Continuous Phase Control Research Articles

A Fully Reconfigurable 1×4Filtering Beamforming Network With Continuous Phase and Amplitude Control

A Fully Reconfigurable 1×4Filtering Beamforming Network With Continuous Phase and Amplitude Control

Efficient and Continuous Carrier-Envelope Phase Control for Terahertz Lightwave-Driven Scanning Probe Microscopy.

The fundamental understanding of quantum dynamics in advanced materials requires precise characterization at the limit of spatiotemporal resolution. Ultrafast scanning tunneling microscopy is a powerful tool combining the benefits of picosecond time resolution provided by single-cycle terahertz (THz) pulses and atomic spatial resolution of a scanning tunneling microscope (STM). For the selective excitation of localized electronic states, the transient field profile must be tailored to the energetic structure of the system. Here, we present an advanced THz-STM setup combining multi-MHz repetition rates, strong THz near fields, and continuous carrier-envelope phase (CEP) control of the transient waveform. In particular, we employ frustrated total internal reflection as an efficient and cost-effective method for precise CEP control of single-cycle THz pulses with >60% field transmissivity, high pointing stability, and continuous phase shifting of up to 0.75 π in the far and near field. Efficient THz generation and dispersion management enable peak THz voltages at the tip-sample junction exceeding 20 V at 1 MHz and 1 V at 41 MHz. The system comprises two distinct THz generation arms, which facilitate individual pulse shaping and amplitude modulation. This unique feature enables the flexible implementation of various THz pump-probe schemes, thereby facilitating the study of electronic and excitonic excited-state propagation in nanostructures and low-dimensional materials systems. Scalability of the repetition rate up to 41 MHz, combined with a state-of-the-art low-temperature STM, paves the way toward the investigation of dynamical processes in atomic quantum systems at their native length and time scales.

Novel Passive Vector-Sum Amplitude-Variable Phase Shifter With Integrated Reconfigurable Filtering Function

In this article, a novel passive vector-sum amplitude-variable phase shifter with integrated reconfigurable filtering function is proposed for the first time. It is constructed using conventional trisection filtering topology, with all the couplings between adjacent resonators being implemented with controllable mixed electric&#x2013;magnetic couplings. This not only achieves a reconfigurable filtering response but also forms an intrinsic <inline-formula> <tex-math notation="LaTeX">$I/Q$ </tex-math></inline-formula> signal generator inside the filter, which can be directly utilized to achieve continuous phase control based on the vector-sum mechanism. In such a manner, an integrated filtering phase shifter (FPS) without the need for an extra <inline-formula> <tex-math notation="LaTeX">$I/Q$ </tex-math></inline-formula> generation network and individual filtering device is obtained. By properly choosing the coupling types and coupling strengths between adjacent resonators, a continuous phase control from 0&#x00B0; to 360&#x00B0;, covering the full four quadrants, is successfully realized. Closed-form equations associating the circuit parameters and insertion phase at center frequency are deduced, providing a quantitative theoretical guideline for determining the parameters of the FPS. Subsequently, a novel tuning mechanism for independent <inline-formula> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula>-factor and resonant frequency control of the resonator is proposed and applied in the circuit to further exploit the amplitude control ability of the phase shifter. Measured results show that the proposed amplitude-variable FPS is capable of achieving a continuous phase control range of 360&#x00B0; and an amplitude control range of 10 dB within a center frequency tuning range of 0.75&#x2013;0.95 GHz. The measured root-mean-square (rms) amplitude error and the rms phase error are less than 2.58 dB and 8.45&#x00B0;, respectively.

A Piecewise Monotonic Smooth Phase Variable for Speed-Adaptation Control of Powered Knee-Ankle Prostheses

Researchers are currently making progress in unifying the entire gait cycle of powered prostheses by using a human-inspired phase variable, but constructing a robust phase variable to more accurately estimate the gait phase and desired joint trajectories of prostheses during varying walking speeds remains an open problem. Firstly, this study proposed a piecewise monotonic and smooth phase variable to predict the gait phase from only the measured thigh angle. Compared to the two most widely used methods, thigh angle integral vs. thigh angle and thigh angular rate vs. thigh angle, the proposed method addressed the drift problem of the integral-based method and the noise problem of the angular rate-based. Then a predictive tuning-free model that represents gait kinematics as a continuous function of proposed phase variable and walking speed was constructed to generate desired joint virtual constraints for speed-adaptation control of powered knee-ankle prosthesis during continuously varying walking speeds. Experiments were conducted with six able-bodied participants wearing inertial measurement units and performing periodic and non-periodic (quick start and stop) tasks, and one transfemoral amputee wearing a powered knee-ankle prosthesis walking on a treadmill. Experimental results illustrated that the root mean squared error of the gait phase estimated by the proposed approach was 75% lower than the integral-based and angular rate-based methods, and the proposed approach performed well in the continuous phase control of a powered knee-ankle prosthesis during varying walking speeds.

Novel Passive Vector-Sum Reconfigurable Filtering Phase Shifter With Continuous Phase-Control and Tunable Center Frequency

In this article, a novel reconfigurable filtering vector-sum phase shifter (RFPS) with a continuous phase shift range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ge 300^{\circ }$ </tex-math></inline-formula> and tunable operating frequency range from 1.05 to 1.3 GHz is proposed. It consists of two identical wideband Wilkinson power dividers (or power combiners) (WPDs) and a reconfigurable filtering quadrature coupler (RFQC) that is connected between the two WPDs. Through the first WPD, the split waves are fed into the RFQC and are then combined at the output ports of the RFQC. The phase of the combined waves can be continuously tuned by adjusting different combinations of coupling types between interstage resonators of the RFQC, and the resulted output waves are then summed up through the second WPD with the desired output phase. Different from the conventional active vector-sum phase shifter, the vector summing is realized by the proposed RFQC and is a pure passive design, resulting in a low-cost, low-noise, easy-design, and highly flexible system. A prototype is designed and fabricated to demonstrate the proposed technique. Detailed theoretical analysis and design procedure have been given. The experimental results show that the proposed RFPS features the continuous phase-control range of more than 300° with a tunable filtering response covering the frequency range from 1.05 to 1.3 GHz.

Versatile metasurface platform for electromagnetic wave tailoring

The emergence of metasurfaces provides a novel strategy to tailor the electromagnetic response of electromagnetic waves in a controlled manner by judicious design of the constitutive meta-atom. However, passive metasurfaces tend to perform a specific or limited number of functionalities and suffer from narrow-frequency-band operation. Reported reconfigurable metasurfaces can generally be controlled only in a 1D configuration or use p-i-n diodes to show binary phase states. Here, a 2D reconfigurable reflective metasurface with individually addressable meta-atoms enabling a continuous phase control is proposed in the microwave regime. The response of the meta-atom is flexibly controlled by changing the bias voltage applied to the embedded varactor diode through an elaborated power supply system. By assigning appropriate phase profiles to the metasurface through voltage modulation, complex beam generation, including Bessel beams, vortex beams, and Airy beams, is fulfilled to demonstrate the accurate phase-control capability of the reconfigurable metasurface. Both simulations and measurements are performed as a proof of concept and show good agreement. The proposed design paves the way toward the achievement of real-time and programmable multifunctional meta-devices, with enormous potential for microwave applications such as wireless communication, electromagnetic imaging, and smart antennas.

Catenary-based phase change metasurfaces for mid-infrared switchable wavefront control.

Active wave manipulation by ultracompact meta-devices is highly embraced in recent years, but a major concern still exists due to the lack of functional reconfigurability. Moreover, the phase or amplitude discontinuities introduced by collective response of discrete meta-atoms make current meta-devices far from practical applications. Here, we demonstrate actively tunable wavefront control with high-efficiency by combining catenary-based meta-atoms for intrinsic continuous phase regulation with the chalcogenide phase change material (PCM) of Ge2Sb2Te5. First, switchable beam deflection is demonstrated in a wide mid-IR range between 8 μm and 9.5 μm with 'on' and 'off' states for beam steering between anomalous and normal specular reflections. Second, a switchable meta-axicon for zero order Bessel beam generation is demonstrated with full width at half maximum (FWHM) as small as ∼0.41 λ (λ = 12 µm). As a result, our scheme for active and continuous phase control potentially paves an avenue to construct active photonic devices especially for applications where large contrast ratio is highly desirable, such as optoelectronic integration, wavefront engineering and so on.

Advances in strain engineering on oxide heteroepitaxy

Advances in strain engineering on oxide heteroepitaxy

Reflective Quasi-Continuous Metasurface with Continuous Phase Control for Light Focusing.

Benefitting from the arbitrary and flexible light modulation, metasurface has attracted extensive attention and been demonstrated in different applications. However, most reported metasurface-based devices were normally composed of discrete micro or nano structures, therefore the discretization precision limited the performance of the device, including the focusing efficiency, stray light suppression, and broadband performance. In this work, an all-metallic reflective metasurface consisting of numerous quasi-continuous nanostructures is proposed to realize high-efficiency and broadband focusing. The constructed quasi-continuous metasurface (QCMS) is then verified numerically through electromagnetic simulation, and the numerical results show a higher focusing efficiency and a better stray light suppression effect, compared to a binary-phase-based metalens. Through the same design strategy, a QCMS with the ability to overcome the diffraction limit can also be constructed, and a focal spot with the size of 0.8 times the diffraction limit can be achieved. We expect that this quasi-continuous structure could be utilized to construct other high-performance devices that require continuous phase controls, such as the beam deflector, orbital angle momentum generator, and self-accelerating beam generator.

Continuous Phase Control of Vanadium Dioxide Films

Abstract Vanadium dioxide (VO2) undergoes a metal-insulator transition (MIT) at approximately 68 °C, with associated sharp changes in its physical (e.g., optical, electrical, and mechanical) properties. This behavior makes VO2 films of interest in many potential applications, including memory devices, switches, sensors, and optical modulators. For ON/OFF like digital applications, an abrupt switching behavior is ideal. However, to continuously change VO2 metal/insulator phase ratio for analog-like operation, the intrinsic hysteresis characteristic of VO2 MIT renders the phase control becoming a formidable challenge. This paper considers the problem of controlling and tracking desired optical transmittance via continuous phase ratio change. The problem becomes worse while considering the differences of individual thin-film samples and the hysteresis associated with the phase change within a narrow temperature range. This paper reports a robust feedback controller using an optical transmittance measurement and based on an uncertainty and disturbance estimator (UDE) architecture. The proposed controller is capable of mitigating the adverse effect of hysteresis, while also compensating for various uncertainties. The effectiveness of the proposed methodology is demonstrated with experimental validation.

Analysis of polarization-dependent continuous 2π phase control mechanism for trapezoidal nano-antennas through multipole expansion method

In order to explore the polarization-dependent continuous 2π phase control mechanism of nano-antennas and to provide theoretical bases for the subsequent design of polarization beam splitters, unidirectional radiation antennas, and other devices, we design a trapezoidal nano-antenna structure with high transmission efficiency and polarization-dependent continuous 2π phase variation under the wavelengths of 600–1000 nm. Then we analyze the relationship between phase control and the excited electric/magnetic dipoles and quadrupoles under different linearly polarized incident light beams. The results show that, in the y -direction, the antenna mainly realizes polarization-dependent continuous 2π phase control at the wavelengths where the first Kerker’s condition is satisfied. As the antenna’s unidirectional angular radiation is mainly achieved by compensating the wavefront phase, based on the above analysis, the relationship between the maximum radiation angle of unidirectional angular radiation and the excited electric/magnetic dipoles and quadrupoles in the antenna is further analyzed. Finally, we also briefly consider the influence of the structural sizes of the designed antenna on the resonances and coupling of the excited electric/magnetic dipoles and quadrupoles under different linearly polarized incident light beams for future applications.

Continuous phase control of second harmonic generation from metasurfaces composed of complementary split ring resonators

We demonstrate the realization of a continuous control over the phase change from zero to 2π for second harmonic generation (SHG) from the complementary split-ring resonators (CSRRs) by adjusting their geometrical parameters and reversing their orientations. We verify this concept by designing and fabricating nonlinear metasurfaces consisting of CSRRs with desired nonlinear phase profiles, which can bend and focus the SHG signals. The ability to provide a continuous and subwavelength phase control of the local second-order nonlinearities makes the CSRRs good candidates for applications, such as nonlinear holograms and integrated nonlinear nanophotonic elements that combine the coherent generation and manipulation of harmonic waves.

Microwave Phase Shifting Using Coherent Photonic Integrated Circuits

An optically coherent silicon-on-insulator circuit for microwave phase shifting is presented. Such photonic integrated circuits provide advantages over more-complicated incoherent methods and coherent techniques implemented in bulk fiber-optic components. The circuit is described theoretically with supporting experimental data. Continuous microwave phase control at 49 GHz is demonstrated, with an electrical power to achieve 2π phase shift of 80 mW and a 3-dB phase modulation bandwidth of 170 kHz.

Spin and wavelength multiplexed nonlinear metasurface holography.

Metasurfaces, as the ultrathin version of metamaterials, have caught growing attention due to their superior capability in controlling the phase, amplitude and polarization states of light. Among various types of metasurfaces, geometric metasurface that encodes a geometric or Pancharatnam–Berry phase into the orientation angle of the constituent meta-atoms has shown great potential in controlling light in both linear and nonlinear optical regimes. The robust and dispersionless nature of the geometric phase simplifies the wave manipulation tremendously. Benefitting from the continuous phase control, metasurface holography has exhibited advantages over conventional depth controlled holography with discretized phase levels. Here we report on spin and wavelength multiplexed nonlinear metasurface holography, which allows construction of multiple target holographic images carried independently by the fundamental and harmonic generation waves of different spins. The nonlinear holograms provide independent, nondispersive and crosstalk-free post-selective channels for holographic multiplexing and multidimensional optical data storages, anti-counterfeiting, and optical encryption.

Ultrathin gradient nonlinear metasurface with a giant nonlinear response

Gradient metasurfaces have recently been demonstrated to provide control of the phase of scattered fields over subwavelength scales, enabling a broad range of linear optical components in a flat, ultrathin, integrable platform. Additionally, the development of nonlinearmetasurfaces has disrupted conventional nonlinear optical device design by relaxing phase matching constraints, reducing size and dimensionality, and providing record values of localized nonlinear responses. However, extending the “flat optics” paradigm to the nonlinear case faces important challenges, since we are required to simultaneously achieve efficient frequency conversion and sub-diffractive phase control. Here, we experimentally demonstrate continuous phase control of the giant nonlinear second harmonic optical response from metasurfaces tied to intersubband transitions in semiconductor multi-quantum wells, establishing an exciting path toward realizing the vision of flat, nonlinear optics.

Continuous control of the nonlinearity phase for harmonic generations.

The capability of locally engineering the nonlinear optical properties of media is crucial in nonlinear optics. Although poling is the most widely employed technique for achieving locally controlled nonlinearity, it leads only to a binary nonlinear state, which is equivalent to a discrete phase change of π in the nonlinear polarizability. Here, inspired by the concept of spin-rotation coupling, we experimentally demonstrate nonlinear metasurfaces with homogeneous linear optical properties but spatially varying effective nonlinear polarizability with continuously controllable phase. The continuous phase control over the local nonlinearity is demonstrated for second and third harmonic generation by using nonlinear metasurfaces consisting of nanoantennas of C3 and C4 rotational symmetries, respectively. The continuous phase engineering of the effective nonlinear polarizability enables complete control over the propagation of harmonic generation signals. Therefore, this method seamlessly combines the generation and manipulation of harmonic waves, paving the way for highly compact nonlinear nanophotonic devices.

An Array of Coherent Sources Based on Novel Dual-Loop PLL Infrastructure

In this paper, a novel array of coherent sources based on dual-loop phase-locked loop (PLL) is proposed. An advanced low-cost frequency and phase control technique for a group of PLLs is presented. A novel dual-loop PLL infrastructure consists of a conventional PLL loop and a microcontroller-unit-controlled phase-detector-array loop, which achieves real-time calibration on both frequency and phase by reducing the effect of component aging and environmental issues. This technique has its advantages of building a phased transmitter array. For the purpose of demonstration, a four-element phased array has been designed and implemented by using commercially available components at S-band. Near-perfect local oscillator (LO) beamforming performance and array pattern self-compensation realization are presented and analyzed. Due to analog continuous phase control and individual programmable transmit frequency, the dual-loop PLL-based coherent-source array in this paper offers considerable practical advantages when implementing beamforming, as compared to other beamforming techniques.

Continuous Active Phase Shifter Design and Analysis for Millimeter-Wave Circuits

This brief presents a continuous active phase shifter for millimeter-wave phased-array transceivers. Having an all-pass network frequency response, the proposed phase shifter provides continuous insertion phase control and nearly constant insertion loss regardless of the insertion phase variation. A complete analysis for the phase shifter is provided along with circuit measurement results. The phase shifter is fabricated in a 0.13-μm commercial CMOS technology. A phase tuning range larger than 90 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> and -7 dB of insertion loss are achieved for the phase shifter.

Application of the method of Lyapunov periodic functions

The paper is concerned with asymptotic behavior of continuous and discrete phase control systems involving periodic differentiable nonlinear vector functions and featuring nonunique equilibrium state.

Strong phase-controlled fiber Bragg gratings for dispersion compensation.

Dispersion-compensating fiber Bragg gratings with approximately 99.9% reflectivity that are made by continuous apodization and phase control are demonstrated. These strong dispersion-compensating gratings provide precision second-order, third-order, or even more complex dispersion compensation, as well as sufficient transmission isolation to be used at add-drop stages without additional filtering. A 99.84% grating with a constant approximately 700-ps/nm dispersion and a 99.94% grating with dispersion varying linearly from 1000 to -1000 ps/nm are demonstrated.