Pixelated non-volatile programmable photonic integrated circuits with 20-level intermediate states

Multi-level programmable photonic integrated circuits(PICs)and optical metasurfaces have gained widespread attention in many fields,such as neuromorphic photonics,opticalcommunications,and quantum information.In this paper,we propose pixelated programmable Si_(3)N_(4)PICs with record-high 20-level intermediate states at 785 nm wavelength.Such flexibility in phase or amplitude modulation is achieved by a programmable Sb_(2)S_(3)matrix,the footprint of whose elements can be as small as 1.2μm,limited only by the optical diffraction limit of anin-house developed pulsed laser writing system.We believe our work lays the foundation for laser-writing ultra-high-level(20 levels and even more)programmable photonic systems and metasurfaces based on phase change materials,which could catalyze diverse applications such as programmable neuromorphic photonics,biosensing,optical computing,photonic quantum computing,and reconfigurable metasurfaces.

Theory and verification of moiréfringes for x-ray three-phase grating interferometer

Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging.Dual-phase grating interferometers have been relatively completely studied and discussed.In this paper,the corresponding imaging fringe formula of the three-phase grating interferometer is provided.At the same time,the similarities and differences between the three-phase grating interferometer and the dual-phase grating interferometer are investigated and verified,and that the three-phase grating interferometer can produce large-period moiréfringes without using the analyzing grating is demonstrated experimentally.Finally,a simple method of designing three-phase grating and multi-grating imaging systems from geometric optics based on the thin-lens theory of gratings is presented.These theoretical formulas and experimental results provide optimization tools for designing three-phase grating interferometer systems.

A high precision time-to-digital converter based on multi-phase clock implemented within Field-Programmable-Gate-Array

In this paper, the design of a coarse-fine interpolation Time-to-Digital Converter (TDC) is implemented in an ALTERA’s Cyclone FPGA. The carry-select chain performs as the tapped delay line. The Logic Array Block (LAB) having a propagation delay of 165 ps in the chain is synthesized as delay cell. Coarse counters triggered by the global clock count the more significant bits of the time data. This clock is also fed through the delay line, and LABs create the copies. The replicas are latched by the tested event signal, and the less significant bits are encoded from the latched binary bits. Single-shot resolution of the TDC can be 60 ps. The worst Differential Nonlinearity (DNL) is about 0.2 Least Significant Bit (LSB, 165 ps in this TDC module), and the Integral Nonlinearity (INL) is 0.6 LSB. In comparison with other architectures using the synchronous global clock to sample the taps, this architecture consumed less electric power and logic cells, and is more stable.

Laser Doppler Vibrometer Without Directional Ambiguity Using Rectangular Phase Grating

The two-phase detection method for directional discrimination in laser Doppler measurements is discussed.The diffraction efficiency of a sin- gle period rectangular phase grating is analysed and a kind of back-scattered laser Doppler vibrometer without directional ambiguity using the single peri- od rectangular phase grating as the beam-combiner described.The principles of this kind of vibrometer are explained in detail,and some experimental re- sults are given.In this kind of vibrometer,the rectangular phase grating, without the zero diffracted order and even orders,is used to eliminate use- less stray light and to combine the useful signal light.Differential electronics is employed to reject signal noise.Therefore,the signal-to-noise ratio of Doppler signals and the measurement accuracy of the instrument are im- proved and the range of application is expanded.

Comparative analysis of phase extraction methods based on phase-stepping and shifting curve in grating interferometry

Two phase extraction methods which are based separately on phase-stepping and shifting curve are mainly used in phase-sensitive imaging in gating interferometry to determine the x-ray phase shift induced by an object in the beam. In this paper, the authors perform a full comparative analysis and present the main virtues and limitations of these two methods according to the theoretical analysis of the grating interferometry.

Electrically tunable holographic polymer templated blue phase liquid crystal grating

In this paper, we demonstrate an alternative approach to fabricating an electrically tunable holographic polymer tem- plated blue phase liquid crystal grating. This grating is obtained by preforming a polymer template comprised of periodic fringes, and then refilling it with a blue phase liquid crystal. Compared with conventional holographic polymer dispersed liquid crystal gratings, our grating can remarkably reduce its switching voltage from 200 V to 43 V while maintaining a sub-millisecond response time. The holographic polymer templated blue phase liquid crystal （HPTBPLC） grating is free from electrode patterning, thus leading to a lower cost and more flexible applications.

DEFORMATION MEASUREMENT USING DUAL-FREQUENCY PROJECTION GRATING PHASE-SHIFT PROFILOMETRY

2π phase ambiguity problem is very important in phase measurement when a deformed object has a large out of plane displacement. The dual-frequency projection grating phaseshifting profilometry （PSP） can be used to solve such an issue. In the measurement, two properchosen frequency gratings are utilized to synthesize an equivalent wavelength grating which ensures the computed phase in a principal phase range. Thus, the error caused by the phase unwrapping process with the conventional phase reconstruct algorithm can be eliminated. Finally, experimental result of a specimen with large plastic deformation is given to prove that the proposed method is effective to handle the phase discontinuity.

A modified phase diversity wavefront sensor with a diffraction grating

The phase diversity wavefront sensor is one of the tools used to estimate wavefront aberration, and it is often used as a wavefront sensor in adaptive optics systems. However, the performance of the traditional phase diversity wavefront sensor is limited by the accuracy and dynamic ranges of the intensity distribution at the focus and defocus positions of the CCD camera. In this paper, a modified phase diversity wavefront sensor based on a diffraction grating is proposed to improve the ability to measure the wavefront aberration with larger amplitude and higher spatial frequency. The basic principle and the optics construction of the proposed method are also described in detail. The noise propagation property of the proposed method is also analysed by using the numerical simulation method, and comparison between the diffraction grating phase diversity wavefront sensor and the traditional phase diversity wavefront sensor is also made. The simulation results show that the diffraction grating phase diversity wavefront sensor can obviously improve the ability to measure the wavefront aberration, especially the wavefront aberration with larger amplitude and higher spatial frequency.

Fast generation of controllable equal-intensity four beams based on isosceles triangle multilevel phase grating realized by liquid crystal spatial light modulator

Liquid crystal spatial light modulator （LCSLM） realizing equal-intensity multiple beams often has some features, i.e., phase valley between two adjacent pixels, flybaek region when phase decreases immediately from 2~r to 0, and inevitable backplane curvature, which are different from those of most conventional diffractive optical elements （DOEs）, such as static DOEs. For optimal intensity uniformity, equal-intensity multi-beam generation must be considered for these artifacts. We present a tunable-grating method in which the intensity uniformity can be improved by considering the LCSLM artifacts. For instance, tuning phase modulation depth of the grating, called isosceles triangle multilevel phase grating （ITMPG）, can be used not only to improve the intensity uniformity, but also to fast steer four beams with narrow beamwidths, determined by the same effective aperture of ITMPG. Improved intensity uniformity and high relative diffraction efficiency are demonstrated through experiments with phase-only LCSLM.

COMPACT PHASE GRATING INTERFERENCE SENSOR FOR MICRO-DISPLACEMENT

On the basis of existing techniques, a compact micro-displacement sensor of phase grating interference （PGI） is described, which adopts cylindrical hologram diffraction grating as the calibration standard. The optical principle of the sensor is explained, and the relation between the grating motion displacement and the phase shift of interference stripes is deduced. The improvement of the integral structure and the method of photoelectric signal processing are described in detail. With the software system based on the virtual instrument development platform Labwindows/CVI and other hardwares such as the precision displacement worktable, the surfaces of typical parts are measured and the characterization results are given. The sensor has wide measuring range and high resolution, its sensitivity and resolution being independent of the wavelength of the incident light. The vertical measuring range is 0-6 mm, and the vertical resolution is 0.005μm. The experimental results show that the sensor can be used to measure and characterize the surface topography parameters of the plane and curved surface.

Analysis of period and visibility of dual phase grating interferometer

Dual phase grating interferometer may simultaneously achieve large field of view and high x-ray dose efficiency.Here,we develop a simple theoretical method to better understand the imaging process of the dual phase grating interferometer.The derivation process of fringe period and the optimal visibility conditions of the dual phase grating interferometer are given in detail.Then,we theoretically prove that the fringe period and optimal visibility conditions of the dual phase grating interferometer include that of the Talbot interferometer.By comparing our experimental results with those of other researchers,we find that when the positions of phase gratings are far away from the positions where the fringe visibility is optimal,the fringe period of the dualπ-phase grating interferometer is twice the theoretical results under the illumination of polychromatic x-ray.This conclusion may explain the contradictory research results of dual phase grating interferometer among different researchers.

Quantitative coherence analysis of dual phase grating x-ray interferometry with source grating

Dual phase grating x-ray interferometry is compatible with common imaging detectors,and abandons the use of an absorption analyzer grating to reduce the radiation dose.When using x-ray tubes,an absorbing source grating must be introduced into the dual phase grating interferometer.In order to attain a high fringe visibility,in this work we conduct a quantitative coherence analysis of dual phase grating interferometry to find how the source grating affects the fringe visibility.Theoretical analysis shows that with the generalized Lau condition satisfied,the fringe visibility is influenced by the duty cycle of the source grating and the transmission through the grating bar.And the influence of the source grating profile on the fringe visibility is independent of the phase grating type.Numerical results illustrate that the maximum achievable fringe visibility decreases significantly with increasing transmission in the grating bar.Under a given transmission,one can always find an optimal duty cycle to maximize the fringe visibility.These results can be used as general guidelines for designing and optimizing dual phase grating x-ray interferometers for potential applications.

Large Spacing Array with Offset Phase Center Elements for Highly Integrated Applications

A scanning and uniform array architecture with large spacing,low complexity and high scalability is presented for high integration massive array applications.It is constructed by offset phase center elements arranged in a uniform and regular way,but its spacing can be larger than that of traditional arrays.An ideal model of the offset phase center element is established and its far-field distribution is derived.To suppress grating lobes,the phase center of any element is designed to be movable without changing its physical position.Using genetic algorithm(GA),a new constraint condition limiting the number of phase center changes is proposed to solve the objective function of the minimum values of grating lobes(GLs)and side lobes(SLs).It is shown that the optimal results can be achieved by two changes of phase centers.A multimode circular patch is developed and designed,and characteristics of the offset phase center are analyzed and verified.A prototype array of 12×12 offset phase center elements is implemented based on multi-mode circular patches.Full wave simulation results of radiation patterns show that the level of grating lobes is suppressed at least 7dB with 1.12λ spacing,while the scanning angle is 20°.

Profilometry with Grating Projection Based on One-step Phase Shift

An optical technique for 3 D shape measurement is presented. This technique, based on a deformed projected grating pattern which carries 3 D information of the measured object, can automatically and accurately obtain the phase map of a measured object by using one step phase shift algorithm.In comparison with traditional phase shift technique, the technique is much faster, with the equivalent accuracy. Only one frame image is sufficient for measuring. Experimental result of typical object is presented.

Theory and method of dual-energy x-ray grating phase-contrast imaging

The principle of dual-energy x-ray grating phase-contrast imaging(DEPCI) is clarified by using the theory of x-ray interference and Fresnel diffraction. A new method of retrieving phase from the two interferograms is proposed for DEPCI,and its feasibility is verified via simulation. Finally, the proposed method applied to DEPCI experiment demonstrates the effectiveness of the method. This paper lays the theoretical foundation for performance optimization of DEPCI and the further integration of DEPCI and computed tomography.

Fiber Bragg Grating Sensor Array System Based on Digital Phase Generated Carrier Demodulation and Reference Compensation Method

A novel fiber Bragg grating （FBG） sensor array system based on digital phase generated carrier （PGC） demodulation and reference compensation method is proposed and set up. Experimental results confirm that the digital PGC demodulation can be used for wavelength-division-multiplexed FBG sensor array and the reference compensation method can reduce the environmental interference by approximately 40 dB in the frequency range from 20 Hz to 2 kHz. The minimum detectable wavelength-shift of the sensor system is 1 × 10^-3 pm/Hz^1/2.

Phase grating in a doubly degenerate four-level system

In this paper, we suggest a doubly degenerate four-level system, in which the transition takes place between the hyperfine energy 52S1/2 F = 1 and 52P3/2 F = 2 in rubidium 87 D2 line, for studying atomic phase grating based on the cross-Kerr and phase conjugation effects. The phase grating with high efficiency can be obtained by tuning phase shift Ф between the coupling and probe field, when the coupling intensity is much stronger than the strength of probe field. Under different coupling intensities, a high diffraction efficiency can be maintained. A new and simple way of implementing phase grating is presented. However, in such an atomic system, two main limitations must be taken into account. First, the independence between steady state probe susceptibility and the coupling intensity, when the population decay rate is larger than the Rabi frequency of the coupling field, cannot result in diffraction grating; second, the sample to be prepared should not be too long.

Single-shot grating-based x-ray differential phase contrast imaging with a modified analyzer grating

X-ray grating interferometer has attracted widely attention in the past years due to its capability in achieving x-ray phase contrast imaging with low brilliance source. However, the widely used phase stepping information extraction method reduces system stability and prolongs data acquisition time by several times compared with conventional x-ray absorption- based imaging. The mechanical stepping can be avoided by using a staggered grating, but at the cost of low vertical spatial resolution. In this paper, employing a modified staggered grating and the angular signal radiography, we proposed a single-shot grating-based x-ray differential phase contrast imaging with decent vertical spatial resolution. The theoretical framework was deduced and proved by numerical experiments. Absorption, phase, and scattering computed tomography can be performed without phase stepping. Therefore, we believe this fast and highly stable imaging method with decent resolution would be widely applied in x-ray grating-based phase contrast imaging.

PHOTOINDUCED HOLOGRAPHIC PHASE GRATINGS BURIED IN AZOBENZENE SIDE-CHAIN POLYMER FILMS WITH A CHIRAL GROUP

An optically active polymer (PM1) containing azobenzene moieties with a chiral group (s-2-methyl-butyl) wassynthesized by homopolymerization of monomer, 4-[2-(methacryloyloxy)ethyloxy-4'-(s-2-methyl-1-butyl oxycarbonyl)azobenzene, using the free radical polymerization method. The polymer dissolved in tetrahydrofuran (THF) could be easilyprocessed into high optical quality films. The optical anisotropy of the polymer films was investigated by polarizing opticalmicroscopy (POM). The experimental results showed that irradiation with a circularly polarized beam could align theorientation of the molecules in the polymer films. Moreover, the holographic phase gratings of photo-induced polymer filmswere detected by atomic force microscopy (AFM) and POM. In comparison with polymer containing no chiral group, it wasfound from the preliminary measurement of the photo-induced holographic phase gratings that PM1 containing a chiralgroup could form holographic phase gratings buried in the films.

Optical phase front control in a metallic grating with equally spaced alternately tapered slits

A technique capable of focusing and bending electromagnetic （EM） waves through plasmonic gratings with equally spaced alternately tapered slits has been introduced. Phase resonances are observed in the optical response of transmission gratings, and the EM wave passes through the tuning slits in the form of surface plasmon polaritons （SPPs） and obtains the required phase retardation to focus at the focal plane. The bending effect is achieved by constructing an asymmetric phase front which results from the tapered slits and gradient refractive index （GRIN） distribution of the dielectric material. Rigorous electromagnetic analysis by using the two-dimensional （2D） finite difference time domain （FDTD） method is employed to verify our proposed designs. When the EM waves are incident at an angle on the optical axis, the beam splitting effect can also be achieved. These index-modulated slits are demonstrated to have unique advantages in beam manipulation compared with the width-modulated ones. In combination with previous studies, it is expected that our results could lead to the realization of ootimum designs for plasmonic nanolenses.