A new technique for measuring the degenerate spectra of optical vortices and orbital angular momentum (OAM) of singular beams is theoretically studied and experimentally verified. The technique is based on measuring the intensity moments of higher orders of a beam containing vortices with both positive and negative topological charges. The appropriate choice of the vortex mode amplitudes of the combined beam forms anomalous regions in the form of resonant dips and bursts in the OAM spectrum. Since the intensity moments for vortices with positive and negative topological charges are the same (degenerate) for an axially symmetric beam, it was necessary to break the symmetry of the beam, so measurements were taken at the plane of the double focus of a cylindrical lens. The calibration measurements showed that the experimental error is not higher than 3.5%. The technique was implemented for measuring and analyzing combined beams with OAM anomalies. It was found that the dips and bursts in the OAM spectrum are caused by the vortex avalanche induced by weak perturbations of the holographic grating responsible for shaping the beam. The OAM dips or bursts are controlled by the ratio between the energy fluxes of the vortex avalanche with positive or negative topological charges.

Measurement of the vortex and orbital angular momentum spectra with a single cylindrical lens.

We investigate both analytically and numerically the propagation dynamic of on-axis and off-axis cosine-Gaussian (CG) beams in a linear medium with quadratic external potential. CG beam propagation evolves periodically with a period depended on the potential depth (α) and whether the beam shape is symmetrical with respect to optical axis. In each period, the CG beam first splits into two sub-beams with different accelerated direction; they then reverse the accelerated direction owing to the quadratic external potential and finally merge again to reproduce its initial shape, and the whole process repeats periodically. The intensity oscillation period of the off-axis CG beam is double times than that of the on-axis one. At the special position, the beam (or spectral) shape is strongly related to the initial spectral (beam) shape. The corresponding scaled relationship is that the spatial intensity Ix (or spatial frequency axis k) is α times the spectral intensity Ik (or space axis x). The interaction of two spatially separated CG beams still exhibit periodic evolution with complex structure in the regime of focal point. The propagation dynamics of two-dimensional CG beams are also presented. When the propagation distance is exactly an integer multiple of half period, there are four focal points in the diagonal position.

Controlling cosine-Gaussian beams in linear media with quadratic external potential

The weak force sensing based on a coherent quantum noise cancellation (CQNC) scheme is presented in a hybrid cavity optomechanical system containing a trapped ensemble of ultracold atoms and an optical parametric amplifier (OPA). In the proposed system, the back-action noise can be completely eliminated at all frequencies and through the proper choice of the OPA parameters, and the noise spectral density can also be reduced at lower frequencies. This leads to a significant enhancement in the sensitivity of the cavity optomechanical weak force sensor, and the noise spectral density also surpasses the standard quantum limit (SQL) even for the small input power at the lower detection frequency. Furthermore, the experimental feasibility of this scheme is also briefly discussed. This study can be used for the realization of a force sensor based on hybrid cavity optomechanical systems and for the coherent quantum control in macroscopic systems.

Enhanced weak force sensing based on atom-based coherent quantum noise cancellation in a hybrid cavity optomechanical system

Optical sensing techniques are well-known for electromagnetic immunity and thus have been widely considered in high-performance vibration sensors such as accelerometers and seismometers. In the progress of miniaturization, however, the force feedback control has rarely been developed due to associated complexity of the optical loops. Aiming to further explore the application of interferometry in geophysics, a force-rebalanced micro-optics accelerometer is developed in this work. This device operates relying on a grating-based MEMS interferometer, where a 3D sensing structure is microassembled to serve as the moveable reflector. In the meantime, a soft robber magnet is arranged on the proof mass and then the feedback mechanism is constructed in combination with a wound coil. The open-loop test indicates this feedback system can generate a drive force of 43.39 nN/mA, and possesses a resultant displacement-regulating capacity of 20.7 nm/mA. Implemented with a digital PI control, the closed-loop device demonstrates an improved dynamic range of 1.012 mg, equal to 10 times of the open-loop state, along with a scale factor of 3250 V/g and a <inline-formula> <tex-math notation="LaTeX">$\text{R}^{{2}}$ </tex-math></inline-formula> coefficient of 0.99927. Additionally, the instrumental noise is tested as 10 ng/<inline-formula> <tex-math notation="LaTeX">$\sqrt {\text {Hz}}$ </tex-math></inline-formula> from 0.2 Hz to 10 Hz, and a bias stability of 36 ng is available at room temperature. Further considering the compact footprint of 4cm <inline-formula> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 6cm <inline-formula> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 3.15cm, this device exhibits great utility for microseismic observations in confined environments.

Nano-g Micro-Optics Accelerometer With Force Feedback Control and Improved Dynamic Range

Precision measurements of local gravitational acceleration variations are of great importance in geophysical surveys. With advantages such as cost-effectiveness and portability, micro-electromechanical system (MEMS)-based gravimeters have shown the potential for long-term gravity measurements. In this article, aiming to further improve the stability of the instrument, the design considerations and system evaluations of an MEMS gravimeter are presented. With a linear spring design for the silicon proof mass, a low natural frequency of <inline-formula> <tex-math notation="LaTeX">$\sim 14$ </tex-math></inline-formula> Hz and a large linear range of <inline-formula> <tex-math notation="LaTeX">$\sim 10300$ </tex-math></inline-formula> mGal are achieved with an ultralow self-noise floor of <inline-formula> <tex-math notation="LaTeX">$1.2~\mu $ </tex-math></inline-formula>Gal/<inline-formula> <tex-math notation="LaTeX">$\surd $ </tex-math></inline-formula>Hz@1 Hz. By implementing a vacuum chamber system, the pressure variation is reduced from hundreds of Pa/day in atmosphere to a linear variation of <inline-formula> <tex-math notation="LaTeX">$\sim 6$ </tex-math></inline-formula> Pa/day. In addition, an active temperature control system can suppress temperature fluctuations by 2–3 orders of magnitude within the band from <inline-formula> <tex-math notation="LaTeX">$1\times 10^{-4}$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$1\times 10^{-2}$ </tex-math></inline-formula> Hz. The stability of the proposed MEMS gravimeter is demonstrated via long-term Earth tides observations within a 30-day time span, giving a correlation coefficient of 0.957 with the reference. An excellent bias instability of <inline-formula> <tex-math notation="LaTeX">$\le 4~\mu $ </tex-math></inline-formula>Gal is demonstrated within the 8–3000-s averaging time range, representing one of the best performances to date in terms of stability for MEMS gravimeters. This shows the potential of high-performance MEMS gravimeters for petroleum and mineral prospecting, seismology, and other geophysical applications.

A Highly Stable and Sensitive MEMS-Based Gravimeter for Long-Term Earth Tides Observations

A portable and high-resolution optomechanical accelerometer employing a deformable grating-based micro-electro-mechanical system (MEMS) interferometer is presented in this Letter. The movable reflective mirror of this interferometer is realized by a low-frequency vertical sensing structure with a three-dimensional (3D)-spring construction, which, to the best of our knowledge, is first proposed and fabricated in this work. All the components of the sensor are packaged in a metal case with a compact size of 4 cm×6 cm×3.15 cm. The micrometer-scale springs permit the device to have a high mechanical sensitivity of 893.23 µm/g and a resultant self-noise below 2 ng/H z from 2 to 7 Hz. Meanwhile, the measured voltage responsivity is as high as 15,874 V/g, demonstrating it is one of the most sensitive accelerometers reported to date.

2 ng/√Hz-resolution optomechanical accelerometer employing a three-dimensional MEMS interferometer.

We generate and measure the versatile vortex linear light bullet, which combines a high-order Bessel beam and an Airy pulse. This three-dimensional optical wave packet propagates without distortion in any medium, while carrying an orbital angular momentum. Its non-varying feature in linear propagation is verified by a three-dimensional measurement. Such a novel versatile linear light bullet can be useful in various applications such as micromachining.

http://www.opticsjournal.net/ViewFull0.htm?aid=OJ170222000032aGdJfM

Generation of three-dimensional versatile vortex linear light bullets (Invited Paper)

We generate a three-dimensional (3D) autofocusing wave packet by combining counter-propagating Airy pulses and an Airy ring beam. A 3D profile measurement reveals unique 3D autofocusing of such wave packet in a linear medium.

Three-dimensional abruptly autofocusing optical wave packet

We demonstrate a versatile vortex linear light bullet as a vortex Airy-Bessel wave packet for the first time. Its non-varying three-dimensional (3D) vortex field in linear propagation is verified by 3D measurements.

Generation of versatile vortex linear light bullet

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2 ng/√Hz-resolution optomechanical accelerometer employing a three-dimensional MEMS interferometer.

Generation of three-dimensional versatile vortex linear light bullets (Invited Paper)

Three-dimensional abruptly autofocusing optical wave packet

Generation of versatile vortex linear light bullet