Reflectivity properties of an anisotropic slab waveguide with isolated substrate

The scattering properties for both TE and TM modes of an abruptly ended two-layered slab waveguide with anisotropic core and isolated substrate are examined by an improved iteration technique, which is based on the integral equation method with accelerating parameters. The relative dielectric constants of the core for the three Cartesian directions are considered to be different, but cases with isotropic core are also considered. The electric field distribution on the terminal plane and the reflection coefficients of the dominant TE and TM guided modes, as well as the near-field distribution and the far-field radiation pattern, are computed, while numerical results are presented for several cases of the core anisotropy.     

Reflectivity properties of an abruptly ended asymmetrical slab waveguide for the case of transverse magnetic modes

We deal with the scattering phenomenon from an abruptly terminated asymmetrical slab waveguide for the case of transverse magnetic (TM) modes. The analysis uses both the integral equation method and the variational technique. The reflection coefficient of the dominant TM guided mode and the far-field radiation pattern are computed, and the discontinuity of the electric field distribution on the core-clad interface is exhibited. Numerical results are presented for several cases of abruptly ended waveguides, including the three-layer slab guide and the structure with variable profile of the refractive index.     

Scattering of the transverse magnetic modes from an abruptly ended strongly asymmetrical slab waveguide by an accelerated integral equation technique.

We study the problem of the scattering of the first TM guided mode from an abruptly ended strongly asymmetrical slab waveguide by an improved iteration technique, which is based on the integral equation method with "accelerating" parameters. We demonstrate that the values of these parameters are related to the variational principle, and we save approximately 1-2 iterations compared with the case in which these parameters are not employed. The tangential electric-field distribution on the terminal plane, the reflection coefficient of the first TM guided mode, and the far-field radiation pattern are computed. Furthermore, a simple technique based on the Aitken extrapolation procedure is employed for faster computation of the higher-order solutions of the reflection coefficient. Numerical results are presented for several cases of abruptly ended waveguides, including systems with variational profile, while special attention is given to the far-field radiation pattern rotation and its explanation.     

Analysis of mode scattering from an abruptly ended dielectric slab waveguide by an accelerated iteration technique

A new modification of the integral equation method using an iteration technique with "accelerating" parameters is presented to solve the problem of guided-mode scattering from an abruptly ended asymmetrical slab waveguide. The optimal choice of the parameters is shown to be closely connected with the variational principle. The electric-field distribution at the terminal plane, the reflection coefficient of the guided mode, and the far-field radiation pattern are computed. Numerical results are presented for several cases of abruptly ended waveguides, including the systems with constant and variable profiles of the refractive indices. The phenomenon of the radiation pattern rotation is examined in detail.     

Numerical simulation of an arbitrarily ended asymmetrical slab waveguide by guided-mode extracted integral equations

The scattering phenomenon from an arbitrary-shaped end of a asymmetrical slab waveguide for the cases of TE and TM guided modes is simulated by means of boundary integral equations that are called guided-mode extracted integral equations. The integral equations that we derive can be solved by the conventional boundary-element method. Numerical results are presented for problems of three-layer asymmetrical waveguides with tilted ends. The reflection coefficient, reflected and scattered powers, and radiation patterns are calculated numerically for the cases of incident TE and TM guided modes.     

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.     

Modeling and experimental observation of an on-chip two-dimensional far-field interference pattern

In this paper, we model and experimentally observe the far-field radiation produced by interfering beams propagating in two-dimensional (2D) slab waveguides. Using a transmission-line analogy, we compare the 2D propagation with standard three-dimensional (3D) far-field representations and derive the 2D conditions for using standard far-field approximations. Then we test our theoretical results by experimentally observing the 2D far-field pattern produced by a 1×3 multimode interference (MMI) coupler on a silicon nanomembrane. The MMI outputs are connected to a slab silicon waveguide, and the far field is observed at the edge of the silicon slab. This represents the observation of 2D far-field pattern produced by an array of on-chip radiators.     

Evanescent surface-wave modes in a slab with application to miniaturised waveguide components

Characteristics of surface-wave modes in a slab with either negative permittivity or negative permeability are considered. It is shown that this kind of slab is a monomode structure which supports TM mode when the permittivity is negative and TE mode when the permeability is negative. It is shown that tightly bound surface-wave modes exist, also backward waves, in a slab with small thickness. These surface-wave modes will certainly have applications in trying to miniaturise waveguide components in microwave techniques and in optics. As an example, characteristics for a planar plasma waveguide are given     

TM and TE propagating modes of photonic crystal waveguide based on honeycomb lattices

The waveguide based on the honeycomb photonic crystal has propagating modes for both the TE and TM polarizations. The group index-normalized frequency curves are U-shaped for the two polarizations. The average group index of the TE mode is approximately 3, while the average group index of the TM mode is over 10, which implies that the TM mode is a slow light mode. With the shift value 0 ≤ δx ≤ 0.025a, the group index is over 10 and the normalized delay-bandwidth product is from 0.316 to 0.349, which is ideal for the slow light mode of the TM polarization. In the group velocity dispersion of the waveguide, there is a very large "zero" dispersion region for both the TM and TE modes, which is far larger than that of other photonic crystal waveguides. The TM mode of this kind of waveguide structure is a slow light mode with wide bandwidth and a large "zero" dispersion region.     

A slab optical waveguide with negative effective thickness

Two new asymmetric slab optical waveguides with a left-handed media (LHM) cover or substrate are studied. The effective thickness is derived by using normalized waveguide parameters. An analytical method is then proposed to calculate the universal effective thickness. We show that negative effective thickness exists in the waveguide with a LHM substrate, unlike in conventional waveguide or other LHM waveguides studied previously. However, for the waveguide with a LHM substrate, the shape of high-order mode behaves like that of a traditional slab waveguide, and neither the fundamental mode nor the other higher order modes have the novel phenomena of negative effective thickness. Both TE and TM modes are discussed.     

Metal iris influence on guided-mode diffraction

The effects of the presence of metal irises on guided-mode propagation through a symmetrical three-layer slab waveguide are examined by using the integral equation method. The aperture electric field distribution is expressed in terms of a finite series of Chebyshev polynomials. The modal reflection and transmission coefficients, the near-field structure, and the far-field radiation pattern are calculated, while numerical results are presented for several iris apertures.     

Transverse electric modes in planar slot waveguides

Transverse electric (TE) modes in symmetrical planar slot waveguides are analytically solved, and a comprehensive knowledge about them is provided. It has been shown that there are four types of TE modes in planar slot waveguides just as the TM modes. Their field solutions, characteristic equations and cut-off conditions are derived. The cut-off conditions and the power confinement factors of the TE and TM modes are compared. It is demonstrated that there may be degeneration points between TE and TM modes. Because a three-dimensional waveguide has similar modal characteristics as its planar counterpart, our work presents a foundation of recognizing and utilizing the three-dimensional slot waveguides.     

包含左手介质的4层平板波导的转移矩阵和模式本征方程

研究了一个芯子层由左手介质构成、其他3层由普通介质构成的4层平板光波导系统。从波动方程出发,根据电磁场的边界条件,得到了TE波的转移矩阵和模式本征方程,并用图解法对这种左手介质4层平板波导中TE波的场分布分别进行了数值模拟。     

Excitation of waveguide modes in organic light-emitting diode structures by classical dipole oscillators

Analytical techniques known in the literature are used to (i) identify all the planar waveguide modes in four top-emitting organic light-emitting diode (OLED) structures over the visible spectrum, and (ii) compute both TM and TE power spectra for classically radiating dipoles in the emissive layers of these OLED structures. Peaks in the computed power spectra are identified with the waveguide modes in the OLED devices, and areas associated with these peaks are used to estimate the excitation probability of the waveguide modes. In cases where ambiguities arise because of overlapping peaks, it is shown that computed power spectra can be approximated as sums of Lorentzian line shapes. It is found that for all four structures, the dipoles couple almost 80% of their radiant energy into TM modes with only about 20% going into TE modes. Furthermore, except for a narrow spectral band, the excited TM modes are primarily short-range surface plasmon polaritons. Excitations in the narrow spectral band correspond to TM and TE Fabry-Perot microcavity modes. Finally, the analysis shows that, in the absence of grating couplers, only light in the microcavity modes escapes into the air cover.     

Polarization eccentricity of the transverse field for modes in chiral core planar waveguides.

The general solution for modes in an asymmetric planar waveguide with a homogeneous and isotropic chiral core is given in terms of a pair of parameters related to the eccentricity of the polarization ellipse for the transverse electric field. This formulation provides insight into the transition, with increasing chirality of the core, from TE/TM modes to right-handed and left-handed circular polarization modes. Mode polarization as a function of waveguide thickness and of frequency is discussed in detail. Beyond a mode-dependent maximum thickness (or frequency), the left-handed elliptical modes consist of a slow-wave component whose cutoff properties are examined. The limiting case of a symmetric waveguide is also discussed.     

Spinor–electron waveguided optics based on the Dirac equation

A preliminary quantum analysis, based on the Dirac equation, of the propagation of spinor–electron waves in electron waveguides is presented. The wave equations for spin-up (SU) and spin-down (SD) electron waves in electron guides are derived and their analogy with TE and TM light modes in dielectric guides is stressed. The spinor–electron waveguided propagation in a electron wave slab waveguide is solved exactly using the Dirac equation, that is, the exact amplitudes and dispersion equations of the spinor–electron waveguided modes are calculated. The main consequences related to the spinor modal structure are discussed: phase retardations (spin polarization), modal cutoff conditions and the non-relativistic limit.     

Single-scattering theory of light diffraction by a circular subwavelength aperture in a finitely conducting screen

A perturbation theory based on a single-scattering approximation is developed from the rigorous differential theory of diffraction in cylindrical coordinates. It results in analytical formulas in the inverse space for the field amplitudes providing results that are in quantitative agreement with the results of the rigorous method, in both the near- and far-field regions, when a proper correction to the incident field inside the aperture is made by using the renormalized Born approximation. When working in reflection by a screen having permittivity high in modulus, the method proposes an equivalence with the simple model consisting of the emission by a single magnetic dipole excited inside the pierced layer, emission that is then transferred back into the cladding following the Fresnel's coefficients of transmission from the layer into the cladding. The theory predicts a directivity of the radiation pattern that increases for smaller values of modulus of permittivity, both for dielectrics and metals, thus independently of the possibility of plasmon surface wave excitation along the interface. The theory can take into account such surface wave resonances, as well as the waveguide supported by a dielectric slab, but cannot implicitly recognize the modes carried out by the cylindrical waveguide corresponding to the aperture. This fact limits its domain of validity when used in transmission, although the far- and near-field maps can be reconstructed sufficiently well within a multiplicative factor corresponding to the enhanced transmission due to the excitation of these modes.     

Integrated optical polarization splitter based on photobleaching-induced birefringence in azo dye polymers

An integrated optical polarization splitter has been fabricated by utilizing the photobleaching-induced birefringence in an azo dye polymer. It consists of a Y-branch waveguide formed by the reactive ion etching with one of the two arms photobleached. The refractive index of the photobleached arm is decreased for the TE mode and increased for the TM mode. The performance of the splitter was measured as a function of the energy of the photobleaching beam and compared to a wave propagation simulation of the device. The measured cross talks are less than -28 dB for the TM mode and -24 dB for the TE mode at a wavelength of 1310 nm. The measured excess losses for the TE and TM modes, which measure the effect of the Y branch and the photobleaching, are 0.3 and 0.4 dB, respectively. The insertion loss was 5 dB, which includes the input fiber to waveguide coupling loss.     

Single-arm double-mode double-order planar waveguide interferometric sensor

A sensor is described for which interference measurements of the phase delay between two propagating modes of different orders in a slab thin-film waveguide are used as the sensing technique. The basic building block of the sensor is a polymer film doped with an indicator dye such as Bromocresol Purple. The modes of two orders such as TM(0) and TM(1) are simultaneously excited in the light-guiding film with a focusing optics and a prism coupler. The modes are decoupled from the film and recombined to produce an interference pattern in the face of an output optical fiber. The sensitivity of the sensor to the ambient temperature change is 1.5 degrees C, and the sensitivity to NH(3) is 200 parts in 10(6) for one full oscillation of the signal.