Mode Field Patterns Research Articles

Surface plasmon-like modes on structured perfectly conducting surfaces

Surface plasmon-like (SPL) modes are the electromagnetic surface eigenmodes supported by the structured perfectly conducting surfaces. The standard eigenvalue-solving method is adopted to solve these SPL modes. The field patterns of the SPL modes in the square holes for in-plane wavevectors k(x) = 2pi / 2d and k(x) = 2pi /d are TE(10)-like and TE(11), respectively. However, the field patterns can no longer be identified as any particular waveguide mode for other in-plane wavevectors. The dispersion relations of the SPL modes are obtained numerically. The change in mode character with wavevector prevents the dispersion relation from being derived by assuming only the fundamental mode in the holes. On a thin perfect conductor perforated with structures, the SPL mode splits into a high-frequency anti-symmetric mode and a low-frequency symmetric mode, which is caused by the mutual interaction of the electromagnetic evanescent fields on both sides.

Surface modes in two-dimensional photonic crystal slabs with a flat dielectric margin

We report numerical simulations of surface modes in two-dimensional high-index-contrast photonic crystal slabs with a flat dielectric margin of width on the order of the photonic crystal periodicity. Our calculations using plane wave expansion method reveal multiple surface guided modes within the photonic band gap, with some high-order modes exhibit relatively flat dispersion curves. We calculate the finite-length surface waveguide modes transmission and field patterns using two dimensional finite-difference time-domain method. We verify the surface mode dispersion curves by using spatial Fourier transform of the mode field patterns. Our study on surface modes under small ambient refractive index changes (5 x 10(-3)) shows that lower order modes exhibit larger wavelength shifts on the order of 1 nm. We also design a 4-port 3-channel bidirectional coupler using a conventional dielectric waveguide side coupled to the multimode surface waveguide.

Two-mode photonic crystal fibers

Index-guiding photonic crystal fibers with appropriate structural parameters support the fundamental and second order modes over a practically infinite wavelength range. The polarization principal axes and mode field patterns of the modes can be made stable by having different size air-holes along the orthogonal directions. The potential applications of such two-mode PCFs are discussed.

Spectral shift and Q change of circular and square-shaped optical microcavity modes due to periodic sidewall surface roughness

Radiation loss and resonant frequency shift due to sidewall surface roughness of circular and square high-contrast microcavities are estimated and compared by using a boundary integral equations method. An effect of various harmonic components of the contour perturbation on the Whispering-Gallery (WG) modes in the circular microdisk and WG-like modes in the square microcavity is demonstrated. In both cases, contour deformations that are matched to the mode field pattern cause the most significant frequency detuning and Q-factor change. Favorably mode-matched deformations have been found, enabling one to manipulate the Q-factors of the microcavity modes.

Analysis of strictly bound modes in photonic crystal fibers by use of a source-model technique.

We describe a source-model technique for the analysis of the strictly bound modes propagating in photonic crystal fibers that have a finite photonic bandgap crystal cladding and are surrounded by an air jacket. In this model the field is simulated by a superposition of fields of fictitious electric and magnetic current filaments, suitably placed near the media interfaces of the fiber. A simple point-matching procedure is subsequently used to enforce the continuity conditions across the interfaces, leading to a homogeneous matrix equation. Nontrivial solutions to this equation yield the mode field patterns and propagation constants. As an example, we analyze a hollow-core photonic crystal fiber. Symmetry characteristics of the modes are discussed and exploited to reduce the computational burden.

Photonic crystal power-splitter based on directional coupling

We propose a new power-splitting scheme in two-dimensional photonic crystals that can be applicable to photonic integrated circuits. The proposed power-splitting mechanism is analogous to that of conventional three-waveguide directional couplers, utilizing coupling between guided modes supported by line-defect waveguides. Through the analysis of dispersion curve and field patterns of modes, the position in propagation direction, where an input field is split into a two-folded image, is determined by simple mode analysis. Based on the calculated position, a photonic crystal power-splitter is designed and verified by finite-difference timedomain computation.

Planar corner-cut square microcavities: ray optics and FDTD analysis

We analyze corner-cut square microcavities as alternative planar microcavities. Ray tracing shows open-ray orbits that are 90-degree-rotated can oscillate between each other upon reflections at the 45-degree corner-cut facets, and have the same sense of circulation. Our two-dimensional finite-difference time-domain simulations suggest that a waveguide-coupled corner-cut square microcavity with an optimum cut size supports traveling-wave resonances with desirable add-drop filter responses. The mode-field pattern evolutions confirm the concept of modal oscillations. By applying Fourier transform on the mode-field patterns, we analyze the modal composition in k-space. The add-drop filter responses can be optimized by fine-tuning the waveguide width.

Mode field patterns and preferential mode coupling in planar waveguide-coupled square microcavities

We report a numerical and analytical study of mode field patterns and mode coupling in planar waveguide-coupled square microcavities, using two-dimensional (2-D) finite-difference time-domain (FDTD) method and k-space representation. Simulated mode field patterns can be identified by k-space modes. We observe that different mode number parities permit distinctly different mode field patterns and spectral characteristics. Simulation results suggest that k-space modes that nearly match the waveguide propagation mode have a relatively high coupling efficiency. Such preferential mode coupling can be modified by the mode number parity.

On the field patterns of the TE modes in antipodal ridge waveguide by finite element method

AbstractIn this paper, the field patterns of the TE modes in antipodal ridge waveguide (ARW) and double antipodal ridge waveguide (DARW) are presented by finite element method. The figures in this paper are useful in the design of antipodal waveguide components for wideband microwave transmission. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 79–82, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10679

Field patterns of the TE modes in ridge-trough waveguide

A single-ridge waveguide with a symmetrical longitudinal trough, designated as a ridge-trough waveguide has been used as a transition in a V-band (50-75 GHz) wafer probe recently. In this paper, the field patterns for the dominant TE mode and the first higher TE mode in ridge-trough waveguide with different configurations are presented by finite element method. The field patterns in this paper have important values for us to understand the transmission characteristics of ridge-trough waveguide, and will be of practical significance in designing ridge-trough waveguide components in microwave and millimeter wave engineering.

Surface plasmon polaritons on metal cylinders with dielectric core

Metal-cladded dielectric cylinders with submicron diameters may serve to model coated tips used in near-field scanning optical microscopy. The signal measured may be greatly influenced by resonance effects due to eigenmodes of the probe. Especially, using a photon scanning tunneling microscope setup, gold-coated tips have been found to detect a signal proportional to the magnetic field distributions [E. Devaux et al., Phys. Rev. B 62, 10 504 (2000)]. This effect is attributed to cylindrical surface plasmons. We present here fully retarded calculations of the dispersion and field patterns of the nonradiative plasmon modes in cylindrical geometry. We study the effect of varying the cylinder radius on the surface plasmon dispersion, thus justifying that the cylinder is a useful model for near-field probes in spite of their slightly conical shape.

Finite element analysis of the field patterns of higher-order TE and TM modes in rectangular-groove guide

The field patterns of the different TE and TM modes in a rectangular-groove guide are analysed by finite element method. The electric field, magnetic field and energy distributions in the groove guide for the dominant TE mode, the lowest TM mode and the 1st, 2nd, and 3rd higher-order TE,TM modes are presented. The results show that the low-loss characteristic of rectangular-groove guide seems unreliable. The results in this paper will be of benefit for us to understand the transmission characteristics of rectangular-groove guide, and will be of practical significance in designing groove guide components.

Three-dimensional electromagnetic modeling of fiber-core effects on the coupling characteristics of weakly fused tapered fiber-optic couplers

Based on the full-wave formulations, which combine the finite element method add the boundary element technique, and the step-like approximation method, a three-dimensional (3-D) electromagnetic modeling approach is proposed in this work to investigate the fiber-core effects on the coupling characteristics of the weakly fused tapered couplers. We find the fiber cores have significant effects on the mode field patterns, coupling coefficients, and birefringence for the coupler with large normalized frequencies. The influence of the fiber cores on the coupling behavior for the real couplers, such as 3 dB power dividers, polarization beam splitters, and wavelength demultiplexing/multiplexing couplers, are also studied in 3-D view. It is found that the effects of fiber-cores in the weakly fused tapered couplers have to be considered for accurately modelling their coupling behavior, although the model with no core assumption can predict the trend of the coupling characteristics for the real couplers.

Boundary-element calculations of electromagnetic band-structure of photonic crystals

A boundary element method is developed for calculating the photon modes of periodic structures whose unit cells consist of piecewise homogeneous dielectric materials of arbitrary shapes. Green’s function techniques are used to derive integral equations for these structures. These equations involve integrals over the boundaries between the regions, which are discretized and solved numerically. Thus the full set of Maxwell’s equations with boundary conditions in d independent variables is changed into an integral equation in d−1 variables. This allows for the calculation of mode frequencies and field patterns for wave vectors throughout the Brillouin zone, thus allowing the determination of photonic band gaps. An illustrative example is given here for a two-dimensional system.

Electromagnetic properties of periodic cavities coupled to a radiating antenna

The electromagnetic properties of spatially periodic cavities determines both the linear and nonlinear interaction between the waves and the electron beam in high-power backward-wave oscillators. A corrugated cavity is usually left open at one end for extraction of the useful microwave energy; however, reflections at the open end are large so that a cavity is still formed. In contrast to a previously studied N period closed cavity where the number of axial modes with frequencies falling in the lowest pass band of the structure is equal to N+1, an open cavity was found to support only N axial modes. In this paper the resonance frequencies, quality factors and the field patterns of the axial modes in an open cavity were all investigated experimentally and the results are in very good agreement with those obtained using a new, time-dependent, quasi-three dimensional code. It was also demonstrated that a short interface section between the periodic cavity and the radiating antenna can drastically reduce the quality factors to the diffraction limit over a very wide frequency band. This is expected to substantially increase the starting current and allow operation at high-beam current without degradation of spectral purity.

Composition of LP 11 modes in ellipticallycored fibre

The composition of the LP/sub 11/ modes in elliptically cored fibre is derived from the field and power density patterns of the individual higher order modes, and is confirmed by experiment. >

Composition of LP 11 modes in elliptically cored fibre

The composition of the LP11 modes in elliptically cored fibre is derived from the field and power density patterns of the individual higher order modes, and is confirmed by experiment. [This article has been reprinted due to the significance of the corrections. The article appears in 1994, issue 12, p.993-994.]

Bend-induced loss for the higher-order spatial mode in a dual-mode fiber

Measured loss for the LP(11) mode in a dual-mode fiber subjected to a uniform bend shows a strong dependence on the orientation of the mode-field pattern relative to the plane of the fiber bend. Wavelength and bend-radius dependence of the loss indicates that operation within ~40 nm of cutoff is feasible in dispersion compensators based on dual-mode fibers operated in the LP(11) spatial mode near cutoff.

Optical channel waveguides in AlGaAs multiple-quantum-well structures formed by focused ion-beam-induced compositional mixing

Optical channel waveguiding in a AlGaAs multiple-quantum-well structure was demonstrated in a channel formed by compositional mixing induced by focused ion beam (FIB) implantation. Selective mixing was achieved by FIB implanting Si/sup ++/ with a dose of 5*10/sup 14/ cm/sup -2/ followed by rapid thermal annealing at 950 degrees C for 10 s. Raman microprobe spectra were used to characterize the lateral variation of compositional mixing. Channel waveguide loss of 17.2 dB/cm was measured, compared to 10-12 dB/cm measured for planar waveguiding. Mode field pattern measurements indicate that a change in effective index of 2.7*10/sup -4/ was induced, corresponding to an approximate mixing depth of 270 nm. >

Variational coupled-mode theory of optical couplers

A scalar coupled-mode theory is developed from the variational principle. The formulation is variational in the sense that the mode parameters are adjustable and can be optimized subject to the coupling between the guides. The theory is applied to slab and fiber couplers. In comparison with the conventional scalar coupled-mode theory in which only the amplitudes of the modes in the individual guides are adjustable, the variational scalar coupled-mode theory predicts more accurate propagation constants and field patterns of the normal modes of the couplers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>