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.     

一种新型混合双包层光子晶体光纤的色散特性研究

以多极法理论为基础,设计了一种混合双包层结构的光子晶体光纤.通过改变其五层空气孔的四个结构参数（内层空气孔直径、外层空气孔直径、六边形孔间距和八边形孔间距）,理论上实现了色散绝对值在144—20 μm的波段内变化仅为125 ps·km^-1·nm^-1的平坦色散特性.在此情况下对其损耗进行了数值模拟,使所设计的光纤在144—20 μm的宽波段范围内具有小于0005 dB/km的低限制损耗特性. 关键词： 光子晶体光纤 多极法 平坦色散 限制损耗     

Design of double cladding dispersion flattened photonic crystal fiber with deformation insensitive outer cladding air-holes

A design of double cladding dispersion flattened photonic crystal fiber (DF-PCF) is proposed. To employ traditional stack and draw technology, the cladding of the DF-PCF is consisted of triangular periodic air-holes with the same hole to hole pitch. Simulation results show that the small air-holes in the inner cladding are mainly for dispersion management. The large air-holes in the outer cladding are mainly used for light confinement and have little impact on the dispersion tailoring. Thus, the dispersion profile of the double cladding DF-PCFs is insensitive to the deformation of air-holes in the outer cladding. Considering that the larger air-holes are apt to deform in the drawing procedure, the characteristics mentioned above make the realization of DF-PCFs relative easy by employing conventional stack and draw technology and modest air-hole rings (less than 10 rings) in the cladding.     

Uniform silicon slow light waveguide

An uniform silicon waveguide is proposed featuring ultralow-dispersion slow light. The core of the waveguide consists of one silicon trip and two pairs of air/silicon strip and the cladding is composed of several alternative silicon and air strips, which form a transverse band gap to confine propagating light in the core. The waveguide has several nearly linear photonic bands in a large frequency range, which can support broadband slow modes with a group velocity of 0.03–0.08c and tolerable group velocity dispersion.     

Photonic-crystal fibers with a photonic band gap tunable within the range of 930–1030 nm

The physical principles of photonic-crystal fibers with a photonic band gap tunable in the visible and near-IR spectral ranges are demonstrated. Direct numerical integration of the Maxwell equations with the use of the finite-difference time-domain technique reveals the possibility of creating holey fibers with a photonic-crystal cladding whose photonic band gap lies within the frequency range characteristic of widespread solid-state femtosecond lasers. The fabrication of holey fibers with a pitch of the two-dimensional periodic structure of the cladding less than 500 nm allowed us to experimentally observe a photonic band gap in transmission spectra of holey fibers tunable within the range of 930–1030 nm. This photonic band gap is satisfactorily described within the framework of the proposed numerical approach based on the finite-difference time-domain method.     

Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals

The frequency bands for self-collimation at both TE and TM polarizations in square lattice annular photonic crystals are studied systematically by plane-wave expansion and finite difference time domain methods. By increasing the inner ring radius or reducing the outer ring radius, the self-collimation band will be moved to a lower frequency. Compared with the TM modes, TE ones have different frequency sensitivities to both the inner ring radius and outer ring radius tuning. Using these features, a polarization insensitive self-collimation waveguide in a high dielectric contrast system with bandwidth up to 102.9 nm is demonstrated as an example of the implementation of photonic integration circuits.     

Extremely large birefringence and shifting of zero dispersion wavelength of photonic crystal fibers

Three different types of photonic crystal fibers have been investigated which promise very large birefringence. The first type fiber is band gap guiding, the second index guiding, while the third type is index guiding with high refractive index circular and elliptical regions in the innermost ring. The birefringence, group velocity dispersion, modal effective index and mode field area of these fibers have been numerically estimated by employing finite difference time domain method. When elliptical regions are introduced in the first and second rings with the combination of small circular regions, each of these proposed fibers exhibits large birefringence with shifted zero dispersion point. Among these three different types of fibers, the band gap guiding photonic crystal fiber promises the largest birefringence (～5.45×10^?2) reported so far. The value of the birefringence and group velocity dispersion of these fibers can be controlled by controlling the hole pitch. Largest birefringence is achieved with a specific value of hole pitch.     

Variation of spontaneous emission in the opal stop-band with an enhanced refractive-index contrast

Photoluminescence spectra of an opal with an anatase layer grown on its inner surface were studied. Measurements were carried out with a high angular resolution at various pump power levels and detection angles. The intensity and probability of emission were found to acquire an anisotropy corresponding to the frequency and angular dispersion of the first opal photonic band gap. As the pump power increases, the suppression of spontaneous emission in the photonic band gap is shown to be replaced by its amplification. The amplification of spontaneous emission is tentatively assigned to the existence of localized defect optical modes in the photonic band gap.     

基于双芯光子晶体光纤的低非线性宽带色散补偿光纤的设计

采用矢量光束传输法数值模拟了基于模式耦合的双芯光子晶体光纤的色散和非线性与其结构的关系。结果表明:通过在包层中移除一层空气孔以形成外纤芯并调整内外纤芯之间的距离及包层空气孔的占空比,内外纤芯间的模式耦合可以在宽带范围内发生,导致产生大负色散。同时,由于光场分布在两个纤芯内,增大了模场面积,产生低非线性,可以实现低非线性宽带色散补偿。     

双芯复合格点光子晶体光纤的负色散特性

介绍了一种双芯复合格点负色散光子晶体光纤,其包层是由连续电介质纯硅背景上挖出的两种大小不同的空气孔构成,芯区是由掺锗的高折射率的材料构成。为了实现负色散,还移去了包层中的一圈空气孔。采用频域有限差分法对其负色散特性进行分析表明,通过调整空气孔间距和两种空气孔的尺寸,可以得到不同程度的宽带负色散。当内芯半径取0.95μm,孔间距取2.15μm,大空气孔直径取1.9μm,小空气孔直径取1.1μm时,可在1.55μm处实现宽带负色散,其半峰全宽超过了200 nm。这种光纤的包层中空气孔呈六边形分布,空气孔的尺寸均大于1μm,降低了制作的难度。这种光纤可以用于波分复用光纤通信系统中的宽带色散补偿。     

矩形晶格高偏振、低损耗铋锗镓光子晶体光纤的结构设计及性能分析

非对称结构光子晶体光纤应用广泛。其良好的偏振特性、灵活的色散调控能力以及低限制损耗品质,对于优化与改善偏振光纤器件、非线性光学光纤、光通信光纤、光纤传感器等性能发挥着关键的作用。选用高折射率铋锗镓激光玻璃为材料,设计了八边形阵列、矩形晶格排列的光子晶体光纤,纤芯缺陷区包层及外包层均为圆形空气孔。模拟实验数据显示,结构参数为M=0.5,0.6时,在波长为1.55 μm处的双折射系数分别为1.16×10?2和1.33×10?2;在近红外波段短波区,矩形晶格结构光子晶体光纤的色散范围分别在±30 ps·nm?1·km?1之间及?18～32 ps·nm?1·km?1之间。色散斜率较低,曲线具有零色散点,展现了良好的连续谱调控能力;在1.00～1.90 μm波段内,当M=0.5,0.6时,光纤限制损耗稳定在10?7～10?9 dB·km?1之间;在1.55 μm处,限制损耗测量值分别为2.32×10?7和1.62×10?8 dB·km?1。     

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.     

光子晶体光纤的导波模式与色散特性

利用有效折射率方法基于标量近似理论对光子晶体光纤的传播模式和色散特性进行了数值模 拟，发现通过调节光纤包层的空气填充率或包层空气穴节距及其有效芯径可以在很宽的波长 范围实现单模传播，可以设计零色散波长小于1.27μm的光子晶体光纤和在较宽的波段接近 于零色散的色散平坦光纤，以及具有较大的正常色散值的色散补偿光纤. 关键词： 光子晶体光纤 有效折射率 标量近似 导波模式     

Controlled light localization and nonlinear-optical interactions of ultrashort laser pulses in micro-and nanostructured fibers with a tunable photonic band gap

Physical principles behind the control of light localization and nonlinear-optical interactions in micro-and nanostructured fibers are demonstrated. Transmission measurements on the cladding of nanostructured fibers having a form of a two-dimensional periodic structure with a pitch less than 500 nm have revealed the existence of a photonic band gap tunable within the range from 930 to 1030 nm. The influence of the structure of the holey-fiber cladding on the effective area of the waveguide mode and the spectral broadening of Ti:sapphire and Cr:forsterite femtosecond laser pulses is experimentally studied. It is shown that the increase in the air-filling fraction of a holey-fiber cladding results in a considerable enhancement of spectral broadening of short laser pulses due to the increase in the light localization degree in the fiber core.     

Optical guided dispersions and subwavelength transmissions in dispersive plasmonic circular holes

The light transmission through a dispersive plasmonic circular hole is numerically investigated with an emphasis on its subwavelength guidance. For a better understanding of the effect of the hole diameter on the guided dispersion characteristics, the guided modes, including both the surface plasmon polariton mode and the circular waveguide mode, are studied for several hole diameters, especially when the metal cladding has a plasmonic frequency dependency. A brief comparison is also made with the guided dispersion characteristics of a dispersive plasmonic gap [K.Y. Kim, et al., Opt. Express 14, 320–330 (2006)], which is a planar version of the present structure, and a circular waveguide with perfect electric conductor cladding. Finally, the modal behaviour of the first three TM-like principal modes with varied hole diameters is examined for the same operating mode.     

Ultra-wideband single-polarization single-mode, high nonlinearity photonic crystal fiber

We report a novel design of photonic crystal fiber (PCF) with a rectangular array of four closely-spaced, highly elliptical air holes in the core region and a circular-air-hole cladding. The proposed PCF is able to support ultra-wideband single-polarization single-mode (SPSM) transmission from the visible band to the near infrared band. With the aid of the inner cladding formed by the central air holes, one polarization of the fundamental mode can be cut off at very short wavelengths and ultra-wideband SPSM propagation can be achieved. The inner cladding also suppresses the higher order modes and allows large air filling fraction in the outer cladding while the proposed fiber remains SPSM, which significantly reduces the mode effective area and the confinement loss. Our simulation results indicate that the proposed PCF has a 1540 nm SMSP range with <0.25 dB/km confinement loss and an effective area of 2.2 μm². Moreover, the group velocity dispersion (GVD) of the proposed PCF can also be tuned to be flat and near zero at the near infrared band (∼800 nm) by optimizing the outer cladding structure, potentially enabling many nonlinear applications.     

Special control of the cutoff frequencies in a 2D photonic crystal coupled-cavity waveguide

We show theoretically that the upper and lower cutoff frequencies of the guided band in a 2D photonic crystal coupled-cavity waveguide can be controlled independently or synchronously by changing two configuration parameters of the waveguide simultaneously. The independent control range for the lower and upper cutoff frequencies can be as large as 68.6% and 67.9% of photonic band gap, respectively. The two cutoff frequencies can also be tuned in the same direction over equal distances up to 25.7% of photonic band gap. These results offer an efficient way for designing the various dispersion relations for photonic crystal waveguides.     

等效折射率模型研究光子晶体光纤的色散特性

应用等效折射率模型对折射率导模光子晶体光纤的群速度色散特性进行了详细的讨论。由于光子晶体光纤由单一材料(SiO2)制成,光纤的波导色散决定了总色散,因此讨论中将群速度色散分解为波导色散和材料色散,研究了波导色散与光子晶体光纤的结构参量孔距∧、相对孔径f的关系。分析表明,在f一定的情况下,光子晶体光纤的波导色散与孔距∧的关系符合麦克斯韦方程的比例性质;而在孔距∧确定的情况下,光子晶体光纤的波导色散的零点、极小值点位置与f在所讨论的波长范围内存在线性关系。最后举例说明了通过调整光子晶体光纤的结构参量,可以灵活地设计其色散特性。     

Loss and dispersion tailoring in 1D photonics band gap Bragg reflection waveguides: finite chirped claddings as a design tool

We exploit a simple and accurate matrix method to analyze the effects of introducing a linear chirp either in thickness or in refractive index of the cladding layers on the propagation characteristics (loss and dispersion) of 1D photonic band gap planar Bragg reflection waveguides (BRWs). We show that an appropriate chirp in the otherwise periodic claddings of finite extent BRWs could be gainfully exploited to tailor its leakage loss and waveguide dispersion features. In particular, we theoretically demonstrate that for some reported sample BRWs, leakage loss and waveguide dispersion could be significantly reduced by a factor of 30–50 and by about two orders of magnitude, respectively as compared to un-chirped BRWs. Furthermore, we also show that in contrast to un-chirped BRWs, how chirped BRWs could be designed with attractive feature like much less number of cladding layers and nearly wavelength independent losses. Our analysis and proposal should serve as a useful design tool to tailor the propagation characteristics of BRWs.     

Influences of supercell termination and lateral row number on the determination of slow light properties of photonic crystal waveguides

We systematically analyze the effects of the use of an inaccurate supercell termination and an insufficient supercell size of plane-wave expansion method on the dispersion and the slow light properties of the photonic crystal waveguides. The inattentive use of supercells of photonic crystal waveguides appeared in the literature is found to be yielding errors in the dispersion and slow light characteristics of the fundamental guided mode of photonic crystal waveguides. In addition, extra modes appear in the photonic band gap of the photonic crystal waveguide due to inaccurate supercell termination. By examining the field distribution of the modes, the extra modes can be determined and removed from the band diagram. The dispersion, group index and bandwidth characteristics are observed to be less affecting from inaccurate supercell termination as the number of rows adjacent to the waveguide increases. Moreover, the dispersion and the group index-frequency curves of the fundamental guided mode of correctly terminated supercells are found to be converging as the lateral row number along the line-defect is increased.