Temporal Waveform Research Articles

Waveform metrology: signal measurements in a modulated world

We review the waveform metrology program developed over many years at the National Institute of Standards and Technology. The goal of this program is to provide a measurement service capable of characterizing both temporal and frequency-domain instrumentation used with high-speed communication systems. Under our program, full waveforms as functions of both time and frequency are the target measurands. From these functional waveforms, traditional parametric descriptions can be derived. Furthermore, we give temporal waveforms and their frequency-domain representations consistent and equal consideration, with traceability to the International System of Units. To support this traceability, we emphasize voltage and current waveforms, their relationships, and the ability to transform both nominal values and their uncertainties from one domain to the other.

Wavelength–time domain transformation-based demodulator for wavelength-encoded optical sensor

As for the issue of the rapid wavelength interrogation of optical fiber wavelength-encoded sensor, a demodulation method combining spectrum-to-time domain information mapping and photonics time stretch technology is proposed. Using group velocity dispersion effect of dispersive elements, the spectrum of optical pulse will be mapped to a temporal waveform whose intensity mimics the spectrum. The temporal waveform is further stretched in timescale so that it is slow enough to be captured by electronic analog-to-digital converter. The performance of the proposed demodulation method is experimentally demonstrated to demodulate a wavelength-encoded sensor.

Airy pulse shaping using time-dependent power-law potentials

We investigate the temporal and spectral evolutions of finite-energy Airy pulses in the presence of power-law optical potentials. The potentials are generated by the time-dependent pumped light, which propagates together with the Airy pulses in a highly nonlinear optical fiber. We show that the intrinsic acceleration of Airy pulses can be modified by an external force that stems from a linear potential, and hence unidirectional frequency shift can be realized. When a triangle potential is employed, the pulse will exhibit self-splitting both in temporal and spectral domains. Additionally, as a parabolic potential is utilized, both the temporal waveform and frequency spectrum of the Airy pulse will exchange alternately between the Airy and Gaussian profiles. By using higher-order power-law potentials, we also realize both revival and antirevival effects for the Airy pulses. The study may find wide applications in pulse reshaping and spectral-temporal imaging for both optical communication and signal processing.

Phased-locked two-color single soliton microcombs in dispersion-engineered Si3N4 resonators.

We propose and theoretically investigate a dispersion-engineered Si3N4 microring resonator, based on a cross section containing a partially-etched trench, that supports phase-locked, two-color soliton microcomb states. These soliton states consist of a single circulating intracavity pulse with a modulated envelope that sits on a continuous wave background. Such temporal waveforms produce a frequency comb whose spectrum is spread over two widely-spaced spectral windows, each exhibiting a squared hyperbolic secant envelope, with the two windows phase-locked to each other via Cherenkov radiation. The first spectral window is centered near the 1550nm pump, while the second spectral window is tailored based on straightforward geometric control, and can be centered as short as 750nm and as long as 3000nm. We numerically analyze the robustness of the design to parameter variation, and consider its implications to self-referencing and visible wavelength comb generation.

On Nonuniform Transient Electromagnetic Field Coupling to Overhead Transmission Lines

Transient electromagnetic fields can couple to overhead power transmission and distribution lines, causing damage to the connected equipment. In real cases, incident electromagnetic fields exhibit different spatial and temporal waveform distributions along the line. Normally, to ensure the accuracy of the simulation results, a large number of observation points are needed along the line, which is difficult to obtain. This paper proposes a new approach to address this problem. The proposed approach is based on Agrawal et al.’s coupling model, in which the amplitude and phase distributions of the horizontal exciting electric field along the line are, respectively, represented by the Fourier series and polynomial functions in the frequency domain using two kinds of least squares methods. As a result, the source terms along the line can be accurately evaluated starting from a limited number of observation points. The proposed approach has been validated experimentally.

Tailoring nonlinear processes for quantum optics with pulsed temporal-mode encodings

The time-frequency degree of freedom is a powerful resource for implementing high-dimensional quantum information processing. In particular, field-orthogonal pulsed temporal modes offer a flexible framework compatible with both long-distance fibre networks and integrated waveguide devices. In order for this architecture to be fully utilised, techniques to reliably generate diverse quantum states of light and accurately measure complex temporal waveforms must be developed. To this end, nonlinear processes mediated by spectrally shaped pump pulses in group-velocity engineered waveguides and crystals provide a capable toolbox. In this review, we examine how tailoring the phasematching conditions of parametric downconversion and sum-frequency generation allows for highly pure single-photon generation, flexible temporal-mode entanglement, and accurate measurement of time-frequency photon states. We provide an overview of experimental progress towards these goals, and summarise challenges that remain in the field.

Identification of Coherent and Incoherent Spectral Sidebands in an Ultrafast Fiber Laser

Ultrafast fiber lasers, as the soliton pulse sources, offer great platforms for the investigations of soliton dynamics. Since both the coherent and incoherent spectral sidebands could be shown on the soliton spectrum, herein we proposed a method to identify them by using the dispersion Fourier transformation (DFT) technique. According to the principle of DFT technology, for the coherent spectral sidebands, that is, Kelly sidebands in the mode-locked fiber laser, they could be mapped to the temporal waveforms after the DFT process. However, the incoherent spectral sidebands, namely continuous waves, would disappear on the shot-to-shot spectra after DFT due to their uncertain phase relation. The obtained results would deepen our understanding of spectral sidebands.

Laser-induced damage of fused silica optics at 355 nm due to backward stimulated Brillouin scattering: experimental and theoretical results.

Forward pump pulses with nanosecond duration are able to generate an acoustic wave via electrostriction through a few centimeters of bulk silica. Part of the incident energy is then scattered back on this sound wave, creating a backward Stokes pulse. This phenomenon known as stimulated Brillouin scattering (SBS) might induce first energy-loss, variable change of the temporal waveform depending on the location in the spatial profile making accurate metrology impossible, and moreover it might also initiate front surface damage making the optics unusable. Experiments performed on thick fused silica optics at 355 nm with single longitudinal mode pulses allowed us to detect, observe and quantify these backward pulses. Experimental results are first compared to theoretical calculations in order to strengthen our confidence in metrology. On this basis a phase-modulator has been implemented on the continuous-wave seeders of the lasers leading to pulses with a wide spectrum that suppress SBS and do not exhibit temporal overshoots that also reduce Kerr effects. The developed set-ups are used to check the reduction of the backward stimulated Brillouin scattering and they allow measuring with accuracy the rear surface damage of thick fused silica optics.

Deterministic control of radiative processes by shaping the mode field

Quantum dots (QDs) interacting with confined light fields in photonic crystal cavities represent a scalable light source for the generation of single photons and laser radiation in the solid-state platform. The complete control of light-matter interaction in these sources is needed to fully exploit their potential, but it has been challenging due to the small length scales involved. In this work, we experimentally demonstrate the control of the radiative interaction between InAs QDs and one mode of three coupled nanocavities. By non-locally moulding the mode field experienced by the QDs inside one of the cavities, we are able to deterministically tune, and even inhibit, the spontaneous emission into the mode. The presented method will enable the real-time switching of Rabi oscillations, the shaping of the temporal waveform of single photons, and the implementation of unexplored nanolaser modulation schemes.

TI Workbench, an integrated software package for electrophysiology and imaging.

TI Workbench is a software package that serves as a control and analysis center for cellular imaging and electrophysiological experiments. It is unique among general-purpose software packages where it integrates the control of cellular imaging and electrophysiological devices, as well as sophisticated data analyses, which provides superior usability in imaging experiments combined with electrophysiology. During the development over the last 20 years, the range of supported image acquisition devices has expanded from cooled charge-coupled device (CCD) cameras to multi-photon microscope systems. In this review, I outline the concept of TI Workbench together with its unique functions and features derived from ideas emerging during daily experiments in my own lab and in those of my collaborators over the last 20 years. TI Workbench includes standard functions required for time-lapse multicolor fluorescence imaging and electrophysiological experiments, in addition to specialized functions such as random-scan or conventional raster-scan two-photon microscopy packages and fluorescence life time imaging (FLIM) utilities. Data analysis modules, e.g. digital data filters for temporal waveforms of time-lapse image data and electrophysiology and for 2-D image data, and fluorescence correlation spectroscopy (FCS) analysis functions, are well integrated with data acquisition functions. A notebook function holds formatted text, graphs, image and movie data altogether, which are linked to the actual data files. TI Workbench uses Igor Pro software as a back-end output for publishing. In addition, TI Workbench imports several different formats of image and electrophysiology data, serving as a general-purpose data analysis software package.

Real-Time Optical Spectrum Fourier Transform With Time–Bandwidth Product Compression

We propose and experimentally demonstrate a photonic technique for Fourier transformation of broadband optical spectrum and compression of time-bandwidth product (TBP) simultaneously. Conventionally, an optical spectrum could be Fourier transformed based on the so-called time-spectrum convolution technique with a linearly dispersive delay line. In this paper, a nonlinearly dispersive delay line is implemented by the convolution of an input optical spectrum in the spectral domain with a nonlinearly chirped temporal sinusoidal waveform in the time domain. By specially designing the chirp rate variation of the temporal waveform, an anamorphic Fourier transformation functionality is realized to compress the TBP of output waveform. The key feature of this paper is that it is the first time to our knowledge to carry out the Fourier transformation of an optical spectrum with TBP compression. In addition, since the dispersive delay line could be programmable with high resolution, this technique is adaptable for different optical spectra and realizable for a reconfigurable TBP compression ratio. Experimental results show that the TBP compression ratio is programmable from 1.6 to 3 by engineering the nonlinear dispersive delay line. After reconstructing the Fourier transform of optical spectrum from the output waveforms, the error rate of the recovered waveform is calculated quantitatively. Also, we discussed and proved the possibility to recover the input spectrum only with intensity information. This proposed method is promising to break the big data limitation of the conventional real-time optical spectrum Fourier transformation technique based on the TBP engineering for data compression.

Altered erector spinae activity and trunk motion occurs with moderate and severe unilateral hip OA.

People with hip osteoarthritis (OA) demonstrate altered movement patterns in the hip joint, as well as the pelvis and spine. While kinematic changes have been described in the literature, little is known about the associated erector spinae (ES) activity. Increased or prolonged ES activity may contribute to the low back pain often associated with hip OA. Using a cross-sectional cohort study, 3D trunk motions and ES surface electromyography were recorded on 19 individuals with severe OA (SOA), 20 with moderate hip OA (MOA), and 19 asymptomatic (ASYM) individuals during treadmill walking, using standardized collection and processing procedures. Principal component analysis was used to derive electromyographic amplitude and temporal waveform features. Three-dimensional thoracic motion in a global system, and thoraco-lumbar motion was calculated. Various statistical analyses determined between group differences (α = 0.05). In the sagittal plane, thoracic motion was greater in the SOA group (p < 0.001), whereas the ASYM group used less thoraco-lumbar motion than either OA group (p ≤ 0.002). Greater frontal plane angular excursion during early stance was found in the thoracic region in the SOA group (p ≤ 0.001) . With increasing OA severity, bilateral ES activity increased during the swing phase of gait (p < 0.001), whereas during stance, the SOA ipsilateral ES activity was higher than other groups (p < 0.001). Statement of clinical significance: with moderate and severe OA, sagittal, and frontal trunk motion increases during gait. ES activity during the entire gait cycle is more sustained with increased disease severity, which may aide our understanding of low back pain associated with hip OA. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:1826-1832, 2018.

In-fiber high-speed recognition of incoherent-light broadband energy spectrum patterns.

A fiber-optic system is proposed and experimentally demonstrated for real-time, on-the-fly identification of an incoherent-light energy spectrum pattern based on dispersion-induced time-spectrum convolution. In the proposed system, the incoming frequency-spectrum patterns to be identified are modulated by a time-mapped version of the target intensity profile. Following propagation through a suitable fiber-optic dispersive medium, the measured output temporal waveform provides a correlation of the incoming spectra with the programmed target pattern. This enables direct, real-time detection of the matching energy spectra, without any further numerical post-processing. We experimentally demonstrate successful recognition of a target infrared spectral pattern, extending over a bandwidth of 1.5THz with a resolution of ∼12 GHz, with sub-megahertz update rates. A path for further performance improvements is also suggested.

Cognitive Control and Brain Network Dynamics during Word Generation Tasks Predicted Using a Novel Event-Related Deep Brain Activity Method

There is a growing interest in the diagnosis and treatment of patients with dementia and cognitive impairment at an early stage. Recent imaging studies have explored neural mechanisms underlying cognitive dysfunction based on brain network architecture and functioning. The dorsal anterior cingulate cortex (dACC) is thought to regulate large-scale intrinsic brain networks, and plays a primary role in cognitive processing with the anterior insular cortex (aIC), thus providing salience functions. Although neural mechanisms have been elucidated at the connectivity level by imaging studies, their understanding at the activity level still remains unclear because of limited time-based resolution of conventional imaging techniques. In this study, we investigated temporal activity of the dACC during word (verb) generation tasks based on our newly developed event-related deep brain activity (ER-DBA) method using occipital electroencephalogram (EEG) alpha-2 powers with a time resolution of a few hundred milliseconds. The dACC exhibited dip-like temporal waveforms indicating deactivation in an initial stage of each trial when appropriate verbs were successfully generated. By contrast, monotonous increase was observed for incorrect responses and a decrease was detected for no responses. The dip depth was correlated with the percentage of success. Additionally, the dip depth linearly increased with increasing slow component of the DBA index at rest across all subjects. These findings suggest that dACC deactivation is essential for cognitive processing, whereas its activation is required for goal-oriented behavioral outputs, such as cued speech. Such dACC functioning, represented by the dip depth, is supported by the activity of the upper brainstem region including monoaminergic neural systems.

Memory Effect on Adaptive Decision Making with a Chaotic Semiconductor Laser

We investigate the effect of a memory parameter on the performance of adaptive decision making using a tug‐of‐war method with the chaotic oscillatory dynamics of a semiconductor laser. We experimentally generate chaotic temporal waveforms of the semiconductor laser with optical feedback and apply them for adaptive decision making in solving a multiarmed bandit problem that aims at maximizing the total reward from slot machines whose hit probabilities are dynamically switched. We examine the dependence of making correct decisions on different values of the memory parameter. The degree of adaptivity is found to be enhanced with a smaller memory parameter, whereas the degree of convergence to the correct decision is higher for a larger memory parameter. The relations among the adaptivity, environmental changes, and the difficulties of the problem are also discussed considering the requirement of past decisions. This examination of ultrafast adaptive decision making highlights the importance of memorizing past events and paves the way for future photonic intelligence.

Optical Sinc-Shaped Nyquist Pulses Generation From Frequency-Quadrupled Rectangular Frequency Comb

Frequency-quadrupled rectangular optical frequency comb (OFC) generation with Nyquist temporal waveforms using a dual-parallel Mach–Zehnder modulator (DP-MZM) and a remodulation structure is proposed. The remodulation structure is formed by a coupler, a photodiode, and an intensity modulator. Its function is similar to optical carrier suppression (OCS) modulation index amplifier, which can achieve the modulation index improve of approximately 77.9% in the OCS modulation. This result in no special modulation index is needed in the proposed scheme. By using a 4 GHz sinusoid signal, a 4-tones frequency-quadrupled OFC with sideband spacing of 16 GHz and flatness within 0.5 dB is experimentally generated. The temporal waveform is sinc-shaped Nyquist pulse with duty cycle 23% and the repetition rate is quadrupling that of the local oscillator frequency, which shows great potential in generating a cost-effective pulses. Moreover, being benefited from the filter-free structure, the high flexibility of the generated Nyquist pulse has also been demonstrated.

Random Number Generation From Intermittent Optical Chaos

We propose a method to generate physical random numbers based on intermittent optical chaos. Intermittent chaotic output is produced in a semiconductor laser subjected to optical feedback embedded in a photonic integrated circuit. This dynamics is characterized by a temporal waveform organized in a succession of laminar regions of low amplitude and bursts of high amplitude. The temporal randomness ruling the alternation of successive laminar regions and bursts is used as an entropy source to generate sequences of random bits. We compare the performances of the exclusive OR and reverse methods implemented in the bit generation process and evaluate the quality of the random bits with the Rabbit test of TestU01 for different bit sequences lengths.

Ultrasonic bandgaps and interlaminar interface echoes of composite laminates: Analysis and experiments

Increasing applications of carbon fiber reinforced plastics (CFRP) in aerospace industry highlight the importance of nondestructive methods to characterize their mechanical properties as well as defect concentrations. In CFRP laminate structures, thin resin layers, typically of a few micron thickness, are present between plies. Their spatially periodic nature causes bandgaps for ultrasonic waves having wavelengths comparable to the ply thickness. Features of the reflection and transmission spectra of ultrasonic waves including such bandgaps can be utilized for nondestructive characterization of CFRP laminates. In particular, the oscillatory frequency dependence of the reflection or transmission spectra of ultrasonic waves near the band gaps can be used to identify the equivalent stiffnesses of interlaminar interfaces. These interfacial stiffnesses contain rich information of the mechanical soundness of the interlaminar interfaces which are otherwise difficult to evaluate with traditional ultrasonic methods working in relatively low frequencies. The evidence of ultrasonic bandgaps of CFRP laminates can also be observed as long-standing signals following the surface echo in the temporal reflection waveforms of CFRP laminates (interlaminar interface echoes). In this presentation, the physical phenomena behind the ultrasonic bandgaps and interlaminar interface echoes of CFRP laminates are discussed together with their applications to nondestructive characterization of these materials.

All‐optical reconfigurable multicast canonical logic units based on four‐wave mixing

Canonical logic units (CLUs) are basic building blocks for complex all-optical logic operations, and multicast of CLUs can improve the computing capacity and operating flexibility. The authors thus propose and experimentally demonstrate all-optical reconfigurable multicast two-input CLUs (i.e. minterms) at 40 Gb/s by using four-wave mixing in a single highly non-linear fibre. Each type of CLUs with clear temporal waveform and wide eye opening is achieved in five parallel channels simultaneously. The extinction ratios are >10.3 dB, while the optical signal-to-noise ratios are >21 dB. Based on the demonstrated scheme, a method of realising simultaneous full set of two-input logic operations is proposed and discussed. The proposed scheme can be extended to higher data rates and transferred to on-chip platforms.

How To Drive a Flashing Electron Ratchet To Maximize Current.

Biological systems utilize a combination of asymmetry, noise, and chemical energy to produce motion in the highly damped environment of the cell with molecular motors, many of which are "ratchets", nonequilibrium devices for producing directed transport using nondirectional perturbations without a net bias. The underlying ratchet principle has been implemented in man-made micro- and nanodevices to transport charged particles by oscillating an electric potential with repeating asymmetric features. In this experimental study, the ratcheting of electrons in an organic semiconductor is optimized by tuning the temporal modulation of the oscillating potential, applied using nanostructured electrodes. An analytical model of steady-state carrier dynamics is used to determine that symmetry-breaking motion of carriers through the thickness of the polymer layer enables even temporally unbiased waveforms (e.g., sine) to produce current, an advance that could allow the future use of electromagnetic radiation to power ratchets. The analysis maps the optimal operating frequency of the ratchet to the mobility of the transport layer and the spatial periodicity of the potential, and relates the dependence on the temporal waveform to the dielectric characteristics and thickness of the layer.