Analysis of Bragg reflection waveguides with finite cladding: An accurate matrix method formulation

Ideal Bragg reflection waveguides (BRWs) are assumed to have an infinitely extended periodic cladding whereas in practice, the cladding of BRWs is of a finite extent. Bloch theorem is widely used to analyze the propagation characteristics of the BRWs. Since Bloch theorem is ideally valid only for an infinitely extended periodic medium, its application to study such BRWs is an approximation. We present a matrix method for a more accurate analysis of finite-clad BRWs and estimate the extent of errors involved in the values of the propagation constant obtained by the Bloch wave formalism. The proposed method can be used to obtain the mode effective indices as well as the radiation loss of a finite-clad BRW without resorting to solving any complex transcendental equation. In addition, since the method does not inherently assume a periodic cladding, it can also be used to analyze symmetric multi-channel BRWs, chirped structures and directional couplers.     

高斯脉冲在半导体光放大器中传输的解析表征

采用解析方法,在考虑材料损耗和色散的情况下,详细研究了无啁啾高斯脉冲和啁啾高斯脉冲在半导体光放大器中传输的物理过程,分析了强度增益、脉冲宽度和频率啁啾与线宽增强因子、色散系数、小信号增益特征参数及初始啁啾之间的关系。结果表明:当输入变换极限的高斯脉冲时,色散会引起增益压缩,脉冲展宽和频率啁啾;同样情况下,线宽增强因子越大,脉宽加宽越明显,输出脉冲啁啾越大,且随着线宽增强因子的增大,输出脉冲啁啾极大值向特征参数值较小的一边移动。当输入啁啾高斯脉冲时,初始脉冲啁啾越大,增益压缩越明显,啁啾系数为正时,脉冲单纯展宽,输出啁啾随特征参数的增大而逐渐减小,啁啾系数为负时,初始啁啾与群速度色散导致的啁啾相互竞争,致使脉冲先被压缩后被展宽;脉冲最窄处对应的特征参数随线宽增强因子的增大而先增大后减小,输出啁啾随特征参数的增大而经历振荡后趋于平稳。     

Large-core single-mode channel waveguide based on geometrically shaped leaky cladding

We propose a leaky channel waveguide structure for large-mode-area single-mode operation. The proposed structure is characterized by a uniform rectangular core and a specially designed cladding, through which all the confined modes are leaky. Single-mode operation is ensured by choosing the waveguide parameters properly so that the differential leakage loss between the first two modes is sufficiently high. A general power-law cladding geometry profile is considered, which is solved by the effective-index method in conjunction with the transfer-matrix-method to obtain the effective indices and leakage losses of the modes. We show that, with a suitable choice of cladding parameters, the waveguide can demonstrate extended single-mode operation in the wavelength range 750–1600 nm with a core area as large as 100 μm². Such a large confinement area for mode propagation can effectively suppress nonlinear optical effects. The waveguide is expected to find applications in the design of high-power lasers and amplifiers. PACS 42.82.-m; 42.82.Et; 42.79.Gn; 42.55.-f; 42.82.Bq     

Analysis of Planar Dielectric Waveguide with Mirror-Conjugate Chiralities in the Core and the Cladding

The propagation characteristics of a planar waveguide with mirror-conjugate chiralities filled in the core and the cladding (mirror-conjugate chirality waveguide) are presented. The effects of chirality on cutoff, dispersion and field distribution characteristics of the waveguide are studied. The results show that the waveguide with desired features can be made by appropriately selecting the chiralities of the core and the cladding, because the core chirality and cladding chirality have different influences on waveguide propagation characteristics.     

Propagation loss in a two-dimensional triangular photonic crystal waveguide

By means of a plane-wave-based transfer-matrix method, we present an extensive study of propagation loss in two-dimensional (2D) photonic crystal waveguides with limited cladding wall thickness. We examine the dependence of propagation loss on both the propagation direction and the waveguide wall thickness. It is shown that the propagation loss is a function of excitation frequency, wall thickness and waveguide outermost surface morphology. The conclusion that the propagation loss essentially decays exponentially with respect to the cladding wall thickness of a waveguide is valid only to a certain degree. In addition, we find that the propagation loss exhibit very complex behavior with respect to the excitation frequency.     

An analytical study of a doubly clad compressed ellipse optical waveguide

Using an analytical method based on boundary matching technique, the modal behavior and cutoff frequencies of a compressed ellipse doubly clad optical waveguide is studied. The proposed waveguide consists of a core region of higher refractive index with two cladding regions: one is inner cladding and the other is outer cladding. We take appropriate orthogonal coordinates for the proposed structure and impose the boundary conditions to obtain the characteristic equation. The effect of the width of inner cladding layer on the dispersion characteristic is observed. It is found that the width of inner cladding is able to tailor the dispersion characteristic and cutoff condition of the waveguide up to a certain limit.     

Analysis of Planar Dielectric Waveguide with Chiral Cladding

The propagation characteristics of a planar waveguide with chiral media filled in the cladding are presented. The effect of chirality on cutoff, dispersion and field distribution of the waveguide are studied. The results show that the cladding chirality may lead to a single-mode operation in the planar waveguide.     

A New Type of Terahertz Waveguides

A new type of THz waveguides, which employs a solid polyethylene rod as the core and polyethylene tubes in a periodic array of square lattice as the cladding, is proposed. Optical properties of this new THz waveguide, especially in dispersion, confinement loss and single mode property, are investigated in detail with the plane wave expansion method and the beam propagation method. Numerical results demonstrate that the new THz waveguide can reach not only low dispersion but also low confinement loss at single mode propagation. Therefore, the square lattice structure is a better candidate as THz waveguides than the triangular ones.     

Analysis of a Metal-Coated Planar Dielectric Waveguide with Chiral Cladding

The propagation characteristics of a metal-coated planar waveguide with chiral media filled in the cladding are presented. The effects of chirality on cutoff, dispersion characteristics and field distributions of the waveguide are studied. The results show that cladding chirality brings phase chopping to the transverse electric field component of those modes with odd mode numbers.     

Effect of plasma on modal dispersion characteristics of elliptical Bragg waveguide

In this paper, the dispersion characteristics of a plasma filled elliptical Bragg waveguide is investigated. The modal characteristic equations of the proposed Bragg waveguide for both ω > ω_p and ω < ω_p are derived. The effects of plasma frequency, numbers of cladding layers and the eccentricity of elliptical Bragg waveguide on the dispersion characteristics are studied. The analysis shows that the introduction of plasma in the proposed waveguide allows to control the propagation of modes.     

Analysis of Circular Dielectric Waveguide with Chiral Cladding

The propagation characteristics of a circular dielectric waveguide with chiral media filled in the cladding are investigated. The relation between the cutoff frequency and the chiral admittance, the dispersion curves for some modes with different angular mode numbers and the transverse distribution of fields are presented. Some new features different from the ordinary circular dielectric waveguide are resulted. The results show that the cladding chirality may lead to a single-mode operation in the circular dielectric waveguide.     

Design and characterization of arrayed waveguide gratings using ultra-low loss Si3N4 waveguides

Planar waveguides with ultra-low propagation loss are necessary for integrating optoelectronic systems that require long optical time delay or narrowband optical filters. In this paper, we review an ultra-low loss planar waveguide platform that uses thin (<150 nm) Si₃N₄ cores and thick (>8 μm) SiO₂ cladding layers. In particular, we discuss the performance of arrayed waveguide gratings (AWGs) fabricated with the platform. We propose the use of a practical design method that takes the statistical nature of worst-case crosstalk into account. We also demonstrate the measurement of amplitude and phase error distributions in an AWG using an optical backscatter reflectometer. We show that the waveguides have phase errors small enough to achieve AWG crosstalk below ?30 dB, while crosstalk below ?40 dB should also be possible with optimization of the component design.     

650 nm聚合物阵列波导光栅波分复用器设计

选择在可见光波段具有较低吸收损耗的聚甲基丙烯酸甲酯-甲基丙烯酸环氧丙酯 共聚物作为波导包层材料,使用双酚A型环氧树脂作为折射率调节剂,根据材料的折射率设计了单模波导截面尺寸;然后,采用束传播法优化设计出16信道阵列波导光栅(AWG)器件的版图结构。利用Optiwave软件模拟了AWG器件的光传输特性,结果显示,器件的信道间隔为0.845 01 nm,插入损耗小于14 dB,串扰小于-25 dB。     

A theoretical study of the modal dispersion characteristics of an annular circular waveguide with helical winding as the outer cladding

In this present communication, we introduce a new type of annular optical waveguide whose outer cladding is made of sheath helix. The sheath helix is made up of the dielectric material of lower refractive index than the core materials. Using vector approach, the general characteristic equation for the proposed waveguide has been derived. The modal dispersion characteristics for the lowest-order modes for different pitch angles are determined and analyzed. We observe that there is no effect of pitch angles on dispersion curve nearly up to 89° but drastic change is observed at 90° and above pitch angle. On comparison of helically inner cladded annular circular waveguide, we have found that there is not the existence of the negative dispersion curve and photonic band gap in the helically outer cladded annular circular waveguide. It means only the inner cladding is responsible for the negative dispersion as well as photonic band gap. There is no effect of the outer cladding.     

Existence of negative dispersion and band gap in a helically inner cladded annular circular waveguide

Helical waveguide, a different type of waveguide structure, has been considered for analysis of modal dispersion characteristics. This paper deals with the study of a new type of annular waveguide, in which the inner cladding is made by the helical windings i.e. sheath helix and the outer cladding is as usual simple step-index cladding. Using vector approach, the general characteristic equation for the proposed waveguide has been derived. The modal dispersion characteristics for the lowest order modes for different pitch angles and thickness are determined and analyzed. We have found that there is an existence of the negative dispersion curve in the helically inner cladded annular circular waveguide. It means that the inner cladding is responsible for the negative dispersion which is generally obtained in a photonic band gap.     

Influence of the initial chirp on the supercontinuum generation in silicon-on-insulator waveguide

We propose a practical method to broaden the bandwidth of supercontinuum generated in silicon-on-insulator (SOI) waveguide by controlling the initial chirp of inputting femtosecond pulses, which has the main impact on the initial stage of the spectral broadening caused by the self-phase modulation (SPM) effect. The numerical results show that the bandwidth and flatness of the supercontinuum generated in SOI waveguide are sensitive to the initial chirp of inputting femtosecond pulses, the supercontinuum bandwidth can be remarkably enhanced by inputting positive chirp femtosecond pulses with a decreased propagation distance required by soliton fission, and the maximum bandwidth of supercontinuum can be increased to 1500 nm.     

各向异性内包层对双包层光纤特性影响的分析

提出了单轴各向异性材料为内包层，且其主轴沿光纤轴线（z轴）方向的双包层光纤模型，推出了矢量模特征方程，重点研究了主轴折射率比kcl对波导色散的影响，针对从矢量模特征方程求解波导色散因表达式极为复杂而无法直接求解的困难，提出了一种求解波导色散的有效方法，研究结果发现可以在不改变光波导结构参量的条件下，通过改变kcl可有效地改变光纤的波导色散，也分析了kcl、几何参量S、光学参量R对低次模的传输和截止特性的影响。研究结果为获得更为理想的色散补偿、色散平坦光纤及设计新型无源光器件提供了重要的依据。     

The effect of an inhomogeneous cladding of a gradient optical waveguide on the mode and envelope characteristics of a soliton pulse

The nonlinear dynamics of a short pulse in a gradient waveguide layer is studied analytically taking into account the occurrence of a cladding layer and the longitudinal inhomogeneity of the two layers. The class of functions is presented in terms of which the transverse profiles of the refractive indices of both the gradient and the cladding layers can be represented, and, at the same time, the mode structure of the pulse can be explicitly described in terms of a hypergeometric equation. Expressions are presented that describe the variations of the propagation constant and transverse distribution of the wave field under the action of the longitudinal inhomogeneities of the gradient and cladding layers. It is shown that the envelope of the pulse satisfies the generalized nonlinear Schrödinger equation the coefficients of which are functions of the longitudinal coordinate and are expressed via the refractive indices of the waveguide layer and cladding.     

Anomalous dispersion and group velocity properties in subwavelength uniaxial metamaterial waveguide with metal cladding

We investigate propagation behavior of electromagnetic waves in a slab uniaxial metamaterial waveguide with metal cladding and discuss the dispersion relation, group velocity and energy flux distribution of transverse electric guided modes in two kinds of uniaxial metamaterial waveguides with different orientations of optical axis in detail. The numerical results show that there exist anomalous dispersion properties such as backward modes existing in low-frequency range, and the group velocity can be negative or approach zero. If the orientation of optical axis is selected properly, each guided mode has two dispersion curves—one is normal dispersion and another belongs to anomalous dispersion and shows a transition from a backward mode to a forward one with the angular frequency increasing. In addition, the condition of the existence of cutoff frequency is clarified. These properties may have potential applications in optical information storage, optical communication, integrated optics and nanophotonic devices.     

Multi-layer cladding leaky planar waveguide for high-power applications

We design a multi-layer cladding large-core planar waveguide that supports a single guided mode. The waveguide works on the principle of higher-order mode discrimination. The cladding of the waveguide is formed by alternate low- and high- index regions, which helps leaking out of higher-order modes while retaining the fundamental mode over the entire length of the waveguide. The structure is analyzed by the transfer-matrix method and the leakage losses of the modes have been calculated. We show that a waveguide formed in silica with numerical aperture 0.24 and core width 10 μm can be designed to exhibit single-mode operation at 1550-nm wavelength. Such a structure should find applications in high-power planar waveguide lasers and amplifiers.