Quantum amplifiers at microwave frequencies using Josephson junctions

Abstract

Josephson junctions are quantum mechanical devices with sinusoidal nonlinearity and their use as amplifiers of non-classical microwaves in cavities at low temperatures, is discussed. Self-pumped amplifiers as well as externally pumped three- and four-photon amplifiers are considered, and a quantum theory that describes their operation is developed. It is shown that the sinusoidal nonlinearity can be expanded into a series of terms, the first few of which are familiar from quantum optical amplifiers that use nonlinear optical materials, while the others are higher order corrections.     

Nonlinear modes in optical fibers

It is shown that the electromagnetic field generated in an optical fiber operating in a nonlinear regime has the form of nonlinear guided modes—cnoidal (periodic) waves which transform into monochromatic fiber modes in the linear operating regime. The cnoidal modes are generated due to nonlinear polarization effects in the dielectric medium. These effects can be described by equations with sinusoidal nonlinearity.     

Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid

This paper investigates the effect of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force on the transverse vibration of the double-walled carbon nanotubes conveying fluid and the interaction between two types of nonlinearities. By using the Hamilton’s principle, the nonlinear governing equations of the double-walled carbon nanotubes conveying fluid are deduced. The effects of two types of nonlinearities on the coaxial and noncoaxial vibrations of the double-walled carbon nanotubes conveying fluid are discussed in numerical examples. The results show that the effect of geometric nonlinearity on the amplitude–frequency properties can be neglected if two types of nonlinearities are simultaneously considered. Compared with the uncoupling, the coupling between the longitudinal and transverse vibrations has little effect on the amplitude–frequency properties with considering two types of nonlinearities simultaneously. However, the coupling has significant effect on the amplitude–frequency properties with only considering the geometric nonlinearity.     

Physical Mechanisms of Nonlinear Optical Activity in Crystals

Possible mechanisms of nonlinear optical activity (NLOA) in crystals connected with electronic nonlinearities are considered in this work. Relations are obtained that describe nonlinear changes in the structure of light polarization in a medium having weak, arbitrary nonlinearity. It is shown that in media with third-order nonlinearity, NLOA may be linked either with the distribution of nonlinearity in the medium or with the anisotropy of nonlinear absorption-so-called absorptive and dispersive NLOA.     

Frequency domain analysis of nonlinear systems driven by multiharmonic signals

This paper examines the output properties of static power-series nonlinearities driven by periodic multiharmonic signals with emphasis given to their effect on linear frequency response function (FRF) measurements. The analysis is based on the classification of nonlinear distortions into harmonic and interharmonic contributions. The properties of harmonic contributions are examined in detail and explicit formulae are derived, by which the number of harmonic contributions generated at the test frequencies can be calculated for odd-order nonlinearities up to, and including, the ninth order. Although an analytic solution for any odd-order nonlinearity is still under investigation, a heuristic methodology is developed that solves this problem. It is shown that the derived formulae provide a useful tool in the examination of the behavior of FRF measurements in the presence of nonlinear distortions. Based on these formulae, different approaches in classifying nonlinear distortions are then compared with respect to their suitability in assessing the influence of system nonlinearities on linear FRF measurements.     

Numerical determination of electric field forces and capacitance of pressure condenser microphone

Nonuniform deflection of a pressure condenser microphone membrane causes nonlinearities of a relationship between peak deflection of the membrane and the induced voltage. This paper describes how the numerical analysis carried out with the finite element method can help in more accurate determination of this nonlinearity. The dependence of the inverse capacitance (proportional to the induced voltage) on the deflection can be well approximated with the third-order polynomial and the electric field force with the second-order polynomial. There is a major influence of the nonlinearity of the inverse capacitance compared to the nonlinearity of the overall force on the microphone's overall nonlinearity. The deflection profile of the analyzed microphone's membrane is deduced from the values for a 1" microphone.     

Noise figure measurements on nonlinear devices

A study of the effect of a cubic nonlinearity on the Y-factor method for measuring noise figure is performed. By hypothesis, the Y-factor technique does not take nonlinearities into account. It is shown that the presence of the nonlinearity largely influences the measured noise figure value. An alternative, single-tone noise figure measurement setup is proposed to correct the problem     

杜芬型滑移系统振动非线性评估

以叠加原理为判别准则,通过计算杜芬型滑移系统对双频简谐激励作用的动力响应,分析系统的振动非线性及其影响因素。结果表明,恢复力非线性与阻尼非线性存在相互作用机制,一定条件下摩擦阻尼的增加可以抑制恢复力非线性的发挥,系统整体振动的非线性并非两者效应的简单累加。外部激励的影响体现在其幅值和频率两个方面,双频激励强度均较大时会激发系统的振动非线性。     

Hot‐Electron‐Assisted Femtosecond All‐Optical Modulation in Plasmonics

The optical Kerr nonlinearity of plasmonic metals provides enticing prospects for developing reconfigurable and ultracompact all‐optical modulators. In nanostructured metals, the coherent coupling of light energy to plasmon resonances creates a nonequilibrium electron distribution at an elevated electron temperature that gives rise to significant Kerr optical nonlinearities. Although enhanced nonlinear responses of metals facilitate the realization of efficient modulation devices, the intrinsically slow relaxation dynamics of the photoexcited carriers, primarily governed by electron–phonon interactions, impedes ultrafast all‐optical modulation. Here, femtosecond (≈190 fs) all‐optical modulation in plasmonic systems via the activation of relaxation pathways for hot electrons at the interface of metals and electron acceptor materials, following an on‐resonance excitation of subradiant lattice plasmon modes, is demonstrated. Both the relaxation kinetics and the optical nonlinearity can be actively tuned by leveraging the spectral response of the plasmonic design in the linear regime. The findings offer an opportunity to exploit hot‐electron‐induced nonlinearities for design of self‐contained, ultrafast, and low‐power all‐optical modulators based on plasmonic platforms.     

Stability of steady-state vibrations of a nonlinear,imperfectly elastic two-mass system subjected to harmonic excitation

A study is made of the stability of steady-state vibrations of harmonically excited two-mass systems with allowance for the imperfect elasticity of the materials and cubic nonlinearities. It is shown that, in the general case, when imperfect elasticity is accounted for by the model constructed by G. S. Pisarenko, an increase in the inflection of the skeleton curves with an increase in the amplitude of the vibrations may lead to the appearance of regions of instability and amplitude jumps. The averaging method is used to determine the conditions under which the amplitudes will be stable. Resonance curves of amplitude are constructed for a two-mass system modeling an imperfectly elastic dynamic vibration damper. The range of stable amplitudes is also determined for this system. It is shown that a cubic nonlinearity can either reinforce or offset the inflections caused by inelasticity.Translated from Problemy Prochnosti, No. 8, pp. 69–76, August, 1994.     

Essential Nonlinearity of Phase-Sensitive Detector Characteristics

The effect of essential nonlinearity of phase-sensitive detector characteristics is studied and determined theoretically in detail, assuming that the input signal is a sine wave in the presence of additive narrow-band Gaussian noise. Minimum, maximum, and limiting values of nonlinearities of detector characteristics as functions of the input signal-to-noise ratio and the phase angle between the input signal and the reference wave are determined by means of computer-aided analysis. A set of curves that can be used to evaluate in detail the essential nonlinearities of detector performance and characteristics over a wide range of operating conditions and significant parameters is presented. Particular emphasis is placed on the determination of optimum detector operating conditions for minimum essential nonlinearities in wide-band Fourier-transform high-resolution nuclear magnetic-resonance and electron-spin-resonance spectrometers.     

Optimal signal processing of nonlinearity in swept-source and spectral-domain optical coherence tomography

We demonstrate the efficiency of the convolution using an optimized Kaiser-Bessel window to resample nonlinear data in wavenumber for Fourier-domain optical coherence tomography (OCT). We extend our previous experimental demonstration that was performed with a specific swept-source nonlinearity. The method is now applied to swept-source OCT data obtained for various simulated swept-source nonlinearities as well as spectral-domain OCT data obtained from both simulations and experiments. Results show that the new optimized method is the most efficient for handling all the different types of nonlinearities in the wavenumber domain that one can encounter in normal practice. The efficiency of the method is evaluated through comparison with common methods using resampling through interpolation prior to performing a fast-Fourier transform and with the accurate but time-consuming discrete Fourier transform for unequally spaced data, which involves Vandermonde matrices.     

A REVIEW OF THE MATHEMATICAL APPROACHES TO NONLINEAR GRINDING AND A SUGGESTED GENERAL TREATMENT FOR ENVIRONMENTAL NONLINEARITIES BASED ON THE USE OF INFLUENCE FUNCTIONS

Grinding processes such as rod milling and fine dry ball milling sometimes exhibit nonlinear breakage characteristics. These nonlinearities may be due to either sample heterogeneity which gives an apparent nonlinearity or environmental effects which are truly nonlinear. Previous treatments of both of these types of nonlinearities are reviewed and discussed and a new general treatment is proposed for the latter based on the use of influence functions. This treatment allows for both “shielding” and “cushioning” effects and provides a general framework for treating environmental grinding nonlinearities. Simulated results are given for both types of environmental nonlinearities with the influence function approach and methods of applying the approach are discussed.     

Phase-Sensitive Detector Nonlinearity at the Signal Detection in the Presence of Noise

The essential nonlinearity characteristics of a phase-sensitive detector are studied theoretically, assuming that the input signal is a sine wave in the presence of additive narrow-band Gaussian noise. Three interesting cases of the nonlinearity of the phase-sensitive detector characteristics are analyzed by means of the expression which has been derived for the output signal-to-input noise ratio as a function of the input signal-to-noise ratio, the reference wave-to-noise ratio, and the phase angle between the input signal and reference wave. In the first case, the detector nonlinearity NA as a function of the input signal-to-noise ratio is determined. In the second and third cases, the detector nonlinearities NB and NC as a function of the phase angle between the input signal and the reference wave are obtained. The results are presented as closed-form analytical expressions. Several interesting cases are plotted as a function of the significant parameters. Besides being important in themselves, the results are of a general interest because they may be used to estimate essential nonlinearities in some other more complicated cases.     

The generation of binary and near-binary pseudorandom signals: an overview

Pseudorandom signals have been widely used for system identification. Maximum length binary (MLB) signals are the best known class of pseudorandom signals, because of their ease of generation using feedback shift registers, but it is less well known that there are several other classes of binary and near-binary signals with identical, or nearly identical properties. An overview of these classes of signals is given, and the design of a new MATLAB routine incorporating all these classes of signals is described. The importance of the choice of MLB signal to use in particular applications is illustrated with the identification of a Wiener system having a quadratic nonlinearity and a cubic nonlinearity. Using correlation analysis to estimate the linear system weighting function, errors due to the nonlinearities can be reduced if an appropriate choice is made of feedback connections and of data length used for the estimation.     

Polarization Effects in Heterodyne Interferometry

Abstract

A detailed analysis of the polarization effects which lead to nonlinearity in the non-ideal optical heterodyne interferometer is presented. Extensive use is made of the coherency matrix representation by setting up a ‘cross-coherency matrix’ representation. A generalized treatment of periodic phase errors (nonlinearity) is then presented. Individual contributions to the nonlinearity have been characterized as either ‘independent’ or ‘dependent’ phase errors. In the single-pass plane-mirror heterodyne system, to which the approach is applied, phase errors for rotational misalignment of the nominally orthogonal linearly polarized input states, beam splitter leakage, non-orthogonality, ellipticity and the effect of misaligned polarizer-mixer are explicitly considered. The latter effect is found to produce nonlinearity only when in combination with any one of the first three and is therefore a dependent phase error. The nonlinearity arising from ellipticity is identical with that from rotational misalignment except that it has an offset. Rotational misalignment and ellipticity produce nonlinearity at the second harmonic and are second order for practical set-ups. It is also found that combinations of positive (anticlockwise) and negative (clockwise) angular misalignments of the azimuth of the states, non-orthogonality and misorientations of the polarizer-mixer, all relative to the polarizing beam splitter axes, lead to different peak-to-peak nonlinearities in the given system.     

Electromechanical modeling and analytical investigation of nonlinearities in energy harvesting piezoelectric beams

Piezoelectric materials are extensively applied for vibrational energy harvesting especially in micro-scale devices where other energy conversion mechanisms such as electromagnetic and electrostatic methods encounter fabrication limitations. A cantilevered piezoelectric bimorph beam with an attached proof (tip) mass for the sake of resonance frequency reduction is the most common structure in vibrational harvesters. According to the amplitude and frequency of applied excitations and physical parameters of the harvester, the system may be pushed into a nonlinear regime which arises from material or geometric nonlinearities. In this study nonlinear dynamics of a piezoelectric bimorph harvester implementing constitutive relations of nonlinear piezoelectricity together with nonlinear curvature and shortening effect relations, is investigated. To achieve this goal first of all a comprehensive fully-coupled electromechanical nonlinear model is presented through a variational approach. The governing nonlinear partial differential equations of the proposed model are order reduced and solved by means of the perturbation method of multiple scales. Results are presented for a PZT/Silicon/PZT laminated beam as a case study. Findings indicate that material nonlinearities of the PZT layer has the dominant effect leading to softening behavior of the frequency response. At the primary resonance, different frequency responses of the extracted power can be distinguished according to the excitation amplitude, which is due to harmonic generation as a result of piezoelectric nonlinearity. The extracted power is analytically computed and validated with a good agreement by a numerical solution.     

Effect of competing cubic-quintic nonlinearities on the modulational instability in nonlocal Kerr-type media

We investigate analytically and numerically the modulational instability (MI) of plane waves under competing nonlocal cubic-local quintic nonlinearities. The generic properties of the MI gain spectra are then demonstrated for the Gaussian response function, exponential response function, and rectangular response function. Special attention is paid to competing nonlocal cubic-local quintic nonlinearities on the MI. We observe that the focusing local quintic nonlinearity increases the growth rate and bandwidth of instability contrary to the small values of defocusing local quintic nonlinearity which decrease the growth rate and bandwidth of instability. Numerical simulations of the full model equation describing the dynamics of the waves are been carried out and leads to the development of pulse trains, depending upon the sign the quintic nonlinearity.     

Periodic and solitary wave solutions for ultrashort pulses in negative-index materials

Abstract

We present a detailed analysis for the existence of dark and bright solitary waves as also fractional-transform solutions in a nonlinear Schrödinger equation model for competing cubic–quintic and higher-order nonlinearities with dispersive permittivity and permeability. Parameter domains are delineated in which these ultrashort optical pulses exist in negative-index materials (NIMs). For example, dark solitons exist for the case of normal second-order dispersion, anomalous third-order dispersion, self-focusing Kerr nonlinearity, and non-Kerr nonlinearities, while the bright solitons exist for the case of anomalous second-order dispersion, normal third-order dispersion, self-focusing Kerr nonlinearity, and non-Kerr nonlinearities. This is contrary to the situation in ordinary materials.     

Second-harmonic generation in silicon waveguides strained by silicon nitride

Silicon photonics meets the electronics requirement of increased speed and bandwidth with on-chip optical networks. All-optical data management requires nonlinear silicon photonics. In silicon only third-order optical nonlinearities are present owing to its crystalline inversion symmetry. Introducing a second-order nonlinearity into silicon photonics by proper material engineering would be highly desirable. It would enable devices for wideband wavelength conversion operating at relatively low optical powers. Here we show that a sizeable second-order nonlinearity at optical wavelengths is induced in a silicon waveguide by using a stressing silicon nitride overlayer. We carried out second-harmonic-generation experiments and first-principle calculations, which both yield large values of strain-induced bulk second-order nonlinear susceptibility, up to 40 pm V(-1) at 2,300 nm. We envisage that nonlinear strained silicon could provide a competing platform for a new class of integrated light sources spanning the near- to mid-infrared spectrum from 1.2 to 10 μm.