Eigenvector method for unstable resonator simulations

Eigenvector method is a numerical method for laser resonator with which all the eigenmodes and eigenvalues can be solved at the same time. This method is extended for unstable resonators combined with the Collins formula and the ABCD ray matrix in this paper. The mode behavior in a resonator with arbitrary irregular structures can be studied exactly and conveniently. An asymmetrical practical unstable resonator and a non-confocal practical unstable resonator are numerically simulated under varying structure parameters, and some new characteristics are found.     

Axisymmetric eigenmodes of magnetic type in an open resonator with spherical mirrors

We develop a rigorous mathematical model describing axisymmetric eigenmodes of magnetic type of open resonators with spherical mirrors. On the assumption that the spectrum of complex eigenfrequencies of an open resonator exists, it is proved that this spectrum is discrete and has finite multiplicity with a single accumulation point at infinity. Theoretical analysis of the spectral characteristics of an open resonator is performed in the case where the wavelength is comparable with the resonator sizes. The limits of applicability of the well-known asymptotic models of open resonators are established. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 9, pp. 787–798, September 2006.     

On classification of eigenmodes of an open resonator with spherical mirrors

A rigorous mathematical model describing eigenmodes of open resonators with spherical mirrors is proposed. Theoretical analysis of the spectral characteristics of an open resonator is performed for the case where the wavelength is comparable with the resonator size. Specification and significant generalization of eigenmode classification based on approximate open-resonator models are proposed. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 12, pp. 1051–1060, December 2008.     

Theory and design of a free-electron maser with two-dimensional feedback driven by a sheet electron beam

The use of two-dimensional Bragg resonators of planar geometry, realizing two-dimensional (2D) distributed feedback, is considered as a method of producing spatially coherent radiation from a large sheet electron beam. The spectrum of eigenmodes is found for a 2D Bragg resonator when the sides of the resonator are open and also when they are closed. The higher selectivity of the open resonator in comparison with the closed one is shown. A time-domain analysis of the excitation of an open 2D Bragg resonator by a sheet electron beam demonstrates that a single-mode steady-state oscillation regime may be obtained for a sheet electron beam of width 100-1000 wavelengths. Nevertheless, for a free-electron maser (FEM) with a closed 2D Bragg resonator, a steady-state regime can also be realized if the beam width does not exceed 50-100 wavelengths. The parameters for a FEM with a 2D planar Bragg resonator driven by a sheet electron beam based on the U-2 accelerator (INP RAS, Novosibirsk) are estimated and the project is described.     

Noise control in enclosures: modeling and experiments with T-shaped acoustic resonators

This paper presents a theoretical and experimental study of noise control in enclosures using a T-shaped acoustic resonator array. A general model with multiple resonators is developed to predict the acoustic performance of small resonators placed in an acoustic enclosure. Analytical solutions for the sound pressure inside the enclosure and the volume velocity source strength out of the resonator aperture are derived when a single resonator is installed, which provides insight into the physics of acoustic interaction between the enclosure and the resonator. Based on the understanding of the coupling between the individual resonators and enclosure modes, both targeted and nontargeted, a sequential design methodology is proposed for noise control in the enclosure using an array of acoustic resonators. Design examples are given to illustrate the control performance at a specific or at several resonance peaks within a frequency band of interest. Experiments are conducted to systematically validate the theory and the design method. The agreement between the theoretical and experimental results shows that, with the help of the presented theory and design methodology, either single or multiple resonance peaks of the enclosure can be successfully controlled using an optimally located acoustic resonator array.     

正三角形及正方形微光学腔模式特性研究

微谐振腔模式特性研究是利用微腔研制新型光电器件的基础．为了研制出能采用平面工艺制作的定向输出的微腔激光器，文章采用解析和数值模拟方法深入研究了正三角形及正方形光学微腔的模式特性，并得到与数值模拟结果符合非常好的解析场分布及模式波长．对正方形光学微腔，把模式组合成满足正方形对称性的场分布，发现其类WG模式只存在品质因子比它小一个数量级以上的偶然简并模式，因此正方形微腔有利于实现真正的单模工作．     

基于异向传输线的亚波长谐振腔设计

 提出了一种新型的谐振腔,该谐振腔的谐振条件与普通谐振腔不同,其两个端面的总相移不必是180°的正整数倍。这种谐振腔由异向传输线和右手传输线两种不同性质的传输线级联构成,它利用耦合腔链作为异向传输线实现负相移,同轴波导作为右手传输线实现正相移,使谐振腔两个端面的总相移为零,满足谐振腔的谐振条件。由于它与传统谐振腔谐振条件不同,理论证明这种谐振腔的长度可远远小于传统谐振腔,设计实例的仿真结果表明这种新型谐振腔的长度最短仅为传统谐振腔的1/7。     

A chiral elastic metamaterial beam for broadband vibration suppression

One of the significant engineering applications of the elastic metamaterial (EMM) is for low-frequency vibration attenuation because of its unusual low-frequency bandgap behavior. However, the forbidden gap from many existing EMMs is usually of narrow bandwidth which limits their practical engineering applications. In this paper, a chiral-lattice-based EMM beam with multiple embedded local resonators is suggested to achieve broadband vibration suppression without sacrificing its load-bearing capacity. First, a theoretical beam modeling is suggested to investigate bandgap behavior of an EMM beam with multiple resonators. New passbands due to dynamic interaction between resonators are unpleasantly formed, which become a design barrier for completely broadband vibration suppression. Through vibration attenuation factor analysis of the resonator, an EMM beam with section-distributed resonators is proposed to enable broadband vibration attenuation function. Required unit number of the resonator in each section is quantitatively determined for complete vibration attenuation in a specific frequency range. Finally, the chiral-lattice-based EMM beam is fabricated, and experimental testing of the proposed structure is conducted to validate the design.     

Why are the eigenmodes of stable laser resonators structurally stable?

Optical resonators are usually examined wave optically. We consider geometrical imaging in stable canonical resonators. We show that, with important exceptions related to eigenmode degeneracy, stable resonators generally image all transverse planes into each other. This insight leads to an intuitive understanding of important properties of the corresponding eigenmodes, most notably their well-known structural stability, i.e., the property that the eigenmodes retain their shape on propagation.     

The scattering cross section of a resonator in a multimode waveguide

The scattering of sound by a single monopole-dipole resonator in a multimode pipe is investigated. The resonator has the form of a Helmholtz resonator connected through a small bar to the pipe wall. In fact, this resonator is a combination of a monopole resonator and a dipole one positioned at the same point. The scattered fields of these resonators are orthogonal to each other. The scattering cross sections of the monopole and dipole resonators in a multimode pipe are calculated. The scattering cross section of the monopole-dipole resonator is determined as the sum of the scattering cross sections of the monopole and the dipole resonators. The friction in a resonator (the monopole or dipole resonator) reduces its scattering cross section by a factor of (1 + β)², where β is the ratio between the friction resistance and the radiation resistance of this resonator.     

Effect of resonator dimensions on nonlinear standing waves

An investigation of the effect of resonator dimensions on nonlinear standing waves in shaped resonators is conducted. Simple forms of the shear viscosity term in the momentum equations are developed for an axisymmetric (2D) resonator and a low aspect ratio rectangular (3D) resonator. The cross sections of the resonators are exponentially expanded and the one-dimensional wave equations are solved by using the Galerkin's method. The quality factors, pressure waveforms, compression ratios, and resonance frequencies are calculated for different dimensionless cross sections and lengths of the resonators. The results show that, apart from the resonator length, the ratio of the cross-section dimension to the length of the resonator is an important parameter. If the ratio is greater than 0.04, the characteristics of the shaped resonator are not affected significantly. However, when the ratio is less than 0.01, the resonance becomes weak, the compression ratio drops substantially, and the frequency response changes as well.     

A candidate three-dimensional GHz left-handed metamaterial composed of coplanar magnetic and electric resonators

GHz left-handed metamaterials (LHMs) composed of coplanar magnetic and electric resonators were proposed in this paper. On each of the unit cells, the electric resonator is placed in the center space of the magnetic resonator. By adjusting the geometrical dimensions of the resonators, negative magnetic response of the magnetic resonator and negative electric response of the electric resonator can be tuned to be coexistent at the same frequencies. The effective constitutive parameters were retrieved. The results verified simultaneous negative permeability and permittivity as well as negative index of the proposed LHMs. Based on the above work, two- and three-dimensional LHMs that make use of coplanar magnetic and electric resonators were proposed. The work done in this paper is of great reference values in fabricating three-dimensional LHMs.     

Fundamental transverse mode of a 3D ring resonator containing selecting elements

The fundamental mode in ring optical resonators containing selecting elements, as well as field absorbing and amplifying media, is described. In such a case, the elements of the ABCD matrix corresponding to a round-trip over the resonator are complex-valued. The stability conditions for such resonators, which differ qualitatively from those for real-valued matrices, are considered. The concepts of bilateral (bidirectional) and unilateral (unidirectional) stabilities introduced earlier for planar resonators are generalized to 3D resonators, including those with complex astigmatism and noncoplanar optical contours. An example of a resonator with unidirectional stability is considered.     

Ultraefficient cooling of resonators: beating sideband cooling with quantum control

The present state of the art in cooling mechanical resonators is a version of sideband cooling. Here we present a method that uses the same configuration as sideband cooling-coupling the resonator to be cooled to a second microwave (or optical) auxiliary resonator-but will cool significantly colder. This is achieved by varying the strength of the coupling between the two resonators over a time on the order of the period of the mechanical resonator. As part of our analysis, we also obtain a method for fast, high-fidelity quantum information transfer between resonators.     

Coupled magnetic resonator optical waveguides

Optical resonators are important devices that control the properties of light and manipulate light–matter interaction. Various optical resonators are designed and fabricated using different techniques. For example, in coupled resonator optical waveguides, light energy is transported to other resonators through near‐field coupling. In recent years, magnetic optical resonators based on LC resonance have been realized in several metallic microstructures. Such devices possess stronger local resonance and lower radiation loss compared with electric optical resonators. This study provides an overall introduction on the latest progress in coupled magnetic resonator optical waveguide (CMROW). Various waveguides composed of different magnetic resonators are presented and Lagrangian formalism is used to describe the CMROW. Moreover, several interesting properties of CMROWs, such as abnormal dispersions and slow‐light effects, are discussed and CMROW applications in nonlinear and quantum optics are shown. Future novel nanophotonic devices can be developed using CMROWs.     

Experimental investigation of the sound absorption performance of compartmented Helmholtz resonators

An experiment was derived in the present study to investigate the effects of coupling up two Helmholtz resonators on their overall sound absorption performance. The effect of compartmenting the cavity of a resonator on its sound absorption property was also discussed. Such cavity compartmentation in fact creates a coupled resonator with a front and a rear resonator. The results show that the coupling in many cases can improve the sound absorption capacity and widen the working bandwidth of the resonators provided that the uncoupled resonance frequency of the front resonator is larger than or equal to that of the rear resonator. Results also suggest that the best compartmentation is that with these uncoupled resonance frequencies very close to each other. It is also found that the undamped plane wave approach is sufficient to predict the resonance frequencies of the coupled resonators within engineering tolerance.     

Noise suppression for micromechanical resonator via intrinsic dynamic feedback

We study a dynamic mechanism to passively suppress the thermal noise of a micromechanical resonator through an intrinsic self-feedback that is genuinely non-Markovian. We use two coupled resonators, one as the target resonator and the other as an ancillary resonator, to illustrate the mechanism and its noise reduction effect. The intrinsic feedback is realized through the dynamics of coupling between the two resonators: the motions of the target resonator and the ancillary resonator mutually influence each other in a cyclic fashion. Specifically, the states that the target resonator has attained earlier will affect the state it attains later due to the presence of the ancillary resonator. We show that the feedback mechanism will bring forth the effect of noise suppression in the spectrum of displacement, but not in the spectrum of momentum.     

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.     

Noise suppression for micromechanical resonator via intrinsic dynamic feedback

We study a dynamic mechanism to passively suppress the thermal noise of a micromechanical resonator through an intrinsic self-feedback that is genuinely non-Markovian. We use two coupled resonators, one as the target resonator and the other as an ancillary resonator, to illustrate the mechanism and its noise reduction effect. The intrinsic feedback is realized through the dynamics of coupling between the two resonators: the motions of the target resonator and the ancillary resonator mutually inthence each other in a cyclic fashion. Specifically, the states that the target resonator has attained earlier will affect the state it attains later due to the presence of the ancillary resonator. We show that the feedback mechanism will bring forth the effect of noise suppression in the spectrum of displacement, but not in the spectrum of momentum.      

Broadband locally resonant beams containing multiple periodic arrays of attached resonators

The plane wave expansion method is extended to study the flexural wave propagation in locally resonant beams with multiple periodic arrays of attached spring-mass resonators. Complex Bloch wave vectors are calculated to quantify the wave attenuation performance of band gaps. It is shown that a locally resonant beam with multiple arrays of damped resonators can achieve much broader band gaps, at frequencies both below and around the Bragg condition, than a locally resonant beam with only a single array of resonators, although the two systems have the same total resonator masses.