导中的净能流出现负值. 关键词： 单负介质 平板波导 快波与慢波 传播常数