Leaky Mode Propagation Research Articles

Angular dependent light emission from planar waveguides

We have investigated the angular dependence of amplified spontaneous emission (ASE) and laser emission from an asymmetric and free-standing polymer thin films doped with rhodamine 6G, which is transversely pumped by a pulsed Nd:YAG laser. A semi-leaky waveguide or quasi-waveguide structure has been developed by spin coating technique. In these waveguides, the light was confined by the film/air-film/glass substrate interfaces. At the film/substrate interface, a portion of light will reflect back into the film (guided mode) and the remaining refracted to the substrate resulting in cutoff modes. A blue-shift in ASE has been observed when the pump power was increased from 8 to 20 mW allowing a limited range of tuning of emission wavelength. To study the directionality of the ASE from the waveguide, we have measured the output intensity and FWHM of emission spectra as a function of viewing angle (θ) from the plane parallel to film. From the detailed examination of the output emission spectra, as +θ increases from 0° there has been an initial decrease in output intensity, but at a particular angle ≈10° an increase in output intensity was observed. This additional peak in output intensity as +θ is a clear indication of coexistence of the cutoff mode. We also present a compact solid-state laser based on leaky mode propagation from the dye-doped polymer free-standing film (∼50 μm thickness) waveguide. The partial reflections from the broad lateral surfaces of the free-standing films provided the optical feedback for the laser emission with high directionality. For a pump power of 22 mW, an intense line with FWHM <0.2 nm was observed at 578 nm.

Application of conditional simulation of heterogeneous rock properties to seismic scattering and attenuation analysis in gas hydrate reservoirs

Abstract We present a conditional simulation algorithm to parameterize three-dimensional heterogeneities and construct heterogeneous petrophysical reservoir models. The models match the data at borehole locations, simulate heterogeneities at the same resolution as borehole logging data elsewhere in the model space, and simultaneously honor the correlations among multiple rock properties. The model provides a heterogeneous environment in which a variety of geophysical experiments can be simulated. This includes the estimation of petrophysical properties and the study of geophysical response to the heterogeneities. As an example, we model the elastic properties of a gas hydrate accumulation located at Mallik, Northwest Territories, Canada. The modeled properties include compressional and shear-wave velocities that primarily depend on the saturation of hydrate in the pore space of the subsurface lithologies. We introduce the conditional heterogeneous petrophysical models into a finite difference modeling program to study seismic scattering and attenuation due to multi-scale heterogeneity. Similarities between resonance scattering analysis of synthetic and field Vertical Seismic Profile data reveal heterogeneity with a horizontal-scale of approximately 50 m in the shallow part of the gas hydrate interval. A cross-borehole numerical experiment demonstrates that apparent seismic energy loss can occur in a pure elastic medium without any intrinsic attenuation of hydrate-bearing sediments. This apparent attenuation is largely attributed to attenuative leaky mode propagation of seismic waves through large-scale gas hydrate occurrence as well as scattering from patchy distribution of gas hydrate.

Distributed feedback leaky laser emission from dye doped gel-glass dispersed liquid crystal thin film patterned by soft lithography

Gel-glass dispersed liquid crystal (GDLC) thin films doped with organic laser dye Rhodamine 6G (R6G) were prepared via a sol–gel procedure of tetraethyl orthosilicate (TEOS) and ethyl triethoxisilane (ETES). As characterized by scanning electronic microscope (SEM), surface-relief structures were successfully patterned on lower refractive index GDLC thin films by soft lithographic technology, which support distributed feedback (DFB) laser emission based on leaky mode propagation. The performance of the DFB laser emission was investigated and the spectral narrowing of the emitted radiation and the fine structure pattern were found to be controlled by the doping concentration of liquid crystal (LC) 4-cyano-4′-pentylbiphenyl (5CB). We also showed the synchronous excitation of a DFB lasing with random lasing mediated by light scattering inside the same GDLC leaky waveguide.

Seismic modeling of multidimensional heterogeneity scales of Mallik gas hydrate reservoirs, Northwest Territories of Canada

In hydrate‐bearing sediments, the velocity and attenuation of compressional and shear waves depend primarily on the spatial distribution of hydrates in the pore space of the subsurface lithologies. Recent characterizations of gas hydrate accumulations based on seismic velocity and attenuation generally assume homogeneous sedimentary layers and neglect effects from large‐ and small‐scale heterogeneities of hydrate‐bearing sediments. We present an algorithm, based on stochastic medium theory, to construct heterogeneous multivariable models that mimic heterogeneities of hydrate‐bearing sediments at the level of detail provided by borehole logging data. Using this algorithm, we model some key petrophysical properties of gas hydrates within heterogeneous sediments near the Mallik well site, Northwest Territories, Canada. The modeled density, and P and S wave velocities used in combination with a modified Biot‐Gassmann theory provide a first‐order estimate of the in situ volume of gas hydrate near the Mallik 5L‐38 borehole. Our results suggest a range of 528 to 768 × 106 m3/km2 of natural gas trapped within hydrates, nearly an order of magnitude lower than earlier estimates which did not include effects of small‐scale heterogeneities. Further, the petrophysical models are combined with a 3‐D finite difference modeling algorithm to study seismic attenuation due to scattering and leaky mode propagation. Simulations of a near‐offset vertical seismic profile and cross‐borehole numerical surveys demonstrate that attenuation of seismic energy may not be directly related to the intrinsic attenuation of hydrate‐bearing sediments but, instead, may be largely attributed to scattering from small‐scale heterogeneities and highly attenuate leaky mode propagation of seismic waves through larger‐scale heterogeneities in sediments.

Laser emission from transversely pumped dye-doped free-standing polymer film

We present a compact solid-state laser based on leaky mode propagation from a dye-doped polymer free-standing film waveguide. The edge emitted spectrum clearly indicated the existence of periodic resonant modes. The reflections from the lateral faces of the free-standing film provided the optical feedback thus giving rise to a Fabry?Perot like optical cavity. This together with the guidance through the gain medium gave rise to intense narrow emission lines. For a pump energy of 1.82?mJ/pulse, an intense line with FWHM ~0.4?nm was observed at 576.5?nm.

Modal properties of surface and leaky waves propagating at arbitrary angles along a metal strip grating on a grounded slab

A full-wave analysis is presented of the dispersion properties of modes supported by a grounded dielectric slab periodically loaded with metal strips, which represents a canonical configuration employed in planar microwave antennas and arrays and in the realization of artificially hard and soft surfaces. Propagation of surface and leaky modes at arbitrary angles is considered here, without any restrictive assumption on the values of the involved physical and geometrical parameters. Spectral properties of modes are studied, by deriving generalized conditions for establishing the proper or improper nature of the spatial harmonics in the Floquet representation of the fields. The proposed approach, based on a full-wave moment-method discretization of the relevant electric-field integral equation in the spectral domain, is validated through comparisons with the available data in the literature. Novel results are presented which illustrate the continuous evolution of modes as a function of the propagation angle along the grating, both in surface and leaky propagation regimes.

Design of Planar Optic Sensors for Hydrocarbon Detection

A realistic design of evanescent field optical sensors, constituted by three different kinds of planar waveguides covered by a sensing polymeric overlay, is performed. More precisely, the slab, the embedded strip and the ridge waveguides are considered. The sensor operation is simulated, in both the cases of lossy guided and leaky mode propagation, via a home made computer code. The optimal waveguide transverse section and length are identified, the advantages and drawbacks are shown. The ridge waveguide sensor exhibits appreciable characteristics: for a concentration Cw = 200 ppm of toluene in water, the absorbance pertaining to a device L = 2.6 cm long and for the guided quasi-TE00 mode is A ≅ 5, while it is A ≅ 0.054 for a device long L ≅ 24.1 μm and the leaky quasi-TE10 mode. The simulation results suggest that a selective excitation of the suitable propagation mode can enhance the sensor performance.

Multiple defect characterization in finite-size waveguiding photonic bandgap structures

A powerful and efficient model recently proposed by the authors based on the leaky mode propagation method is used to characterize photonic bandgap structures incorporating multiple defects, having arbitrary shape and geometrical parameter values. The importance of the defect-mode characterization in photonic bandgap materials is due to the intensive use of defects for light localization to design very promising optical devices. This paper provides a new, efficient method to model defects in waveguiding, finite-size photonic bandgap devices and analytical and closed-form expressions for the reflection and transmission coefficients and out-of-plane losses,which is very useful and easily implemented under any operating conditions. Moreover, the method has been applied to examine the capabilities of waveguiding photonic bandgap devices in dense wavelength division multiplexing filtering applications. Therefore, the design of two optical filters for such applications has been carried out and optimal design rules have been drawn using the new model.

Modelling of photonic bandgap devices by the leaky mode propagation method

AbstractMain modelling approaches used for investigating the Photonic bandgap (PBG) devices are reviewed. In particular, the model based on Leaky Mode Propagation (LMP) method is described.A complete analysis of the propagation characteristics, including the determination of modal propagation constants, electromagnetic field harmonics and total field distribution, transmission and reflection coefficients, total forward and backward power flow in the structure, guided and radiated power, and total losses, can be carried out by a computer program based on the LMP approach.The numerical results have been validated by comparisons with those obtained by using other more complex and expensive models.The new model shows some significant advantages in terms of very low computational time, absence of any a priori theoretical assumptions and approximations, capability of simulating the actual physical behaviour of the device and fast determination of the bandgap position.Copyright © 2003 John Wiley & Sons, Ltd.

Analysis of the propagation of leaky magnetostatic modes in normally magnetized microstrip and slot lines

The propagation of leaky forward magnetostatic (MS) volume waves along ferrite-loaded microstrip and slot lines is analyzed. This phenomenon is studied by means of a numerical approach based on the residue calculus technique because of its good numerical convergence and stability. The proposed method allows for a quick and accurate computation of the phase and attenuation constants of the leaky MS modes. A comparative analysis between both microstrip lines and slot lines is carried out, and some new physical effects, such as MS resonances in the radiation loss, are reported. The advantages of the proposed method of analysis over other numerical methods, such as Galerkin's or moment methods, are also discussed.

Modeling of fully etched waveguiding photonic bandgap structures

Modeling of a 1-D finite-height, finite-length fully etched waveguiding photonic bandgap structures, based on the leaky mode propagation method, is proposed for the first time. So far only infinitely long gratings have been modeled by this approach. Finite extension structures having deep grooves, high refractive index contrast, and an arbitrary profile of the etched region can be modeled in very short computer time, starting from the infinitely-long photonic bandgap structure. Useful analytical and closed-form expressions for the reflection and transmission coefficients and out-of-plane losses are derived, which are valid for any operating conditions. One of the most important applications of the model relevant to 1-D photonic bandgap devices is to determine the losses occurring also in 2-D devices. Comparisons of results in terms of transmittance, losses, bandgap position and complex propagation constant with those obtained by the bi-directional mode expansion and propagation method and an exact vectorial method show an excellent agreement together with a strongly reduced CPU time for our method. Full investigations of three different etching profiles (i.e., rectangular, triangular and saw-tooth) are carried out. Particular attention is paid to the physical behavior around the first and second Bragg interaction regions. We demonstrate that the rectangular shape exhibits the highest losses and the widest bandgap, while the saw-tooth grating exhibits the lowest losses and the narrowest bandgap. Quick and accurate determination of the out-of-plane losses in a large variety of photonic bandgap devices is also demonstrated.

Modelling waveguiding photonic bandgap structuresby leakymode propagation method

A model of one-dimensional fully etched waveguiding photonic bandgap (FWPBG) structures, based on the leaky mode propagation (LMP) method, is proposed for the first time, to perform a complete analysis of the propagating characteristics including the radiation loss for a structure of finite extension.

Very fast and accurate modeling of multilayer waveguiding photonic bandgap structures

A model of one-dimensional (1-D) waveguiding photonic bandgap (PBG) structures, based on leaky mode propagation (LMP) method, is proposed for the first time. A complete analysis of the propagation characteristics, including the determination of modal propagation constants, electromagnetic field harmonics and total field distribution, transmission and reflection coefficients, total forward and backward power flow in the structure, guided and radiated power, and total losses, has been carried out for a finite extension configuration. The numerical results have been compared with those obtained by using other methods, showing a very good agreement together with some significant advantages in terms of very low computational time, absence of any a priori theoretical assumptions and approximations, capability of simulating the actual behavior of the device as a reflector, and fast determination of the bandgap position.

Cladding-mode-resonances in air-silica microstructure optical fibers

We present a comprehensive study of mode propagation in a range of different air-silica microstructured fibers. The inscription of both Bragg and long-period gratings (LPGs) into the photosensitive core region of microstructured air-silica fibers has allowed us to generate complex transmission spectra from a range of fibers with various fill fractions and with increasing air-clad hole diameters. The spectral characteristics for typical air-hole geometry's are explained qualitatively and modeled using beam propagation simulations, where the numerical modeling corroborates the experimental measurements. Specifically, the data reveal the propagation of higher order leaky modes in fibers with periodically spaced air-holes, and relatively small air-fill fraction. And as the air-hole diameter increases, spectra show cladding modes defined solely by the inner air-clad region. We describe these measurements and corresponding simulations and discuss their implications for the understanding of such air-hole structures.

Optimal design of grating-assisted directional couplers

In this paper, a rigorous leaky mode propagation method has been used to investigate the influence of the grating period and grating index profile on the design of grating-assisted directional couplers (GADC's). A detailed explanation of resonance condition and radiation loss in terms of electromagnetic field contribution in the grating region as a function of the grating period and profile is given. Optimal design parameters hare been found for well-defined structures in order to achieve either minimum coupling length or maximum coupling efficiency. A very fast method to extract the resonance condition in any grating-assisted structure by using a sinusoidal profile is proposed. Numerical results are presented for both moderately and strongly asymmetric structures in terms of normalized propagation constant, mode radiation loss, coupling length and coupling efficiency. Comparisons with grating period and coupling length predictions obtained by other methods are also shown. The rectangular profile with optimized duty cycle has been demonstrated to be the best choice in order to minimize the GADC coupling length.

Leaky cladding mode propagation in long-period fiber grating devices

We investigate leaky-mode propagation of the cladding modes of an optical fiber through coupling with a long-period fiber grating. A one-dimensional ray propagation model is applied. Experimental measurements are compared to a transfer-matrix model to estimate the cladding mode losses. Losses are also measured using an all-fiber Mach-Zehnder mode interferometer. The measured losses are somewhat greater than predicted by the simple theory.

Modal and Focusing Properties of Plasma Based Waveguides for X‐Ray Beams

AbstractModal and focusing properties of the plasma based waveguide having a parabolic profile of the electron density are treated for x‐ray beams with the ray‐transfer and paraxial‐envelope equations. Conditions on the single mode, multimode and leaky mode propagation in straight and tapered plasma channels are evaluated. The near‐ and far‐field patterns of these modes are calculated. The main result is that the mode structure is guide length and wavelength dependent, resulting in the guide length and wavelength dependent conditions for the guiding and focusing. The modal analysis finds its application in the field of x‐ray lasers, extremly high harmonic generation and x‐ray beam focusing, in which it may be helpful to design guides for optimum beam propagation. Futhermore, the mode properties are extremly simple and provide an idealised model for the real plasma waveguides.

Nonperturbative calculation of bend loss for a pulse in a bent planar waveguide

Conformally transforming the scalar Helmholtz equation for a step-index planar waveguide with a constant bend radius and assuming a bend radius large in comparison to the core half-width yields a differential equation whose solutions can be written in terms of Airy functions. A correct expansion of the leaky mode field in terms of these Airy functions and matching the field and its derivative across boundaries yields an eigenvalue equation whose complex roots give the leaky mode propagation constant and bend loss directly. This allows a second-order Taylor series expansion for the bend loss as a function of wavelength over the spectrum of a pulse to be determined. A comparison between bend loss for a cw wave and a pulse with the same carrier frequency is made.

Comparison Between the Performance of Ti:LiNbO3 and H:LiNbO3 Rotated Optical Axis Waveguides - Summary

Guided and leaky mode propagation in three-layered and five-layered c-rotated anisotropic waveguides is examined. The considered dielectric tensor configurations are the polar, longitudinal and equatorial ones. The modal characteristics of titanium diffused lithium niobate (Ti:LiNbO3 ) and proton exchanged lithium niobate (H:LiNbO3 ) waveguides are compared. The experimental results for a three layered Y-cut Ti:LiNbO3 waveguide agree very well with the calculated ones.

On the nature of critical points in leakage regimes of a conductor-backed coplanar strip line

Leaky dominant mode propagation regimes of a conductor-backed coplanar strip line are rigorously analyzed using the concept of critical or equilibrium points from catastrophe and bifurcation theories, in conjunction with a full-wave integral equation solution. The existence of nondegenerate or Morse critical points (MCPs) and degenerate or fold (turning) critical points (FPs) in coupling and leakage regions are associated with the occurrence of improper real and complex (leaky) solutions. The locations and types of critical points determine the stability and instability of the transmission line system with respect to small changes in geometrical parameters. The dispersion behavior of improper real and complex (leaky) solutions are efficiently reproduced in the local neighborhood of MCPs and FPs using a Taylor series expansion about those points. The qualitative and quantitative dynamic behavior of the transmission line modes can be investigated by examining the evolution of nondegenerate and degenerate points versus some structural parameter, such as strip width. The proposed analysis enables the prediction of bifurcation situations and the existence of improper real and complex solutions and gives a complete description of the system's structural behavior.