Arbitrary Spectral Shape Research Articles

Fast likelihood-free reconstruction of gravitational wave backgrounds

We apply state-of-the-art, likelihood-free statistical inference (machine-learning-based) techniques for reconstructing the spectral shape of a gravitational wave background (GWB). We focus on the reconstruction of an arbitrarily shaped signal (approximated by a piecewise power-law in many frequency bins) by the LISA detector, but the method can be easily extended to either template-dependent signals, or to other detectors, as long as a characterisation of the instrumental noise is available. As proof of the technique, we quantify the ability of LISA to reconstruct signals of arbitrary spectral shape (blind reconstruction), considering a diversity of frequency profiles, and including astrophysical backgrounds in some cases. As a teaser of how the method can reconstruct signals characterised by a parameter-dependent template (template reconstruction), we present a dedicated study for power-law signals. While our technique has several advantages with respect to traditional MCMC methods, we validate it with the latter for concrete cases. This work opens the door for both fast and accurate Bayesian parameter estimation of GWBs, with essentially no computational overhead during the inference step. Our set of tools are integrated into the package GWBackFinder, which is publicly available in GitHub.

On the non-uniqueness of the kernel of the Zakharov equation in intermediate and shallow water: the connection with the Davey–Stewartson equation

The Zakharov equation describes the evolution of weakly nonlinear surface gravity waves for arbitrary spectral shape. For deep-water waves, results from the Zakharov equation are well established. However, for two-dimensional propagation, in intermediate and shallow water, there are problems related to the treatment of apparent singularities in the contribution of the wave-induced set-up to the evolution of the surface gravity waves. More specifically, the kernel in the integral term is characterized by a regular and an apparent singular contribution. Here, we show that the Davey–Stewartson equation can be directly derived from the Zakharov equation, also in the shallow water limit. This result provides guidance on how to treat the singular contribution to the evolution of the action variable. A relevant result that is obtained is that the growth rate obtained from the stability analysis of a plane wave in shallow water does not depend on the singular part of the kernel of the Zakharov equation.

In-fiber duplex optical antenna and its programmable spectral filter application.

In this Letter, we have proposed an in-fiber duplex optical antenna based on a 45° radiated titled fiber grating (RTFG), in which the 45° RTFG not only radiates the light from the fiber core to the free space, but also harvests the light from the free space back into the fiber core. Using the finite difference time domain method, we have theoretically analyzed the light recoupling efficiency of the RTFG. The simulated results have shown that the RTFG-based optical antennas have a maximum coupling efficiency of 10%. The recoupling wavelength and efficiency are related to the grating period and horizontal incidence angle. Furthermore, we demonstrate a programmable spectral filtering system based on the 45° RTFG antennas, which could achieve filtering with arbitrary spectral shapes. The spectral resolution is 0.4 nm and the insertion loss is around 20 dB. The proposed programmable spectral filtering system has a compact structure compared with the traditional filter.

Exact solution of polaritonic systems with arbitrary light and matter frequency-dependent losses.

In this paper, we perform the exact diagonalization of a light-matter strongly coupled system taking into account arbitrary losses via both energy dissipation in the optically active material and photon escape out of the resonator. This allows us to naturally treat the cases of couplings with structured reservoirs, which can strongly impact the polaritonic response via frequency-dependent losses or discrete-to-continuum strong coupling. We discuss the emergent gauge freedom of the resulting theory and provide analytical expressions for all the gauge-invariant observables in both the Power-Zienau-Woolley and the Coulomb representations. In order to exemplify the results, the theory is finally specialized to two specific cases. In the first one, both light and matter resonances are characterized by Lorentzian linewidths, and in the second one, a fixed absorption band is also present. The analytical expressions derived in this paper can be used to predict, fit, and interpret results from polaritonic experiments with arbitrary values of the light-matter coupling and with losses of arbitrary intensity and spectral shape in both the light and matter channels. A Matlab code implementing our results is provided.

Analysis and Design Specifications for Full-Duplex Radio Transceivers Under RF Oscillator Phase Noise With Arbitrary Spectral Shape

In this paper, the effects of oscillator phase noise (PN) with arbitrary spectral characteristics on the self-interference (SI) cancelation capability of a full-duplex radio (FDR) transceiver are addressed, and design considerations for optimized phase-locked loop (PLL) design in FDR are given. This paper first presents a full-duplex transceiver model that inherently mitigates most of the phase-noise effects from the SI signal. The remaining effect of the PN is then analyzed, and closed-form expressions for the SI power are derived. In the simulations part, a practical PLL-type oscillator is used, which is based on the arbitrary mask phase-noise model. Analytical derivations are verified with the simulations, and the SI cancelation performance is thoroughly studied with various parameters. Design considerations are finally given for oscillator design in FDR transceivers, with the help of tangible parameters of the PLL-type oscillators.

Waveform Design With Unit Modulus and Spectral Shape Constraints via Lagrange Programming Neural Network

To maximize the transmitted power available in active sensing, the probing waveform should be of constant modulus. On the other hand, in order to adapt to the increasingly crowed radio frequency spectrum and prevent mutual interferences, there are also requirements in the waveform spectral shape. That is to say, the waveform must fulfill constraints in both time and frequency domains. In this work, designing these waveforms is formulated as a nonlinear constrained optimization problem. By introducing auxiliary variable neurons and Lagrange neurons, we solve it using the Lagrange programming neural network. We also analyze the local stability conditions of the dynamic neuron model. Simulation results show that our proposed algorithm is a competitive alternative for waveform design with unit modulus and arbitrary spectral shapes.

Spectrum-Sliced Microwave-Photonic Filter Based on Fourier Transform of Modified Optical Spectrum

A new technique is presented to reconfigure the dispersion-induced RF fading in a spectrum-sliced microwave photonic filter to an arbitrary spectral shape, including the flat-top response with rectangular shape and operating frequencies beyond conventional baseband. The technique is based on the Fourier transform of the modified optical source power spectrum, which is realized by applying a designed optical amplitude and phase manipulation using a diffraction-based spectral pulse shaper to the ports of a dual-output Mach-Zehnder electro-optic modulator in combination with a broadband light source. This scheme is fundamentally different from earlier finite-impulse-response-based spectrum-sliced microwave-photonic filters that require specific slicing elements for optical taps, but offers the same flexibility in realizing various filter passband characteristics with the added benefit of widely shape-invariant tuning and a single passband response. Experimental results verify the technique and demonstrate a continuously tunable dispersion-induced RF fading up to 20 GHz, exhibiting shape invariance and a flat-top response.

Arbitrary holographic spectral shaping of plasmonic broadband excitations.

We demonstrate a new method for controlling the broadband excitations of surface plasmons. This method is based on computer-generated holographic gratings and enables not only the coupling of the broadband illumination with surface plasmons, but also the arbitrary shaping of their spectra. As an example, we demonstrate several spectral shapes numerically and measure them experimentally, finding a good agreement with the simulation results. In addition, we show the potential for shaping the plasmonic spatial profile simultaneously with its spectral profile. This method may be useful for on-chip communication and light filtering as well as for sensing and temporal manipulation of ultrashort pulses.

All-fiber arbitrary and precise pulse spectral shaping

A fiber-loop-based electro-optic (EO) modulation system is proposed and demonstrated to realize both broadband and high-resolution spectral shaping of laser pulses through direct phase modulation. With this fiber-loop EO modulator, arbitrary spectral shape can be carved and the modulation precision is up to 0.004 nm. The laser spectral bandwidth can be steadily broadened from several MHz to several nanometers through tuning the pulse cycle times and the programmable driving signal. One representative shaped spectrum is presented with a <0.01 nm mismatch to the simulated results, which is used to effectively pre-compensate the pulse spectral distortion during amplification.

On a random time series analysis valid for arbitrary spectral shape

AbstractWhile studying the problem of predicting freak waves it was realized that it would be advantageous to introduce a simple measure for such extreme events. Although it is customary to characterize extremes in terms of wave height or its maximum it is argued in this paper that wave height is an ill-defined quantity in contrast to, for example, the envelope of a wave train. Also, the last measure has physical relevance, because the square of the envelope is the potential energy of the wave train. The well-known representation of a narrow-band wave train is given in terms of a slowly varying envelope function ${\it\rho}$ and a slowly varying frequency ${\it\omega}=-\partial {\it\phi}/\partial t$ where ${\it\phi}$ is the phase of the wave train. The key point is now that the notion of a local frequency and envelope is generalized by also applying the same definitions for a wave train with a broad-banded spectrum. It turns out that this reduction of a complicated signal to only two parameters, namely envelope and frequency, still provides useful information on how to characterize extreme events in a time series. As an example, for a linear wave train the joint probability distribution of envelope height and period is obtained and is validated against results from a Monte Carlo simulation. The extension to the nonlinear regime is, as will be seen, fairly straightforward.

Analysis of SBS Gain Shaping and Threshold Increase by Arbitrary Strain Distributions

Fibers with a longitudinal strain distribution can be used to shape the stimulated Brillouin scattering (SBS) gain spectrum or to increase the SBS threshold power. Theoretical analysis and experimental results on the SBS gain spectrum of coiled fibers with a continuous and arbitrary distribution of longitudinal strain are presented. The concept of a critical gain factor for determining the SBS threshold power with a simple formula is reviewed for fibers with different parameters and spectral shapes. A fiber coiling machine for high coiling forces is described for realizing permanent strain distributions with a maximum strain of more than 3%. SBS spectra were broadened to a spectral width of 1.7 GHz. Measurements verify a significant SBS gain suppression by a factor of 40, which is in excellent agreement with the theoretical analysis. Finally, synthetic triangular and broadened Lorentzian SBS spectral shapes with a spectral width of 550 MHz are demonstrated. The results can be used to suppress SBS in high-power fiber lasers and amplifiers or to tailor almost any arbitrary SBS spectral shapes, which could be useful for slow-light or active optical filter applications.

Spectral broadening of incoherent nanosecond pulses in a fiber amplifier

Amplification of incoherent light pulses in a relatively short active fiber is treated. Spectral broadening due to the self-phase modulation effect at negligibly small dispersion has been studied theoretically. The expression for the shape of the output spectrum has been obtained for input pulses of arbitrary temporal and spectral shape at various gain coefficients. The expression is found to be simplified in case of a hyperbolic secant temporal shape. The calculated shapes have been compared with the experimentally measured spectra for Q-switched fiber laser nanosecond pulses amplified in Yb-doped fiber, demonstrating excellent agreement of theory and experiment. The spectrum of the output pulse is shown to be composed of two different-scale structures: a narrow central part copying the initial shape and broad exponential tails that grow with increasing output power.

利用光参量啁啾脉冲放大进行任意光谱整形方案的稳定性分析

利用光参量啁啾脉冲放大进行任意光谱整形方案的稳定性分析

利用光参量啁啾脉冲放大进行任意光谱整形方案的稳定性分析

利用光参量啁啾脉冲放大进行任意光谱整形方案的稳定性分析

利用光参量啁啾脉冲放大进行任意光谱整形方案的稳定性分析

利用光参量啁啾脉冲放大进行任意光谱整形方案的稳定性分析

A Unified Framework for Interference Analysis of Noncoherent MFSK Wireless Communications

This paper presents a new unified analytical technique for accurate interference analysis of noncoherent M-ary frequency shift keying (MFSK) wireless communication systems in the presence of additive white Gaussian noise (AWGN) and multiple arbitrary interfering signals. New exact bit error rate expressions are derived for nonorthogonal noncoherent binary FSK in the presence of an arbitrary number of interfering signals having arbitrary spectral shapes at arbitrary frequency offsets. Furthermore, tight upper bounds for the symbol and bit error rates are given for noncoherent MFSK with arbitrary tone spacings. These results are extended to include MFSK signals experiencing Rayleigh, Nakagami-m or Rician fading. Some specific interference scenarios are analyzed in details, including jammers with a given Doppler-spread, direct sequence spread spectrum and orthogonal frequency division multiplexing signals, and a Poisson field of arbitrary interferers.

Generalized Theory of Code Tracking with an Early-Late Discriminator Part II: Noncoherent Processing and Numerical Results

Code tracking is an important attribute of receivers for Global Positioning System (GPS) and other global navigation satellite systems (GNSS). This paper and its antecedent provide analytical expressions for performance of code-tracking loops using early-late discriminators, under small-error conditions. Expressions are provided for output signal-to-noise-plus-interference ratio (SNIR) and code-tracking error, for arbitrary signal spectra, and Gaussian noise and interference having arbitrary spectral shapes. This second paper addresses noncoherent early-late processing (NELP) for given receiver precorrelation bandwidth and given early-late spacing, comparing the results to results for coherent early-late processing (CELP) and to a lower bound (LB) on code-tracking error. Theoretical expressions are derived and compared, and numerical results are provided to examine the effect of different modulation designs and interference conditions.

Generalized Theory of Code Tracking with an Early-Late Discriminator Part I: Lower Bound and Coherent Processing

Code tracking is an important attribute of receivers for Global Positioning System (GPS) and other global navigation satellite systems (GNSS). This paper and its sequel provide analytical expressions for performance of code-tracking loops using early-late discriminators, under small-error conditions. Expressions are provided for output signal-to-noise-plus-interference ratio (SNIR) and code-tracking error for arbitrary signal spectra, and Gaussian noise and interference having arbitrary spectral shapes. This first paper addresses coherent early-late processing (ELP) for given receiver precorrelation bandwidth and given early-late spacing, also providing a tight lower bound on code-tracking error independent of discriminator design. Theoretical expressions are derived, showing that code-tracking accuracy depends on more than merely signal-to-noise ratio and early-late spacing - the shape of signal and interference spectra are important, as is the receiver precorrelation bandwidth.

Few-cycle femtosecond field synthesizer

We report on an optical field synthesizer consisting of a CEO-phase stabilized octave-spanning Ti:sapphire laser oscillator, a double-LCD prism-based pulse shaper, and a SPIDER pulse characterization apparatus. This field synthesizer allows for generating pulses with durations as short as 3.6 fs and enables to control the electric field on a sub-cycle scale. Within the limits of the ultrabroad spectrum arbitrary spectral and temporal pulse shapes and pulse sequences can be realized. Together with the ability to stabilize the pulses with respect to their CEO-phase, this system forms a versatile tool for coherent control experiments of field sensitive processes and precision spectroscopy.

Prediction of Bandlimited Fading Envelopes with Arbitrary Spectral Shape

In mobile radio, fading-envelope prediction can improve the performance of adaptive modulation techniques that require up-to-date channel-state information for optimal performance. We show how to compute the minimum mean squared prediction error of a mobile-radio fading envelope modeled as a stationary, bandlimited process arising from a diffuse set of local scatterers. For bandlimited processes, it is difficult to solve for the Wiener predictor using the usual spectral-factorization approach. Our method reduces the prediction problem to an eigenvalue decomposition, and is appropriate when the prediction is to be based on error-corrupted estimates of a narrowband fading process. We also show how to bound the error in the computation due to truncation of infinite series