Phase Mismatch Research Articles

PET-Based Instant Inkjet-Printed 4 × 4 Butler Matrix Beamforming Network

In this paper, a novel planar Butler matrix (BM) utilizing only 3dB3⁢dBhybrid couplers and a crossover are implemented using a low-cost silver-nano inkjet printing technique. Unlike in the conventional design of BM where a phase shifter is required, this novel design does not need a phase shifter to be implemented. However, the use of delicate substrates like polyethylene terephthalate (PET) in the design makes it unique. This is not possible with the conventional thermal curing process, as PET substrate cannot be subjected to an excessively feverish temperature. The results obtained show good return loss and transmission coefficients better than 26.1026.10 and 23.54dB23.54⁢dB, respectively, at the center frequency. Similarly, an amplitude imbalance of less than 2.4dB2.4⁢dB with phase mismatch within ±0.25∘±0.25∘ is achieved at the center frequency. The BM has a −10dB-10⁢dB bandwidth of 24.79% with a beam pattern produced at +13∘+13∘,−40∘-40∘, +40∘+40∘, and −13∘-13∘ when ports 1-4 of the BM are energized.

Elimination of the Phase Mismatch Error in PP Probe Using Synchronous Measurement Technique

The paper presents a modification of the pressure-pressure (PP) sound intensity measurement method. In the proposed solution simultaneous measurement with a pair of microphones (used in the classical PP probe) is replaced by a sequence of measurements taken with a single microphone placed in successive positions. This approach requires an additional (reference) microphone to synchronize the successive measurements. Although, in the process of calculating the sound intensity only the signal from the measurement microphone is used. Thanks of this the errors associated with differences in the frequency responses of the measurement microphones (especially phase mismatch error) that occurs in the classical PP method are eliminated. This approach simultaneously increases the random error and limits the measurements to periodic signals only. The article presents the principle of operation of the classical PP probe and the currently used methods of phase mismatch error elimination based on pre-calibration of the probe. Next, the theoretical basis of the proposed measurement method is described. To verify the effectiveness of phase mismatch error elimination in the proposed method, an experiment was conducted. It consisted in estimation the angle of incidence of an acoustic wave under controlled conditions in an anechoic chamber. The measurement was carried out with the classical PP probe and with the modified method. Measurements were made for different sound sources (a loudspeaker set and a small electrical device). In the final part of the paper, the results are discussed, both methods (classical and modified) are compared and potential applications of the proposed method are indicated.

Method for Estimating and Compensating the Phase Imbalance of Quadrature Signal Components

Currently, methods of direct modulation using complex signals are widely used. A complex signal consists of in-phase I (In-phase) and quadrature Q (Quadrature) components. When a signal passes through a communication channel and a receiving path, mismatches of the signal components occur as a result of interference. The mismatch, in turn, leads to increase in bit error rate (BER) during signal demodulation. The quality of the received signal is expressed in terms of bit error rate. The article considers phase imbalance of the quadrature components of a complex signal. Phase imbalance occurs in the receive path and depends on the quality of the receiver's local oscillators, on the operating temperature and the difference in propagation time of the I and Q components. The article shows an algorithm for estimating the phase imbalance of the quadrature signal components for digital modulation methods. Examples of signal constellation distortions in case of phase imbalance of quadrature signal components are considered. The phase imbalance estimation is based on the modulation constellation method for measuring signal parameters. Formulas for calculating the angle of phase error and the magnitude of quadrature error are given. Formulas for compensating the phase imbalance are also given, taking into account the calculated quadrature error. A mathematical model of the transmitter, communication channel and receiver has been developed to study the method for estimating and compensating for phase imbalance. The mathematical model is built in the Matlab software environment and is an m-script software model. With the help of the mathematical model, method for estimating and compensating for phase imbalance has been studied. In the course of the study, relationships of error probability due to the mismatch of the quadrature components of the signal were obtained. The noise immunity of the receiver paths with and without compensation for the phase mismatch of the quadrature signal components is compared. Based on the results of the study, diagrams of the error probability and the phase mismatch of the receiver's local oscillators were obtained. The study shows that phase mismatch of the receiver local oscillators at a fixed signal-to-noise ratio leads to an increase in the probability of received bit errors. But when applying the phase imbalance compensation method, the error probability remains fixed as the phase mismatch of receiver local oscillators increases at a fixed signal-to-noise ratio.

Research of the Influence of the Quadrature Components Mismatch on the Noise Immunity of OFDM and UFMC Signals

The method of direct modulation using complex signals is used to implement signal paths of transmitters in base stations of cellular communication systems. In the process of modulation, there are mismatches of the gain coefficient and the phase of the quadrature components of the signal. Mismatch degrades the Error Vector Magnitude (EVM) at the receiver, which in turn results in an increased Bit Error Rate (BER). The quality of the received signal is expressed in bit error rate. The mismatch of the amplitude and phase of the quadrature components is one of the most important factors making the greatest contribution to the amplitude of the error vector, and which must be investigated. The paper presents a research of the influence of the mismatch on the OFDM (Orthogonal frequency-division multiplexing) and UFMC (universal filtered multi-carrier) technologies. A model of the transmitter, communication channel and receiver for OFDM and UFMC signals has been developed. The model was built in the MatLab software environment. In the work, by studying the simulation model, the dependence of the noise immunity of technologies was studied by changing the parameters of the communication channel, such as the amplitude and phase mismatch of the quadrature components of the signal, as well as the signal-to-noise ratio. Also, a comparative analysis of such signal parameters as the occupied bandwidth, peak to average ratio, frequency of occurrence of bits with an error was carried out. Based on the results of the study, graphs of the dependence of the error probability and the signal peak to average ratio on the mismatch of the quadrature components were obtained for two technologies, OFDM and UFMC. The study allows us to highlight the advantages of UFMC technology, which are expressed in spectral efficiency, noise immunity and the level of the signal peak to the average ratio.

Shortcut to adiabaticity in bent waveguide couplers with a sign flip of the phase mismatch.

Bending the axis of a waveguide coupler can result in phase mismatch between the evanescently coupled waveguides. Using a bent waveguide coupler, we realize a shortcut to adiabatic light transfer between waveguides with a sign flip of the phase mismatch. Counterdiabatic driving with unitary transformation cancels non-adiabatic coupling in the waveguide coupler so that light evolution follows the adiabatic modes at short lengths. The counterdiabatic driving protocol is implemented in the waveguide coupler by engineering the waveguide spacing and axis bending profile. The bent waveguide coupler is compact and robust against parameter variations.

Control Scheme of Phase-Shifter for Photon Energy Scan

Variable gap undulator widely used in X-ray free-electron laser (XFEL) enables the photon energy scan by changing its gap. A phase-shifter should be incorporated to compensate for the phase mismatch between the electron bunches and X-ray pulses arising while those traverse the drift space between undulator segments. The uncertainties in both the undulator parameter and the drift space distance introduce an error in calculating the optimum gap distance of the phase-shifter for the different undulator K. The phase-shifter gap needs to be set where the error is within the tolerable range. The control scheme we propose can maintain full FEL intensity over the scanned photon energies.

EPI phase error correction with deep learning (PEC-DL) at 7T.

The phase mismatch between odd and even echoes in EPIcauses Nyquist ghost artifacts. Existing ghost correction methods often suffer from severe residual artifacts and are ineffective with k-space undersampling data. This study proposed a deep learning-based method (PEC-DL) to correct phase errors for DWI at 7Tesla. The acquired k-space data were divided into 2 independent undersampled datasets according to their readout polarities. Then the proposed PEC-DL network reconstructed 2 ghost-free images using the undersampled data without calibration and navigator data. The network was trained with fully sampled images and applied to two- and fourfold accelerated data. Healthy volunteers and patients with Moyamoya disease were recruited to validate the efficacy of the PEC-DL method. The PEC-DL method was capable to mitigate the ghost artifacts in DWI in healthy volunteers as well as patients with Moyamoya disease. The fourfold accelerated results showed much less distortion in the lesions of the Moyamoya patient using high b-value DWI and the corresponding ADC maps. The ghost-to-signal ratios were significantly lower in PEC-DL images compared to conventional linear phase corrections, mini-entropy, and PEC-GRAPPA algorithms. The proposed method can effectively eliminate ghost artifacts for full sampled and up to fourfold accelerated EPI data without calibration and navigator data.

Phase mismatch induced suppression of eigenmode resonance in terahertz metasurfaces.

In this paper, we observe the distinguishable modulation of the different eigenmodes by lattice mode in terahertz U-shaped metasurfaces, and a remarkable lattice induced suppression of the high order eigenmode resonance is demonstrated. With the quantitative analysis of Q factor and loss of the resonances, we clarify that the peculiar phenomenon of suppression is originated from the phase mismatch of the metasurfaces via introducing the phase difference between the neighboring structures. These results provide new insights into the phase mismatch mediated transmission amplitude of eigenmode resonance in metasurfaces and open a new path to developing terahertz multifunctional devices.

Fading Suppression for Distributed Acoustic Sensing Assisted With Dual-Laser System and Differential-Vector-Sum Algorithm

The sensing performance is severely affected by the intensity fading in the phase-sensitive optical time domain reflectometry ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula> -OTDR) based distributed acoustic sensing (DAS) system. The intensity fading manifests a stochastic amplitude fluctuation in the scattering signal. To suppress the fading noise, a heterodyne <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varphi $ </tex-math></inline-formula> -OTDR system assisted with dual lasers with independent frequency, polarization, and initial phase is established to generate two pulses responses with different fading components at the same time. The backscattering signals from two individual probe pulses present different fading positions but possess the same phase change rate which is induced by the external disturbance. Through the differential-vector-sum algorithm including vectorization and phase differential, two complex Rayleigh backscattering beat signals from the two laser probes are efficiently synthesized, to simultaneously suppress the fading phenomenon caused by the inner pulse interference, polarization mismatch and phase mismatch. In the experimental validation, the probability of the fading channels in dual-laser scheme was significantly reduced from 9.4% to 1% compared with the single laser system, which is based on the resolution threshold of 2.1n <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon / \surd $ </tex-math></inline-formula> Hz at 10Hz. Moreover, the dual-laser scheme also proves the polarization insensitivity by inducing a rapid polarization perturbation for two probe lasers. Owing to the fading noise suppression, the dynamic signal’s SNR of the dual-laser system was improved more than 20dB in the intensity fading channels, while the temporal and spatial resolution were not deteriorated. The proposed fading suppressed distributed sensing system possesses the excellent performance, which makes it play an important role for practical distributed acoustic sensing.

Orbital angular momentum sidebands in second harmonic generation of a vortex beam by a nonlinear crystal with inhomogeneous refractive index

The manipulation of the orbital angular momentum (OAM) spectrum in new wavelengths generated by frequency conversion has a wide range of applications in quantum information technology and modern communications. Here, the second harmonic generation of a vortex beam in a nonlinear crystal with an inhomogeneous refractive index is considered. It is shown that by using a segmented oven and generating a controllable temperature gradient along the thickness of the nonlinear crystal, a transverse phase mismatch can be induced in the vortex beam. Accordingly, the OAM spectrum of the vortex beam can be changed by generating new OAM components in the spectrum. Compared with the nonlinear Bragg diffraction method, the presented method has the advantage of longer interaction length and higher efficiency.

A Transformation-Optics-Based Flat Metamaterial Luneburg Lens Antenna With Zero Focal Length

The transformation optics (TO) technique has been widely applied in the volume reduction of Luneburg lens (LL) in both optical and microwave regimes. However, it is found that the focus is usually not located on the surface of the transformed LL anymore after applying TO. The focus location shift results in a limited volume reduction, severe reflection from the new lens surface, and limited scanning range with increased spillover loss. This article theoretically studies and proposes a TO-based LL antenna with zero focal length by considering the phase mismatch caused by space discontinuity. The study first reveals that the transformation of an LL alone without sustaining the original boundary inherently deteriorates the original focusing property even before exerting any approximation. To validate the idea, a flat metamaterial LL antenna using TO is proposed, approximated, and fabricated using an integrated dielectric and conductive 3-D printing manufacturing process. The feeding patch antenna remains on the surface of the transformed lens. The thickness of the proposed antenna is reduced to 1/3 of a traditional LL in its boresight, while a ±20° beam scanning range is achieved with linearly shifted feedings. The study verifies that it is essential to ensure phase matching at the radiation boundary to maintain the original focusing property of an LL. The information derived from the study evidences the conditions of the enforcement of TO in electromagnetic problems such as dielectric lenses.

Sinusoidal and nonsinusoidal patterns in amplitude envelope synchronization.

In this work, amplitude envelope synchronization (AES), as a general phenomenon characterized with highly correlated amplitude envelope but uncorrelated phases and frequencies in coupled nonidentical nonlinear systems, is investigated theoretically and numerically. Two different types of AES patterns, including sinusoidal and nonsinusoidal, are widely observable in coupled periodic and/or chaotic oscillators. They both come from modulation of phase mismatch on amplitude but show different patterns due to different behaviors of phase mismatch. With increase of frequency mismatch, the system tends to crossover from nonsinusoidal to sinusoidal AES. With the aid of synchronization manifold and transverse stability analyses of the AES state, the physical mechanism and scale relations for the AES are well revealed. We expect that all these results could uncover the generality of AES in coupled nonlinear oscillators and help to understand the rich dynamics of phase and amplitude coupling in multidisciplinary fields.

High extinction ratio and broadband polarization beam splitter based on bricked subwavelength gratings on SOI platform

A compact asymmetrical directional coupler (ADC) based on coupling between a conventional subwavelength grating (SWG) and a bricked subwavelength grating (BSWG) is proposed to realize broadband polarization beam splitter (PBS) with high extinction ratio (ER) on silicon-on-insulator (SOI) platform. Apart from conventional SWG structural parameters (duty cycle and period), the BSWG is utilized to provide a new design space to control TE and TM modal effective index for accurate phase match. Accordingly, as to the TM mode, it is possible to satisfy phase-matching condition and then can be coupled more efficiently with higher ER by introducing the BSWG. Meanwhile, there is a significant phase mismatch for the TE mode. In this way, the proposed PBS that separates TE and TM mode to the through and cross ports can be realized. Simulation results show that the proposed PBS with a compact coupling length of 8.4 μm can achieve a high ER of 35.06 dB and an insertion loss of 0.25 dB for the TM mode at 1.55 μm, while the ER is 18.92 dB and insertion loss is 0.01 dB for the TE mode. Moreover, the operating bandwidth is up to 300 nm (1400∼1700 nm) for the TE mode and 155 nm (1487∼1642 nm) for the TM mode when the ER is >15 dB.

Higher-order optical rabi oscillations

Rabi oscillations express a phenomenon of periodic conversion between two wave states in a coupled system. The finding of Rabi oscillation has led to important applications in many different disciplines. Despite great progress, it is still unknown whether the Rabi oscillating state can be excited in the framework of the higher-order vector vortex regime. Here, we demonstrate in theory that the higher-order vector vortex light beams can be Rabi oscillating during evolution in an optical coupling system. This new classical oscillating state of light is characterized by a topologically shaped wavefront and coupled with spatially varying polarization. The vector vortex state exhibits a harmonic oscillatory property in the resonant and nonresonant conditions but differs greatly in Rabi oscillating frequencies. During Rabi oscillation, the complex state maintains its topology and intensity profile, while its intrinsic polarization pattern varies adiabatically in a periodic manner. We present an interpretation of the Rabi oscillation of the higher-order wave states in terms of the coupled-mode theory. Furthermore, we reveal a symmetry-protected transition between two Rabi oscillating modes, driven by a slowly varying phase mismatch. This Rabi transition has not been reported in either quantum mechanics or any other physical setting. This work advances the research of Rabi oscillation into the higher-order regime, and it may lead to novel applications in classical and quantum optics.

2×2 MIMO Equalizer Enabled Transmitter Side IQ Imbalance Compensation for Optical Single Sideband Direct Detection System

Recently, optical single sideband (SSB) based direct detection (DD) has been considered as a promising candidate for inter data center interconnects (inter-DCIs). Kramers-Kronig (KK) receiver is always applied to eliminate the signal-to-signal beating interference (SSBI) caused by the square law-detection of a single-ended photodiode (PD) in SSB DD system. The electro-to optical (E/O) conversion of the complex signal can be realized by IQ modulator (IQM). However, IQ imbalance exists at the transmitter since the in-phase and quadrature-phase ports of IQM are driven by the real and imaginary parts of the signal, respectively. In this paper, we show the theoretical analysis of the transmitter side (Tx-side) IQ imbalance includes time delay, amplitude mismatch and phase mismatch. Tx-side IQ imbalance will seriously deteriorate the system performance. To deal with the impairment caused by Tx-side IQ imbalance, a 22 real-value multiple-input multiple-output (MIMO) equalizer is proposed and implemented, and the system with the impact of these three factors are investigated in simulation, respectively. Besides, a transmission of 180 Gb/s/ discrete Fourier transform spread (DFT-S) orthogonal frequency division multiplexing (OFDM) signal over 80-km single mode fiber (SMF) is experimentally demonstrated with bit error rate (BER) below the soft-decision forward error correction (SD-FEC) threshold of 210-2 enabled by the proposed 22 MIMO equalizer.

Design and Demonstration of Compact and Broadband Wavelength Demultiplexer Based on Subwavelength Grating (SWG)

An ultracompact and broadband silicon wavelength demultiplexer based on SWG-assisted directional coupler is designed and experimentally demonstrated for wavelength splitting of 1310 and 1550 nm. The embedded SWG enables significantly reduced footprint, due to the precise phase matching at 1550 nm and large phase mismatch at 1310 nm. As a result, the fabricated device has a length of only 9 &#x03BC;m, and provides high extinction ratios (ERs) of 23 dB and 19 dB at 1310 and 1550 nm, respectively. Its 3-dB bandwidths are 85 nm for O-band (ER &gt; 15 dB) and 140 nm for C-band (ER &gt; 10 dB).

Temperature-dependent second-harmonic generation from color centers in diamond.

Under infrared ultrashort pulse laser stimulation, we investigate temperature-dependent second-harmonic generation (SHG) from nitrogen-vacancy (NV)-introduced bulk diamond. The SHG intensity decreases in the temperature range of 20-300°C, due to phase mismatching caused by refractive index modification. We discover that optical phonon scattering outperforms acoustic phonon scattering in NV diamond by fitting the temperature dependence of the SHG intensity using a model based on the bandgap change via the deformation potential interaction. This study presents an efficient and viable way for creating diamond-based nonlinear optical temperature sensing.

Spectral analysis of Brillouin dynamic gratings in polarization-maintaining fibers.

Experiment observations show that the spectra of Brillouin dynamic gratings in polarization-maintaining fibers based on a polarization decoupled scheme are quite broad and usually have multiple peaks. In this paper, we measure the birefringence distribution along polarization-maintaining fibers with high spatial resolution using optical frequency-domain reflectometry. Based on birefringence measurements, both the simulation and experiment are carried out to determine the spectra of Brillouin dynamic gratings generated within the same polarization-maintaining fibers, indicating quantitatively that spectral broadening and irregularity are mainly due to phase mismatch caused by the non-uniformity of birefringence along polarization-maintaining fibers.

Exchange of orbital angular momentum of light via noise-induced coherence

The noise-induced coherence created via the quantum interference of incoherent radiation in atomic three-level systems of V and \ensuremath{\Lambda} types driven by a pair of weak laser pulses is shown to result in exchange of optical vortices. In the three- level V-type atom-light coupling the system is populated in its ground level, while in the \ensuremath{\Lambda} model the system is initially prepared in an electromagnetically induced transparency state. By solving the quantum optical Maxwell-Bloch equations and with quantum interference of incoherent radiation present, we show that the orbital angular momentum (OAM) of the vortex probe beam can be transferred to a generated signal field. While the exchange efficiency in the V configuration is higher, the losses are less in the \ensuremath{\Lambda} scheme when we consider such a noise-induced coherence. We further discuss the effects of phase mismatching and inhomogeneous broadening on the energy conversion between light beams carrying OAM.

Generation of entangled photons via parametric down-conversion in semiconductor lasers and integrated quantum photonic systems

We propose and design a high-brightness, ultra-compact electrically pumped GaSb-based laser source of entangled photons generated by mode-matched intracavity parametric down-conversion of lasing modes. To describe the nonlinear mixing in highly dispersive and dissipative waveguides, we develop a nonperturbative quantum theory of parametric down-conversion of waveguide modes which takes into account the effects of modal dispersion, group and phase mismatch, propagation, dissipation, and coupling to noisy reservoirs. We extend our theory to the regime of quantized pump fields with a new approach based on the propagation equation for the state vector which solves the nonperturbative boundary-value problem of the parametric decay of a quantized single-photon pump mode and can be generalized to include the effects of dissipation and noise. Our formalism is applicable to a wide variety of three-wave mixing propagation problems. It provides convenient analytic expressions for interpreting experimental results and predicting the performance of monolithic quantum photonic systems.