Integrated liquid-crystal switch for both TE and TM modes: proposal and design

An integrated optical switch is proposed and designed based on a weak-anchoring liquid-crystal (LC) cell with a substrate integrating planar lightwave circuits. It consists of a polarization splitter, two switchable polarization converters and a polarization combiner. The polarization splitter/combiner is a directional coupler with an etched slot and filled-in LC covering layer. The switchable polarization converters are straight waveguides with a designed length and covering LC. The proposed configuration is superior to the existing integrated LC switches, as it works for both the TE and TM modes.     

Calculation of radiation modes by the Lanczos-Fourier expansion

For construction of the TE radiation modes of planar waveguides several methods are employed that are based on collocation techniques. The field representation in the core is based on the Lanczos-Fourier sinusoidal series. The numerical codes are very simple and give accurate results. The validity of these methods is checked for constant refractive-index profiles, while numerical results are also given for parabolic profiles. Furthermore, the validity of the orthogonality condition between the guided and the radiation modes is checked. These methods are demonstrated to be effective and can also be employed to study the TM case and waveguides of lossy media, as well as anisotropic and chiral structures.     

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.     

Modal behavior in single-mode slab waveguides consisting of inhomogeneous cores

We present an analytical method for TE and TM modes in weakly guiding inhomogeneous single-mode slab waveguides. Based on our results, the modal behavior or propagation constants depend on index profiles of the waveguides. It is important to know how the modal behavior depends on the index profile in single-mode waveguides, because it determines wave-front characteristics of propagating modes.     

Stable and accurate method for modal analysis of multilayer waveguides using a graph approach

A method for calculating the propagation constants of allowed guided and leaky modes in multilayer planar waveguides is presented. We develop a two-way graph model to describe the tangential fields propagating in the waveguides. According to the special structure of the graph model, it is convenient to employ a topology scheme to derive analytical and closed-form dispersion equations for TE and TM modes. By comparing the dispersion equations formulated by series-expansion methods, approximation methods, and transfer-matrix methods, we find that the use of these equations for finding the eigenmodes has some benefits. First, this method can be easily employed to solve eigenmodes accurately in numerical computation without using series truncation. Second, the dispersion equations are exact. Moreover, all the eigenmodes can be determined according to the formulas without losing roots or causing numerical instability even for a waveguide with thick layers.     

Reflectivity of buried slab waveguides

The scattering properties of an abruptly ended buried slab waveguide for both TE and TM modes are examined by an improved iteration technique that is based on the integral equation method with "accelerating" parameters. The waveguide is considered a symmetrical slab, for which the weakly guiding conditions are invalid, and it is embedded in a different dielectric material. The tangential electric field distribution on the terminal plane, the reflection coefficient of the first TE and TM guided modes, and the far-field radiation pattern are computed. Numerical results are presented for several ended waveguides, while special attention is given to the far-field radiation pattern rotation and the terminal field distributions.     

Characterization of a compact silicon-based slot-to-strip waveguide crossing

A compact crossing scheme for a silicon-based slot-to-strip (or vice versa) waveguide is proposed and analyzed by using a finite-difference time-domain method, where a strip–multimode waveguide (SMW) crossing is used at the center and two logarithmically tapered slot-to-strip mode converters are incorporated into the ports with slot waveguides. For the input ports with slot waveguides and output ports with strip waveguides, the guided modes are efficiently transformed through the mode converter, and then enter into the SMW, where the fields converge at the center of the intersection due to the self-imaging effect. Hence, the size of the input beam is much smaller than the width of the SMW at the crossing center, leading to significant reductions of both crosstalk and radiation loss. The numerical results show that a slot-to-strip waveguide crossing operating at a wavelength of 1.55?μm can be achieved with insertion loss, crosstalk, and reflection of 0.134/0.182, ?36.18/?38.6, and ?35.8/?42.02?dB for input ports with slot/strip waveguides, respectively.     

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.     

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.     

Measurement of the modal birefringence of single-mode K(+) ion-exchanged planar waveguides with polarimetric interferometry

The polarimetric interference pattern on the surface of single-mode planar waveguides made by potassium ion exchange in soda-lime glass substrates can be observed through a 45 degrees analyzer, which allows for the high-precision measurement of the modal birefringence of samples in a wide range of 0 to 5 x 10(-4). Using this method, believed to be new, we investigated the effects of exchange temperature and time on the modal birefringence of single-mode potassium ion-exchanged waveguides. The modal birefringence profile was achieved by measurement of the variation of the phase difference between the TE(0) and the TM(0) modes with hydrofluoric-acid-etching depth of the sample.     

Segmented multimode to dual port slot couplers as compact optical sensors with improved sensitivity

A segmented silicon based multimode to dual port slot structure on silicon-on-insulator platform is proposed which can be used as a refractive-index sensing device. The introduction of segmentation leads to tuning the effective index of the device which results in increasing compactness of the sensing device. Although the structure supporting TM mode is more compact than TE mode, but TE mode is considered here as vertical slots in the output section enhances optical signal in the slots for TE mode only. By considering dual output, the device length is reduced further as dual self-imaging length is less compared to single self-imaging distance for symmetrical multimode section input. The surface sensitivity of the structure has a typical value of～2249?nm/RIU. Relative sensitivity can be calculated from the ratio of field amplitudes of the arms of the dual output. Matrix method and 2D FDTD is used for the entire analysis.?     

Analysis of Metallic Waveguides by Using Least Square-Based Finite Difference Method

This paper demonstrates the application of a meshfree least square-based finite difference (LSFD) method for analysis of metallic waveguides. The waveguide problem is an eigenvalue problem that is governed by the Helmholtz equation. The second order derivatives in the Helmholtz equation are explicitly approximated by the LSFD formulations. TM modes and TE modes are calculated for some metallic waveguides with different cross-sectional shapes. Numerical examples show that the LSFD method is a very efficient meshfree method for waveguide analysis with complex domains.     

A single-mode single-polarization monolithically silica waveguide ring resonator used in microoptic gyro

A single-mode single-polarization waveguide (SMSPW) ring resonator for the microoptic gyro (MOG) was proposed, and it could be monolithically integrated onto a silica planar lightwave circuit. We have presented the design of a three-dimensional SMSPW ring resonator in which the TM mode cuts off and the TE mode transmits by taking into consideration the stress-induced birefringence effect of the Si-based silica waveguide using the effective-index method. The characteristics of the light propagation across the SMSPW resonator were studied by a three-dimensional finite difference beam propagation method. Numerical simulation results showed the SMSPW ring resonator has a high extinction ratio over 50 dB cm^?1 for the TM mode, low propagation loss of 0.055 dB cm^?1 for the TE mode, and a high finesse of 36. A rate detection limit of 0.8° h^?1 can be achieved. Without increasing the complexity of the waveguide fabrication process, this structure can solve the MOGs output bias instabilities induced by polarization fluctuations and provide a new solution for MOGs.     

Compact hybrid TM-pass polarizer for silicon-on-insulator platform

Hybrid waveguides consisting of a metal plane separated from a high-index medium by a low-index spacer have recently attracted a lot of interest. TM and TE modes are guided in two different layers in these structures and their properties can be controlled in different manners by changing the waveguide dimensions and material properties. We examine the effects of different parameters on the characteristics of the two modes in such structures. We show that by properly choosing the dimensions, it is possible to cut off the TE mode while the TM mode can still be guided in a well-confined manner. Using this property of the hybrid guide, we propose a TM-pass polarizer. The proposed device is very compact and compatible with the silicon-on-insulator platform. Finite-difference time-domain simulation indicates that such a polarizer can provide a high extinction of the TE mode for a reasonable insertion loss of the TM mode.     

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     

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.     

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.     

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.     

Attenuation in thin film optical waveguides due to roughness-induced mode coupling

Marcuse's mode-coupling theory for symmetrical planar optical waveguides was extended to cover the asymmetrical case. Computer programs were written to study the particular case of coupling between the zeroth order guided transverse electric (TE) mode and the radiation modes as a function of interface roughness.It is shown that a simple expression proposed by Tien gives results which correspond to the most pessimistic results obtained by the mode-coupling theory. R.f. sputtered thin film planar optical waveguides were prepared. The zeroth order TE guided mode having a vacuum wavelength of 0.6328 μm was excited in the thin film by means of a prism coupler. The attenuation of this mode was inferred from the reduction in intensity of the radiation modes which was measured with a photomultiplier. A Talystep was used to obtain the film thickness and also profiles of the roughness of the film-substrate and film-superstrate interfaces. The roughness profiles were computer-processed to determine the r.m.s. amplitude and the correlation length of the interface roughness. The refractive index was determined from the film thickness and the synchronous coupling angle using the reduced SYNCANG method. These data were used to compute the attenuation of the zeroth order guided TE mode from the mode-coupling theory. The correlation coefficient between the theoretical and experimental results was 0.96.     

Photosensitivity in silica-based waveguides deposited by atmospheric pressure chemical vapor deposition

By using a Mach-Zehnder interferometer, we evaluated photosensitivity in silica-based waveguides deposited by atmospheric pressure vapor deposition. Our results show that photosensitivity with ArF excimer laser irradiation was ten times greater than photosensitivity with KrF excimer laser irradiation. ArF excimer laser irradiation induced a refractive-index change of greater than 2 x 10(-3) at 1.55 mum and a birefringence between TE and TM modes of less than 6 x 10(-5). It has also been determined that the photoinduced absorption change of 90 dB/mm at 210 nm cannot account for a refractive-index change greater than 10(-3).