Mode Field Patterns Research Articles

High-order modes of spoof surface plasmonic wave transmission on thin metal film structure

Recently, conformal surface plasmon (CSP) structure has been successfully proposed that could support spoof surface plasmon polaritons (SPPs) on corrugated metallic strip with ultrathin thickness [Proc. Natl. Acad. Sci. U.S.A. 110, 40-45 (2013)]. Such concept provides a flexible, conformal, and ultrathin wave-guiding element, very promising for application of plasmonic devices, and circuits in the frequency ranging from microwave to mid-infrared. In this work, we investigated the dispersions and field patterns of high-order modes of spoof SPPs along CSP structure of thin metal film with corrugated edge of periodic array of grooves, and carried out direct measurement on the transmission spectrum of multi-band of surface wave propagation at microwave frequency. It is found that the mode number and mode bands are mainly determined by the depth of the grooves, providing a way to control the multi-band transmission spectrum. We have also experimentally verified the high-order mode spoof SPPs propagation on curved CSP structure with acceptable bending loss. The multi-band propagation of spoof surface wave is believed to be applicable for further design of novel planar devices such as filters, resonators, and couplers, and the concept can be extended to terahertz frequency range.

Mode analysis for metal-coated nanocavity by three-dimensional S-matrix method

Three-dimensional scattering matrix method is proposed to investigate mode characteristics for metal-coated nanocavities, with the vertical waveguide structure of an active region confined by upper and lower cladding layers. For a nanocavity with radius of 800 nm, Q factors of well-confined modes with wavelength around 1550 nm first decrease with the increase of the metallic layer thickness due to the metallic absorption and the increase of radiation loss as the metallic layer thickness is less than 10 nm, and then rise with the increase of the metallic layer. However, for a weak confined nanocavity with a radius of 500 nm, the mode Q factor increases with the metallic layer thickness first, reaches a maximum value at an optimal metallic thickness, then decrease with the further increase of the metallic layer. For nanocavities confined by a thick metallic layer, the Q factors approach constants limited by the metallic absorption. However, mode field patterns, including the vertical field distributions, are affected by the metallic layer, which not only influences the metallic layer absorption but also the optical confinement factor in the active region.

Optical properties of three-dimensional woodpile photonic crystals composed of circular cylinders with planar defect structures

The optical properties of three-dimensional woodpile photonic crystals (PhCs) composed of circular cylinder rods with a planar defect structure at the central layer are theoretically investigated using the parallel finite-difference time-domain method and plane-wave expansion method. Three types of planar defects are introduced into the PhC by alternating respectively the dielectric constant, cylinder diameter, and misalignment of the rods at the defect layer. The transmission spectrum and band diagram of each planar defect structure are systematically studied. The resonance and transmission properties of the defect structures can be characterized by two distinct resonant modes, the defect mode and the band-edge resonant mode, which have been identified by detailed spectrum analysis, calculated mode profiles and field patterns. It is shown that, by modifying the rod diameter or the dielectric constant of materials at the defect layer, the resonant modes can be varied and controlled. Also, by applying dislocation to a layer of dielectric rods, the photonic band edges can be shifted.

耦合微盘及带输出波导的单微盘腔的耦合模式特性

The optical microresonators with high Q factor and ultra-small mode volume have attracted great attentions for applications in optoelectronic devices. For a coupled-microdisks and a single microdisk connected with an output waveguide, coupled mode characteristics resulting from the structure asymmetry are investigated by the finite-difference time-domain(FDTD) method and the Pade′ approximation. Mode field patterns and mode Q factors are calculated, and the relative energies of mode-field components with different angular wave numbers are estimated from the coupled mode-field distribution. For coupled microdisk resonator, the higher-order modes introduced by the mode coupling usually reduces the mode Q factor of the coupled mode greatly. For a single microdisk resonator with a radius of1μm and a refractive index of3.2 connected with a0.2-μm-wide output waveguide, a coupled mode at the wavelength of1.52μm is observed with the mode Q factor of268 and a triangle mode-field pattern, which is the coupled mode between whispering-gallery modes TE9,1 and TE6,2 with a wavelength difference of6.6 nm.

Design principles of microwave applicators for small-scale process equipment

In this work, we bridge fundamental electromagnetics and chemical process engineering with the aim to develop tailor-made (microwave or high frequency radiowave) applicators for heating of micro- and small-structured process equipment. In this context, two simple configurations with well-defined single mode field patterns, namely a cylindrical and a rectangular cavity both containing a homogeneous cylindrical load were analyzed either analytically or numerically. We present design charts that illustrate how important operating, geometric and materials parameters relate with each other. It was found that load size, heating uniformity and desired frequency mutually constrain one another. The required cavity volume increases with increasing heating uniformity or with increasing load permittivity for a given heating uniformity requirement. At the popular frequency of 2.45 GHz the load is restricted to a small size, compared to the cavity size, in order to achieve high heating uniformity. Opting for lower resonance frequencies allows for bigger load volumes to be heated uniformly. Furthermore, we show that the relations found for the operating, structural and material properties on the basis of these simple configurations can provide design guidelines and first approximations for more realistic process equipment geometries.

Compensation of Multimode Fiber Dispersion by Optimization of Launched Amplitude, Phase, and Polarization

In previous work, a technique was proposed for compensation of modal dispersion in multimode fiber (MMF) systems by using adaptive optics. A spatial light modulator (SLM), with amplitude and phase adjustable over discrete blocks, was used to control the field launched into a MMF. The system impulse response was found as a function of the SLM settings and the field patterns of the MMF principal modes, which were assumed to be known. Using principles of convex optimization, an optimal solution for the SLM settings was obtained, which minimizes intersymbol interference (ISI) subject to physical constraints. Here, we extend the previous method to include control over launched polarization. We propose five adaptive optics configurations, some permitting control only of overall polarization, and others permitting block-wise polarization control. For each configuration, we find optimal adaptive optics settings, which minimize ISI. We show that the best performance is obtained by two configurations that permit independent block-wise control of amplitude, phase and polarization.

Multimode resonances in metallically confined square-resonator microlasers

Directional emission InP/AlGaInAs square-resonator microlasers with a side length of 20 μm are fabricated by standard photolithography and inductively coupled-plasma etching technique. Multimode resonances with about seven distinct mode peaks in a free-spectral range are observed from 1460 to 1560 nm with the free-spectral range of 12.1 nm near the wavelength of 1510 nm, and the mode refractive index versus the photon energy E (eV) as 3.07152+0.18304E are obtained by fitting the laser spectra with an analytical mode wavelength formula derived by light ray method. In addition, mode field pattern is simulated for cold cavity by two dimensional finite-difference time-domain technique.

High-Q unidirectional emission properties of the symmetric half-spiral microcavities

Mode field patterns and light emissions of novel symmetric half-spiral microcavities (SHSMs) are investigated by the two-dimensional (2-D) finite-difference time domain (FDTD) method. The calculation results show that an SHSM can support high-quality (Q) (Q>104) distorted whispering-gallery modes with directional emissions. Moreover, artificial controls on the Q factor and emission directionality are realized in the coupled size-mismatched SHSMs, and unidirectional emission from the coupled cavity structure with a divergence of 19° is achieved.

Mode Analysis for Equilateral-Triangle-Resonator Microlasers with Metal Confinement Layers

Mode characteristics are analyzed for electrically injected equilateral-triangle-resonator (ETR) semiconductor microlasers, which are laterally confined by insulating barrier SiO2 and electrode metals Ti-Au. For the ETR without metal layers, the totally confined mode field patterns are derived based on the reflection phase shifts, and the Q -factors are calculated from the far-field emission of the analytical near field distribution, which are agreement very well with the numerical results of the finite-difference time-domain (FDTD) simulation. The polarization dependence reflections for light rays incident on semiconductor- SiO2-Ti-Au multi-layer structures are accounted in considering the confinement of TE and TM modes in the ETR with the metal layers. The reflectivity will greatly reduce with a Ti layer between SiO2 and Au for light rays with incident angle less than 30deg especially for the TE mode, even the thickness of the Ti layer is only 10 nm. If the ETR is laterally confined by SiO2 -Au layers without the Ti layer, the Fabry-PEacuterot type modes with an incident angle of zero on one side of the ETR can also have high Q-factor. The FDTD simulation for the ETR confined by metal layers verifies the above analysis based on multi-layer reflections. The output spectra with mode intervals of whispering-gallery modes and Fabry-Perot type modes are observed from different ETR lasers with side length of 10 mum, respectively.

Analysis of mode characteristics for equilateral-polygonal resonators with a center hole

Mode characteristics for equilateral triangles, squares, and hexagonal resonators with a center hole are numerically simulated by the finite-different time domain (FDTD) technique. The center hole does not break the symmetry behavior of the original resonators and can result in modification of the mode field patterns and mode Q factors. In an equilateral triangle resonator the center hole can suppress the symmetry state of degenerate states with the merit of single mode operation. In a square resonator, the Q factor can be enhanced for some modes with a suitable size of the hole. For a hexagonal resonator with a side length of 1 μm and a refractive index of 3.2, the mode Q factors first gradually decrease with the increase of the hole diameter for modes at a wavelength of about 1500 nm, then the modes transform to that of a microdisk with a jump of the mode wavelength as the hole diameter approaches 0.7 μm. Finally, the mode Q factors greatly enhance as the hole diameter reaches about 1 μm. The results indicate that the center hole can greatly modify mode characteristics, especially that of the mode Q factor.

Multiple Defect Modes in Diamond Photonic Crystal

Defect frequencies, degeneracy and mode field patterns of defect modes in diamond based photonic crystal (PC) are analyzed. An efficient method to create multiple defect frequency levels in the photonic band gap by degeneracy lifting is proposed. The degenerate dipole mode is split into two defect frequency levels by upsetting the symmetry about the origin. The diamond PC with our proposed defect structure has four defect frequency levels with two dipole and two quadrupole mode field patterns. It is shown that non-degenerate monopole and hexapole modes can be obtained by pulling up the acceptor levels from the dielectric band in diamond photonic crystals. Our proposed structure has a monopole and a hexapole mode that are very close in frequency. However, C6v symmetry of the triangular lattice guarantees their non-degeneracy.

Compensation of Multimode Fiber Dispersion Using Adaptive Optics via Convex Optimization

In this paper, we propose a provably optimal technique for minimizing intersymbol interference (ISI) in multimode fiber (MMF) systems using adaptive optics via convex optimization. We use a spatial light modulator (SLM) to shape the spatial profile of light launched into an MMF. We derive an expression for the system impulse response in terms of the SLM reflectance and the field patterns of the MMF principal modes (PMs). Finding optimal SLM settings to minimize ISI, subject to physical constraints, is posed as an optimization problem. We observe that our problem can be cast as a second-order cone program, which is a convex optimization problem. Its global solution can, therefore, be found with minimal computational complexity, and can be implemented using fast, low-complexity adaptive algorithms. We include simulation results, which show that this technique opens up an eye pattern originally closed due to ISI. We also see that, contrary to what one might expect, the optimal SLM settings do not completely suppress higher order PMs.

A Cerenkov generator with coaxial slow wave structure

Results of analytic theory, numerical simulation, and experimental studies on a Ceronkov generator with coaxial slow wave structure are presented. The dispersion curves and the field patterns of the axial modes are given in the analytic theory, showing the operation mode of quasi-TEM mode. The numerical simulation results indicate that the device is featured by the resonance characteristics, the microwave frequency spectrum illustrates high purity, the dominant frequency remains fairly constant over a wide range of diode voltage, and the optimized efficiency of more than 37% is obtained. In preliminary experiment, a microwave pulse with frequency of 7.7GHz, power of 1.3GW, and efficiency of 28% was obtained.

Measurement and numerical simulation of the bandgap in hollow-core photonic crystal fibers

The full-vector plane-wave method was used to calculate the bandgaps of the photonic crystal fiber with triangular structure. The transmission spectrum of the hollow-core photonic crystal fiber fabricated by Yanshan University was measured, and we obtained the relation between the transmission intensity and the wavelength in visible region. In the subsequent experiment, the mode field patterns were observed. The theoretical simulation is well consistent with the experimental result.

Comparison of $Q$-Factors Between TE and TM Modes in 3-D Microsquares by FDTD Simulation

Mode characteristics of three-dimensional (3-D) microsquare resonators are investigated by finite-difference time-domain (FDTD) simulation for the transverse electric (TE)-like and the transverse magnetic (TM)-like modes. For a pillar microsquare with a side length of 2 mum in air, we have Q-factors about 5 times 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> for TM-like modes at the wavelength of 1550 nm, which are one order larger than those of TE-like modes, as vertical refractive index distribution is 3.17/3.4/3.17 and the corresponding center layer thickness is 0.2 mum. The mode field patterns show that TM-like modes have much weaker vertical radiation coupling loss than TE-like modes. TM-like modes can have high Q-factors in a microsquare with weak vertical field confinement.

Guided modes of one-dimensional photonic bandgap waveguides

Using a ray-optics model, we analyze the guided modes of a slab waveguide that consists of a low-index layer sandwiched between two photonic bandgap structures. Normalized band diagrams and dispersion curves for the TE and TM waves are investigated in detail, and a nomenclature system for the guided modes based on the mode-field patterns in the waveguide is proposed. The cutoff conditions and the confinement factors of the modes are discussed. The effects of varying the physical parameters of the waveguide on the dispersion characteristics of the modes are also analyzed.

Mode coupling between first- and second-order whispering-gallery modes in coupled microdisks

The mode characteristics for two coupled microdisks are investigated by the finite-difference time-domain technique. In the two coupled micodisks, mode coupling between the same order whispering-gallery modes (WGMs) results in coupled WGMs with split mode wavelengths. The numerical results show that the split mode wavelengths of the coupled first- and second-order WGMs can have a crossing point in some cases, which can induce anticrossing mode coupling between them and greatly reduce the mode Q factor of the coupled first-order WGMs. The time variation of mode field pattern shows the transformation between the coupled first- and second-order WGMs.

Analyses of cladding modes in photonic crystal fiber

Characteristics of cladding modes in a photonic crystal fiber (PCF) are numerically analyzed using the plane wave expansion method. The presence of the outer silica ring in the PCF tends to push the optical fields of the cladding modes toward the rim of the PCF, which creates 'ring modes' whose fields are tightly confined in the outer ring. The dispersion of the cladding modes are determined mainly by the dispersive property of the holey cladding structure. The optical field patterns of the cladding modes and the beatlengths between the fundamental mode and the cladding modes are also investigated.

Reciprocal transmissions and asymmetric modal distributions in waveguide-coupled spiral-shaped microdisk resonators

We report transmission spectra and mode-field distributions of a waveguide-coupled spiral-shaped microdisk resonator on a silicon nitride-on-silica substrate. Our measured and simulated transmission spectra reveal reciprocal transmissions between clockwise and counterclockwise travelingwaves of such microcavity that lacks mirror symmetry. Our measured out-of-plane scattering intensity distributions and simulated steady-state mode-field patterns, however, indicate asymmetric modal distributions that depend on the sense of lightwave circulations and the input-coupling mechanisms. We discuss implications of the observed reciprocal transmissions with asymmetric modal distributions to unidirectional lasing from spiral-shaped microcavities reported in the literature.

Novel Dual-Mode Bandpass Filters Using Hexagonal Loop Resonators

Novel dual-mode hexagonal loop resonators with the patch and notch perturbation are proposed in this paper. The field patterns of the degenerate modes and their mode splitting characteristics are investigated. The applications of the dual-mode hexagonal loop resonator as bandpass filters are presented. It is shown that different responses can be realized using only a single dual-mode resonator by changing the position of the perturbation. A coupling and routing scheme is presented to model the operations of these filters. Two- and four-pole filters of this type are demonstrated for the first time. All the theoretical analysis and design procedures have been verified by experimental results