Deep Waveguide Research Articles

Deep subsurface waveguides with circular cross section produced by femtosecond laser writing

A combination of low numerical aperture focusing optics, in order to minimize spherical aberration, and beam shaping with a slit has been used to produce waveguides in fused silica by femtosecond laser writing. Waveguides with circular cross section and low losses are produced over a large depth window (>7mm) without changing any experimental parameter. Diffraction induces beam divergence along the axis perpendicular to the slit, leading to a shift of the focal plane. The focal intensity distribution can be predicted by a hybrid model combining Gaussian beam propagation with imaging of the slit into the material.

Guided waves at subduction zones: dependencies on slab geometry, receiver locations and earthquake sources

SUMMARY We investigate the geometry of deep subduction zone waveguides (depth >100 km). The wavefield characteristics for up-dip profiles are described and compared with data recorded at the Chile–Peru subduction zone. Observed distorted P onsets at stations in northern Chile near 21°S can be matched by 2-D finite difference simulations of a thin low-velocity layer (LVL) atop the slab in an IASP91 velocity model. The replacement of the LVL by simple random velocity undulations in the slab in the same model cannot explain the observations. Varying slab geometries are investigated and the distribution of guided wave onsets originating in deep waveguides is predicted relative to the slab surface. Further, double couple source position and orientation is explored and found to be closely limited by the guided wave observations. Sources situated above the layer and at distances more than 2 layer widths below the subducted Moho are not suitable. For the remaining favourable source locations, a strong link between pulse shapes and fault plane dip angle is evident. We conclude that up-dip guided wave observations at subduction zones follow a simple pattern given by slab geometry and modified by source position. The resulting onsets are shaped by layer thickness and velocity contrast and further influenced by the shape of the slab surface.

Mean and variance of the 3-D field forward propagated through random internal waves in continuously stratified deep and shallow water ocean waveguides

A general modal solution for the mean and covariance of an acoustic field propagating through 3-D random inhomogeneities in an ocean waveguide [Ratilal and Makris, J. Acoust. Soc. Am. 114, 2428 (2003)] is applied to propagation through a general 3-D internal wave field. Our previous two-layer internal wave parameterization is extended to continuous stratification and applied in both continental shelf and deep ocean waveguides. Physical and statistical properties of the internal waves are modeled with the Garret-Munk and other theoretical and empirical formulations. The mean and variance of the forward field propagating through internal waves is expressed in terms of the stochastic moments of the medium’s scatter function density. This is formulated with the Rayleigh-Born approximation to Green’s theorem in terms of the medium’s compressibility and density fluctuations. In this way, the effect of both internal-wave sound speed and density variations on the forward propagated field are quantified. Density variations are shown to greatly affect high order modal propagation in some cases. Two-dimensional models of propagation through random internal wave fields are shown to become inaccurate after exceeding threshold ranges where 3-D scattering becomes important.

A dry electromigration process for fabricating deep optical channel waveguides on glass and their characterization

A dry electromigration technique was developed to fabricate deep multimode channel and planar waveguides on BK7 optical glass. In contrast to earlier ion exchange processes based on thermal diffusion, a relatively high electric field (∼440 V/mm) was applied on the glass to accelerate the field-driven ion exchange process by expeditiously replacing host sodium ions in the glass with silver ions. As a result, the process temperature is significantly reduced, leading to lower optical attenuation on the waveguides. Lowest optical loss was achieved on waveguides fabricated at 320 °C. The increase on the index of refraction for the planar waveguide was determined to be 0.076 using the prism coupling method. The optical loss for channel waveguides was measured using the edge coupling technique with a 0.6328 μm He–Ne laser. Loss of 2 dB/cm was obtained for channel waveguides of 25 μm in depth, relatively low for waveguides of such depth at red wavelength. The scanning electron microscope (SEM) with energy-dispersive X-ray (EDX) spectroscope was utilized to obtain the concentration profile of silver ions in the waveguide region. A modified Huggins–Sun model with Gladstone–Dale relation was employed to deduce the refractive index profile from the silver ion concentration profile. A nearly step-like profile was observed from every deep multimode waveguide fabricated.

Conductance quantization in deep mesa-etched gate-controlled ballistic electron waveguides

We present a theoretical study of the ballistic conductance in electron waveguides created by deep mesa etching from quantum-well structures with a two-dimensional electron gas (2DEG) in the well. The widths of the waveguides are controlled by gate bias voltages. We consider three different cases: the etched waveguide is completely covered by a gate [continuous gate (CG)], the gate is deposited on top of the waveguide [top gate (TG)], and when the gates are located on the etched side walls [side gate (SG)]. The number and periodicity of the quantized conductance steps, as well as the energy separation of the one-dimensional subbands near the Fermi level are determined as functions of the parameters of the device. The CG device provides a fairly periodic quantized conductance staircase. The highest subband separation is achieved for the TG device etched well below the 2DEG layer and for the SG device etched slightly below it.

Wave-theory modeling of oceanic T-phase coupling at continental margins and seamounts

The role of seismo-acoustic seabed scattering as a mechanism for coupling of seismic energy into oceanic teleseismic waves or T-phases is investigated using a new versatile modeling capability for seismo-acoustic propagation in laterally inhomogeneous or range-dependent ocean waveguides. The Virtual Source Approach (VISA) uses a local Rayleigh–Kirchhoff approximation to handle the transmission and reflection of plane waves at the vertical interfaces separating horizontally ocean stratified sectors. Combined with the wavenumber integration approach which inherently computes the plane-wave decomposition of the seismo-acoustic field in stratified fluid-elastic waveguides, this approach provides a robust approximation to the seismo-acoustic coupling phenomena in shallow and deep ocean waveguides. The VISA approach has been implemented in the OASES seismo-acoustic modeling framework and used to investigate the role of seismo-acoustic conversion and scattering by seabed topography and roughness in generating oceanic T-phases at continental margins and seamounts. It is demonstrated that the excitation of the oceanic T-phases can be explained by the coupling of crustal shear body-waves into seismic interface waves, or seabed Scholte waves, which then subsequently scatter into the waterborne modal spectrum. This wavenumber conversion mechanism implies that the excitation of the T-phases will be significantly stronger by earthquakes producing crustal SV-waves than those producing predominantly P-waves. This in turn suggests that earthquakes associated with dip-slip failure modes excite significantly stronger T-phases than buried explosive sources.

Analytic mean and variance of forward propagated field through random internal waves and subbottom anomalies with Rayleigh–Born scattering

The mean and variance of the field propagated through a waveguide containing random internal waves or subbottom anomalies is modeled using a modal solution [Ratilal and Makris, J. Acoust. Soc. Am. 114, 2428 (2003)] that analytically expresses the effects of dispersion, attenuation, and redistribution of modal energy due to multiple scattering in the forward direction. The scatter function of an elemental volume of inhomogeneity in density and compressibility is modeled using the Rayleigh–Born approximation. Simulations in both continental shelf and deep water waveguides quantitatively show how the relative magnitude of coherent versus incoherent intensity varies with range in typical internal wave fields and subbottom environments.

Spatial harmonics analysis of deep waveguide Bragg gratings

The spectral properties of a single-mode planar deep waveguide Bragg grating (DWBG) operating on the first diffraction order are investigated by a spatial harmonics theoretical approach. This analytical method allows us to evaluate the most important features of the propagating fields. In particular, the slowdown of the group electromagnetic propagation near the photonic band-edges is accurately modelled with a minimal computational effort, which makes this tool useful for preliminary analysis of periodic waveguides.

Proton-exchanged optical waveguides fabricated by glutaric acid

In this paper, we first report that a new proton source, glutaric acid, has been used to fabricate optical waveguides in Z-cut lithium niobate crystals. The relationship was experimentally established between proton-exchanged (PE) waveguide parameters and fabrication conditions. It is shown that this new organic acid can be used to obtain deep PE waveguides in fast diffusion speed ( 0.275 μm 2/ h at 221°C) and with low loss ( ∼0.2 dB/cm ). It provides an alternative approach for fabricating PE waveguides in lithium niobate substrate.

High-Q silicon micromachined cavity resonators at 30 GHz using the split-block technique

Bulk micromachining of silicon wafers is a promising technique for use in deep three-dimensional waveguide fabrication. Past efforts to realise a high-quality cavity resonator with such a procedure have resulted in lower than expected unloaded quality factors (Q0). A new design for micromachined cavities is presented, that is based upon the split-block technique used in traditional waveguides. Specifically, this design solves poor contact issues involved with the final stages of fabrication encountered in previous topologies of micromachined cavities. Measurement results of four resonant modes between 30 GHz and 52 GHz for a coaxial-fed micromachined cavity are presented. These are compared with simulated values from Ansoft's high frequency structure simulator (HFSS). A measured unloaded Q0 of 4550 for the dominant TE101 mode at 29.326 GHz compares very well with the simulated value of 4490.

Fabrication of a deep polyimide waveguide grating for wavelength selection

Abstract A deep polyimide waveguide grating with transmission of −21 dB is demonstrated. A simple lithography process is used to fabricate the raised waveguide, including a deeply corrugated holographic grating. To accurately control the grating period, a rotatable optical setup is used to adjust the interference angle for the holographic process. The corrugation fabricated holographically is 80 nm much deeper than that written directly by an electron beam. The waveguide is thus a promising low-cost wavelength selective device that can be applied to metro networks. The design principles of the optimum mode-matching condition and the efficient transmission for such a deep waveguide grating are also discussed in this paper.

Low-loss deep glass waveguides produced with dry silver electromigration process

We report an effective, simple dry silver electromigration technology designed to fabricate low-loss deep channel waveguides on a specially chosen BF450 glass substrate with refractive index of 1.472. The simplicity is achieved by using two stainless-steel electrodes to facilitate the electromigration process. In contrast to earlier ion exchange waveguides reported, a relatively high electric field of 545 V/mm was applied to the glass to speed up the migration and also to prevent silver ions driven into the glass from reducing into silver atoms, a major contributor to waveguide loss. The deep channel waveguides thus fabricated showed no discoloration or cracks, and attenuation losses of less than 0.1 dB/cm were measured using our 0.6328 /spl mu/m He-Ne laser edge-coupling setup. A scanning electron microscope equipped with an energy-dispersive X-ray (EDX) detector was adopted to obtain the concentration profile of silver ions distributed in the channel waveguide region after the exchange. The EDX measurements were then utilized along with the Gladstone-Dale relation to deduce the refractive index profile; a nearly step-like profile was deduced from every deep channel waveguide fabricated.

Analysis of deep waveguide gratings: an efficient cascading and doubling algorithm in the method of lines framework

In this work, a computationally fast, numerically stable, and memory-efficient cascading and doubling algorithm is proposed within the method of lines framework to model long planar waveguide gratings having thousands of periods in the propagation direction. This algorithm can model 2/sup n/ grating periods in n calculational steps and needs N/sup 2/ matrices for N sample points in the problem space. It can model periodic, quasi-periodic, symmetric, and asymmetric gratings efficiently. Different deep waveguide gratings are modeled using this scheme and results for the fundamental TE mode spectral reflectivity are compared with published results showing excellent agreement.

Time-reversal in a waveguide

Experimental evidence of time-reversal has been performed at an ultrasonic scale (1.5–3.5 MHz) in a 70 long cm, 1 cm deep waveguide. This laboratory experiment allow us to get rid of noise or ocean fluctuations classically observed. Spatial and temporal time-focusing are studied and interpreted by the method of images in a waveguide or matched-field theory. For a wide band source array, an algorithm based on time-reversal is presented to achieve depth and range shifting without any knowledge of the waveguide properties.

Fabrication of Optical Wave-Guides in Silica-on-Silicon by Nickel Electroplating and Conventional Reactive Ion Etching

A novel process for the fabrication of deep optical waveguides in silica-on-silicon for optical processing applications has been developed. It makes use of nickel electroplating to conform precisely e-beam written smooth curved structures and to use the deposited nickel to etch deeply (up to 8 µm) into silica layers. It is demonstrated that nickel plating offers substantial advantages in terms of resistance and resist mold fidelity than more conventional etch masks such as patterned metal layers. The etching process, that is based on conventional fluorine reactive ion etching, has been optimized by making use of a design of experiment technique, details of process optimization and comparative analysis of different etching mask performances are also given.

Performance comparison of finite-element approaches for electromagnetic waveguides

The accuracy of finite-element-method techniques used for waveguide modal analysis has usually been assessed by testing the precision of the propagation constant. As a consequence, no useful criteria have been proposed for checking the spatial distribution of the evaluated unknown field. To overcome this lack, two error figures have been introduced and applied to different finite-element-method formulations. In particular, the following approaches have been compared: the one based on the transverse magnetic field, those based on the so-called edge elements, and a new one presented by the authors. The new approach, obtained by simply operating on the matrices of the original node-based formulation, directly solves for the propagation constant at a given frequency, preserves the matrix sparsity, and directly evaluates all of the unknown magnetic field components. Results demonstrate the applicability of the proposed approach and the usefulness of the introduced figures for a deep waveguide analysis.

Vibrating object sound field within a closed water area

Using the methods of boundary integral equations, the radiating object’s field within the closed water area is defined. A Green’s function for the closed water area with different boundary impedances is built. The sound-pressure field around the object is calculated on the basis of predicted (already measured) discrete pressure levels on the object’s surface that is irritated by the a priori unknown inner vibration sources of various nature. The algorithm of computation is used to find out the potentials of a single (or double) layer at the separate points (spots) on the object surface on the basis of sound-pressure amplitude and relative phase measurements in these very points. The experimental data within the frequency range of 2–256 Hz corresponded well enough to the suggested theoretical model of the problem. The differences between calculated pressure amplitudes and measured ones did not exceed the value of 6 dB. The 128-channel phase measurements have been run within the narrow frequency band after the signals’ time processing. The phase shift at the separate points has been defined with respect to the reference hydrophone located at the bow side of the object. The methods of noisy object’s sound field prediction (recomputation) from the closed water area measurements to the open sea deep water waveguides’ conditions are suggested. The methods are based upon the modified reciprocity principle.

Passive fiber optic bus using bidirectional integrated optic bus access couplers

The feasibility of a passive fiber optic bus that uses bidirectional integrated optics bus access couplers is studied. The number of bus nodes can be increased when an optimized asymmetric bus access coupler is used instead of a symmetric one. A modified Ag-Na ion exchange process provides the possibility of manufacturing integrated optics asymmetric couplers for the bus. The process is suitable for the processing of integrated optics components that combine deep multimode waveguides with different core sizes on a single substrate. An access coupler is designed, modeled, and processed. The coupler is optimized for seven nodes; the asymmetry of the coupler is 5 dB.

Three-dimensional method for simulation of multimode interference couplers

A three-dimensional (3-D) method for modeling multimode interference devices based on a finite element formulation is presented as an alternative to models having one-dimensional cross-sections only. The method is tested for couplers with two different strongly confined waveguides structures. The results show that full treatment of two-dimensional cross-section is of special importance for design and simulation of waveguide devices for which the effective index approximation is no longer valid. For deep rib waveguide geometries, excess loss greater than 15 dB can be obtained if the 3-D method is not used in the design of the couplers.

Wave Propagation In Connected Waveguides Of Varying Cross-section

The spectral element method is extended to problems involving arbitrary non-uniform waveguides by introducing an approximate tapered element. The depth of the cross-section is assumed to vary linearly, thus allowing an arbitrary variation to be modelled as a collection of piece-wise linear segments. The frequency dependent stiffness relation is established using the displacement fields of the uniform deep waveguide (both longitudinal and transverse) as the Ritz functions. The element is verified by comparison with a 2-D finite element solution.