Gap solitons in a two-channel microresonator structure

We show that, when two channel waveguides are coupled by a sequence of periodically spaced microresonators, the group-velocity dispersion is low in the vicinity of the gap associated with the resonant frequency of the resonators. This low dispersion permits the excitation of a gap soliton with much lower energy than in a gap of similar width caused by Bragg reflection.     

Coupled mode analysis of in-plane channel drop filters with resonant mirrors

A channel drop filter system that consists of two waveguides and three cavities is studied. One cavity couples with both waveguides, while the other two work as resonant mirrors to reflect the selected channel back into the system. The operation of this configuration is analyzed, using coupled mode theory. The conditions to achieve 100% in-plane channel transfer are derived. A method to suppress the side lobes of reflection and backward drop is also proposed. The direct coupling between the cavities is not required. The analysis is verified by two-dimensional finite difference time domain simulations in 2D hexagonal photonic crystals.     

Modeling of grating assisted standing wave,microresonators for filter applications in integrated optics

A wide, multimode segment of a dielectric optical waveguide, enclosed by Bragg reflectors and evanescently coupled to adjacent port waveguides, can constitute the cavity in an integrated optical microresonator. It turns out that the device can be described adequately in terms of an approximate coupled mode theory model which involves only a few guided modes as basis fields. By reasoning along the coupled mode model, we motivate a simple design strategy for the resonator device. Rigorous two dimensional mode expansion simulations are applied to verify the predictions of the approximate model. The results exemplify the specific spectral response of the standing wave resonators. As refinements we discuss the single resonance of a device with nonsymmetrically detuned Bragg reflectors, and the cascading of two Fabry–Perot cavities, where the coupling across an intermediate shorter grating region establishes a power transfer characteristic that is suitable for an add-drop filter.     

Simplified universal dispersion curves for channel waveguides

Simplified universal dispersion curves for graded-index diffused channel waveguides have been obtained with the new normalized WKB equation using the effective index method. It is shown that, similarly to planar guides, the propagation constant of all the guided modes of a particular channel can be obtained by two parameters, called the normalized mode orders. The dispersion relations between the propagation constant and the normalized mode order of the channel have been obtained for a number of profile shapes and waveguide dimensions.     

Improved photonic crystal directional coupler with short length

We investigate a photonic crystal (PC) waveguide coupler which is formed by two closely spaced linear waveguides in a two-dimensional triangular lattice of air holes. Our study shows that shifting one row of the air holes between the waveguides affects the dispersion curves of the guided modes and if the triangular lattice of air holes between the waveguides is replaced by a rectangular lattice, this modification results in an ultra-short coupling structure with coupling length less than 3a, where a is the lattice constant. Also, we investigate the effect of changing the radii of air holes that are adjacent to or between the waveguides on the coupling length and show that increasing the radius of air holes between the waveguides decreases the coupling length. We analyze the output spectrum of an ultra-short channel drop filter designed based on this structure.     

Light guidance in a photonic bandgap slab waveguide consisting of two different Bragg reflectors

By means of a zigzag-wave model, we perform a comprehensive analysis of the guided modes of a photonic bandgap slab waveguide that consists of a low-index guiding layer placed between two different Bragg reflectors. We show that the guided modes of the waveguide operate inside the overlapped bandgaps of the two Bragg reflectors. We label each mode with three mode orders, which reflect the features of the mode-field distribution in the guiding layer and the two Bragg reflectors, respectively. We discuss in detail the transmission characteristics of the guided modes, including the dispersion curves, the cutoff conditions, and the confinement factors, and highlight the mode-selection characteristics of the waveguide. We also study the effects of truncating the Bragg reflectors by deriving an analytical expression to show the dependence of the leakage losses of the modes on the numbers of the periods in the truncated Bragg reflectors.     

Surface electromagnetic waves at the interface between a homogeneous medium and a system of coupled waveguides

An analysis is made of the experimental investigations of the surface waves existing at the interface between a homogeneous medium and a periodically stratified medium that represents a bounded system of coupled waveguides. It is shown that, in all cases of the observation of surface waves, the bounded system of coupled waveguides has its own spectrum of guided modes and a spectrum of leaky modes that become surface waves of the system. It is also demonstrated that a biosensor can successfully operate when two surface waves serve as leaky modes of a Bragg waveguide in which the periodic system of waveguides is used as a distributed Bragg mirror of this waveguide. A structure supporting surface waves is designed on the basis of ten pairs of Nb₂O₅-SiO₂ layers and implemented experimentally. The surface waves are detected with a K8 glass prism according to the Kretschmann scheme.     

A novel polarization channel drop filter based on two-dimensional photonic crystals

<正>A novel polarization channel drop filter(PCDF) based on two-dimensional(2D) photonic crystals(PCs) is presented.It consists of two line defect waveguides and two point defect micro-cavities.In the line-defect waveguides,the transverse-electric(TE) and transverse-magnetic(TM) polarization lights are guided using photonic band-gap and total internal reflection effect,respectively.The light at the resonant frequency for TE polarization can be transferred from one waveguide to the other using the proposed system.Compared with the existing four-port PCDF based on PCs,the three-port structure can realize a multi-channel wavelength system of PCDF more easily and can be an essential device in future polarization wavelength division multiplexing(PWDM) systems.     

Analysis of non-linear multilayer waveguides with Kerr-like permittivities

This paper presents a semi-analytical method for calculating the dispersion relationships for stationary non-linear TE waves guided by general multilayer waveguides with Kerr-like permittivities. The non-linear wave equations are solved rigorously for each layer, and the mode index and field distribution are systematically determined so as to satisfy the boundary conditions at all interfaces. To verify the validity of the present method, a non-linear graded-index waveguide is approximated by a number of step layers and the resultant multilayer waveguide is analysed numerically. The convergence properties of mode index and total power flow are presented, and these are compared with direct solutions of the non-linear wave equation by the numerical integration method. The dispersion relationships for a non-linear multiple-quantum-well waveguide have also been investigated under two simple permittivity models. The present method is useful for the analysis of non-linear graded-index waveguides in addition to non-linear multilayer waveguides such as the multiple-quantum-well structure.     

Supermode dispersion and waveguide-to-slot mode transition in arrays of silicon-on-insulator waveguides

In this Letter, we report group index measurements of the supermodes of an array of two strongly coupled silicon-on-insulator waveguides. We observe coupling-induced dispersion that is greater than the material and waveguide dispersion of the individual waveguides. We demonstrate that the system transforms from supporting the two supermodes associated with two coupled waveguides to the single mode of a slot waveguide within the investigated spectral range. During the cutoff of the antisymmetric supermode, an anti-crossing between the symmetric TM and antisymmetric TE supermodes has been observed.     

A search-and-track algorithm for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles

A search-and-track algorithm is proposed for controlling the number of guided modes of planar optical waveguides with arbitrary refractive index profiles. The algorithm starts with an initial guess point in the parameter space that supports a specific number of guided modes. Then, it searches for, and tracks, the boundaries of this space or another space supporting different number of modes. It does so by monitoring the sign of a unified cutoff dispersion function. The algorithm is applied to both symmetric and asymmetric silicon-based parabolic-index waveguides. It shows that unlike asymmetric waveguides, the single-mode condition of symmetric waveguides is controlled by TM-, as opposed to TE-, polarization. This abnormal polarization control is strongest for high index contrast waveguides of sub-micrometer core sizes. The results are verified by full-vectorial beam propagation method.     

Dispersion properties of planar Bragg waveguides

We reformulate the leaky mode condition of planar Bragg waveguides as two simple, separate conditions on the propagation constant; a phase match condition and a loss formula. These relations enable efficient numerical calculations of the mode properties. Furthermore, we use the phase match condition as a starting point to discuss the dispersion of waveguides with advanced cladding structures. In particular, we point out that chirped claddings, where the effective reflection point is dependent on frequency, do not give dispersion characteristics significantly different from metallic waveguides or waveguides with periodic claddings.     

Prediction and suppression of strong dispersive coupling in microracetrack channel drop filters

For a four-port microracetrack channel drop filter, unexpected transmission characteristics due to strong dispersive coupling are demonstrated by the light tunneling between the input-output waveguides and the resonator, where a large dropping transmission at off-resonance wavelengths is observed by finite-difference time-domain simulation. It causes a severe decline of the extinction ratio and finesse. An appropriate decrease of the coupling strength is found to suppress the dispersive coupling and greately increase the extinction ratio and finesse, a decreased coupling strength can be realized by the application of an asymmetrical coupling waveguide structure. In addition, the profile of the coupling dispersion in the transmission spectra can be predicted based on a coupled mode theory analysis of an equivalent system consisting of two coupling straight waveguides. The effects of structure parameters on the transmission spectra obtained by this method agree well with the numerical results. It is useful to avoid the strong dispersive coupling region in the filter design.     

Comparison of numerical methods for light propagating in fibers with high steps of refractive index

Fast development of complex structures like microstructural fibers, photonic nanowires or slot waveguides requires numerical tools to predict a light propagation. There are many works concerning weakly guided case, but the microstructural fibers need algorithm for a high step of the refractive index. In this paper, three approximate methods are compared. The comparison concerns a structure consisting of circular cores surrounded by cladding for different values of the refractive index steps. Application of these methods in chromatic dispersion case is also presented. It is shown that certain conditions prefer two dimensional scalar algorithms (based on approximated methods) than three dimensional ones. This allows us to implement more efficient and less complicated methods.     

可调谐集成光学Ti:LiNbO3光波导定向耦合滤波器

波分复用技术是当今光纤通信系统中的关键技术之一。具有增加光纤通信系统容量的巨大潜力,集成光学复用技术对于单模光纤通信系统特别重要本文给出了一种集成光学复用器件的设计和制作,这种集成光学滤波器是在之切LiNbO₃衬底上用非对称钛扩散条波导定向耦合器构成,它适于1.32μm和1.55μm波长耦合滤波。为了使单模光纤和条波导有效耦合,我们研制出了硅V型槽,并给出了一种光纤与波导的连接结构。提供了一种切实可行的途径。     

Polymer optical waveguide based on integrated optics

The fabrication and characterization of refractive index profiles of multimode mode polymer optical waveguides is reported. Effect of annealing temperature on guided losses of polymer (polystyrene) thin film optical waveguide is also presented. Efficient coupling over a 110 nm spectral bandwidth was experimentally demonstrated with a prism-coupler designed to match the dispersion of a particular waveguide.     

Nonreciprocal frequency doubling of electromagnetic waves through double resonance and Bragg reflection in photonic crystals

A computational study of the uni-directional second-harmonic generation in a one-dimensional dual photonic crystal structure made of GaAs, AlAs and SiO₂ with quadratic optical nonlinearity and material dispersion is presented. The computational approach uses a shooting method to solve nonlinear wave equations for coupled fundamental and second-harmonic fields and the invariant imbedding method to obtain the linear transmittance and group index spectra. The dual structure consists of two substructures, the conversion structure creating a strongly enhanced second-harmonic signal and the filter structure blocking the fundamental frequency field by Bragg reflection while permitting the passage of the second-harmonic field. The conversion structure is built with an elementary cell consisting of four sublayers whose thicknesses are systematically varied. Doubly resonant second-harmonic generation with very high conversion efficiency is achieved for light incident from the conversion structure side by choosing the geometrical parameters of the elementary cell optimally and controlling the band structure. A new mechanism to enhance second-harmonic generation by controlling the energy flow between the fundamental frequency and second-harmonic fields has also been found.     

All-optical generation of 40 Gb/s single sideband signals using a fiber Bragg grating

In this work, we demonstrate a reliable all-optical technique for performing optical double sideband (ODSB) to single sideband (OSSB) format conversion of a 40 Gb/s non-return-to-zero signal. It is based on the optimization of a detuned optical filter, which was implemented on a fiber Bragg grating (FBG) with a complex apodization profile. An OSSB signal with negligible distortion was obtained, as the FBG presented a nearly ideal frequency response. Higher tolerance to chromatic dispersion enabled by the OSSB signal in comparison to the ODSB signal was demonstrated on both simulation and experimental results.     

A novel wavelength dispersive device with a dispersive element based on staircase-like straight and parallel arrayed waveguides

We propose a new type of arrayed waveguide grating (AWG) multiplexer/demultiplexer based on modified group refractive index. This device is composed by an array of straight and parallel waveguides of equal length and each waveguide consist of two sections with different width. The length of the two sections are changed from a waveguide to the adjacent one following a linear dependence resulting in a wavelength dispersive waveguide array. An example of the device design for silicon-on-insulator (SOI) platform is provided and numerical simulations have been carried out for various arrayed waveguide parameters. We demonstrate that the group index modification can be used for tailoring device dispersion properties, and that it can also result in new dispersion characteristics predicted numerically not observed in conventional AWGs. Additional advantages are that the demultiplexer does not necessarily require bending waveguide sections as in a conventional AWG (de)multiplexers, and thus yields highly compact devices with potentially very low insertion loss. Channel spacing of 1 nm have been predicted for sub-micron waveguides sizes. In this paper it is also proposed a novel wavefront converter based on waveguide array lens-like element with waveguides broadened sections. Numerical results for different input/output geometries are analized.     

Second harmonic generation by modal phase matching involving optical and plasmonic modes

The feasibility of a modal phase matching scheme between optical modes and surface plasmonic modes is demonstrated: in fact, the high effective index of a plasmonic mode allows us to obtain phase matching even in semiconductors showing a large dispersion between fundamental and second harmonic wavelengths. We design a realistic device to obtain Type-II second harmonic generation in AlGaAs-based waveguides; whereas one of the two pumps is carried by a plasmonic mode, the generated second harmonic signal is guided inside the AlGaAs multilayer, and hence it is not hampered by high propagation losses.