多波导定向耦合器耦合特性

利用拉普拉斯变换,将多波导定向耦合器的耦合模方程组变换为三对角线性方程组,并采用追赶法求出了该方程组的通解;进一步,给定初始条件,进行拉普拉斯变换反演,即可严格地求出该耦合模方程组的解。采用该方法研究了5波导定向耦合器光从一个波导入射和等光强从5个波导入射时的耦合特性,求出了耦合模方程组解的解析表达式,给出了每个波导中光功率变化规律曲线。利用该方法,可很方便地求出任意有限数目波导组成的定向耦合器在任意入射条件下耦合模方程组的解,因此对于多波导定向耦合器结构的合理设计,具有非常重要的意义。     

Packing density of conventional waveguides and photonic crystal waveguides

We compare coupling between parallel waveguides within one-dimensional photonic crystals and coupling between conventional waveguides. We consider the situation in which coupling between the waveguides is minimized, so that light in the waveguides propagates essentially independently. Subject to this condition, we compare the minimum mutual distance between conventional planar waveguides and waveguides in one-dimensional photonic crystals. We find that the packing densities of the conventional and periodic structures are comparable.     

多波导阵列耦合研究

提出了一种求解波导阵列耦合特性的方法.采用拉普拉斯变换,将同时考虑相邻和次相邻波导耦合作用的波导阵列耦合模方程组变为一个线性方程组,利用矩阵的LU分解法(将系数矩阵分解为单位下三角阵L与上三角阵U的乘积)求出该线性方程组的解.然后根据给定的初始条件进行拉普拉斯变换反演,求出耦合模方程组的解.采用该方法研究了五波导阵列,光从中间一个波导入射和从五个波导入射时的耦合特性,给出了每个波导中光功率变化规律曲线,并将所得结果与同样条件下仅考虑相邻波导耦合的结果做了比较.采用该方法可以求出任意数目波导组成的阵列,考虑任意波导之间耦合的耦合模方程组的解.     

Directional coupler using gap plasmon waveguides

Here, we demonstrate that efficient nano-optical couplers can be developed using closely spaced gap plasmon waveguides in the form of two parallel nano-sized rectangular slots in a thin metal film or membrane. Using the rigorous numerical finite-difference and finite element algorithms, we investigate the physical mechanisms of coupling between two neighboring gap plasmon waveguides and determine typical coupling lengths for different structural parameters of the coupler. Special attention is focused onto the analysis of the effect of such major coupler parameters, such as thickness of the metal film/membrane, slot width, and separation between the plasmonic waveguides. Detailed physical interpretation of the obtained unusual dependencies of the coupling length on slot width and film thickness is presented based upon the energy consideration. The obtained results will be important for the optimization and experimental development of plasmonic sub-wavelength compact directional couplers and other nano-optical devices for integrated nanophotonics.     

Bending Efficiency of Bent Multiple-Slot Waveguides

The bending efficiency of three-dimensional bent multiple-slot waveguides is studied by applying a combined method of effective-index and modified transfer-matrix methods. The effects of asymmetric structure, asymmetric slots, and asymmetric middle strips on the bending efficiency are investigated. We show that the bending efficiency can be improved by the use of asymmetric structures and asymmetric middle strips. The bending efficiency of different slot waveguides （up to quintuple-slot structure） is compared. It is revealed that although the single-slot waveguide in general provides the lowest bending loss for the same waveguide parameters, it is possible that the multiple-slot waveguide can present a lower bending loss than the single-slot one.     

Coupling constant of microcavity waveguides based on coupled mode theory

We analyze the microcavity waveguides and derive the coupling constant based on the coupled mode theory. The formula contains only two parameters with clear physical meanings, the quality factor of the cavity modes and the phase shift that the lightwave acquires when tunnelling between two cavities. It provides an easy way to express and modulate the properties of the waveguides. Our analytical results are supported by the simulations using the transfer matrix method.     

Modeling of InGaAsP–InP 1.55 μm lasers with integrated mode expanders using fiber-matched leaky waveguides

A new concept for InGaAsP–InP 1.55 μm lasers integrated with spot size converters using leaky waveguides is presented. The large fundamental mode size and the high discrimination of the higher order modes make ARROWs (Antiresonant Reflecting Optical Waveguides) and antiguided waveguides useful for fiber coupling functions. Three-dimensional (3-D) beam propagation method (BPM) results show that the devices have transformation losses lower than 0.22 dB. Fiber-coupling efficiencies of 60% are possible with standard cleaved single-mode fibers (SMF). The horizontal and vertical FWHM can be efficiently reduced to 9.70° (horizontal) and 17.80° (vertical). The fabrication of such devices avoids the growth of thick layers of quaternary material with a low Ga and As fraction, and simplifies the fabrication to one planar epitaxial growth step and one non-critical conventional etch. Received: 16 May 2001 / Published online: 30 October 2001     

Adiabatic three-waveguide directional coupler

We propose a three-waveguide directional coupler based on adiabatic evolution of a single normal mode of the system and analyze its switching properties using coupled mode theory. In our scheme the propagation coefficients of the waveguides are constant and the coupling coefficients are variable. This device works in the case that the propagation coefficients of the two outer waveguides are identical and that the coupling coefficients are designed to act in a counterintuitive order.     

Optical channel waveguides with trapezoidal-shaped cross sections in KTiOPO4 crystal fabricated by ion implantation

Optical channel waveguides were fabricated in KTiOPO₄ crystal by He⁺-ion implantation using photoresist masks with wedged-shaped cross sections. Semi-closed barrier walls with reduced refractive indices inside the crystal constructed the enclosed regions to be channel waveguides with trapezoidal-shaped cross sections. The m-line as well as end-fire coupling arrangements were performed to characterize the waveguides with light at wavelength of 632.8 nm. The propagation loss of the channel waveguides was determined to be as low as ∼2 dB/cm after simple post-irradiation thermal annealing treatment in air.     

Emissions of Photonic Crystal Waveguides with Discretely Modulated Surfaces

Transmission properties of photonic crystal （PC） waveguides with discretely modulated exit surfaces are investigated numerically using the finite-difference time-domain （FDTD） method. Unlike the case of periodically modulated surfaces, where the transmission beam tends to be a single and directional beam, when the exit surfaces are modulated only at several discrete points, the emission power tends to split into multiple and directional beams. We explain this phenomenon using a multiple point source interference model. Based on these results, we propose a 1-to-N beam splitter, and numerically realized high efficiency coupling between a PC sub-wavelength waveguide and three traditional dielectric waveguides with a total efficiency larger than 92%. This simple, easy fabrication, and controllable mechanism may find more potential applications in integrated optical circuits.     

Magneto-optical defects in two-dimensional photonic crystals

We analyze the properties of magneto-optical defect states in two-dimensional photonic crystals. With out-of-plane magnetization, the magneto-optical coupling splits doubly-degenerate TE states into two counter-rotating modes at different frequencies. The strength of magneto-optical coupling strongly depends on the spatial overlap of the cavity domain structures and the cross product of the modal fields. The transport property of the resultant nonreciprocal states is demonstrated in a junction circulator structure with a magneto-optical cavity coupled to three waveguides. By a proper matching of the magneto-optical frequency splitting with the cavity decay rate into the waveguide, ideal three-port circulator characteristics with complete isolation and transmission can be achieved, with an operational bandwidth proportional to the magneto-optical constant. The proposed optical circulator in a bismuth-iron-garnet/air photonic crystal is demonstrated with finite-difference time-domain calculations and is compared to an alternative implementation of silicon/air crystal infiltrated with a single bismuth-iron-garnet domain.     

Efficient omnidirectional couplers achieved by anisotropic photonic crystal waveguides

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated omnidirectional couplers in two-dimensional anisotropic PC structures. The anisotropic PC coupler composed of an anisotropic-dielectric cylinder in air is studied by solving Maxwell's equations using the plane wave expansion method and finite-difference time-domain method. The photonic band structures are found to exhibit absolute bandgaps for the square lattices. Numerical simulations show that the incident light-waves at both transverse electric and transverse magnetic modes have efficient coupling in anisotropic PC coupler with square lattices. The guided modes and coupling length are analyzed by considering various line defect anisotropic PC waveguides and interaction regions of couplers. Such a mechanism of omnidirectional coupling should open up a new application for designing components in photonic integrated circuits.     

Simple low-loss waveguide bends using ARROW effect

A new concept for reducing bend loss in dielectric planar waveguides is presented. It is based on the introduction of a set of antiresonant reflecting optical waveguides (ARROWs) on the outside of the bent core and defined in the same fabrication step as the main bend. It has been ascertained by simulation that the bending loss can be significantly reduced. The method is compatible with other bend-lossreduction strategies, as well as with different waveguiding structures, such as rib and buried waveguides and fibers.This revised version was published online in August 2005 with a corrected cover date.     

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.     

Geometry Parameter Optimization of Large Cross-Sectional S-Shaped Bent Rib Waveguides for Silicon Based Optical Switches

By using a genetic algorithm, geometry parameters of large cross-sectional S-bend rib waveguides are optimized aiming at the least total loss when the propagation loss is considered. Optimized results axe presented as an example of S-bend rib waveguides based on silicon-on-insulator （SOI） 4 × 4 optical switches. The value of 2 dB/cm is given to the propagation loss according to the experimental results. The simulation results indicate that the total loss drops from 1.0002rib down to 0.4375dB without considering a lateral offset. If the offset is adopted, the total loss reduces from 0.5463dB to 0.2365dB. In addition, the effect of the rib height ratio on the loss is analysed, and the optimal ratio is obtained to be 0.55.     

Er-Yb co-doped glass waveguide amplifiers using ion exchange and field-assisted annealing

Er³⁺-Yb³⁺ co-doped waveguide amplifiers fabricated using thermal two-step ion-exchange are demonstrated. K⁺-Na⁺ ion-exchange process was first carried out in pure KNO₃ molten bath, and then field-assisted annealing (FAA) was used to make the buried waveguides. The effective buried depth is estimated to be ∼3.4 μm for the buried FAA waveguides. With the use of cut-back method, the fiber-to-guide coupling loss of ∼4.38 dB, the waveguide loss of ∼2.27 dB/cm, and Er³⁺ absorption loss ∼5.7 dB were measured for a ∼1.24-cm-long waveguide. Peak relative gain of ∼7.0 dB is obtained for a ∼1.24-cm-long waveguide. The potential for the fabrication of compact optical amplifiers operating in the range of 1520-1580 nm is also demonstrated.     

Solutions of the full- and quasi-vector wave equations based on H-field for optical waveguides by using mapped Galerkin method

The mapped Galerkin method in solving the full-vector and quasi-vector wave equations in terms of transverse magnetic fields (H-formulation) for optical waveguides with step-index profiles is described. By transforming the whole x-y space onto a unit square and using two-dimensional Fourier series expansion, the modal distributions and propagation constants for optical waveguides are obtained in the absence of boundary truncation. Results for step-index circular fiber, buried rectangular waveguide, and optical rib waveguide are presented. Solutions are good agreed with exact solutions and numerical results by using vector nonlinear iterative method, Fourier operator transform method, and vector beam propagation method.     

Flexible Control of Light Propagation Using a Novel Photonic Crystal Hetero-Waveguide Based on Silicon-on-Insulator Slab

We demonstrate a photonic crystal hetero-waveguide based on silicon-on-insulator (SOI) slab, consisting of two serially connected width-reduced photonic crystal waveguides with different radii of the air holes adjacent to the waveguide. We show theoretically that the transmission window of the structure corresponds to the transmission range common to both waveguides and it is in inverse proportion to the discrepancy between the two waveguides. Also the group velocity of guided mode can be changed from low to high or high to low, depending on which port of the structure the signal is input from just in the same device, and the variation is proportional to the discrepancy between the two waveguides. Using this novel structure, we realize flexible control of transmission window and group velocity of guided mode simultaneously.     

Improved optimal variational method to analyze optical rib waveguides

We present an improved optimal variational method (Vopt) to overcome the assumption of field separability in the two orthogonal directions. The improved Vopt method is shown to give accurate results with less computational effort. The method is applied to rib waveguides and the results are compared with those obtained using the computationally intensive finite-element method.     

Design, Fabrication, and Measurement of Two-Dimensional Photonic Crystal Slab Waveguides

Two-dimensional photonic crystal slab waveguides on SOI wafer are designed and fabricated. Photonic band gap, band gap guided mode, and index guided mode are observed by measuring the transmission spectra. The experimental results are in good agreement with the theoretical ones.