TM-like Modes Research Articles

Design of a Metamaterial-Based Backward-Wave Oscillator

In this paper, we present the design of a microwave generator using metamaterials (MTMs) in a negative index waveguide interacting with a high-power electron beam. The microwave structure is formed by inserting two MTM plates loaded with complementary split-ring-resonators (CSRRs) into a rectangular waveguide. Electromagnetic simulations using the high-frequency structure simulator code confirm the presence of a negative index TM-like mode suitable for use in a backward-wave oscillator (BWO). Particle-in-cell (PIC) simulations using the computer simulation technology (CST) Particle Studio code are performed to evaluate the efficiency of an S-Band MTM-based BWO (MTMBWO) excited by a 500 keV, 80-A electron beam. After about 250 ns, the MTMBWO reaches a saturated output power of 5.75 MW with an efficiency of 14% at a frequency near 2.6 GHz. The MTMBWO is also modeled by representing the MTM plates, which consist of CSRRs, as dielectric slabs whose effective permittivity is given by a Lorentzian model. The dielectric slab model is also simulated with the CST PIC code and shows good qualitative agreement with the simulations including the CSRR loaded plates. A cold test structure was fabricated from brass to test the theoretical predictions of the microwave transmission versus frequency of the negative index waveguide. Test results using a vector network analyzer showed very good agreement with the simulations for the excitation of the negative index TM-like mode near 2.6 GHz. The proposed structure appears to be promising for use in a MTMBWO high-power microwave generator.

Geometric dependence of metal-coated silicon nanowire plasmonic waveguides

We report the geometric dependences of metal-coated silicon nanowire (Si NW) plasmonic waveguides on their propagation lengths and mode areas. We examined Si NWs with four different cross-sectional shapes. Numerical simulations showed that propagation lengths and mode areas are highly dependent on the cross-sectional geometries of Si NWs. In particular, the TM-like mode in a hexagonal-shaped Si NW plasmonic waveguide without an air void has the longest propagation length of 18.20 μm, which is 4.7 times larger than that of the TM-like mode in a circular-shaped Si NW plasmonic waveguide. This study can be a useful guide for the design and application of metal-coated Si NW plasmonic waveguides.

Tuning the lateral leakage loss of TM-like modes in shallow-etched waveguides using liquid crystals

We examine the tuning effect a liquid crystal (LC) cladding has on the lateral leakage loss of TM-like modes in shallow-etched waveguides. For such waveguides with an air cladding, the guided TM-like mode and the unguided cladding TE-like mode can only be phase matched at precisely one angle. We find that for an anisotropic cladding such as an LC, this phase matching is now possible for a range of angles. Each of these angles corresponds to a given orientation of the molecules in the LC cladding. We show that the waveguide width at which the minimum in leakage loss occurs can be changed by varying the orientation of the LC cladding. We find different tuning regimes, identify a suitable tuning range, and discuss the feasibility of tunable leakage loss experiments.

Interband scattering in a slow light photonic crystal waveguide under electro-optic tuning

The evolution of the transmission spectrum of a photonic crystal waveguide under electro-optic tuning was studied in the band of an odd TE-like mode. The spectral signature of the interband scattering from the TM-like mode to the odd TE-like mode was characterized at various bias levels. The shift of the odd-mode band was determined based on a statistical approach to overcome the spectral noise. Simulations were performed to explain the spectral shift based on electro-optic and thermo-optic effects in the active photonic crystal structures. Potential impact of interband scattering on indirect interband-transition-based optical isolators is discussed and potential remedies are offered.

Compact Polarization Rotator Based on Surface Plasmon Polariton With Low Insertion Loss

An ultracompact mode-evolution-based polarization rotator is proposed. The polarization rotator consists of silicon wire waveguide covered by silica buffer layer and linearly tapered thin aluminum. Numerical simulations using 3-D finite element method demonstrate that it is possible to obtain an 11-μm-long polarization rotator with about -20-dB extinction ratio and less than 4.7-dB loss in C-band for both polarization conversions from TM-like mode to TE-like mode and from TE-like mode to TM-like mode.

A design method of lithium niobate on insulator ridge waveguides without leakage loss

We evaluate structural dependency of leakage losses in lithium niobate on insulator ridge waveguides. Generally, shallow ridge waveguides based on isotropic materials have inherent leakage loss for TM-like mode. On the other hand, lithium niobate is anisotropic material, thus the optical properties of lithium niobate based ridge waveguides are different from those of isotopic material based ridge waveguides. In this paper, we investigate leakage losses of lithium niobate on insulator ridge waveguides. We show that the shallow ridge waveguide structure without leakage loss can be realized by choosing the waveguide parameters adequately.

Q-factor optimization for TM-like modes in pillar-based photonic crystal cavities with planar slot waveguides

We propose a design for high Q-factor, pillar-based photonic crystal cavities, with the goal of enhancing radiation–matter interaction in planar slot waveguides. The Q-factor is optimized for transverse-magnetic-like (TM-like) cavity modes, and it is found that a maximum Q ≃ 45000 can be reached by proper design of the pillars defining the cavity region. As an application, we study the Purcell enhancement of spontaneous emission rate for a dipole emitter within a thin layer of low index material (slot) grown at the pillars center. The field intensity is enhanced within the slot for TM-like modes, which yields a Purcell factor of the order of 10 4, larger than the corresponding structure without slot. These results directly apply to nanostructures made of a thin active layer of erbium-doped silicon dioxide embedded in silicon pillars, which can be readily fabricated with state-of-the art technology.

Asymmetric Bimodal Accelerator Cavity for Raising rf Breakdown Thresholds

We consider an axisymmetric microwave cavity for an accelerator structure whose eigenfrequency for its second lowest TM-like axisymmetric mode is twice that of the lowest such mode, and for which the fields are asymmetric along its axis. In this cavity, the peak amplitude of the rf electric field that points into either longitudinal face can be smaller than the peak field which points out. Computations show that a structure using such cavities might support an accelerating gradient about 47% greater than that for a structure using similar single-mode cavities, without an increase in breakdown probability.

A silicon nitride microdisk resonator with a 40-nm-thin horizontal air slot

We design and fabricate pedestal-type, 15 microm diameter silicon nitride microdisk resonators on Si chip with horizontal air-slot using selective wet etching between Si, SiO2, and SiNx. As the slot structure is determined by deposition process, air slots that are as thin as 40 nm and as deep as 5 microm with ultra-smooth slot surfaces can easily be fabricated with photolithography only. Fundamental TM-like slot mode in which the E-field is greatly enhanced within slot was observed with an intrinsic Q factor of approximately 34,000 (lambdares=1523.7 nm) and energy overlap in slot region of 21.6%.

Lateral leakage of TM-like mode in thin-ridge Silicon-on-Insulator bent waveguides and ring resonators

We present the first prediction of lateral leakage behavior of the TM-like mode in thin-ridge SOI curved waveguides and ring resonators. A simple phenomenological model is first presented which predicts that the lateral leakage in these structures is significantly impacted by both the ring radius and waveguide width. This prediction is verified using full vectorial mode matching and finite element methods. We show that specific combinations of waveguide width and ring radius can lead to very low-loss propagation in the TM-like mode. This finding is critical for the design of high-Q resonators on such waveguide platforms and will have major impact on the field of silicon lasers and sensing applications.

Enhanced Raman Scattering in Slow-Light Photonic Crystals for Chip-Scale Frequency Conversion and Optical Amplification

We present measurements of enhanced Raman scattering in silicon slow-light photonic crystal waveguides. By utilizing both the Bragg gap edge dispersion of TM-like modes for pump enhancement and the TE-like fundamental mode onset for Stokes enhancement, a six-fold increase in the spontaneous Raman scattering was observed in the double slow-light regime. Both forward and backward Stokes signals are examined, with continuous-wave measurements, in our low-loss photonic crystal membranes. The measured nonlinear enhancement matches well with our numerical model and simulations, and are described in detail in this paper. These observations support the development of chip-scale frequency conversion and optical amplification in silicon nanophotonics.

Deterministic tuning of slow-light in photonic-crystal waveguides through the C and L bands by atomic layer deposition

We demonstrate digital tuning of the slow-light regime in silicon photonic-crystal waveguides by performing atomic layer deposition of hafnium oxide. The high group-index regime was deterministically controlled (redshift of 140±10 pm per atomic layer) without affecting the group-velocity dispersion and third-order dispersion. Additionally, differential tuning of 110±30 pm per monolayer of the slow-light TE-like and TM-like modes was observed. This passive postfabrication process has potential applications including the tuning of chip-scale optical interconnects, as well as Raman and parametric amplification.

Generalized Simple Theory for Estimating Lateral Leakage Loss Behavior in Silicon-on-Insulator Ridge Waveguides

In this paper, we numerically investigate the lateral leakage loss behavior for TM-like modes in silicon-on-insulator ridge wave guides. If the waveguide width is set to satisfy a certain condition, the leakage loss of the TM-like mode leads to be a minimum. When utilizing TM-like modes in the ridge wave guides, it is the main drawback that the tolerance for the variations in the waveguide width and operation wavelength is too small. In this paper, we propose a novel ridge waveguide structure, where a dimple is introduced at the ridge region. It is shown from the finite-element analysis that the ridge waveguide with a dimple is both low loss and fabrication tolerant.

Design of miniaturized silicon wire and slot waveguide polarization splitter based on a resonant tunneling

We propose an ultra-small polarization splitter based on a resonant tunneling phenomenon. This polarization splitter consists of two identical horizontally oblong silicon wire waveguides separated by a vertical slot waveguide. The structural parameters of the central resonant slot waveguide are designed to couple only the TM-like mode between the left and right side silicon wire waveguides. Results from numerical simulation with the full-vectorial beam propagation method show that a 16-mum-long polarization splitter with extinction ratio better than -20 dB on the entire C-band is achieved.

Full-vectorial analysis of high-index-contrast coupled channel waveguides

Coupling of two identical channel waveguides separated by an air gap is analyzed. The coupled structure exhibits a strong refractive index contrast in both the transverse and longitudinal dimensions, which necessitates the use of a full-vectorial model. The 3D full-vectorial bidirectional method-of-lines beam propagation is utilized for this purpose. The effect of the transverse and longitudinal displacements on the modal reflectivity and modal transmissivity of the fundamental TE-like and TM-like modes is reported. Numerical results are presented for both the full-vectorial model and the approximate semivectorial model. A significant difference between the predictions of these two models is seen.

Full-vectorial analysis of bending waveguides using finite difference method based on H-fields in cylindrical coordinate systems

A full-vectorial (FV) analysis of optical dielectric waveguide bends by using finite difference (FD) method in terms of magnetic field components is developed in a local cylindrical coordinate system. The perfectly matched layer absorbing boundary conditions via the complex coordinate stretching technique are incorporated into the FV wave equations for effectively demonstrating the leaky nature of waveguide bends, and a six-point FD scheme is constructed to approximate the cross-coupling terms for improving the convergent behavior. The leaky modes of a typical rib waveguide bend are calculated and the complex propagation constants and the field patterns for TE- and TM-like modes are obtained. Solutions are good agreement with those from the film mode matching method, which shows the validity and utility of the established method.

Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers

The transverse-magnetic to transverse-electric (TM-TE) mode coupling properties and the lateral leakage loss behavior of the propagating TM-like mode in silicon-on-insulator thin-ridge waveguides and directional couplers are investigated. Accurate calculation of the lateral leakage is performed by a mode matching technique in which the calculation window is left fully open in the lateral direction.

Lateral leakage in TM-like whispering gallery mode of thin-ridge silicon-on-insulator disk resonators

The leakage loss due to TM-TE mode coupling of TM-like whispering gallery mode in silicon-on-insulator (SOI) thin-ridge disk resonators is investigated for the first time to the best of our knowledge. We show that the propagation losses of TM-like mode in thin-ridge SOI disk resonators are significantly impacted by the radius of the disk. This behavior is predicted by a simple phenomenological model as well as a rigorous mode matching simulation.

Observation of spontaneous Raman scattering in silicon slow-light photonic crystal waveguides

We report on the observation of spontaneous Raman scattering in silicon photonic crystal waveguides. Continuous-wave measurements of both forward scattered and backscattered Stokes emissions are reported in single line-defect waveguides in hexagonal lattice photonic crystal silicon membranes. By utilizing the Bragg gap edge dispersion of the TM-like mode for pump enhancement and the TE-like fundamental mode onset for Stokes enhancement, the spontaneous Raman scattering coefficient was observed to increase by up to six times in the region of slow group velocity. The results show explicit nonlinear enhancement in a silicon photonic crystal slow-light waveguide device.

Design of high-Q photonic crystal microcavities with a graded square lattice for application to quantum cascade lasers

A high-Q photonic crystal (PC) microcavity for TM-like modes, which can be applied to quantum cascade lasers (QCLs), was successfully designed in an air-hole based PC slab with semiconductor cladding layers. In spite of no photonic badgaps for TM-like modes in air-hole based PC slabs, cavity Q reached up to 2,200 by utilizing a graded square lattice PC structure. This is approximately 18 times higher than those previously reported for PC defect-mode microcavities for QCLs. This large improvement is attributed to a suppression of the coupling between the cavity mode and the leaky modes thanks to the dielectric perturbation in the graded structure. We also predicted a dramatic reduction of the threshold current in the designed cavity down to one-fifteenth of that of a conventional QCL, due to a decreased optical volume.