Individual Waveguides Research Articles

Interaction Between Negative and Positive Index Medium Waveguides

The coupling between negative and positive index medium waveguides is investigated theoretically in this paper. A coupled mode theory is developed for such a waveguide system and its validity is verified. Interesting phenomena in the coupled waveguides are demonstrated, which occur in the case when the negative index medium waveguide in isolation guides its mode backward. A new type of coupled mode solution that varies exponentially with the coupling length is found in the special case when the propagation constants of two individual waveguides are nearly the same. A coupler operating in this case is insensitive to the coupling length, and its coupling efficiency can reach 100% as long as the coupling length is long enough. However, when the propagation constants of the two individual waveguides differ greatly, the coupled mode solution is still a periodic function of the coupling length, but the coupled power is output backward. In addition, the modes in the composite waveguide system are also studied using the coupled mode theory, and their fundamental properties are revealed.

Evanescent coupling in arrays of type II femtosecond laser-written waveguides in bulk x-cut lithium niobate

We report on the first fabrication of evanescently coupled planar arrays of type II waveguides in x-cut lithium niobate (LiNbO3) by femtosecond laser inscription. A particular choice of writing parameters allows the evanescent field of the individual waveguide modes to extend significantly beyond the damage lines into the neighboring guides, thus realizing a coupling constant of 2.2 cm−1 at a wavelength of 633 nm.

Peculiar properties of photonic crystal binary waveguide arrays

We discuss the peculiar properties of binary waveguide arrays composed of identical photonic crystal waveguides with nonuniform spacing. Coupled-mode theory is used in order to demonstrate that, as a result of the excitation of the individual waveguides's modes, two different array modes characterized by opposite transverse velocity can propagate. Approximated expressions for the evaluation of the diffraction curves and the percentage of energy carried by each array mode are calculated and tested through numerical examples.

Tight-Binding Theory for Coupling Asymmetric Photonic Crystal Waveguides

Tight-Binding Theory for Coupling Asymmetric Photonic Crystal Waveguides Chih-Hsien Huang and Wen-Feng Hsieh Department of Photonics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. Szu-Cheng Cheng Department of Physics, Chinese Culture University, Taipei, Taiwan, R.O.C. (Received 21 August 2007) The physical properties of asymmetric photonic-crystal directional couplers are studied under the tight-binding model, which assumes that the eld distribution of photonic-crystal waveguides is localized around periodic defects. The couplings of nearby defects between two asymmetric waveguides cause two dispersion relations to split further whereas the couplings of nearby defects within an individual waveguide cause the sinusoidal modulations of the dispersion curves. The eld-envelope distributions of the coupler are expressed by using the eigenmodes of the tightbinding equations and are consistent with the comparing results from nite-di erence time-domain simulations. PACS numbers: 71.15.Ap, 42.70.Qs, 42.79.Gn, 42.82.Et

Two-dimensional coherent superposition of blue-shifted signals from an array of highly nonlinear waveguiding wires in a photonic-crystal fiber

Frequency-shifted dispersive optical waves generated as a result of soliton dynamics of 30-fs Ti: sapphire-laser pulses in an array of waveguiding wires, implemented on a platform of a photonic-crystal fiber (PCF), are shown to produce regular stable interference patterns with high visibility, indicating a high coherence of frequency-shifted fields. For a hexagonal array of waveguides built into a silica PCF, the field intensity at the main peak of a six-beam interference pattern was found to be a factor of 22 higher than the intensity of a frequency-shifted signal from an individual waveguide in the array and 3.7 times higher than the field intensity attainable through an incoherent superposition of the same fields.

Mode scalability in bent optical fibers

This paper introduces a simple, analytical method for generalizing the behavior of bent, weakly-guided fibers and waveguides. It begins with a comprehensive study of the modes of the bent step-index fiber, which is later extended to encompass a wide range of more complicated waveguide geometries. The analysis is based on the introduction of a scaling parameter, analogous to the V-number for straight step-index fibers, for the bend radius. When this parameter remains constant, waveguides of different bend radii, numerical apertures and wavelengths will all propagate identical mode field distributions, except scaled in size. This allows the behavior of individual waveguides to be broadly extended, and is especially useful for generalizing the results of numerical simulations. The technique is applied to the bent step-index fiber in this paper to arrive at simple analytical formulae for the propagation constant and mode area, which are valid well beyond the transition to whispering-gallery modes. Animations illustrating mode deformation with respect to bending and curves describing polarization decoupling are also presented, which encompass the entire family of weakly-guided, step-index fibers.

Supermode Si/III-V hybrid lasers, optical amplifiers and modulators: A proposal and analysis

We describe a hybrid laser structure which consists of an amplifying III-V waveguide proximity-coupled to a passive Si waveguide. By operating near the synchronism point (where the phase velocities of the individual waveguides are equal), we can cause the optical power to be confined to any of the two waveguides. This is accomplished by control of waveguides' geometry. In the portion of the supermode resonator where amplification takes place, the mode is confined nearly completely to III-V guide thus realizing a near maximal gain. Near the output facet, the mode power is confined to the Si waveguide thus optimizing the output coupling. This is to be contrasted with approaches which depend on evanescent field penetration into the III-V medium to obtain gain.

Three-dimensional analysis of scattering losses due to sidewall roughness in microphotonic waveguides

We present a three-dimensional (3-D) analysis of scattering losses due to sidewall roughness in rectangular dielectric waveguides valid for any refractive-index contrast and field polarization. The analysis is based on the volume current method and uses array factors to introduce significant mathematical simplifications to better understand the influence of individual waveguide parameters on scattering losses. We show that the typical two-dimensional (2-D) analyses can substantially overestimate scattering losses in small waveguides and that scattering losses exhibit considerable polarization dependence. We produce scattering-loss estimates for a wide variety of waveguides and provide guidelines for design of waveguide cross sections that are less sensitive to sidewall roughness.

Restricted homogeneous system of tunnel-coupled waveguides and Bragg diffraction of light in it

A system of tunnel-coupled straight waveguides is studied. The dependence of the number of modes in this system on the number N of waveguides, the distance between waveguides, and the number of modes in an individual waveguide is considered. It is shown that modes of the order m=N and N+1 in the system of coupled waveguides are Bragg modes, i.e., the angle between their propagation direction and the system axis is close to the Bragg angle. The effective refractive indices n* of these modes are different, i.e., the dependence n*(m) changes abruptly. It is found that radiation modes play an important role in the formation of Bragg modes if an individual waveguide of the system is single-mode and the distance between the waveguides is sufficiently large. It is shown that the angular excitation regions of guided and radiation modes of the system near Bragg angles are overlapped.

Numerical characterization of nanopillar photonic crystal waveguides and directional couplers

We numerically characterize a novel type of a photonic crystal waveguide, which consists of several rows of periodically arranged dielectric cylinders. In such a nanopillar photonic crystal waveguide, light confinement is due to the total internal reflection. A nanopillar waveguide is a multimode waveguide, where the number of modes is equal to the number of rows building the waveguide. The strong coupling between individual waveguides leads to the proposal of an ultrashort directional coupler based on nanopillar waveguides. We present a systematic analysis of the dispersion and transmission efficiency of nanopillar photonic crystal waveguides and directional couplers. Plane wave expansion and finite difference time domain methods were used to characterize numerically nanopillar photonic crystal structures both in two- and three-dimensional spaces.

Soft lithography molding of polymer integrated optical devices: Reduction of the background residue

Soft lithography molding is a promising technique for patterning polymer integrated optical devices, however the presence of a background residue has the potential to limit the usefulness of this technique. We present the soft lithography technique for fabricating polymer waveguides. Several effects of the background residue are investigated numerically, including the modal properties of an individual waveguide, the coupling ratio of a directional coupler, and the radiation loss in a waveguide bend. Experimentally, the residue is found to be reduced through dilution of the core polymer solution. We find that the force with which the soft mold is depressed on the substrate does not appreciably affect the waveguide thickness or the residue thickness. Optical microscope images show that the residue is thinnest next to the waveguide.

Chapter 11: The Heating and Current Drive Systems of the FTU

High-frequency wave systems with high-power density launching capability have been the preferred choice to heat the Frascati Tokamak Upgrade (FTU) because of physics arguments (electron heating at very high density) and space constraints from the compactness of the machine design (8-cm-wide port). They do include an 8-GHz lower hybrid current drive (LHCD) system, a 140-GHz electron cyclotron resonance heating (ECRH) system, and a 433-MHz ion Bernstein waves system (IBW). The technical aspects of these systems will be reviewed in this article. The main features of the design include the following: (a) a very compact conventional LHCD grill with a compact window to keep the vacuum on 48 (12 columns, 4 rows) individual waveguides allowing the maximum flexibility in spectra generation to be achieved; power handling up to [approximately equal to]10 kW/cm2 has been achieved, (b) ECRH launchers designed as a quasi-optical system (implementing ITER relevant solutions) retaining the maximum flexibility in the equatorial launcher (poloidal/toroidal steerability) to exploit a variety of scenarios, (c) a two-waveguides launching array making the IBW experiment on FTU unique. Other technical aspects (sources, transmission lines, etc.) are also reviewed. The development of a new ITER relevant lower hybrid launcher, the passive active multijunction, is described.

Ionospheric D region electron density profiles derived from the measured interference pattern of VLF waveguide modes

The altitude profile of electron density in the D region is determined using an array of GPS‐phase‐referenced VLF receivers, allowing for the simultaneous broadband (i.e., phase coherent) measurement of a 24.0 kHz signal at multiple sites ranging in propagation path length from 3060 to 3353 km. Measured data are compared with results of model calculations for four electron density profiles used in previous work, assuming a single density profile to be in effect along the entire signal path from transmitter to receiver. Interpolation between model profiles is used to find a new profile which best fits the data. Phase coherent measurements over a range of path lengths also allow for the identification of the parameters for individual waveguide modes. Measured mode parameters agree with model calculations, within the limitations imposed by the configuration of the present array. A methodology of analysis and the required set of measurements is described, which would allow the decomposition of a VLF signal into all of its constituent waveguide modes, and accurate measurement of the characteristic parameters of each mode, namely phase velocity, attenuation rate, amplitude, and phase.

Scattering matrix approach to large-scale photonic crystal circuits.

We propose a scattering matrix approach to the modeling of large-scale photonic crystal circuits and show that the transmission properties of complex circuits can be accurately calculated on the basis of scattering matrices of individual photonic crystal devices and waveguides that connect them. In addition, we show that functional devices such as waveguide bends generally exhibit a discontinuous frequency dependence in the phases associated with their complex reflection and transmission coefficients and emphasize its importance for the adequate modeling of photonic crystal circuits.

Electromagnetic particle-in-cell simulations of a lower hybrid grill

The coupling of lower hybrid waves to the plasma is a crucial issue for efficient current drive in tokamaks. In this work, the coupling problem is attacked with a new tool in this context: an electromagnetic particle-in-cell (PIC) code, XOOPIC (Verboncoeur J P et al 1995 Comp. Phys. Comm. 87 199). A model for a grill with 32 waveguides is constructed using perfectly conducting walls. The wave propagation in the waveguides and the coupling to plasma is followed. The wave–plasma interaction is studied and the evolution of the launched spectrum is resolved in the near-field of the grill. The reflection coefficients in the individual waveguides are determined.

Analysis of optical waveguide structures by use of a combined finite-difference/finite-difference time-domain method.

We present a method for full-wave characterization of optical waveguide structures. The method computes mode-propagation constants and cross-sectional field profiles from a straight forward discretization of Maxwell's equations. These modes are directly excited in a three-dimensional finite-difference time-domain simulation to obtain optical field transmission and reflection coefficients for arbitrary waveguide discontinuities. The implementation uses the perfectly-matched-layer technique to absorb both guided modes and radiated fields. A scattered-field formulation is also utilized to allow accurate determination of weak scattered-field strengths. Individual three-dimensional waveguide sections are cascaded by S-parameter analysis. A complete 10(4)-section Bragg resonator is successfully simulated with the method.

Non-evanescent adiabatic directional coupler

A directional coupling mechanism based on an adiabatic coupling between three optical modes is suggested. The optical power transfer between two waveguides which are far apart is mediated by adiabatic coupling between zero-order optical modes of the individual waveguides and a high-order intermediate mode. The analytical model for an adiabatic three-mode coupling based on a scalar wave equation is presented. The directional coupling via the adiabatic mode coupling between copropagating modes is described and compared with a nonadiabatic directional coupling assisted by periodic perturbation. It is shown that adiabatic directional coupling has much less sensitivity to the mode parameters and to the wavelength.

Performance of an array of circular waveguides with strip-loaded dielectric hard walls

An infinite planar periodic antenna array of radiating open-ended circular waveguides is considered. The conducting waveguide walls are covered with dielectric layers loaded with longitudinal conducting strips for providing the hard wall boundary condition. Analysis of the array is carried out by the mode-matching method. The waveguide modes involved in the method are calculated by using the asymptotic strip boundary condition. It is shown that they are split into an independent subsystem of TE modes for the whole cross section and two independent subsystems of TM modes: one is for the central region and another is for the layer region. The calculations show that the operation of the hard waveguides in an array with small element spacing is similar to that of the multimode smooth wall waveguides completely filled with dielectric. For large diameters and element spacing, the hard waveguides have significant advantages over the smooth ones. It is shown that unlike an individual hard waveguide, the aperture efficiency of such a waveguide in the array has a nonmonotonic dependence on the waveguide radius. The results characterizing the behavior of the aperture efficiency and cross-polarization level in a frequency band as well as the contribution of certain waveguide modes in the reflected power are presented and discussed. The examples of the element patterns corresponding to minimal cross polarization are also given.

Analysing distributed feedback waveguides

A novel method for analysing distributed feedback waveguides with arbitrary refractive index profiles is reported. The method considers a waveguide as a number of segments within which the reflection is weak, and thus the relevant transmission loss and multiple reflections can be neglected. By introducing a concept of reflective density formulas are derived for calculating the reflection and transmission coefficients and therefore the transfer matrix of an individual waveguide segment. The global reflection and transmission characteristics of the waveguide are then obtained by multiplying transfer matrices of all the waveguide segments together. The proposed method shows better accuracy than the coupled-mode method and requires less computation time than the effective-index method. The limitation of the coupled-mode method is shown both numerically and analytically for the first time and it is demonstrated that the coupled-mode method is only valid for analysing long Bragg gratings with particular initial phases.

Derivation of Coupling Coefficients of Modes in Slab Couplers: Ray Theory

From the reflection and transmission of light in coupled slabs, we derive the coupling coefficient of modes in coupled waveguides. The present result is found to be similar to that of the conventional coupled-mode theory which requires the evaluation of the overlap integral of modes in each individual waveguide. Our method is simple, especially for analyzing complicated coupled waveguides.