Transmission performance of one waveguide and double micro-ring resonator using 3×3 optical fiber coupler

Abstract

This paper investigates theoretically the transmission characteristics of one waveguide and double micro-ring resonator using 3 × 3 optical fibre coupler. Our analytical solution of transmittance is suitable for either linearly distributed coupler or circularly symmetric distributed coupler. The all-optical analogue to electromagnetic inducted transparency spectrum of one waveguide and double micro-ring resonators can be controlled by changing the coupling strength between waveguide and micro-rings, the absorption coefficient around micro-rings, as well as the asymmetric coupling coefficients between non-adjacent waveguides. The curves show that the transitions of transmission spectra sensitively depend on asymmetric coupling coefficients.     

Propagation losses of copper-ion-exchanged channel optical waveguides

Abstract

We have measured the propagation losses of Cu—Na-ion-exchanged channel glass waveguides using both scattering and interferometric methods. In the first method, the waveguide was coated with a fluorescence film to enhance the scattered optical field along the channel waveguide which was then captured by a charge-coupled device camera. A straight line is adjusted to the intensity profile by the least-squares method, and the slope yields the attenuation coefficient. In the interferometric method, the temperature of the waveguides was changed and the intensity output was, measured. From contrast changes of waveguide's intensity output, the attenuation coefficient is calculated. Also, an analysis of the optical absorption of copper waveguides in the 200–1900 nm range to detect the copper oxidation state is presented.     

Lossy multilayer channel optical waveguides analyzed by the transmission line matrix method

We demonstrate that the three-dimensional vectorial transmission line matrix (TLM) method is applicable to the analysis of lossy multilayer optical waveguiding structures. Any lossy multilayer waveguide geometry, including sharp discontinuities in the transverse plane, can be treated taking into account the coupling between all optical field components. The complex propagation constants (propagation constants and the attenuation coefficients) for the fundamental TE-like and TM-like modes can be determined. These parameters of the fundamental TM-like mode of a typical lossy multilayer rib dielectric waveguide are obtained as functions of free-space wavelength. Calculation of the electric-field pattern is also included. Numerical comparisons with the argument principle method (for the case of lossy multilayer slab waveguides) and the spectral-index technique (for the case of lossy multilayer rib waveguides) are also included, and it is shown that the application of the TLM method to lossy multilayer optical waveguides is accurate.     

A Quick Method to Determine Two-mode Step-index Waveguide Parameters

Abstract

A new method is proposed to evaluate the characteristics of optical two-mode step-index waveguides using the values of the propagation constants. This method provides a higher accuracy of the determination of two-mode waveguide parameters than that obtained by the infinite square well approximation.     

Waveguide properties of optical structures fabricated by oxidation of porous silicon

Results of an investigation of the optical properties of channel waveguides fabricated by oxidation of porous silicon are described. The waveguide parameters are estimated and the existence of optical anisotropy is established. The effective refractive index of the dominant quasi-TM waveguide mode is measured. The results suggest that a buffer layer exists between the waveguide and the silicon substrate. It is hypothesized that a second refractive index peak exists within this layer. Pis’ma Zh. Tekh. Fiz. 23, 86–89 (May 26, 1997)     

Guiding mode expansion of a TE and TM transverse-mode integral equation for dielectric slab waveguides with an abrupt termination.

We propose a rigorous transverse-mode integral equation formulation for analyzing TE and TM electromagnetic radiation fields on the facet of dielectric slab waveguides with an abrupt termination in free space. Both exact waveguide guiding modes and discretized radiation modes are included in the kernels of the integral equation. To reduce the size of the matrix that approximates the exact integral equation, we expand the unknown field at the junctions in terms of guiding modes of a selected waveguide with sufficiently large normalized frequency and core thickness. By direct matrix inversion, we obtain numerical solutions of the scattered fields at the junctions. Our method can be used to study the field distribution as well as the energy reflection and transmission coefficients of dielectric waveguides with multiple step discontinuities.     

Asymptotic Coupling Coefficients of Well-separated Single-mode Optical Waveguides

Abstract

Simple general formulae for the coupling coefficients of the fundamental modes on well-separated parallel optical waveguides are derived. The calculation merely requires accurate knowledge of the propagation constants and core fields of the modes on the individual waveguides, while the far-from-core fields need not be known. Results for coupled circular fibres are identical with the asymptotic expansions of previously derived exact coupling coefficients. Analytical expressions for the coupling coefficients between the fundamental modes on identical weakly guiding channel waveguides are obtained.     

Propagation properties and dispersion characteristics of the tapered gap plasmonic waveguides

Abstract

In this study, we numerically analyse the propagation properties and dispersion characteristics of the tapered gap plasmonic waveguides (TGPWs). Using the finite element method, the waveguide parameters such as modal field distribution and complex propagation constant are calculated for different geometrical parameters over a wide spectral range. Moreover, using a kind of active medium with appropriate gain, the required gains for lossless propagation are obtained. Results show that the propagation properties and dispersion characteristics of the waveguide along with the value of required gain for achieving lossless propagation can be well controlled by adjusting the geometrical parameters of the waveguide. The simulation results indicate that the calculated gain values are obtainable using the existing semiconductor technology such as InGaAsP–InGaAlAs multi-quantum well and InAs/GaAs quantum dot active medium at the wavelength of 1550 nm. The strong mode confinement of the TGPWs can be used for achieving strong nonlinear effects. Furthermore, due to optical energy confinement in nanoscale, optical nanofocusing devices based on TGPWs are attainable. TGPWs can be utilized in the field of nanotechnology to fulfil the photonic devices integration.     

Mode Conversion by Photorefractive Damage in Planar Optical Waveguides: Application to Fully Confined Modes

Abstract

A theoretical analysis of mode conversion induced by photorefractive damage in optical waveguides is presented. The model applies to any geometry and uses the well known coupled-wave approach which has been extended to anisotropic media. The light-induced coupling coefficients have been expressed in terms of the photorefractive space charge field. The formulae have been, then, applied to calculate the initial conversion rate of a fully confined mode in a planar LiNbO₃ waveguide perpendicular to the c axis. The photorefractive field developed by illumination has been obtained under a short-time (initial) approximation, taking into account all transport processes. Some numerical estimates on mode conversion rates are also given and compared to available experimental data.     

Reproduction in free space of fields confined by 3-dimensional optical waveguides

Abstract

It is shown by using the Fresnel-Kirchhoff diffraction theory and the method of images that a scalar field confined by a 3-dimensional optical waveguide can be generated in free space by a suitable light source. In the method the boundaries of a waveguide are replaced by virtual sources. This allows one to present the wave guiding as the interference and diffraction of multiple light beams produced in free space by the guide equivalent source (Fresnel waveguide). Thus, the scalar optics of a 3-dimensional waveguide is presented as the free-space beam optics. The method is illustrated by construction of the Fresnel sources for the triangular, rectangular and hexagonal waveguides. The numerical examples demonstrate the diffraction-free and self-imaging propagation in the free-space of the eigenmodes of the Fresnel rectangular-waveguide.     

Extensions to a lens design program for the ray-optical design of waveguide lenses and prism couplers

Abstract

The design of integrated optical lens systems requires special software because such systems contain both three-dimensional and twodimensional elements (e.g. bulk prisms and planar waveguide lenses), and the waveguides are often anisotropic. We extended the popular optical computer-aided design program OSLO SIX so that it can evaluate and optimize systems that contain coupling prisms and planar waveguide lenses. We describe our software extensions and through examples we demonstrate their usage and benefits. We confirm our computations by measurement results. Finally, we present a ray-optical interpretation of transverse image line inclination and a method for its elimination.     

Quantization of coupled modes propagation in integrated optical waveguides

Abstract

A quantum mechanical analysis of the propagation of coupled modes in integrated optical waveguides is given. The modal orthonormalization property on a cross-section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry are taken into account to derive the quantum momentum operator and Heisenberg's equations giving a quantum-consistent formulation of the coupled mode propagation as a function of forward and backward creation and annihilation operators.     

Optical waveguides for imaging applications: Design by an inverse scattering approach

An inverse scattering theory is used to design optical waveguides capable of transmitting spatial images without degradation. The propagation characteristics of N modes each carrying a pixel of the image are specified by a transverse rational reflection coefficient. The Gel'fand-Levitan-Marchenko inverse scattering theory is used to obtain the unique solution of the permittivity profile of the waveguide from the reflection coefficient     

Quantum statistics and dynamics of nonlinear couplers with nonlinear exchange

Abstract

In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through non-degenerate optical parametric interaction. Main attention is paid to generation and transmission of non-classical light, based on a discussion of the squeezing phenomenon, the normalized second-order correlation function and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed with dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state |1〉 enters the first waveguide and the vacuume state |0〉 enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays a similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light.     

Ferroelectric liquid-crystal waveguide modulation based on a switchable uniaxial-uniaxial interface

Liquid crystals have effective electro-optic coefficients that are orders of magnitude larger than other integrated optical materials such as lithium niobate. However, previous studies of liquid-crystal waveguides have mainly focused on nematic liquid crystals, which exhibit impractically large scattering losses as waveguides. Studies of smectic liquid crystals and liquid crystals under strong confinement suggest the losses in these materials may be more manageable. In this study, the possibility of using ferroelectric liquid crystals in active waveguide modulators is explored through the analysis of several modulator configurations: a cutoff modulator, a deflection modulator, and an input coupler. As a way to study these structures, a mode-matching technique was developed to analyze the effects of a discontinuity in a uniaxial slab waveguide whose optic axis is in the plane of the waveguide. The results from the mode-matching technique were compared with those from simple bulk models. The analysis shows that ferroelectric liquid-crystal modulators have many desirable performance characteristics and could form the basis for practical waveguide modulators.     

Study of optical losses of Nd doped silicon rich silicon oxide for laser cavity

Planar and strip-loaded waveguides made of Nd³⁺-doped silicon rich silicon oxide (SRSO) have been fabricated by reactive magnetron sputtering and characterized, with special emphasis on the optical losses. The refractive index of Nd³⁺-doped SRSO layers was measured by both m-line method and reflectance spectroscopy. From these measurements, the Si volume fraction and also the Nd³⁺-doped SRSO index dispersion were deduced by using the Bruggeman model. At 1.06 μm, Nd³⁺-doped SRSO refractive index was equal to 1.543 corresponding to a Si volume fraction of 6.5%. The opto-geometrical parameters of waveguides have been studied in order to obtain single mode waveguides at 1.06 μm. The optical losses are measured as a function of wavelength and are found to be about 0.8 and 0.4 dB/cm at 1.06 and 1.55 μm, respectively. Measurements are confirmed by theoretical models showing that the losses are essentially attributed to surface scattering. From these optical loss values, a percentage value of the Nd active concentration superior of 14.5% was deduced to have a positive modal gain of waveguide.     

Copper-doped ion-exchanged waveguide characterization

Abstract

Copper-doped planar glass waveguides were prepared by the ion-exchange process. Refractive index and compositional profiles, obtained by m-line spectroscopy and secondary-ion mass spectrometry respectively were used to study the waveguide optical behaviour and the copper diffusion into the glass.     

Characteristic analysis of absorptive multiple-quantum-well optical waveguides

Abstract

By extending the transfer matrix technique from the real domain to the complex, the complex eigenvalue equation is presented for both transverse electric and transverse magnetic modes of absorptive multiple-quantumwell optical waveguides, and a computer program is developed to solve the eigenvalue equation in the complex plane. On the basis of the computed results, the effects of the structural parameters and the refractive index profile on the mode propagation and loss properties are analysed and discussed for In^x Ga^1?xAs/Al^yGa^1?yAs absorptive multiple-quantum-well optical waveguides. The results indicate that, if approximate guided structural parameters and an appropriate refractive index profile are selected, higher-order modes can be controlled and single-mode propagation can be realized in the multiple-quantum-well optical waveguide with lower mode loss.     

Detailed Study of Quasi-bound Modes in Leaky Structures

Abstract

The inconsistency of the progressive wave boundary conditions for the quasi-bound modes in open leaky structures is shown and a new boundary value formulation is developed. The results obtained are tested for leaky waveguides with delta function barriers for which a simple analytical characteristic equation is available. The method is applied for the determination of eigenvalues of prism-loaded multilayer waveguides. The influence of the prism coupler on the waveguide modes is investigated in detail for slab and four-layer waveguides. The method is compared with several approximate methods.