Phase-shifting Element Research Articles

Design of an ultra wideband THz reflectarray antenna based on orbital angular momentum

A Reflectarray antenna (RA) that can generate orbital angular momentum vortex waves in the THz band was proposed. First of all, a reflective phase-shifting element composed of a notched double-shaped ring and a single Matal structure was designed to form a radiation patch. The reflective phase-shifting element has the advantages of good linearity, high smoothness, and a large phase shift range, which is suitable for the subsequent production of reflective array antennas. Then, the phase distribution of the reflected wave of the OAM vortex wave carrying mode l=+1、+2、+3、+4 is given, and the size of each element is determined based on the reflected phase of each element. Using the proposed element, an OAM reflectarray antenna operating within the waveguide standard WR-5 (120GHz–220GHz) is designed. The optimal frequency band for antenna operation in mode l=+1 is 150GHz–190 GHz, and the maximum gain of the reflector array antenna is 19.4 dBi, and the minimum divergence angle of the antenna array is 5.2°, which has good directivity and beam radiation ability. The spiral structure of the OAM beam space generated by the RA in this paper is clearly visible, proving that the implementation of OAM vortex waves in the THz frequency band is feasible. This design also provides a new method for generating OAM vortex waves in wireless and microwave wireless communications. The proposed RA is suitable for 6G wireless communication systems.

Synthesis and design of miniaturized poly-phase differential phase shifters with filtering function

In this paper, a class of miniaturized poly-phase differential phase shifters with filtering function is proposed, synthesized and developed. The proposed design is constructed by using parallel-coupled microstrip lines as the phase-shifting element in all branches. Operational mechanisms for these parallel-coupled microstrip lines are given. Closed-form formulas of insertion phase and phase slope are derived to guide a practical design procedure for phase shifters with arbitrary shifted phases and minimized phase errors. Benefitting from the compact size of those parallel-coupled microstrip lines, the proposed design is much smaller when compared with state-of-the-art works. To validate the proposed concept and synthesis method, a class of five-way poly-phase (ΔΦ = 45°, 90°, 135°, and 180°) differential phase shifter centered at 3 GHz is designed, fabricated, and measured. Measured results indicate that, achieved relative phase shifts are 45° ± 2.7°, 91° ± 2.9°, 135° ± 3.2°, and 181° ± 3.9° within a 33 % fractional bandwidth, with amplitude imbalances smaller than 0.2 dB among different ways.

Envelope modulated x-ray grating interferometry

X-ray dark-field and phase contrast imaging using grating interferometry (GI) have demonstrated great potential for medical and industrial applications. GI relies on the fabrication of high-quality absorption gratings, which has revealed to be quite challenging. This paper proposes an interferometer for dark-field and differential phase contrast imaging using a single phase-shifting element. This proposal simplifies the setup without penalizing the image quality. The proposed interferometer consists of a single dual-period phase grating having two distinct periods, which generates intensity modulation with a period large enough to be resolved directly by the detector. This makes the proposed GI system easily adaptable as there are no stringent alignment requirements. We show the utility of this method for a possible diagnostic task by imaging smoked murine lung samples. The simplicity of the proposed setup compared to a conventional Talbot(-Lau) interferometer suggests that it could be easily and widely used for a variety of applications.

Optofluidic phase-shifting digital holographic microscopy for quantitative measurement of microfluidic diffusion dynamics

In this work, an integrated optofluidic phase-shifting element, along with an image processing algorithm, was proposed to enable quantitative analysis for microfluidic applications using a digital holographic microscopic configuration. The advantages of the proposed system lie in its compactness, that the phase-shifting element can be simultaneously fabricated with other microfluidic functional components on a single chip, its robustness to resist environmental vibrations as no mechanical movement is involved for phase-shifting, and its capability of capturing transient events of fluid dynamics for quantitative measurement. The performance of the proposed system was validated with quantitatively label-free monitoring of concentration gradients under various conditions in microchannels.

Interferometric measurement of micro-g acceleration with levitated atoms

The sensitivity of atom interferometers is usually limited by the observation time of a free falling cloud of atoms in Earth’s gravitational field. Considerable efforts are currently made to increase this observation time, e.g. in fountain experiments, drop towers and in space. In this article, we experimentally study and discuss the use of magnetic levitation for interferometric precision measurements. We employ a Bose–Einstein condensate of cesium atoms with tuneable interaction and a Michelson interferometer scheme for the detection of micro-g acceleration. In addition, we demonstrate observation times of 1s, which are comparable to current drop-tower experiments, we study the curvature of our force field, and we observe the effects of a phase-shifting element in the interferometer paths.

Single-Layer Circularly Polarized Wide Band Reflectarray Antenna with High Aperture Efficiency

A circularly polarized broadband low-cost reflectarray in Ku-band is presented using a novel single-layer subwavelength phase-shifting element. The proposed subwavelength element consists of the concentric split ring and the crossed bowtie. The linear reflected phase response curve with 360° phase coverage is obtained. For experimental verification, an array of 25 × 25 reflectarray prototype has been designed and manufactured by employing the angular rotation technique. The measurements are in good agreement with the simulations. The measured gain at the center frequency of 12.5 GHz is 26.6 dBi, corresponding to the aperture efficiency of 52.5%, and the 1 dB gain bandwidth is 26.4%.

Circularly polarized low-cost wide band reflectarray antenna constructed with subwavelength elements

A novel single-layer subwavelength patch element is proposed to design the circularly polarized reflectarray in Ku band. The radiation characteristics of the phase-shifting element are investigated. The relative linearly reflected phase response curve with 360° phase coverage is achieved. A reflectarray model constructed with the proposed element is designed and fabricated, and the angular rotation technique has been employed for obtaining reflected phase curve to compensate the spatial delay. The measurements are in good agreement with the simulations. The superior bandwidth and efficiency performance have been verified. The measured gain at the center frequency of 12.5 GHz is 26.5 dBi, corresponding to the aperture efficiency of 51.9%, and the obtained 1 dB gain and 3 dB AR bandwidth can reach 24.8% and 35.2%, respectively.

Development of phase-shifting device for implementation of three-step interferometric method with arbitrary phase shifts of reference wave

Two basic approaches to the implementation of procedures of a wavefront stepwise and smooth phase shifts in a two-beam optical interferometer are considered. Advantages and lacks of both procedures are analyzed. It is noted that the smooth phase shift procedure removes the oscillations of a phase shifting element (PSE) that occur during the stepwise procedure. A phase-shifting device that is used to realize the three-step phase shifting interferometry (PSI) method with two arbitrary phase shifts of the reference wave within the angular interval (0, π) is developed. This device does not need the calibration procedure, because the three step PSI method allows defining any phase shift angle by calculating the correlation coefficient between two recorded interferograms. The correlation coefficient can be considered as a normalized scalar product of two interferograms that can be represented by centered multidimensional vectors or as a cosine of a phase shift angle between these vectors. Therefore, the developed device is much simpler and cheaper than its calibrated prototypes. It contains a PSE consisting of a piezoelectric transducer (PZT) and a mirror attached to the PZT, and an electronic unit for smooth linear motion of the mirror in the reference beam of the interferometer. Basic characteristics of the developed electronic unit are considered. The operating principle of the phase-shifting device electronic unit is to provide the smooth rising voltage supply initiated a smooth change of the PZT size. Therefore, the mirror attached to the PZT also moves smoothly. The PSE is located in the reference beam of the two-beam interferometer. If the reference beam in the interferometer enters the mirror in the direction perpendicular to the plane of the mirror, the beam wavefront moves to a distance twice that of the mirror. To verify the reliability of the developed phase-shifting device, we have elaborated the experimental setup dedicated for formation, registration and processing of interferograms of test surfaces and based on the Twyman-Green interferometer architecture. In this setup, the three-step PSI method with arbitrary phase shifts of a reference wave is fulfilled by recording of three interferograms during smooth phase shift of the mirror attached to the PZT. Comparative analysis of stepwise and smooth phase shift procedures for interferograms recording in the experimental setup has shown that their modulation transfer functions (MTFs) are similar for small exposures of interferograms. In particular, it is shown that for interferogram’s small exposure times, whose ratio to the voltage increase time in the angular interval (0, π) does not exceed 0.06, the MTF of the interferogram recorded with the smooth phase shift of the reference beam does not differ from the interferogram MTF obtained by stepwise phase shift. Key words: phase shifting interferometry, phase shift, phase shifting element, interferogram, modulation transfer function

Quantum-enhanced interferometry with weak thermal light

We propose and implement a quantum procedure for enhancing the sensitivity with which one can determine the phase shift experienced by a weak light beam possessing thermal statistics in passing through an interferometer. Our procedure entails subtracting exactly one (which can be generalized to m) photons from the light field exiting an interferometer containing a phase-shifting element in one of its arms. As a consequence of the process of photon subtraction, and somewhat surprisingly, the mean photon number and signal-to-noise ratio of the resulting light field are thereby increased, leading to enhanced interferometry. This method can be used to increase measurement sensitivity in a variety of practical applications, including that of forming the image of an object illuminated only by weak thermal light.

Grazing incidence spin-echo neutron spectrometer

A device for the excitation and detection of neutron magnetic-moment precession, consisting of a pair of magnetic mirrors placed in a magnetic field, is discussed. The device may be used as the phase-shifting element in a spin-echo neutron spectrometer, which measures the correlation time of the oscillations of a medium or the correlation length of its density. It is shown that in a magnetic field with an intensity of up to 1 kOe, the probability of neutron scattering can be measured from the minimum values of the wave vector of 10–7 A–1 and the transmitted energy of 1 peV.

Reflective vertical cavity quantum-well saturable absorber as an all-optical nonlinear phase-shifting element

A scheme of an all-optical nonlinear phase-shifting element is proposed, based on a reflective vertical cavity semiconductor (quantum-well) saturable absorber (R-VCSSA). The nonlinear round-trip phase shift in a low-intensity resonant VCSSA is obtained at an input intensity due to the saturating nonlinearity in index change and optically induced thermal effects. An enhanced large nonlinear positive or negative phase shift incurred in a reflected signal is investigated analytically with the wavelength tuning of the probe signal around the low-intensity resonant wavelength of a Fabry–Perot cavity. The device may be useful in compensating the phase of an input signal, either positive or negative, in long-haul fiber communications. A representative InGaAs/InP quantum-well-based VCSSA is considered to demonstrate the phase shift in the pump–probe configuration. With a device speed of 10 GHz, maximum phase shifts of −0.24 and +0.14  rad at pump power of 19.2 mW are observed for the operations at probe wavelengths of 1555.6 and 1557.8 nm, respectively.

Achromatic registration of quadrature components of the optical spectrum in spectral domain optical coherence tomography

We have thoroughly investigated the method of simultaneous reception of spectral components with the achromatised quadrature phase shift between two portions of a reference wave, designed for the effective suppression of the ‘mirror’ artefact in the resulting image obtained by means of spectral domain optical coherence tomography (SD OCT). We have developed and experimentally tested a phase-shifting element consisting of a beam divider, which splits the reference optical beam into the two beams, and of delay lines being individual for each beam, which create a mutual phase difference of in the double pass of the reference beam. The phase shift achromatism over a wide spectral range is achieved by using in the delay lines the individual elements with different dispersion characteristics. The ranges of admissible adjustment parameters of the achromatised delay line are estimated for exact and inexact conformity of the geometric characteristics of its components to those calculated. A possibility of simultaneous recording of the close-to-quadrature spectral components with a single linear photodetector element is experimentally confirmed. The suppression of the artefact mirror peak in the OCT-signal by an additional relative to the level of its suppression is experimentally achieved when the air delay line is used. Two-dimensional images of the surface positioned at an angle to the axis of the probe beam are obtained with the correction of the ‘mirror’ artefact while maintaining the dynamic range of the image.

Holey-Metal Lenses: Sieving Single Modes with Proper Phases

We study a planar, holey-metal lens made as a set of concentric circular arrays (rings) of nanoscale holes milled in a subwavelength-thick metal film. Each nanohole-a finite-length, circular, single-mode waveguide with a radius-dependent mode index-is used as a phase-shifting element. Our experimental results confirm that the focusing properties of our polarization-independent, holey-metal lens milled in a 380-nm-thick gold film and illuminated with 531 nm light fits the analytical model well. The proposed concept could offer an alternative to conventional refraction microlenses and open up a vital path toward on-chip or fiber-end planar photonic devices for biosensing and imaging.

Computer analysis of two-dimensional images in the Zernike phase contrast method for hard X rays

The problems of the numerical simulation of two-dimensional images in the Zernike phase contrast method in hard X rays are analyzed. Calculations are performed for experimental conditions typical of third-generation synchrotron radiation sources (ESRF, APS, Spring-8, etc.). Schemes are considered where the focusing elements are a refracting lens and a zone plate and the phase-shifting element is situated at the point of the source image. It is shown that the refracting lens allows better resolution than the zone plate. A technique similar to ptychography can be successfully applied to improve the quality of the images obtained by the Zernike phase contrast method.

Stochastic Averaging for Identification of Feedback Nonlinearities in Thermoacoustic Systems

We present algorithms based on stochastic averaging for estimating nonlinear feedback parameters obtained from time series data with application to noise-driven nonlinear vibration systems, with particular emphasis on limit-cycling thermo-acoustic systems. The harmonic and Gaussian components of relevant signals are estimated from the probability density function (pdf) of an output signal from a single experiment. The respective feedback gains, along with a phase-shifting element are fit to a nominal (given) linear oscillator model from which the parameters of a nonlinearity are fit. When input-output data are available from multiple experiments, the feedback nonlinearity can be estimated point-wise via an iterative algorithm, applicable when the appropriate input signals have a constant (Gaussian) variance. The estimation procedures are demonstrated on a benchmark thermo-acoustic model and applied to time-series data obtained from a limit-cycling combustor rig experiment. In the latter case, relations between the feedback parameters and the fuel to air ratio are briefly discussed.

Theoretical analysis of the possibilities of Zernike phase contrast method in hard X rays for nondestructive imaging of micropipes in a silicon carbide single crystal

The possibilities of using Zernike phase contrast in hard X rays for imaging micropipes in a silicon carbide single crystal are analyzed by numerical simulation. Calculations are performed for the experimental conditions characteristic of third-generation synchrotron radiation sources. A scheme is considered where the focusing element is a parabolic refracting lens and the phase-shifting element is mounted at the point of the source image. It is shown that micropipe cross sections by a beam with a longitudinal diameter reaching 10 μm are imaged by the lens without distortions. At the same time, the lens makes it possible to magnify the image several tens of times. The cross sections that are significantly elongated along the beam are imaged with artifacts; however, their structure can also be recovered. It is shown that polychromaticity of radiation does not significantly affect the object imaging.

Noise Properties of Microwave Phase Shifters Based on Semiconductor Optical Amplifiers

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, we present detailed modeling and experiments of the noise properties of a single-stage microwave phase-shifting element based on slow light propagation in a semiconductor optical amplifier. A wideband large-signal model is used to calculate the performance dependencies on gain, input power, and modulation frequency for the case where the red-shifted sideband at the amplifier output is suppressed. </para>

Large-Signal Operation of a Semiconductor Optical Amplifier as a Phase-Shifting Element for Microwave Signals

We investigate the modulation index dependence of the phase shift experienced by a sinusoidal microwave signal carried by an optical carrier and propagating through a semiconductor optical amplifier. We show that for large modulation depths, simple small-signal nonlinear models fail to predict the measured phase shift and we present a large-signal model that fits the experiments well.

Planar Passive Electromagnetic Deflector for Millimeter-Wave Frequencies

A novel passive planar structure is proposed that is able to deflect an incoming electromagnetic (EM) wave into a desired direction. The direction of the outgoing EM wave is determined by the design of this deflector. The deflector can be used to extend coverage of a steerable source with limited scan capabilities. It consists of elements which alter the phase distribution of the incoming EM wave. It is called deflector, because it is designed primarily to deflect incoming EM waves, as opposed to focusing as in the case of the array lens. The design of a compact phase-shifting deflector element is given. Two deflectors have been designed and constructed. Measurements show good agreement with simulations.

The LCPDI: A Compact and Robust Phase-Shifting Point-Diffraction Interferometer Based on Dye-Doped LC Technology

Point-diffraction interferometers, by design, are much less sensitive to environmental disturbances than dual-path interferometers, but, until very recently, have not been capable of phase shifting. The liquid crystal point diffraction interferometer (LCPDI) utilizes a dye-doped, liquid crystal (LC), electro-optical device that functions as both the point-diffraction source and the phase-shifting element, yielding a phase-shifting diagnostic device that is significantly more compact and robust while also using fewer optical elements than conventional dual-path interferometers. These attributes make the LCPDI of special interest for diagnostic applications in the scientific, commercial, military, and industrial sectors, where vibration insensitivity, power requirements, size, weight, and cost are critical issues. Until very recently, LCPDI devices have used a plastic microsphere embedded in the LC fluid layer as the point-diffraction source. The process for fabricating microsphere-based LCPDI devices is low-yield, labor-intensive, very “hands-on,” and great care and skill are required to produce devices with adequate interference fringe contrast for diagnostic measurements. With the goal in mind of evolving the LCPDI beyond the level of a laboratory prototype, we have developed “second-generation” LCPDI devices in which the reference diffracting elements are an integral part of the substrates by depositing a suitable optical material (vapor-deposited thin films or photoresist) directly on the substrate surface. These “structured” substrates eliminate many of the assembly difficulties and performance limitations of previous LCPDI devices as well as open the possibility of mass-producing LCPDI devices at low cost by the same processes used to manufacture commercial LC displays.