Symmetric Amplitude Research Articles

Resolution enhancement in continuous-wave stimulated emission depletion microscopy by excitation beam with modulated vortex-phased azimuthally polarized light

In this paper, we report an optical system that can effectively enhance the resolution of continuous-wave (CW) stimulated emission depletion (STED) microscopy by applying an amplitude-modulated azimuthally polarized light with vortex phase (AV) as an excitation beam. Based on the vector field diffraction theory, we analyzed electric fields near the focal plane for various polarization states and rotationally symmetric amplitude modulation conditions. From the analysis, it was found that by applying the amplitude modulated AV beam by the ring-shaped blocking aperture, the resolution in the lateral direction can be improved while minimizing the degradation of the resolution in the axial direction. The reported novel excitation method was experimentally verified based on the imaging of gold beads and fluorescent nano-beads. Accordingly, it was confirmed that the lateral resolution was improved by ~20% and the spot elongation in the axial direction was effectively suppressed.

Flow-structure interactions of two parallel inverted flags with small separation distances in a water tunnel

In this study, the dynamics and flow fields of two parallel inverted flags are investigated using particle image velocimetry technology. The separation distance between two flags is less than two times the length of the flag, and the length ratio of these two flags is considered in the investigation. The results show that for the dynamic behaviours of two identical flags with a larger separation distance, the anti-phase and in-phase modes occur successively in the periodic oscillation as the flow velocity increases. The anti-phase and in-phase oscillations occur according to the formation position of the low-pressure and recirculation areas at different flow velocities. Moreover, a novel coupled flapping mode is observed at smaller separation distances: the contact anti-phase flapping mode, in which one flag oscillates with a large symmetric amplitude, and the other flag oscillates with a single-side large amplitude. As the separation distance further decreases, the in-phase mode appears for a larger range of flow velocity values, to avoid contact for the largest possible amplitude oscillation. Finally, as the length ratio decreases to 0.75, the oscillation frequency of the shorter flag becomes twice that of the longer flag, causing the in-phase and anti-phase oscillations to occur simultaneously in one cycle (i.e., the multi-phase flapping state). Interestingly, the two flags oscillate out of phase in the flapping apart process to avoid contact at a higher flow velocity. In general, the lower amplitude of the longer flag and two contact flags relative to that of an isolated flag clearly indicates the importance of two equal-length and non-contact flags for energy harvesting.

Improvement of frequency responses of an in-plane electro-thermal cantilever sensor for real-time measurement

Resonance-based sensors ordinarily show a symmetrical amplitude shape, which is accompanied by a monotonic transition as its phase response. At its resonance state, there is a 90° phase difference between the excitation force and the system response. Nevertheless, due to some parasitic factors, resonance-based sensors might show non-ideal frequency response as seen in in-plane electro-thermal piezoresistive cantilever sensors (EtPCSs). Because of a direct thermal parasitic coupling from the excitation part to the sensing part, the sensor output shows an asymmetric amplitude shape and a reversing phase response. In some EtPCS that have relatively lower thermal exposure on their sensing part, a symmetrical amplitude shape could be demonstrated but was still accompanied with a low magnitude of monotonical phase response. In this work, a method of reference subtraction was introduced to enhance the frequency response of the EtPCS at changing ambient conditions (e.g. humidity, temperature, smoke exposure). As a result, we obtained optimized frequency responses suitable for a phase-locked loop-based system to carry out resonant-frequency tracking in real-time.

Splitting and rotating of optical vortices due to non-circular symmetry in amplitude and phase distributions of host beams

Discussed is the dynamics of optical vortices carrying multi-topological charges, which are nested in optical envelopes with non-circular symmetric amplitudes and phases. As a result of the non-circular symmetry either in amplitudes or in phases, the vortices can split in pairs from the centers of the host beams. During the splitting process of every constituent vortex, its carried integer charges evolve into fractional ones. Furthermore, the overall rotations of the host optical envelopes are found to happen in the splitting process. The theoretical results may find potential applications in beam shaping and engineering.

Image-contrast enhancement of wavefront coding systems by combining radially symmetrical phase and amplitude masks

The quartic phase mask is a radially symmetrical phase mask which is commonly used to analyze imaging performance and to apply in many practical applications. In this paper, we propose a simple, novel method to improve the image contrast for extending depth of field in wavefront coding system with radially symmetrical quartic phase mask. An amplitude mask, which improves image contrast in low spatial frequency region, is added on the wavefront coding system with quartic phase mask to obtain the remarkable improvement of imaging performance for extending depth of field. Some evaluation methods are used to show the effectiveness of imaging performance of the proposed method in comparison to previously phase mask. The results demonstrated that the proposed method yields better imaging property in extending depth of field.

A Digital Calibration Technique of MEMS Gyroscope for Closed-Loop Mode-Matching Control.

A digital excitation-calibration technique of dual-mass MEMS gyroscope for closed-loop mode-matching control is presented in this paper. The technique, which takes advantage of the symmetrical amplitude response of MEMS gyroscope, exploits a two-side excitation signal to actuate the sense mode to obtain the corresponding DC tuning voltage. The structural characteristics of dual-mass decoupled MEMS gyroscope and the tuning principle of excitation-calibration technique are introduced firstly. Then, the scheme of digital excitation-calibration system for the real-time mode-matching control is presented. Simultaneously, open-loop analysis and closed-loop analysis are deduced, respectively, to analyze the sources of tuning error and system stability. To verify the validity of the scheme and theoretical analysis, the system model was established by SIMULINK. The simulation results are proved to be consistent with the theoretical analysis, verifying the feasibility of the digital excitation-calibration technique. The control algorithms of the system were implemented with a FPGA device. Experimental results demonstrate that digital excitation-calibration technique can realize mode-matching within 1 s. The prototype with real-time mode-matching control has a bias instability of 0.813/h and an ARW (Angular Random Walk) of 0.0117/. Compared to the mode-mismatching condition, the bias instability and ARW are improved by 3.25 and 4.49 times respectively.

Orbital angular momentum of a laser beam behind an off-axis spiral phase plate.

Here we obtain a simple formula for the relative total orbital angular momentum (OAM) of a paraxial light beam with arbitrary rotationally symmetric complex amplitude, passed through an off-axis spiral phase plate (SPP). The formula shows that the OAM is zero if the incident light is bounded by a diaphragm, and the SPP center is outside it. Another consequence of the obtained formula is that if the incident light is limited by an annular diaphragm then the full angular momentum is the same, regardless of the position of the SPP center inside the shaded circle of the annular diaphragm. This means that it is more appropriate to illuminate the SPP by beams with an annular intensity distribution because, in this case, the inaccurate alignment of the SPP center and the center of the annular intensity distribution do not affect the total OAM of the beam. In addition, we obtain a formula for the OAM density of such a light beam in the initial plane. The experimentally measured OAM is in good agreement with that calculated by the obtained formula.

Pupillary Response as Assessment of Effective Seizure Induction by Electroconvulsive Therapy.

Electroconvulsive therapy (ECT) is reported to be effective for severe neuropsychiatric disorders. In ECT, electrical stimulation is applied to the brain, inducing seizure activity. Adequate seizure induction with ECT is associated with seizure duration, symmetrical high amplitude waveforms during slow-wave activity, postictal suppression, and activation of the sympathetic nervous system. Sympathetic nervous system activation is influenced by anesthetic agents or cardiovascular drugs during ECT. Pupillary responses can reflect sympathetic nervous activity or the degree of brain damage. Pupillary response measurement can be conducted in a simple, precise, and objective way using an automated infrared pupillometer, enabling the measurement of pupil diameter (mm) to two decimal places. The white light used for measuring light reflexes is not overly bright, and patients do not typically report discomfort. Pupillary light reflexes were measured before anesthesia induction and immediately after electrical stimulation using this equipment. Pupil diameter is typically enlarged after brain damage or sympathetic nervous activation. Adequate seizure induction using ECT could induce pupillary enlargement immediately after electrical stimulation. In the current method, the constriction ratio of pupil size was calculated automatically and compared with seizure quality. Pupillary responses immediately after electrical stimulation may provide a useful assessment of the efficacy of seizure induction with ECT.

Real-Time Frequency Tracking of an Electro-Thermal Piezoresistive Cantilever Resonator with ZnO Nanorods for Chemical Sensing

The asymmetric resonance response in electro-thermal piezoresistive cantilever resonators causes a need of an optimization treatment for taking parasitic actuation-sensing effects into account. An electronic reference circuit for signal subtraction, integrated with the cantilever resonator has the capability to reduce the effect of parasitic coupling. Measurement results demonstrated that a symmetric amplitude shape (Lorentzian) and an optimized phase characteristic (i.e., monotonically decreasing) were successfully extracted from an asymmetric resonance response. With the monotonic phase response, real-time frequency tracking can be easier to implement using a phase-locked loop (PLL) system. In this work, an electro-thermal piezoresistive cantilever resonator functionalized with self-assembled monolayers of chitosan-covered ZnO nanorod arrays as sensitive layers has been investigated under different relative humidity (rH) levels. Enhancement of resonance phase response has been demonstrated by implementing the reference signal subtraction. Subsequently, a lock-in amplifier integrated with PLL system (MFLI, Zurich Instruments, Zurich, Switzerland) was then employed for continuously tracking the resonant frequency. As a result, we find a good correlation of frequency shift (∆f0) with change in rH monitored using a commercial reference sensor.

A closed-form analytical solution for the ratcheting response of steel tubes with wall-thinning under inelastic symmetric constant amplitude cyclic bending

Metallic tubes experiences a progressive accumulation of ovalisation, or ratchet, under cyclic inelastic bending. During their life time, the tubes may also suffer from different types of mechanically and/or chemically originated defects. The current paper discusses a closed-form solution for the response analysis of defective circular steel tubes under monotonic and cyclic inelastic bending. The defect in the tube is idealised as a uniform patch type wall thinning.The material model considers the cyclic hardening/softening features based on a combined non-linear hardening law. To account for the non-fading memory characteristics of the steel material, the hardening modulus in each half-cycle is introduced as a state variable. A modified version of the Bailey–Norton law is used for the cyclic growth (cyclic creep) in the ovalisation of the cross-section. In overall, the solution considers the geometrical non-linearity due to the ovalisation as well as the hysteresis effects.The study also includes monotonic and cyclic inelastic bending experiments on small-scale, thick-walled, high strength, low alloy carbon steel defective tubes. The analytical solutions for the inelastic monotonic and cyclic bending of the tubes are validated against these experimental data and reasonable agreements are noticed and reported.

Orbital angular momentum of an arbitrary axisymmetric light field after passing through an off-axis spiral phase plate

We obtain a simple formula for the relative total orbital angular momentum (OAM) of a paraxial light beam with arbitrary rotationally symmetric complex amplitude passed through a spiral phase plate (SPP) whose center is shifted from the optical axis. The formula shows that the OAM equals zero if the incident beam is bounded by an aperture and the SPP center is outside this aperture. For the incident beam bounded by an annular aperture, there is another interesting consequence of the obtained expression. The total OAM of such a beam is the same regardless of the position of the SPP center within the shaded circle of the aperture. Thus, it would be appropriate to illuminate the SPP by beams with an annular intensity distribution, since in this case an inaccurate alignment of the SPP center and the center of the annular intensity distribution does not affect the total OAM of the beam. We also obtain an expression for the OAM density of such a beam in the initial plane.

Enabling Technologies for High-Speed Visible Light Communication Employing CAP Modulation

High-speed light emitting diode (LED) based visible light communication (VLC) system is restricted by the limited LED bandwidth, low detector sensitivity, and linear and nonlinear distortions. Thus, single- and two-cascaded constant-resistance symmetrical bridged-T amplitude hardware pre-equalizers, carrierless amplitude and phase (CAP) modulation, and a three-stage hybrid postequalizer are investigated to increase transmission data rate for a high-speed LED-based VLC system. The schemes utilized by the hybrid postequalizer are modified cascaded multimodulus algorithm, Volterra series based nonlinear compensation algorithm and decision-directed least mean square algorithm. With these technologies, we successfully implement high-speed CAP32, CAP64, and CAP128 VLC experimental system over 1-m free space transmission with bit error rate under the hard decision-forward error correction threshold of 3.8 × 10–3. System performance improvement employing these key technologies is also validated through experimental demonstration. With the superposition of each stage of the hybrid postequalizer, system performance will be improved. And utilizing two-cascaded hardware pre-equalizer will provide more accurate channel compensation than a single pre-equalizer.

Two-dimensional particle-in-cell simulations of standing waves and wave-induced hysteresis in asymmetric capacitive discharges

Asymmetrically excited, high frequency cylindrical capacitive discharges are widely used for materials etching and thin film deposition. Two-dimensional (2D) electrostatic particle-in-cell (PIC) simulations show the existence of standing waves and wave-induced hysteresis of the plasma density, i.e. two different steady states for the same driving rf voltage amplitude, when the voltage is increased from a low value or decreased from a high value. The phenomenon is explored over a range of pressures (10–30 mTorr) and frequencies (60–80 MHz). Examined at 73 MHz, with increasing gas pressure, the hysteresis loop gradually shrinks and vanishes. To understand the hysteresis induced by z-symmetric and z-antisymmetric radial wave propagation modes, the PIC results are compared with a nonlinear transmission line model assuming uniform bulk plasma density, to determine the symmetric and antisymmetric voltage amplitudes. The model results are in good agreement with the PIC observations, showing central-low and central-high profiles of the antisymmetric mode voltage at low density and high density, respectively. The results are then used to determine the parameters of a lumped circuit model of the two modes, from which the hysteresis is induced by the density dependence of the symmetric and anti-symmetric wave mode absorbed electron powers. For the low density state, the discharge is sustained mainly by the symmetric mode excitation. At high density, the discharge is sustained by both symmetric and anti-symmetric modes, with the latter partly showing a spatial resonance. The results are also shown to be frequency dependent, with an onset of the hysteresis at about 66 MHz.

Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams.

A general orbital-angular-momentum (OAM) mode selection principle is put forward involving the rotationally symmetric superposition of chiral states. This principle is not only capable of explaining the operation of vortex generating elements such as spiral zone plate holograms, but more importantly, it enables the systematic and flexible generation of structured OAM waves in general. This is demonstrated both experimentally and theoretically in the context of electron vortex beams using rotationally symmetric binary amplitude chiral sieve masks.

Two-dimensional Gaussian-type spatial solitons in inhomogeneous cubic–quintic–septimal nonlinear media under $$\varvec{\mathcal {PT}}$$ PT -symmetric potentials

A (\(2+1\))-dimensional nonlinear Schrodinger equation with cubic–quintic–septimal nonlinearities and \(\mathcal {PT}\)-symmetric potentials is studied, and two kinds of Gaussian-type spatial soliton solutions are obtained. The compressed behaviors of spatial solitons are investigated in three different diffraction systems with Gaussian, Logarithmic and linear profiles. The real and imaginary parts of \(\mathcal {PT}\)-symmetric potentials, the width, amplitude and phase transition of spatial solitons in different media are compared and studied.

Spiralling elliptic vortex solitons in nonlocal nonlinear media

We have introduced a class of spiralling elliptic vortex (SEV) solitons in nonlocal nonlinear media. The SEV soliton has more complicated structures both in its amplitude and in its phase compared with conventional vortex solitons. Different from the circularly symmetric amplitude profile of vortex solitons, the SEV solitons exhibit the elliptic optical spots. Furthermore, the SEV solitons have the special modulated helical phase structures, which make the SEV solitons rotate. For different topological charges, all the SEV solitons own the same critical power, critical cross-term phase coefficient and the critical angular velocity for fixed semiaxis of the elliptic spots. The stability of the SEV solitons is confirmed by the direct numerical simulations with random noises.

A nonlinear electromagnetics model of an asymmetrically-driven, low pressure capacitive discharge

It is well-known that standing waves having radially center-high voltage profiles exist in high frequency driven capacitive discharges. Capacitive sheaths can also nonlinearly excite driving frequency harmonics near the series resonance that can be spatially near-resonant, and therefore enhance the on-axis power deposition. The powered-electrode/plasma/grounded-electrode sandwich structure of an asymmetrically excited cylindrical discharge forms a three electrode system in which both z-symmetric and z-antisymmetric radially propagating wave modes can exist. We develop a nonlinear electromagnetics model for this system with radially- and time-varying sheath widths, incorporating both symmetric and antisymmetric modes, and the plasma skin effect. Waves generated in the electrostatic wave limit are also treated. The discharge is modeled as a uniform density bulk plasma with either homogeneous or Child law sheaths at the electrodes, incorporating their nonlinear voltage versus charge relations. The model includes a finite power source resistance and a self-consistent calculation of the dc bias voltages. The resulting set of nonlinear partial differential equations is solved numerically to determine the symmetric and antisymmetric mode amplitudes and the nonlinearly-excited radially-varying harmonics. Two examples driven at lower frequency (30 MHz) or at higher frequency (60 MHz) are examined. The first case displays the excited dominant ninth harmonic near the series resonance frequency with the fundamental frequency having a weak standing wave. The higher frequency case shows a more obvious standing wave effect, enhanced by the nonlinear harmonics. The symmetric and antisymmetric modes are of similar amplitudes over the driving electrode, summing to give a larger bottom sheath.

Polarization conversion under focusing of vortex laser beams along the axis of anisotropic crystals

We report the development of an optical system based on diffractive optical elements and uniaxial crystals to produce radially and azimuthally polarized beams, including beams of higher orders. The conditions for the generation of beams with different polarization states in an anisotropic crystal with an arbitrary axially symmetric amplitude distribution are analyzed theoretically. The results of the experimental study on the generation of cylindrical vector beams in a calcite crystal agree with the results of the simulation.

Lateral Leg Pain in an Avid Hiker After a Fall

HISTORY: A 62-year-old female with a history of hip OA and low back discomfort presents with left lateral leg pain that started after a fall onto her back 11 months ago. Pain is described as a constant throbbing in the left lateral calf, ankle, and dorsal foot. Pain worsens with ambulation and is relieved by rest. Noninvasive vascular studies ruled out claudication. Prior treatments included left L5 nerve root block, lumbar ESI, SI joint injection, chiropractic treatment, pain medications, and therapy with limited success. She presents to our sports medicine clinic for a diagnostic ultrasound of the left lateral leg region. PHYSICAL EXAMINATION: Guarded gait favoring weight bearing on right lower extremity. Mild tenderness over the proximal tibiofibular joint. No focal area of tenderness noted at lateral knee joint line or distal iliotibial band. Range of motion about the knee and ankle were both full without pain and strength was intact. Allodynia noted to light touch over left anterolateral leg, ankle, and dorsal foot. Straight leg raise and lumbar facet challenge were negative. Lumbar Spurling’s was positive on the left. DIFFERENTIAL DIAGNOSIS: 1. Superficial peroneal neuropathy 2. Common peroneal neuropathy 3. Lumbar radiculopathy TEST AND RESULTS: -MRI lumbar spine: Mild multilevel DJD without significant stenosis. -MRI left tibia-fibula: Subtle edema in the peroneal muscle area. Diffuse symmetric atrophy in both muscles. -EMG/NCV: Decreased amplitude in left superficial peroneal response (4 mV vs 12 mV on contralateral side) and mildly prolonged peak latency. No signs of lumbar radiculopathy. -Left lateral leg/knee ultrasound: Swollen superficial peroneal nerve at the site of penetration through peroneus longus muscular fascia (0.08 cm proximally and 0.22 cm distally). FINAL WORKING DIAGNOSIS: Left superficial peroneal neuropathy TREATMENT AND OUTCOMES: 1. Sonographically guided superficial peroneal nerve hydrodissection (HD) x 2 resulted in improvement in painless walking distance and decrease in pain scale by 50-60%. 2. Repeat elective EMG/NCV 2 months later demonstrated signs of re-innervation of the left superficial peroneal nerve evidenced by normalized and symmetric sensory response amplitude (8 mV) and peak latency measures with polyphasic motor unit potentials seen in the fibularis longus.

Real-Time 14-Gbps Physical Random Bit Generator Based on Time-Interleaved Sampling of Broadband White Chaos

We experimentally demonstrate a real-time high-speed physical random bit generator using the time-interleaved sampling of broadband white chaos. The white chaos is generated by optical heterodyning of two external-cavity feedback laser diodes. It has a white-noise-like spectrum with a 3-dB bandwidth of 16.7 GHz and a symmetric amplitude distribution and has no time-delay signatures of the external feedback cavities. An analog-to-digital converter (ADC) chip integrated by two time-interleaved sub-ADCs with a maximum sampling rate of 7 GHz is utilized to discretize the white chaos into parallel binary streams. After real-time interleaving combination and exclusive-OR operation in the field-programmable gate array (FPGA), a 14-Gbps binary stream with verified randomness is achieved.