Quadrature Condition Research Articles

Characterization of flexural acoustic waves in optical fibers using a fiber-tip interferometer

An experimental study using a fiber-tip interferometer (FTI) to characterize traveling flexural acoustic waves (TFAWs) along an optical fiber is reported. The measurements carried out with the FTI are performed following two different procedures: one of them relies on adjusting the interferometer at the quadrature condition and the other extracts the information from the amplitudes of the fundamental and second harmonic of the interference signal. From our measurements, the detection limit of the FTI is 0.5 nm and the upper limit of the linear regime is 30 nm. These results validate the use of the FTI to detect nanometric displacements associated to the amplitude of acoustic waves along an optical fiber. Parameters such as the acoustic wavelength, attenuation coefficient, and phase velocity are measured for a range of acoustic frequencies around the 2 MHz region. Furthermore, and supported by the in-fiber acousto-optic (AO) effect produced by TFAWs, parameters associated to an acoustic wave packet such as the group velocity and the group attenuation coefficient are also determined. This set of experimental results provide useful information of the mechanisms underlying the propagation of TFAWs along an optical fiber and its corresponding AO effect.

Silicon Nitride External Cavity Laser With Alignment Tolerant Multi-Mode RSOA-to-PIC Interface

We demonstrate an external cavity laser formed by combining a silicon nitride photonic integrated circuit with a reflective semiconductor optical amplifier. The laser uses an alignment tolerant edge coupler formed by a multi-mode waveguide splitter right at the edge of the silicon nitride chip that relaxes the required alignment to the III-V gain chip and equally splits the power among its two output waveguides. Both the ground and first order mode are excited in the coupler and reach the quadrature condition at the waveguide junction, ensuring equal power to be coupled to both. Two high-quality-factor ring resonators arranged in Vernier configuration close a Sagnac loop between the two waveguides. In addition to wideband frequency tuning, they result in a longer effective cavity length. The alignment tolerant coupler increases the alignment tolerance in the two directions parallel to the chip surface by a factor 3 relative to conventional edge couplers, making it ideal for gain chip integration via pick-and-place technology. Lasing is maintained in a misalignment range of ±6 μm in the direction along the edge of the chip. A Lorentzian laser linewidth of 39 kHz is achieved.

Photodetector optic power optimization to increase the gain on sub-octave microwave photonic link / Optimização da potência óptica do fotodetector para aumentar o ganho na ligação fotónica de microondas sub-octave

An investigation of the optic spectral components beating at the photodetector to recover the RF signal at the output of a sub-octave microwave photonic link is presented, by a theoretical and experimental approach. It is demonstrated the best efficiency is achieved when the carrier to sideband ratio (CSR) is 0 dB at a low bias voltage condition on Mach-Zehnder (MZM) intensity modulator. A RF power link gain improvement of 9.7 dB is demonstrated for a same photodetector incident optic power, compared with a link operating at quadrature bias voltage condition on the MZM.

Bayesian model updating and class selection of a wing-engine structure with nonlinear connections using nonlinear normal modes

This paper presents a Bayesian model updating and model class selection approach based on nonlinear normal modes (NNMs). The performance of the proposed approach is demonstrated on a conceptually simple wing-engine structure. Control-based continuation is exploited to measure experimentally the NNMs of the structure by tracking the phase quadrature condition between the structural response and single input excitation. A two-phase Bayesian model updating framework is implemented to estimate the joint posterior distribution of unknown model parameters: (1) at phase I, the effective Young’s modulus of a detailed linear finite element model and its estimation uncertainty are inferred from the data; (2) at phase II, a reduced-order model is obtained from the updated linear model using Craig-Bampton method, and coefficient parameters of structural nonlinearities are updated using the measured NNMs. Five different model classes representing different nonlinear functions are investigated, and their Bayesian evidence are compared to reveal the most plausible model. The obtained model is used to predict NNMs by propagating uncertainties of parameters and error function. Good agreement is observed between model-predicted and experimentally identified NNMs, which verifies the effectiveness of the proposed approach for nonlinear model updating and model class selection.

Phase Shift and Amplitude Array Measurement System Based on 360° Switched Dual Multiplier Phase Detector

This article presents an amplitude and 360° phase shift array measurement system. The basic cell of the measurement system uses a novel amplitude and phase detector based on switched dual multipliers. The phase shift measurement is characterized using an analog phase detector (mixer), detecting a maximum range of ±90°, and a double multiplication of the input signals, in phase and phase shifted. This method broadens the frequency and amplitude range beyond other solutions that require fulfilling the quadrature condition. This method broadens the frequency and amplitude beyond other solutions requiring fulfilling the quadrature condition or phase and amplitude balance. Thus, it enables to compensate significant phase imbalance in the 90° hybrid or use amplitudes out of the range that ensures the switching operation of mixer diodes. The circuit calibration that allows compensation for errors (amplitude, phase shift, mismatching, etc.) is detailed, and its relation to the required measurement accuracy is discussed. The design can be easily extrapolated to other frequency ranges because it uses commercial RF devices available in a wide frequency range and avoids the need of crossing lines or complex 90° hybrid. A prototype with $3 \times 3$ cells has been built to evaluate various test conditions on $1 \times 3$ cell configurations that show the advantages of the procedure. It should be highlighted that the cell prototype uses devices that will be operating outside the frequency and amplitude ranges recommended by their manufacturers. A calibration from 2.6 to 6 GHz and −15 to −3 dBm was performed to evaluate the measurement errors. An analysis of the isolation between cells and different calibration configurations is performed to analyze the measurement errors. Measurements show compensation of +30°/−25° phase imbalance and 13-dB power lower than mixer manufacturer recommendation.

Digital Demodulation Using I/Q Signals and Optical Phase Control Applied to a Vibrometer

An efficient and cost effective optical phase detection vibrometer based on a modified closed loop homodyne Michelson interferometer is presented. Real-time phase demodulation is carried out, using an embedded platform that performs data acquisition, signal processing, PI (proportional-integral) control and the generation of signals that drive the electrooptic Pockels cell phase shifter and the piezoelectric actuator under test. Two phase quadrature signals are generated from a single interferometric output, using the interleaving action, in alternation, of a digitally generated modulating signal, and then the well-known differential-cross-multiplication technique is applied to perform the computation of the phase shift of interest. The quadrature condition is reached using the PI loop based on an error signal obtained from a Lissajous figure derived from out-of-phase signals. The vibrometer is capable of measuring nanometric displacements, and is simple, inexpensive, accurate, immune to fading and self-consistent. The new method was used to determine the displacement frequency response curves of two prototypes of multi-actuated flextensional piezoelectric actuators. Measurements were made between 500 Hz and 15 kHz, and the results agreed with those obtained by the standard SCM-Signal Coincidence Method.

A method of bunch by bunch measurement at nanoseconds interval by using cavity beam position monitors

The application of RF cavity beam position monitors (CBPM) is essential for precise beam position measurements in X-ray Free-Electron Lasers (XFEL) and linear colliders. This paper addresses the solution to the inter-bunch signal interference when the bunch separation is as short as nanoseconds. The signals can overlap from bunch to bunch, which can induce appreciable error in evaluating beam position. We propose a conceptual method to eliminate the dominant signal overlap under a quadrature phase offset condition. Using this method, the elimination automatically occurs in the process of signal digitalization. The dominant interference that is contributed by the last bunch can be reduced over an order of magnitude in a conventional CBPM system. In addition, the required bandwidth can be effectively reduced by a factor of 2, and the design challenge for a wideband CBPM is relaxed. The method was demonstrated in an analytic approach by simulating the signal evolution in the RF front end of electronics built in MATLAB code. In the practical concern of applying this method, the factors that perturb the elimination have been examined as well. Based on the numerical result, the CBPM prototype has been designed for the pre-research plan of future high repetition rate hard XFEL at Chinese Academy of Engineering Physics. The combined simulations in CST and MATLAB on the CBPM prototype indicate agreement with the result obtained in the analytic approach.

Quadrature phase-stabilized three-wavelength interrogation of a fiber-optic Fabry-Perot acoustic sensor.

In this Letter, we propose a quadrature phase-stabilized three-wavelength demodulation technique for the interrogation of fiber-optic Fabry-Perot acoustic sensors. It is based on accurate and fast tuning of a monolithic modulated grating Y-branch laser. Three quadrature wavelengths are chosen to perform high-speed cavity length demodulation by wavelength switching, thereby avoiding imbalances and disturbances between the three optical paths in conventional three-wavelength quadrature phase-demodulation systems. A feedback-stabilization scheme for maintaining the quadrature phase condition is proposed for the first time, to the best of our knowledge, providing potential for long-term monitoring in harsh environments.

Force appropriation of nonlinear structures.

Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the system response and the applied excitation. This paper demonstrates that this commonly used quadrature condition can give results that are significantly different from the true NNM, in particular, when the excitation applied to the system is limited to one input force, as is frequently used in practice. The system studied is a clamped–clamped cross-beam with two closely spaced modes. This paper shows that the regions where the quadrature condition is (in)accurate can be qualitatively captured by analysing transfer of energy between the modes of the system, leading to a discussion of the appropriate number of input forces and their locations across the structure.

360° Phase Detector Cell for Measurement Systems Based on Switched Dual Multipliers

This letter presents a 360° phase detector cell for performing phase-shift measurements on multiple output systems. An analog phase detector, capable of detecting a maximum range of ±90°, has been used to perform a double multiplication of two signals, both in-phase and phase-shifted. The proposed solution broadens the frequency range beyond other solutions that require to fulfill the quadrature condition. Subsequently, the possibility of reaching the theoretical limit of phase shift within a hybrid coupler ($\varphi$ <;90° ± 90°) is discussed by using four straight-line equations to characterize the phase detector response. The proposed solution allows to extend up to 360° the phase detection range and provide an increased immunity with respect to both impedance mismatching and phase deviations within the hybrid coupler. To demonstrate the feasibility of the proposed design, a phase detector cell prototype has been implemented using a commercial hybrid coupler with a phase shift of 92.5° ± 0.5° at 3.1-5.9 GHz, an external switch and a microcontroller with 2 kB of memory. Measurements show a range of detection of 360° (±180°) across the tested frequency band of 2.7-6 GHz.

Interferometer with bismuth silicon oxide crystal for vibration measurement

We present a small-amplitude, high-frequency vibration measurement system. This system is based on the reflective holographic grating in a crystal of bismuth silicon oxide without applying an external electric field. A quarter-wave plate is applied in the reference beam path, with a polarizer after the crystal, to fulfill the quadrature condition when no electric field is applied to the crystal. A reflection configuration is used to obtain a good overlapping of the interference beams, which increases the beam coupling. The factors that affect the diffraction efficiency, including the signal-to-reference-beam intensity ratio and the recording angle, has been investigated. The experimental results coincide with the theoretical results, and the optimal conditions are obtained. The results of comparisons of our system with the vibrometer TEMPO show that the nanometer vibrations of a piezoelectric transducer can be reliably detected.

Ultra-Wideband VCO Phase-Noise Reduction Loop Based on a Six-Port Phase-Shifterless Delay-Line Discriminator

In this paper, a novel frequency-locked loop (FLL) architecture for phase-noise reduction of wideband voltage-controlled oscillators (VCO) is presented. The circuit makes use of a phase-shifterless frequency discriminator, which completely avoids the use of any control circuitry to keep the loop in its quadrature condition, highly simplifying the loop. The FLL circuit, which can be operated in a completely transparent way, can be easily interchangeable with the original VCO. An FLL prototype, based on a commercial state-of-the-art VCO, has been fabricated and measured exhibiting a phase-noise reduction higher than 9 and 5.5 dB up to 100-kHz and 1-MHz offset from carrier, respectively, in the complete 4.6-9-GHz band. Absolute phase noise results of -106.5 and -124 dBc/Hz at 100-kHz and 1-MHz offset from carrier have been obtained, showing lower phase noise than other wideband FLLs in the literature.

An algebraic perspective on multivariate tight wavelet frames. II

Continuing our recent work in [5] we study polynomial masks of multivariate tight wavelet frames from two additional and complementary points of view: convexity and system theory. We consider such polynomial masks that are derived by means of the unitary extension principle from a single polynomial. We show that the set of such polynomials is convex and reveal its extremal points as polynomials that satisfy the quadrature mirror filter condition. Multiplicative structure of this polynomial set allows us to improve the known upper bounds on the number of frame generators derived from box splines. Moreover, in the univariate and bivariate settings, the polynomial masks of a tight wavelet frame can be interpreted as the transfer function of a conservative multivariate linear system. Recent advances in system theory enable us to develop a more effective method for tight frame constructions. Employing an example by S.W. Drury, we show that for dimension greater than 2 such transfer function representations of the corresponding polynomial masks do not always exist. However, for all wavelet masks derived from multivariate polynomials with non-negative coefficients, we determine explicit transfer function representations. We illustrate our results with several examples.

Quaternionic Wavelets

Quaternion-valued functions have been used as a model for colour images and have recently been studied using various Fourier-type transforms. We develop some fundamental wavelet theory for quaternionic signals using the Fourier kernel introduced by Brackx, De Schepper, and Sommen in [1]. We present several analogs to classical wavelet theory, such as the quadrature mirror filter condition. We also include necessary design conditions for a wavelet basis to have desired regularity and sufficient design conditions which will guarantee compact support. Due to the difficulty in constructing orthogonal wavelet bases, we present some theory for biorthogonal wavelet bases and construct a few examples.

A new approach for setting up and applying a fiber-based Fabry–Perot interferometer

A new approach using fiber-based Fabry–Perot interferometry for constructing highly resistant and highly accurate vibration sensors is presented. The application of a diode array makes it possible to acquire a multitude of interference signals which can be classified into pairs of signals fulfilling the quadrature condition. This approach reaches the sensitivity of single-mode optical fiber interferometers proposed in the past while providing a much higher signal accuracy.

Adaptive interferometers with no external field using reflection gratings in CdTe:Ge at 1550 nm

We demonstrate experimentally the operation of an adaptive two-wave mixing interferometer with no field applied to a photorefractive crystal in which the quadrature condition is introduced by an external π/2 phase step. To achieve high signal to noise ratio the counter-propagating geometry for grating recording is used with a CdTe:Ge crystal, ensuring effective recording of reflection holograms. It is demonstrated that the interferometer with a photorefractive semiconductor crystal provides good sensitivity without the adverse effects that are normally associated with an applied field.

Performance Analysis of Photonic Vector Modulation Techniques for Multi-Gb/s Wireless Links

Broadband access networks evolution towards 10-Gb/s user connectivity will foster the evolution of the photonic and wireless technologies needed to implement multi-Gb/s wireless links. In particular, provision of data rates in excess of 1 Gb/s using wireless technologies is limited by currently available electrical technologies due to the required bandwidths and frequencies of operation in the millimeter-wave (mm-wave) band. Microwave photonic techniques and technologies have shown a clear potential to overcome these limitations. In this paper, the detailed study of a photonic vector modulator (PVM) architecture and its performance limitations are presented. The PVM architecture is based on direct baseband modulation and dispersion induced quadrature condition. The limitation of this architecture is the presence of a local oscillator (LO) component in the generated mm-wave spectrum which limits the system dynamic range. To overcome this limitation, a third continuous-wave (CW) laser is used to remove the unwanted LO component by properly adjusting its wavelength and emitted power. After presenting the theoretical model, the LO suppression feature is demonstrated experimentally by generating a 1.25-Gb/s QPSK 41-GHz modulated carrier. The two options (with and without LO carrier) are compared in terms of relevant performance parameters.

Generation of Multi-Gigabit-per-Second MQAM/MPSK-Modulated Millimeter-Wave Carriers Employing Photonic Vector Modulator Techniques

In this paper, two photonic vector modulator (PVM) architectures are presented, and their use in generating multi-gigabit-per-second M-ary quadrature amplitude modulation/M-ary phase shift keying modulated RF carriers in the millimeter-wave frequency regime is experimentally demonstrated. First, a highly scalable photonic quadrature amplitude modulation (QAM) architecture based on vector summation and dispersive delay lines, which directly generate multilevel signals from parallel in-phase and quadrature components, is proposed and experimentally demonstrated by generating up to 3-Gb/s quadrature phase shift keying (QPSK), four-level amplitude shift keying, and eight-level QAM at 39-GHz-modulated carriers. The possibility of also detecting the baseband components is shown, which allows the simultaneous feeding of baseband/RF signals over the same infrastructure. This architecture is limited to a certain length of fiber, as the quadrature condition is obtained for a certain aggregated dispersion. To overcome this limitation, a second PVM architecture is proposed, which is based on the use of two Mach-Zehnder modulators in parallel and an optical delay line to obtain the quadrature condition. The generation of a 2-Gb/s QPSK signal is experimentally demonstrated, including a 1-km standard single-mode-fiber transmission.

Adaptive interferometry of protein on a BioCD

Adaptive spinning-disk interferometry is capable of measuring surface profiles of a thin biolayer with subnanometer longitudinal resolution. High-speed phase modulation in the signal beam arises from the moving surface height profile on the spinning disk and is detected as a homodyne signal via dynamic two-wave mixing. A photorefractive quantum-well device performs as an adaptive mixer that compensates disk wobble and vibration while it phase-locks the signal and reference waves in the phase quadrature condition (pi/2 relative phase between the signal and local oscillator). We performed biosensing of immobilized monolayers of antibodies on the disk in both transmission and reflection detection modes. Single- and dual-analyte adaptive spinning-disk immunoassays were demonstrated with good specificity and without observable cross-reactivity. Reflection-mode detection enhances the biosensing sensitivity to one-twentieth of a protein monolayer, creates a topographic map of the protein layer, and can differentiate monolayers of different species by their effective optical thicknesses.

The effect of AM noise on correlation phase-noise measurements

We analyze the phase-noise measurement methods in which correlation and averaging is used to reject the background noise of the instrument. All the known methods make use of a mixer, used either as a saturated-phase detector or as a linear-synchronous detector. Unifortunately, AM noise is taken in through the power-to-dc-offset conversion mechanism that results from the mixer asymmetry. The measurement of some mixers indicates that the unwanted amplitude-to-voltage gain is of the order of 5-50 mV, which is 12-35 dB lower than the phase-to-voltage gain of the mixer. In addition, the trick of setting the mixer at a sweet point--off the quadrature condition--where the sensitivity to AM nulls, works only with microwave mixers. The HF-VHF mixers do not have this sweet point. Moreover, we prove that if the AM noise comes from the oscillator under test, it cannot be rejected by correlation. At least not with the schemes currently used. An example shows that at some critical frequencies the unwanted effect of AM noise is of the same order-if not greater--than the phase noise. Thus, experimental mistakes are around the corner.