Higher-order Fourier Components Research Articles

Sensitivity and reproducibility of transverse magneto-optical Kerr effect (T-MOKE) ellipsometry

We report a comprehensive experimental study to analyze the limiting factors and physical mechanisms that determine the achievable performance of transverse magneto-optical Kerr effect (T-MOKE) ellipsometry. Specifically, we explore different approaches to achieve high sensitivity and reduced acquisition times. The best sensitivity is observed for an incident light polarization with balanced s-p components. We also verify experimentally that the method’s theoretical description is accurately describing data for any s-p combination of the incoming light. Furthermore, two alternative measurement strategies are explored by using different measurement sequences for the polarization sensitive optics, which both achieve a very comparable, high quality of results. Signal-to-noise ratios and systematic deviations are measured and analyzed based on a large number of nominally identical measurement repeats, both for entire signal sequences as well as for individual Fourier components of the magneto-optical signal generated by a sinusoidal magnetic field sequence. Hereby, we observe that while higher order Fourier components have a significantly reduced signal amplitude and correspondingly exhibit reduced signal-to-noise and repeatability performance, signal-to-noise ratios always exceed values of 100 even for the lowest signal Fourier component and the lowest signal sample that we investigated, illustrating the extremely precise nature of T-MOKE ellipsometry.

HST/WFC3 Complete Phase-resolved Spectroscopy of White-dwarf-brown-dwarf Binaries WD 0137 and EPIC 2122

Abstract Brown dwarfs in close-in orbits around white dwarfs offer an excellent opportunity to investigate properties of fast-rotating, tidally locked, and highly irradiated atmospheres. We present Hubble Space Telescope Wide Field Camera 3 G141 phase-resolved observations of two brown-dwarf-white-dwarf binaries: WD 0137-349 and EPIC 212235321. Their 1.1–1.7 μm phase curves demonstrate rotational modulations with semi-amplitudes of 5.27% ± 0.02% and 29.1% ± 0.1%; both can be fit well by multi-order Fourier series models. The high-order Fourier components have the same phase as the first-order and are likely caused by hot spots located at the substellar points, suggesting inefficient day/night heat transfer. Both brown dwarfs’ phase-resolved spectra can be accurately represented by linear combinations of their respective day- and nightside spectra. Fitting the irradiated brown dwarf model grids to the dayside spectra require a filling factor of ∼50%, further supporting a hot spot dominating the dayside emission. The nightside spectrum of WD 0137-349B is fit reasonably well by non-irradiated substellar models, and the one of EPIC 21223521B can be approximated by a Planck function. We find strong spectral variations in the brown dwarfs’ day/night flux and brightness temperature contrasts, highlighting the limitations of band-integrated measurements in probing heat transfer in irradiated objects. On the color–magnitude diagram, WD 0137-349B evolves along a cloudless model track connecting the early-L and mid-T spectral types, suggesting that clouds and disequilibrium chemistry have a negligible effect on this object. A full interpretation of these high-quality phase-resolved spectra calls for new models that couple atmospheric circulation and radiative transfer under high-irradiation conditions.

Artifacts in time-resolved Kelvin probe force microscopy.

Kelvin probe force microscopy (KPFM) has been used for the characterization of metals, insulators, and semiconducting materials on the nanometer scale. Especially in semiconductors, the charge dynamics are of high interest. Recently, several techniques for time-resolved measurements with time resolution down to picoseconds have been developed, many times using a modulated excitation signal, e.g., light modulation or bias modulation that induces changes in the charge carrier distribution. For fast modulation frequencies, the KPFM controller measures an average surface potential, which contains information about the involved charge carrier dynamics. Here, we show that such measurements are prone to artifacts due to frequency mixing, by performing numerical dynamics simulations of the cantilever oscillation in KPFM subjected to a bias-modulated signal. For square bias pulses, the resulting time-dependent electrostatic forces are very complex and result in intricate mixing of frequencies that may, in some cases, have a component at the detection frequency, leading to falsified KPFM measurements. Additionally, we performed fast Fourier transform (FFT) analyses that match the results of the numerical dynamics simulations. Small differences are observed that can be attributed to transients and higher-order Fourier components, as a consequence of the intricate nature of the cantilever driving forces. These results are corroborated by experimental measurements on a model system. In the experimental case, additional artifacts are observed due to constructive or destructive interference of the bias modulation with the cantilever oscillation. Also, in the case of light modulation, we demonstrate artifacts due to unwanted illumination of the photodetector of the beam deflection detection system. Finally, guidelines for avoiding such artifacts are given.

Metasurface Enabled Wide-Angle Fourier Lens.

Fourier optics, the principle of using Fourier transformation to understand the functionalities of optical elements, lies at the heart of modern optics, and it has been widely applied to optical information processing, imaging, holography, etc. While a simple thin lens is capable of resolving Fourier components of an arbitrary optical wavefront, its operation is limited to near normal light incidence, i.e., the paraxial approximation, which puts a severe constraint on the resolvable Fourier domain. As a result, high-order Fourier components are lost, resulting in extinction of high-resolution information of an image. Other high numerical aperture Fourier lenses usually suffer from the bulky size and costly designs. Here, a dielectric metasurface consisting of high-aspect-ratio silicon waveguide array is demonstrated experimentally, which is capable of performing 1D Fourier transform for a large incident angle range and a broad operating bandwidth. Thus, the device significantly expands the operational Fourier space, benefitting from the large numerical aperture and negligible angular dispersion at large incident angles. The Fourier metasurface will not only facilitate efficient manipulation of spatial spectrum of free-space optical wavefront, but also be readily integrated into micro-optical platforms due to its compact size.

Nonadiabatic squeezed-photon generation by a Fourier-modified Janszky–Adam scheme

We propose a Fourier-modified Janszky–Adam scheme for the efficient nonadiabatic generation of squeezed photons in a harmonic oscillator with a time-dependent frequency. The higher-order Fourier components of frequency modulations introduce steep frequency changes in the time required for nonadiabatic quantum processes. The proposed Fourier scheme significantly improves the degree of squeezing compared with conventional sinusoidal frequency modulations.

X-ray cross-correlation analysis of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition

We present an x-ray study of liquid crystal membranes in the vicinity of the hexatic-smectic phase transition by means of angular x-ray cross-correlation analysis. By applying two-point angular-intensity cross-correlation functions to the measured series of diffraction patterns the parameters of bond-orientational (BO) order in hexatic phase were directly determined. The temperature dependence of the positional correlation lengths was analyzed as well. The obtained correlation lengths show larger values for the higher-order Fourier components of BO order. These findings indicate a strong coupling between BO and positional order.

Coherent generation and dynamic manipulation of double stationary light pulses in a five-level double-tripod system of cold atoms

We study a five-level double-tripod system of cold atoms for efficiently manipulating the dynamic propagation and evolution of a quantum probe field by modulating four classical control fields. Our numerical results show that it is viable to transform the quantum probe field into a pair of two-color stationary light pulses mutually coupled through two wave packets of atomic spin coherence. The pair of stationary light pulses can be released either from the sample entrance and exit synchronously or just from the sample exit with a controlled time delay. In addition, the two-color stationary light pulses are immune to the fast decay originating from the higher-order Fourier components of atomic spin and optical coherence, and may exhibit the quantum limited beating signals with their characteristic frequency determined by detunings of the four classical control fields. These results could be explored to design novel photonic devices, such as optical routing, beam splitter, and beat generator, for manipulating a quantum light field.

A general non-complex analytical expression for the nth Fourier component of a wavelength-modulated Lorentzian lineshape function

A general, analytical expression for the nth Fourier component of a wavelength-modulated Lorentzian lineshape function in terms of a normalized detuning and a normalized modulation amplitude is derived. The expression is cast in a purely real form and is therefore easier to use than the normally used expression, which is given in terms of various combinations (sums, square roots, and powers) of complex expressions and their complex conjugates. Analytical expressions for the nine first Fourier components ( n =0,…, 8 ), clearly showing their dependence on normalized detuning and modulation amplitude, are explicitly given. Simplified expressions for the even harmonics of the Fourier components on resonance, at which they take their maximum value, solely given in terms of the normalized modulation amplitude, are also explicitly given. It is shown that previously published, numerically calculated conditions for maximization of higher-order Fourier components are incorrect. The normalized modulation amplitudes that maximize the four lowest even harmonics of the Fourier components, i.e. for n=2, 4, 6, and 8, are 2.20, 4.12, 6.08, and 8.06, respectively.

Launch Vehicle Self-Sustained Oscillation from Aeroelastic Coupling Part 2: Analysis

Aeroelastic theory developed in a companion paper is applied to the analysis of a launch vehicle mission, and the corresponding loads are compared with those for other transonic events. Limit cycle amplitudes are computed for several payload fairing lengths using both the present theory and the classical approach for analysis of launch vehicle aeroelastic coupling. Thepresent theory explicitly identie esa generalized timelag as the critical parameter for aeroelastic coupling. The amplitude of the self-sustained oscillation can be signie cantly smaller than that predicted by the so-called stability criterion in the classical theory, depending on the value of this parameter. The singlemode representation forlaunch vehicle aeroelasticanalysis is assessed through transient analysis of the fully coupled system. It is shown that higher-order Fourier components of the oscillating e ow forces can excite system modes other than the bending mode, which was expected to dominatethecoupling. Data exhibiting oscillating e ow states during a e ight of the Titan IV launch vehicle are presented.

A resonant, dielectric micro-motor driven by low ac-voltages (<6V)

An asynchronous, dielectric micro-motor consisting of an Al-SiO2 rotor of 50 to 200 μm diameter was driven with 4 or 8 circularly arranged electrodes in water. The motor elements were fabricated by micromachining. Each electrode was designed to be an oscillatory circuit with a sharp resonance frequency in the upper kHz-range. The resonances at all electrode tips increase the voltage in the stator-rotor gap by a factor of up to 15. As a result, the dielectric rotor operates in a sharp frequency window at 5 Vpp excitation as if driven with more than 75 Vpp. With square wave pulses, the higher order Fourier-components induce several changes in rotor spin direction within two frequency decades. The micro-motor has been driven for hours without noticeable wear. It developed high starting torques and was useful for circular water pumping. The system has the advantage of very sensitive frequency dependence and the low drive voltages (below 10 V) can be produced by most electronic circuits.

Theoretical design of amplitude-modulated pulses for spin decoupling in nuclear magnetic resonance

The problem of low-power spin decoupling over a broad range of chemical shifts in liquid-state nuclear magnetic resonance (NMR) is addressed through the design of periodic amplitude-modulated irradiation schemes. A principal feature of these is the composition of each decoupling period which contains a single modulated pulse in place of a composite-pulse train of the kind used traditionally. To satisfy the theoretical criterion for decoupling, the pulse amplitude is shaped such that the propagator is made cyclic and broadband, meaning here that it equals the identity matrix over a frequency range which is broad compared to the root-mean-square (RMS) pulse amplitude. The method of design is based on the use of the Floquet formalism to provide insight into the influence of the modulation on the dynamics of the irradiated spin-. Modulation functions formed from simple Fourier series are derived in the first instance using perturbation theory to impose the required cyclicity on the propagator. Broader bandwidth solutions are then obtained by the addition of higher-order Fourier components. Finally, numerical refinement of a selected solution is shown to raise the decoupling quality to the standards acceptable in routine high-resolution NMR.

Critical study of multivalley effective-mass equation for donors in silicon.

The applicability of the Twose multivalley effective-mass equation [Phys. Rev. 125, 1560 (1962)] to the shallow donors P, As, Sb, and Bi in silicon is examined critically. It is shown quantitatively that, when the Twose multivalley effective-mass equation is used to estimate the donor binding energies, the error caused by the overestimate of the intervalley potential-energy term exactly compensates for the error due to the omission of the intervalley potential-energy term arising from higher-order Fourier components of the impurity potential. Thus the estimated donor binding energies are reasonable.

Nonlinear-process-induced period doubling of a picosecond transient grating in CdS.

The occurrence of higher-order Fourier components in an originally sinusoidal free-carrier index grating produced in CdS by the interference of two picosecond light pulses is demonstrated by monitoring simultaneously the temporal behavior of the first- and second-order diffraction intensities of transparent probe pulses for the temperature range 10\char21{}140 K. Nonlinear processes which take part in the decay of photoexcited carriers result in a deformation of the shape of the grating, which leads to the occurrence of higher-order Fourier components in the diffraction grating. Theoretical analysis of the experimental results yields the following distinct processes: bimolecular recombination of electrons and holes for the degenerate plasma, free-carrier\char21{}to\char21{}exciton Mott transition for the nondegenerate plasma at low carrier temperatures, and a nonlinear relation between exciton density and free-carrier density at high temperatures.

Mott-transition-induced period doubling in transient-grating experiments in CdS

The occurrence of higher-order Fourier components in an originally sinusoidal free-carrier index grating produced in CdS by interference of two picosecond light pulses is demonstrated by simultaneously monitoring the decay of the first- and second-order diffraction intensity of a transparent probe pulse. A pronounced contribution with doubled period can be attributed to an exciton phase grating formed by binding of electrons and holes of the free-carrier grating.

Resistive Loading by a Finite Plasma Cylinder near the Lower Hybrid Resonance

A theoretical study is carried out for the resistive loading of a finite wave-generating coil concentric with a uniform plasma which is immersed in an axial magnetic field and bounded by conducting end plates. The solutions are used to make a numerical and analytic study of the influence of coupling resonances on resistive loading near the lower hybrid resonance. For proper values of the plasma parameters the coupling resonances are strong and completely mask the hybrid resonance. The higher-order Fourier components of the wave may contribute substantially to the loading resistance affecting both its magnitude and the location of the resonance minima.