Selection of a LGp0-shaped fundamental mode in a laser cavity: Phase versus amplitude masks

Laser beams of a single high-order transverse mode have been of interest to the laser community for several years now. In order to achieve such a mode as the fundamental mode of the cavity, mode selecting elements in the form of a phase or amplitude mask are often placed inside the resonator. Such elements have the role to impose one or several zeros of intensity of the desired mode. In this paper, we consider the use of the most simple phase (amplitude) mask which is a transparent π-plate (absorbing ring) set inside a diaphragmed laser cavity for selecting a pure LG_p0 mode of radial order, p. We analyse, for each type of mask, the origin of the transverse mode selection, and contrary to what one might expect we find that it is not necessary the absorbing mask that results in the highest losses.     

Phase,zeros and poles of the transmission in quantum waveguides with an attached resonator and waveguide superlattices

This work reports on a study of electron transport in two-dimensionally-defined waveguide superlattices modeled by a lateral quantum waveguide with different numbers of attached quantum stubs. It is found that for the system with a single stub, the transmission amplitude exhibits pairs of zeros and poles in the complex-energy plane and the phase of the transmission coefficient drops sharply by π when the transmission passes a zero. This co-occurrence phenomenon of the transmission zero and the phase discontinuity is identical to the feature observed in a recent double-slit-like experiment by Schusteret al.[Nature385, 417 (1997)]. When two or more quantum stubs are attached to the quantum waveguide, each transmission zero seen in the single-stub structure develops into a group of zeros and the phase of the transmission coefficient shows, in correspondence to the group of zeros, a multiple-drop structure. However, not all poles of the waveguide superlattices are found to be paired with zeros and poles that are not paired with zeros are found to be located, in the complex energy plane, at the two sides of a multiple-zero region.     

基于复合超构表面的宽带圆极化双功能器件设计

多功能器件的设计是推动新一代电磁系统发展的重要力量,而超构表面因其对电磁波的幅度、相位和极化等特性的灵活调控在多功能器件领域备受关注.传统的多功能超构表面是利用各向异性单元对相互正交的线极化波具有不同响应的特性,从而设计出适用于线极化的多功能器件.本文提出了一种缝隙加载的环I形复合超构表面单元,通过单元臂长和旋转角度的...     

The effect of dispersive and non-dispersive channels on time delay estimation

The cepstrum and complex demodulation for both wrapped and unwrapped phase outputs are examined as to their performance in the presence of amplitude distortion and dispersion in a channel. With amplitude distortion, complex demodulation is a more powerful processor than cepstrum unless zeros occur in the amplitude spectrum of the distortion. Such singularities disrupt the unwrapped phase output completely and, unless removed, limit the useful region of the wrapped phase output. With phase distortion or dispersion, both the cepstrum and complex demodulation (wrapped phase output) yield biased time delay estimates. A successful phase unwrapping process in complex demodulation enables the correct estimate of the time delay in the presence of dispersion. In addition, the dispersion itself is extracted.     

产生多焦环的衍射相位元件设计的新方法

基于光学变换的一般理论，提出了一种产生多焦环的衍射相位元件的新设计方法，焦环的数目、位置和焦环的宽度可以任意设定．在高斯型激光束照明下进行模拟设计，并讨论了相位量化对结果的影响．理论计算表明，新的设计方法可有效地用于衍射光学元件的设计 关键词：     

Embedded ring resonators for microphotonic applications

We propose a new type of optical resonator that consists of embedded ring resonators (ERRs). The resonators exhibit unique amplitude and phase characteristics and allow designing compact filters, modulators, and delay elements. A basic configuration of the ERRs with two rings coupled in a point-to-point manner is discussed under two operating conditions. An ERR-based microring modulator shows a high operation speed up to 30 GHz. ERRs with distributed coupling are briefly described as well.     

Phase Recovery from the Raman Excitation Profile,Time Domain Information and Transform Theory

The phase recovery from the vibrational Raman excitation profile (REP), which contains only the modulus of the Raman amplitude, is discussed for the general situation where the Raman amplitude, with excitation energy extended in the complex plane, may have zeros in the right-half plane. The focus is on the dispersion method, with all results derived by contour integration. The new results for phase recovery, however, apply to both the dispersion and maximum entropy methods. An iterative procedure, with rapid convergence, is presented to overcome the experimental REP data being given in a limited energy range. The forward transform from the electronic absorption spectrum (ABS) to the REP and the inverse transform from the REP to the ABS are presented in a unified manner. The ubiquitous Hilbert transform is shown to be readily evaluated by the fast Fourier transform algorithm. Calculations are presented for β-carotene, a two-mode harmonic model with diffuse vibrational structure, azulene and iodobenzene to illustrate the theory. © 1997 John Wiley & Sons, Ltd.     

Phase of reflection of very low energy electrons at crystal surfaces

The amplitude coefficients of electron reflection at crystal surfaces are complex numbers, each of which may be characterized by a reflection intensity (the squared modulus of the coefficient) and a phase. The phase of reflection of very low energy (? 10 eV) electron reflection is described on the basis of existing theory, and experimental approaches to phase determination are reviewed. Theoretical properties of the phase are described on the basis of the two-beam dynamical theory of diffraction. The model considered is an idealized substrate crystal with an attached selvedge (surface region). The indirect effect of inelastic scattering (absorption) is included by going to complex values of the electron energy or of the surface-normal component K of the propagation vector. In the absence of a selvedge the phase is determined solely by the band structure of the substrate crystal. If a selvedge is present there are large additional effects on the phase associated with zeros of the amplitude coefficient of reflection on the complex K plane. The experimental approaches considered are: (1) measurement of the kinetic energy distributions of ions produced in the field ion microscope, and (2) measurement of the periodic deviations from the Schottky line in field-assisted thermionic emission and photo-emission. Recent results of phase determination for W (011) surface by method (1) are summarized and compared with theoretical expectations.     

Zeros of the scattering amplitude in the complex angle plane

The possibility of reconstructing the scattering amplitude with the aid of the zeros in the complex cos θ plane of the differential cross section is considered. The reconstruction process is demonstrated in two examples. The location of the zeros of the scattering amplitude is examined for the strong absorption and optical models. It appears that there exists a correlation between the position of the zeros and the strength of the absorption.     

光学变换中的离散取样方法

本文研究了光学变换中的离散取样问题。基于幺正变换的考虑,求得了光学变换中离散取样方法所依据的条件。导出了包含取样单元透光孔作用的光传播矩阵。最后,以自然序Walsh变换为例,具体计算了变换所需全息透镜的振幅与相位分布及相应的误差。 关键词：     

飞秒激光在锥形镀膜探针传输中相位奇异的研究

利用数值模拟的方法对飞秒激光脉冲中光波振荡一个周期内不同时刻的光场进行了计算、比较, 获得了输出端平面内各空间点处光场的最大值及达到最大值时对应的时间, 得到了探针近场的振幅和相位分布. 在研究振幅分布的过程中发现, 在探针输出端的有些区域振幅始终为零, 即在光波振荡的一个周期内这些区域始终为相位奇异点; 通过分析相位分布得到了相位奇异随时间的演化及相位奇异的特点.     

A resolution of the question of ππ and Kπ “anomalies”

By means of considerations on the interplay between harmonic moments and amplitude zeros in ππ and Kπ scattering, we resolve the question of anomalies in the harmonic moments. The systematics of ππ amplitude zeros is also shown to be in qualitative agreement with the hypothesis of the existence of the double-pole-killing dual zeros.     

Microwave Polarimeter with Synchronous Recording of Stokes Parameters

We describe a new method for designing a polarimeter which estimates simultaneously the four polarization parameters of the measured microwave signal, using complex phase and amplitude modulation. It is shown that, by choosing an appropriate modulation law, one can reduce significantly the dependence of the accuracy of measurement of polarization parameters on the systematic error of the meter. A block diagram of the polarimeter is presented and its main characteristics are described.     

Do amplitude zeros persist in higher order?

We consider the phenomenon of amplitude zeros, first discovered in the process d u→W^?γ. Using spin-0 particles, we find that the zeros persist for radiation from internal bubbled. However, when we consider the 1-loop correction to the scalar three-point function (with a photon attached in all possible ways), it is shown, by an explicit calculation, that amplitude zeros do not persist in general.     

Predistortion techniques for synthesizing coupled microring filters with loss

A general method based on the predistortion technique is presented for determining the optimum coupling parameters of multiple-coupled microring filters in the presence of known uniform resonator loss. The technique involves predistorting the filter transfer function by shifting its poles and zeros to compensate for loss in the microring resonators due to material absorption, surface roughness scattering, coupling loss and bending loss. It is shown that by sacrificing some in-band insertion loss, both the amplitude and group delay responses of the filter can be recovered when loss is present. Application of the method to synthesizing lossy microring filters in both the digital z-domain and analog s-domain will be presented. The proposed technique is general in that it can be applied to both amplitude and phase filters constructed of coupled microresonators in the most general two-dimensional coupling topology.     

Structure in S-wave ππ scattering

Phenomenological phase shift data and crossing sum rules clearly indicate the presence of zeros below threshold in both S-wave ππ amplitudes, just as predicted by current algebra. Some preference for a resonant I = 0 amplitude emerges.     

The phase of the Riemann zeta function

We, offer an alternative interpretation of the Riemann zeta functionζ(s) as a scattering amplitude and its nontrivial zeros as the resonances in the scattering amplitude. We also look at several different facets of the phase of theζ function. For example, we show that the smooth part of theζ function along the line of the zeros is related to the quantum density of states of an inverted oscillator. On the other hand, for ℜs>1/2, we show that the memory of the zeros fades only gradually through a Lorentzian smoothing of the delta functions. The corresponding trace formula for ℜs≫1 is shown to be of the same form as generated by a one-dimensional harmonic oscillator in one direction along with an inverted oscillator in the transverse direction. Quite remarkably for this simple model, the Gutzwiller trace formula can be obtained analytically and is found to agree with the quantum result.     

Characterizing the Topological Properties of 1D Non-Hermitian Systems without the Berry–Zak Phase

A new method is proposed to predict the topological properties of 1D periodic structures in wave physics, including quantum mechanics. From Bloch waves, a unique complex valued function is constructed, exhibiting poles and zeros. The sequence of poles and zeros of this function is a topological invariant that can be linked to the Berry–Zak phase. Since the characterization of the topological properties is done in the complex plane, it can easily be extended to the case of non-Hermitian systems. The sequence of poles and zeros allows to predict topological phase transitions.     

存在球差和失焦下电子光学传递函数和脉冲响应函数

根据电子光学理论,球差和失焦引起附加相位移为γ,相干的振幅和相位衬度传递函数为cosγ和sinγ。它们的傅里叶逆变换给出脉冲响应函数的实部和虚部。本文讨论了cosγ和sinγ的零点和极值点,这些点将衍射平面划分为一系列环带。证明了当无量纲失焦量Δ=N^1/2(N为正整数)时各环带上cosγ,sinγ的积分相同,即对脉冲响应函数中心值的贡献相同。本文讨论了使cosγ或sinγ的积分取极大值或极小值,亦即使脉冲响应函数中心值或中心强度取极大值或极小值的条件。本文还讨论了脉冲响应函数最佳均方 关键词：     

High-accuracy measurer of complex reflection coefficient of SHF transmission lines

We describe a new method of constructing a device for simultaneous measurement of the relative amplitude and phase difference of microwave signals, using complex phase manipulation of input signals. It is shown that systematic errors of measurement are significantly lower in the proposed amplitude and phase meter. Root-mean-square values are obtained for a system with nonideal elements. A block diagram of the device is presented and its principal characteristics are described. Institute of Radiophysics and Electronics, Armenian Academy of Sciences, Erevan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 9, pp. 1182–1188, September, 1997.