Analysis of two stacked cylindrical dielectric resonators in a TE₁₀₂ microwave cavity for magnetic resonance spectroscopy

The frequency, field distributions and filling factors of a DR/TE??? probe, consisting of two cylindrical dielectric resonators (DR1 and DR2) in a rectangular TE??? cavity, are simulated and analyzed by finite element methods. The TE(+++) mode formed by the in-phase coupling of the TE??(δ)(DR1), TE??(δ)(DR2) and TE??? basic modes, is the most appropriate mode for X-band EPR experiments. The corresponding simulated B(+++) fields of the TE(+++) mode have significant amplitudes at DR1, DR2 and the cavity's iris resulting in efficient coupling between the DR/TE??? probe and the microwave bridge. At the experimental configuration, B(+++) in the vicinity of DR2 is much larger than that around DR1 indicating that DR1 mainly acts as a frequency tuner. In contrast to a simple microwave shield, the resonant cavity is an essential component of the probe that affects its frequency. The two dielectric resonators are always coupled and this is enhanced by the cavity. When DR1 and DR2 are close to the cavity walls, the TE(+++) frequency and B(+++) distribution are very similar to that of the empty TE??? cavity. When all the experimental details are taken into account, the agreement between the experimental and simulated TE(+++) frequencies is excellent. This confirms that the resonating mode of the spectrometer's DR/TE??? probe is the TE(+++) mode. Additional proof is obtained from B?(x), which is the calculated maximum x component of B(+++). It is predominantly due to DR2 and is approximately 4.4 G. The B?(x) maximum value of the DR/TE??? probe is found to be slightly larger than that for a single resonator in a cavity because DR1 further concentrates the cavity's magnetic field along its x axis. Even though DR1 slightly enhances the performance of the DR/TE??? probe its main benefit is to act as a frequency tuner. A waveguide iris can be used to over-couple the DR/TE??? probe and lower its Q to ≈150. Under these conditions, the probe has a short dead time and a large bandwidth. The DR/TE??? probe's calculated conversion factor is approximately three times that of a regular cavity making it a good candidate for pulsed EPR experiments.     

Two-dimensional imaging of two types of radicals by the CW-EPR method

New EPR resonators were developed by using a ceramic material with a high dielectric constant, epsilon=160. The resonators have a high quality factor, Q=10(3), and enhance the sensitivity of an EPR spectrometer up to 170 times. Some advantages of the new ceramic resonators are: (1) cheaper synthesis and simplified fabricating technology; (2) wider temperature range; and (3) ease of use. The ceramic material is produced with a titanate of complex oxides of rare-earth and alkaline metals, and has a perovskite type structure. The resonators were tested with X-band EPR spectrometers with cylindrical (TE(011)) and rectangular (TE(102)) cavities at 300 and 77K. We discovered that EPR signal strength enhancement depends on the dielectric constant of the material, resonator geometry and the size of the sample. Also, an unusual resonant mode was found in the dielectric resonator-metallic cavity structure. In this mode, the directions of microwave magnetic fields of the coupled resonators are opposite and the resonant frequency of the structure is higher than the frequency of empty metallic cavity.     

Normal modes and quality factors of spherical dielectric resonators: I — shielded dielectric sphere

Electromagnetic theoretic analysis of shielded homogeneous and isotropic dielectric spheres has been made. Characteristic equations for the TE and TM modes have been derived. Dielectric spheres of radii of the order of μm size are found suitable for the optical frequency region whereas for the microwave region radii of the order of mm size are found suitable. Parameters suitable for their application in the optical and microwave frequency ranges have been used to compute the frequencies corresponding to the normal modes for the TE and TM modes. Expressions for the quality factors for realistic resonators, i.e., for a dielectric sphere with a non-zero conductivity and a metal shield with a finite conductivity have also been derived for the TE and TM modes. Computations of the quality factors have been made for resonators with parameters suitable for the optical and the microwave regions.     

Wide tuning of silicon-on-insulator ring resonators with a liquid crystal cladding

Wide electrical tuning of silicon-on-insulator ring resonators is demonstrated using a top cladding layer of nematic liquid crystals. A tuning range of 31?nm is demonstrated for ring resonators guiding the TM mode, covering nearly the entire C-band of optical communications. Ring resonators guiding the TE mode can be tuned over 4.5?nm. The combination of a liquid crystal director calculation and a fully anisotropic mode solver confirms the interpretation of these experimental results. The realization of broad and low-power tuning in silicon-on-insulator opens up new opportunities in the field of tunable lasers, filters, and detectors.     

Modes and Fields of Two Stacked Dielectric Resonators in a Cavity of an Electron Paramagnetic Resonance Probe

An electron paramagnetic resonance (EPR) probe consisting of two dielectric resonators (DRs) and a cavity (CV) is ideal for EPR experiments where both signal enhancement and tuning capabilities are required. The coupling of two DRs, resonating in their \({\text{TE}}_{01\delta }\) mode and a CV resonating in its \({\text{TE}}_{011}\) mode, is studied using energy-coupled mode theory (ECMT). The frequencies and eigenvectors of the three coupled modes are analytically derived. As predicted numerically, ECMT confirms that the \({\text{TE}}^{ + + - }\) and \({\text{TE}}^{ + - - }\) modes are indeed found to be degenerate at a specific distance between the two DRs \(d_{12}\). Additionally, the condition at which degeneracy occurs is specified. For a considerable range, the calculated frequency of the \({\text{TE}}^{ + + + }\) mode changes linearly with respect to \(d_{12}\). The \({\text{TE}}^{ + + + }\) mode showed a 500 MHz frequency change over a distance of 2 cm, when the resonance frequency is around 9.7 GHz. This enables the experimentalist to linearly tune the probe over this large frequency range. Finally the asymmetric configuration, where one of the resonators (DR2) is kept at the cavity center and the other one is allowed to move along the cavity axis, is studied. It is estimated that the frequency changes by 600 MHz over a distance of 1.5 cm. A formula for the magnitude of the magnetic field along the cavity axis, where the EPR samples are usually placed, is developed. This is crucial in determining the magnetic field in the vicinity of the sample and the probe’s filling factor.     

Design of transverse electric ring isolators for ultra-low-loss Si3N4 waveguides based on the finite element method

In this Letter we present the design of a novel (to our best knowledge) integrated TE isolator realized using ultra-low-loss Si(3)N(4) waveguides. The device is made of two straight waveguides coupled to an array of ring resonators including a Ce:YIG garnet grown on their internal side. The analysis demonstrates advantages in loss, isolation, and passband width as the number of rings is increased.     

Electro-optically tunable microring resonators on lithium niobate

Electro-optical tuning of a microring resonator fabricated on lithium niobate (LiNbO3) is presented. The device structure, including microring resonator and couplers, is designed in detail and is produced by titanium diffusion on the wet-etched LiNbO3 ridge surface. The resonance wavelengths for TM and TE polarizations can be tuned by electro-optic effect. The output characteristics of through port and drop port in the microring resonators are measured, and the effect of applied voltage on the shift of resonant wavelength is discussed. The presented microring resonators have the features of fast tuning speed, high material stability, bidirection wavelength shift, and no heating interference. Realization of such a microring resonator on LiNbO3 makes the utilization of electro-optic tuning and nonlinear effects in the versatile photonic applications of microring resonators achievable.     

Polarization-independent omnidirectional band gaps in heterostructures containing negative-index materials

We proposed a type of heterostructure by combining two photonic crystals (PCs) consisting of alternating negative-index materials and positive-index materials layers. It is demonstrated by transfer matrix method that the proposed structure has a polarization-independent omnidirectional band gap (OBG), which is independent of the incident angle for both TE and TM polarizations. Compared to a single PC, the frequency range of the OBG in a heterostructure can be notably enlarged. Such a structure has potential applications in improving planar microcavities, optical fibers, and Fabry-Pérot resonators, etc.     

超材料谐振子间的电耦合谐振理论与实验研究

通过将两个金属开口环谐振器口对口地放置, 实现了超材料谐振子间的电耦合谐振. 对电耦合谐振的微波等效电路进行了理论分析和数值计算, 结果表明耦合后的超材料谐振子能产生两个谐振频率, 其中一个随耦合强度的增加逐渐向低频方向移动, 而另一个固定在单谐振子的谐振频率处不变. 微波透射谱的实验测试和电磁仿真结果表明, 两个谐振峰随耦合强度的增加分别向低频和高频方向移动. 分析表明: 低频谐振峰的位置主要是由超材料谐振子间的电耦合强度决定的; 高频谐振偏离单谐振子的谐振频率主要是由不可避免的磁耦合引起的, 而且在耦合间距越小时磁耦合影响越大. 提出的基于超材料谐振子间的电磁耦合实现的双频谐振及其可调性极大地增加了超材料的设计与应用空间.     

Enhanced nanoparticle detection with liquid droplet resonators

Whispering gallery mode particle sensing experiments are commonly performed with solid resonators, whereby the sensing volume is limited to the weak evanescent tail of the mode near the resonator surface. In this work we discuss in detail the sensitivity enhancements achievable in liquid droplet resonators wherein the stronger internal fields and convenient means of particle delivery can be exploited. Asymptotic formulae are derived for the relative resonance shift, line broadening and mode splitting of TE and TM modes in liquid droplet resonators. As a corollary the relative fraction of internal and external mode energy follows, which is shown to govern achievable sensitivity enhancements of solute concentration measurements in droplet sensors. Experimental measurements of nanoparticle concentration based on whispering gallery mode resonance broadening are also presented.     

Mode characteristics of silver-coated inverted-wedge silica microdisks

The characteristics of whispering gallery modes(WGM) in silver-coated inverted-wedge silica microdisks are theoretically investigated by using finite element method. Dielectric TE mode always exists in silver-coated inverted-wedge resonators; dielectric TM mode tends to couple with SPP modes; only pure interior surface plasmonic polariton(SPP) mode but not pure exterior SPP mode is observed in contrast to the metal-coated cylindrical and toroidal resonators. The dependence of quality factor of different kinds of WGMs on the radius of the resonator and the thickness of the coated silver layer are systematically analyzed. We find that the quality factors of the hybrid WGMs associated with SPP mode can reach 104. The maximum light intensity enhancement in ambient for a hybrid mode consisting of a dielectric TM mode and an exterior SPP mode can be obtained when a silver film of thickness ~40 nm is deposited. The silver-coated inverted-wedge silica resonators may be widely applied in sensing and surface enhanced Raman scattering.     

A high efficiency label-free photonic biosensor based on vertically stacked ring resonators

In this paper we propose an optical biosensor based on two vertically stacked Silicon on Insulator (SOI) micro-ring resonators interacting with a microfluidic ring channel. This device behaves as a resonant optical coupler and it is very sensitive to the variation of the coupling coefficient between the two vertically stacked ring resonators. A ring microfluidic channel is proposed in the coupling region between the two vertically stacked ring resonators. The inner walls of the channel are funzionalized in order to the trap a specific biological species. Assuming a biotin-streptavidin system, the straptividin trapping gives rise to a change of the biological thickness of about 3 nm. This thickness increase of the deposited layer leads to a consequent change in the coupling strength between the two rings. These theoretical predictions have been validated by using both 3D Finite-Difference Time-Domain (FDTD) and 3D full-vectorial Finite Element Method (FEM) approaches. Moreover, by appropriately choosing the design parameters of the micro-resonant structure, we evaluate a sensitivity of the spectral response to the streptavidin adlayer variation of about 20% nm^?1 for TE polarization and 34% nm^?1 for TM polarization, which represents an important achievement to obtain selective SOI bio-sensors with ultra-high resolution.     

Polarization conversion in ring resonator phase shifters

The effect of the polarization rotation induced by curved waveguides on the spectral behavior of phase shifter ring resonators is investigated both theoretically and experimentally. At resonance the polarization rotation that takes place in curved waveguides is strongly enhanced. The effect can be detrimental, or it can be exploited for new devices. The ring vectorial transfer function is derived, together with the conditions for the total conversion of TE polarization into TM polarization. These conditions are verified experimentally.     

Kolmogorov-Arnold-Moser transition and laser action on scar modes in semiconductor diode lasers with deformed resonators

Measurements of the optical spectra of semiconductor injection lasers with deformed cylinder resonators show strong indications of the classical Kolmogorov-Arnold-Moser transition from integrability to chaos for devices with small deformation. At larger deformation, evidence for laser action on scar modes is obtained. The diode lasers operate with TE polarization, resulting in laser action on (partially) chaotic whispering-gallery modes for all deformations.     

Coupling Losses and Discrimination of Annular Waveguide Laser Resonators

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The optimum design model of two resonators system

In this work we present a new theoretical treatment for the design of two resonator system. Our finding shows our model behaves better than previous models when we consider side-coupling loss for two resonators coupled in a ring configuration. In addition, our model is more physical and intuitive for the analysis of the two resonators system. The properties of the system are studied using the model. The optimum separation between the resonators for the parallel-coupled resonators is provided and the effect of the side-coupling on the system is presented.     

Coupling Losses and Discrimination of Annular Waveguide Laser Resonators

An approach of calculating the coupling losses in a coaxial (or annular) waveguide laser resonator is developed by which the computational time is considerably reduced. Computations of the coupling losses for some TE modes of an annular waveguide, as a function of mirror curvature and position, are presented in the limit of large mirror aperture. It is shown that there exist three special configurations to provide low coupling losses. The resonator properties are discussed. The calculating results are useful for design of annular waveguide laser resonators.     

Cold tests of open coaxial resonators in the range 9–17 GHz

A study of selective properties of coaxial open cylindrical resonators have been conducted experimentally and compared with theory. The resonator consists of an inner circular cylinder symmetrically located inside an outer weakly irregular open waveguide. Several fundamental TE modes were identified over the range 9 to 17 GHz through measurements of the resonant frequencies and the associated loaded quality factors. It has been verified that the structure and the number of resonant modes are both strongly dependent on the diameter of the coaxial insert. Such an electrodynamical system proves to be useful in guided wave applications requiring, for example, filters, frequency-tunable resonators and devices for analyzing the modal composition of a signal.     

Hybrid Si-LiNbO₃ microring electro-optically tunable resonators for active photonic devices

Hybrid Si-LiNbO? electro-optic tunable ring resonators have been proposed and demonstrated as a path to achieving ultracompact and high-speed electro-optic devices. Free standing single crystal LiNbO? microplatelets (~mm long and ~1 μm thick) were obtained from a z-cut LiNbO? substrate by ion implantation and thermal treatment. The platelets were transferred and thermally bonded on top of Si resonators that were fabricated in a Si-on-insulator platform by a 0.18 μm standard complementary metal-oxide-semiconductor process. For the hybrid microring resonator, a free spectral range of 16.5 nm, a finesse F of ~1.67 × 102, a Q-factor of ~1.68 × 10?, and an effective r coefficient of ~1.7 pm/V were achieved for the TE mode. These values are in good agreement with the calculated results.     

Coherent interference induced transparency in self-coupled optical waveguide-based resonators

We propose a self-coupled optical waveguide (SCOW)-based resonator to generate an optical resonance analogous to electromagnetically induced transparency (EIT). The EIT-like effect is formed by the coherent interference between two resonance paths inherent to the SCOW resonator. For cascaded SCOW resonators, the spectrum they produce is significantly affected by the phase shift between them, with the EIT-like peak flattened or split as the two extreme cases. We also investigate the dispersion characteristics of an infinite array of SCOW resonators and show that the dispersion relation and group index in the EIT subband can be greatly changed by a small phase shift between the SCOW resonators.