Ultrahigh Order Research Articles

Ultrahigh carrier mobility and anisotropy of the layered semiconductor ATiN2 (A = Ca, Sr and Ba)

Semiconductors with a suitable band gap and high carrier mobility are highly desirable in the electronics, optoelectronic and photovoltaic applications. The mechanical, electronic, optical and transport properties of the layered nitrides ATiN2 (A = Ca, Sr, and Ba) have been systematically studied by theoretical calculations. These nitrides show good ductility with moderate moduli, larger Poisson's ratio than 0.26 and Pugh's modulus ratio exceeding 1.75. CaTiN2 and SrTiN2 are direct bandgap semiconductors, while BaTiN2 is an indirect bandgap semiconductor, showing suitable band gaps (1.54–1.78 eV) and band edge positions for optoelectronic and photocatalytic water-splitting applications. More intriguingly, they possess superhigh carrier mobility with remarkable anisotropy. Particularly, the in-plane electron mobility reaches an ultrahigh order of 104 cm2V−1s−1, whereas those along the out-of-plane direction are almost zero. In addition, the hole mobilities are also very large along the in-plane direction and the anisotropic ratios are as high as about 30 for all these nitrides. Furthermore, these ATiN2 nitrides exhibit high optical absorption coefficients (∼105 cm−1) and lower exciton binding energies. Due to the suitable band gaps and band alignments, ultrahigh carrier mobility and huge anisotropy, excellent visible light absorption performance, the ATiN2 nitrides will be promising candidate semiconductors in electronics, optoelectronic, photovoltaic and photocatalytic applications.

Enhancing secure transmission of ultra-high order QAM via delta-sigma modulation integrated with radial basis function neural network enhanced chaos

This paper proposes and experimentally demonstrates an ultra-high order signal security enhancement method based on delta-sigma modulation (DSM). We employ a radial basis function neural network (RBFnn) to enhance Henon chaos, effectively avoiding the degradation of chaotic dynamics, and increasing the key space from 1054 to 10385. In the experimental demonstration, we achieved high-security transmission of 16384QAM over 25 km in an intensity-modulated direct detection (IMDD) system based on DSM. The experimental results show that the ultra-high order transmission scheme based on RBFNN-chaos and DSM has superior security, with a key sensitivity of up to 10−16.

Ultra-high order mode-assisted optical differentiator for edge detection with high tunability

An optical spatial differentiator based on the photonic spin Hall effect (PSHE) with high tunability is presented. By utilizing the characteristics of ultra-high order modes in the symmetrical metal cladding waveguide, the Fresnel reflection coefficient spectrum exhibits a narrow peak width and low trough at the resonant incident angles, resulting in high sensitivity to changes in the incident angle-induced spatial shift caused by the PSHE (the highest ∂(|r s /r p |)/∂θ value can reach 107). After polarization transformation and extinction, the output field demonstrates differential operation with respect to the input field. When applied to edge detection, our differentiator can achieve tunable resolution edge images by adjusting the incident angle. Our proposed edge detection scheme has potential applications for cellular and molecular imaging through two-dimensional extension via the target rotation.

Cascaded mode converter for generating high-order Poincaré sphere beams of multiple different orders

Structured light fields, especially high-order Poincaré sphere (HOPS) beams, are attracting increasing attention for their intriguing properties and extensive applications. Here, we demonstrate a cascaded mode converter for generating HOPS beams of different orders. The cascaded mode converter is composed of q-plates and half waveplates, which realize switchable generation of HOPS beams of multiple different orders with reliable performance. Exponential growth of the available number of HOPS beams of different orders is achieved. The local polarization state and the order of the HOPS beams can be used as two degrees of freedom to encode 2 bits of information. The proposed method makes it possible to generate multiple and ultrahigh order Poincaré sphere beams and may have potential application in communication systems.

New methods for numerical evaluation of ultra-high degree and order associated Legendre functions

New methods for numerical evaluation of ultra-high degree and order associated Legendre functions

Highly Sensitive Plasmonic Waveguide Biosensor Based on Phase Singularity-Enhanced Goos-Hänchen Shift.

The detection for small molecules with low concentrations is known to be challenging for current chemical and biological sensors. In this work, we designed a highly sensitive plasmonic biosensor based on the symmetric metal cladding plasmonic waveguide (SMCW) structure for the detection of biomolecules. By precisely designing the configuration and tuning the thickness of the guiding layer, ultra-high order modes can be excited, which generates a steep phase change and a large position shift from the Goos–Hänchen effect (with respect to refractive index changes). This position shift is related to the sharpness of the optical phase change from the reflected signal of the SPR sensing substrate and can be directly measured by a position sensor. Based on our knowledge, this is the first experimental study done using this configuration. Experimental results showed a lateral position signal change > 90 µm for glycerol with a sensitivity figure-of-merit of 2.33 × 104 µm/RIU and more than 15 µm for 10−4 M biotin, which is a low molecular weight biomolecule (less than 400 Da) and difficult to be detected with traditional SPR sensing techniques. Through integrating the waveguide with a guiding layer, a strong improvement in the electric field, as well as sensitivity have been achieved. The lateral position shift has been further improved from 14.17 µm to 284 µm compared with conventional SPR substrate with 50 nm gold on single side. The as-reported sensing technique allows for the detection of ultra-small biological molecules and will play an important role in biomedical and clinical diagnostics.

Design of Probabilistic Shaping 4D Ultra High Order Modulation Format With 8APSK Pilot Aided Carrier Phase Recovery

A new four-dimensional (4D) probabilistically shaped (PS) ultra-high order modulation format is proposed with pilot aided carrier phase recovery (PA-CPR) algorithm to improve the general mutual information (GMI) performance. While the structure of the 4D-PS ultra-high order modulation format uses constellation set partitioning (SP) based on amplitude translation, and the PA-CPR applies 8-level amplitude phase shift keying (8APSK) pilot. To demonstrate the feasibility of the scheme, the PS-1024QAM system is designed on the simulation platform. The results show that the proposed 8APSK-PA-CPR algorithm outperforms the QPSK-PA-CPR algorithm. The gain of the optimal 8APSK-PA-CPR is ∼0.4 dB compared with the quadrature phase-shift keying (QPSK) PA-CPR algorithm. The steep drop of blind phase search (BPS) with different PS factors is overcome by 8APSK-PA-CPR when the signal-to-noise (SNR) ratio is lower than 24 dB. The maximum improvement of GMI is 1.3 bit/symbol when the SNR is higher than 26 dB and the complexity of the 8APSK-PA-CPR algorithm is reduced by 99.9% compared with the BPS algorithm. The gain obtained from the proposed 4D modulation scheme is ∼2.8 dB under the condition of GMI = 17.7971 bit/symbol. It demonstrated that this scheme has a strong tolerance to noise, low computational complexity, and high coding gain. It is a feasible and flexible scheme for PS high-order modulation format transmission systems.

Effect of heat treatment on the properties of non-stoichiometric Ba3CoNb2O9 ceramics: Evaluation of crystal structure, order-disorder behavior, and dielectric characteristics

Non-stoichiometric Ba(Co1/3Nb2/3)O3 (BCN) ceramics were synthesized using the solid-state method at 1150 ℃. The heat treatment process was then followed by sintering at 1400–1550 ℃ and annealing at 1300 °C. Systematically varying the extent of the non-stoichiometry and the heat treatment conditions resulted in the division of the BaO−CoO−Nb2O5 system into two categories of compounds: (A) high-order Co/Ba-deficient and Co/Nb-excess ceramics and (B) completely disordered Nb-deficient and Ba-excess ceramics. It was found that a slight deviation from stoichiometry toward the group (A) and subsequent annealing led to a significant improvement in the ordering from 82% to 100% accompanied with the formation of non-equidistant Nb−O bonds. The crystal structure based on the ultra-high order BCN−0.02Ba5Nb4O15 was also designed to display non-equidistant Nb−O bonds. The dielectric characteristics demonstrated that high Q correlates with the 1:2 ordering and the highest Q×f values obtained from BCN−xBa5Nb4O15 ceramics (x = 0.02, 0.04, 0.06): 83, 84.95, and 79.71 THz, respectively.

MEMS based ultra-high order frequency multiplication utilizing superharmonic synchronization effect

Frequency multipliers are widely present in electronic system, which always cooperates with low frequency local oscillator for delivering an output wave with a frequency that an exact integral multiple of the input frequency. Conventional frequency multiplier such as step recovery diode, field-effect transistors, low spurious harmonic, etc., usually has only two or three low multiplication factor. Multi-stage frequency doublers can accumulate the multiplication factor, however, has high power consumption and negative conversion gain. Here, we proposed a novel frequency multiplication mechanism utilizing superharmonic synchronization (SHS) effect in micromechanical resonator. We achieved up to 121th ultra-high frequency amplification with frequency stability of output signal 92 times improved and signal to noise ratio 20% increased. To solve the limitation of narrow synchronization range, a frequency automatic tracking system is designed to expand the working range from 0.62 Hz to 27.5 kHz. The proposed frequency amplification is a promising candidate for frequency multipliers and provides an alternative mechanism for micromechanical sensing and signal processing system.

Suspended AlGaAs waveguide for integrated nonlinear photonics

AlxGa1-xAs compound is one of the promising platforms to realize high performance nonlinear optical devices, which provide ultra-high third order nonlinearity and negligible two-photon absorption in the range of telecom wavelength. To achieve highly efficient optical confinement, the conventional AlGaAs waveguide cladding layer is achieved by using SiO2 via the wafer bonding process or AlGaAs with higher Al concentration, which requires a complex fabrication process. In this work, we demonstrate a suspended Al0.5Ga0.5As waveguide structure directly grown on the GaAs substrate by using the molecular beam epitaxy system. Both self-phase modulation and four-wave-mixing experiments are performed. By solving the nonlinear Schrödinger equations and the degenerated parametric amplification process, the n2 value is calculated to be 1.6 × 10−17 m2/W, and the nonlinear parameter is determined to be 155 W−1 m−1. As the AlGaAs thin film can be directly grown on the Si based substrate, this suspended waveguide platform could potentially be developed on a large scale silicon wafer for integrated nonlinear photonic devices.

Enhanced temperature sensing based on birefringence induced Vernier effect in a symmetrical metal-cladding waveguide

A temperature sensor with high sensitivity based on the birefringence induced Vernier effect in a symmetrical metal-cladding waveguide (SMCW) structure is theoretically proposed. Due to the guiding layer of SMCW is extended to a sub-millimeter scale, the excited ultra-high order modes is highly sensitive to the variation of thermally modulated refractive index (RI) and the obtained comb-like resonance reflectivity spectrum shifts accordingly as changing the ambient temperature. There is a little difference between the RI of the ordinary light and the extraordinary light of the filled nematic liquid crystal (LC), the resulted slight different free spectral range of two orthogonal polarizations makes their superposition of reflectivity spectrum metamorphose into a period envelope with multiple sub-peaks. The dips in the fitting upper envelope possesses a much enhanced temperature dependent spectrum shift which can be measured by a low-cost integrated-type micro-spectrometer. Such a sensor has no reference resonant cavity and its sensing range can be easily controlled by filling with different kinds of LC.

Stability Analysis of Multi-Discrete Delay Milling with Helix Effects Using a General Order Full-Discretization Method Updated with a Generalized Integral Quadrature

A tensor-based general order full-discretization method is enhanced with the capacity to handle multiple discrete delays and helix effects leading to a unique automated algorithm in the stability analysis of milling process chatter. The automated algorithm is then exploited in investigating the effects of interpolation order of chatter states and helix-induced terms on the convergence of milling stability lobes. The enhanced capacity to handle the distributed helix effects is based on a general order formulation of the Newton-Coates integral quadrature method. Application to benchmark milling models showed that high order methods are necessary for convergence of the low speed domain of stability lobes while all the numerically stable orders converge in the high speed domain where the ultra-high order methods are prone to numerical instability. Also, composite numerical integration of the helix-induced integrand beyond the usual zero-th order method leads to higher accuracy of stability lobes especially in the low speed domain.

Numerical experiments on column-wise recurrence formula to compute fully normalized associated Legendre functions of ultra-high degree and order

When using column-wise recurrence formulae to compute modified normalized Legendre functions up to approximate degree and order 3200 in the IEEE double precision environment, the overflow problem occurs. In this paper, we analyze the causes of the overflow problem in detail. We analyze column-wise recurrence formulae for computing fully normalized associated Legendre functions (fnALFs), their first-order derivatives, and the definite integrals of $$ \bar{P}_{nm} \left( {\cos \theta } \right)\sin \theta $$. From our tests, we claim that if fully normalized column-wise recurrence formulae are applied, the computational accuracies of fnALFs and their first-order derivatives up to complete degree and order 64,800 can reach at least 10−11. The computational accuracies of fully normalized column-wise recurrence formulae for computing definite integrals of $$ \bar{P}_{nm} \left( {\cos \theta } \right)\sin \theta $$ are almost 10 times higher than those of the X-number method up to degree 6000. From the statistical results, the computational efficiency of fully normalized column-wise recurrence formulae for computing fnALFs and their first-order derivatives are almost 1.5 times faster than those of the X-number method, and approximately 15–22% faster than those of the dynamical switching X-number method. However, the computational efficiency of definite integrals is slower than that of the X-number method and dynamical switching X-number method.

Ultra-high order harmonic mode-locking of a Raman fiber laser

An ultra-high order harmonically mode-locked Raman fiber laser with a high signal-to-noise ratio has been proposed and demonstrated. We apply the nonlinear polarization rotation (NPR) technique as the mode-locker in the Raman fiber laser. The underlying harmonic mode-locking (HML) mechanism is discussed to achieve ultra-high order HML in the Raman fiber laser. Up to 5044th ultra-high order HML has been obtained with a signal-to-noise ratio of up to 42.5 dB. To the best of our knowledge, this is the highest order of passive HML achieved so far from a Raman fiber laser using NPR or similar techniques.

A generalized massively parallel ultra-high order FFT-based Maxwell solver

Dispersion-free ultra-high order FFT-based Maxwell solvers have recently proven to be paramount to a large range of applications, including the high-fidelity modeling of high-intensity laser–matter interactions with Particle-In-Cell (PIC) codes. To enable a massively parallel scaling of these solvers, a novel parallelization technique was recently proposed, which consists in splitting the simulation domain into several processor sub-domains, with guard regions appended at each sub-domain boundary. Maxwell’s equations are advanced independently on each sub-domain using local shared-memory FFTs (instead of a single distributed global FFT). This implies small truncation errors at sub-domain boundaries, the amplitude of which depends on guard regions sizes and order of the Maxwell solver. For moderate guard region sizes, this ’local’ technique proved to be highly scalable on up to a million cores and notably enabled the 3D modelingof so-called plasma mirrors, for which 8 guard cells only were enough to prevent truncation error growth. Yet, for other applications, the required number of guard cells might be much higher, which would severely limit the parallel efficiency of this technique due to the large volume of guard cells to be exchanged between sub-domains. In this context, we propose a novel parallelization technique that ensures very good scaling of FFT-based solvers with an arbitrarily high number of guard cells. Our ’hybrid’ technique consists in performing distributed FFTs on local groups of processors with guard regions now appended to boundaries of each group of processors. It uses a dual domain decomposition method for the Maxwell solver and other parts of the PIC cycle to keep the simulation load-balanced. This ’hybrid’ technique was implemented in the open source exascale library PICSAR. Benchmarks show that for a large number of guard cells (>16), the ’hybrid’ technique offers up to ×3 speed-up and ×8 memory savings compared to the ’local’ one.

Application of Geoid Anomalies to the Tectonic Research in the East Asian Continental Margin

In this paper, we calculated multi-scale residual geoid anomalies with the method of geoid separation processing, according to EGM2008 ultra-high order gravity field model, remove-restore technique and Stokes integral. The East Asian continental margin was selected as the study area. The residual geoid anomalies have been calculated by programming. On the basis of residual geoid anomalies at various orders, the interlayer geoid anomalies at different depths were calculated to depict the spatial distribution characteristics of the residual geoid. Finally, we conducted a detailed geophysical interpretation for the study area according to the geoid anomalies in combination with other geophysical datasets. Four conclusions can be outlined as follows: 1) it is impracticable that geoid anomalies are used in the interpretation of the shallow objects due to the influence of the terrain; 2) the anomalies of residual geoid can reflect the intensity of small-scale mantle convection in the asthenosphere; 3) the interlayer geoid anomalies can reflect the magmatic activities associated with the mantle convection and mantle plume in different scales; 4) the study of the geoid may provide an approach for the research of the subduction zone, mantle convection and mantle plume.

Using Ultra-High Expansion Orders of Max-Ortho Basis Functions for Analysis of Axially Symmetric Metallic Antennas

Implementation of max-ortho basis functions is proposed in a method for analysis of axially symmetric metallic antennas based on exact kernel of electric field integral equation in combination with Galerkin testing. High-precision evaluation of matrix elements is enabled by: a) representing them as a linear combination of impedance integrals due to the Legendre polynomials and their first derivatives; b) using the singularity cancelation techniques; and c) evaluating the Legendre polynomials and their first derivatives by well-known recurrent formulas. Applicability of max-ortho bases up to expansion order of $n =128$ is illustrated on a full-wave thick dipole antenna.

Theoretical large positive and negative lateral beam shift of the metal cladding waveguide in the mid-infrared region.

A large negative and positive lateral beam shift is presented in the midinfrared region based on the penetration enhancement effect of the ultrahigh order modes in the metal-cladding waveguide. The characteristics of the lateral beam shift have been discussed in theory, and the performance of the ultrahigh order modes is confirmed in an experiment at 5.4µm. The negative and positive lateral shift depends on the derivative of the imaginary part of the propagation constant.

A micromachined device describing over a hundred orders of parametric resonance

Parametric resonance in mechanical oscillators can onset from the periodic modulation of at least one of the system parameters, and the behaviour of the principal (1st order) parametric resonance has long been well established. However, the theoretically predicted higher orders of parametric resonance, in excess of the first few orders, have mostly been experimentally elusive due to the fast diminishing instability intervals. A recent paper experimentally reported up to 28 orders in a micromachined membrane oscillator. This paper reports the design and characterisation of a micromachined membrane oscillator with a segmented proof mass topology, in an attempt to amplify the inherent nonlinearities within the membrane layer. The resultant oscillator device exhibited up to over a hundred orders of parametric resonance, thus experimentally validating these ultra-high orders as well as overlapping instability transitions between these higher orders. This research introduces design possibilities for the transducer and dynamic communities, by exploiting the behaviour of these previously elusive higher order resonant regimes.

Ultralow-threshold continuous-wave lasing assisted by a metallic optofluidic cavity exploiting continuous pump.

We report an ultralow-threshold continuous-wave lasing via a metallic optofluidic resonant cavity based on the symmetrical metal-cladding waveguide. The high quality factor Q and spontaneous emission coupling factor β of the waveguide strengthen the interaction between the gain medium and the ultrahigh order modes (UOMs); hence, the room-temperature, narrowband lasing can be effectively pumped by a continuous laser of low intensity. Rhodamine 6G and methylene blue are chosen to verify the applicability of the proposed concept. Lasing is emitted from the chip surface when the pumped laser is well coupled into the UOMs. For methylene blue with a concentration of 2.57*10-13 mol/ml, the operated emission can be observed with the launched pump threshold as low as 2.1 μW/cm2.