On cycle systems with specified weak chromatic number

AbstractA weak k-colouring of an m-cycle system is a colouring of the vertices of the system with k colours in such a way that no cycle of the system has all of its vertices receive the same colour. An m-cycle system is said to be weakly k-chromatic if it has a weak k-colouring but no weak (k−1)-colouring. In this paper we show that for all k⩾2 and m⩾3 with (k,m)≠(2,3) there is a weakly k-chromatic m-cycle system of order v for all sufficiently large admissible v

Magnetic Scanometric DNA Microarray Detection of Methyl Tertiary Butyl Ether Degrading Bacteria for Environmental Monitoring

A magnetoresistive biosensing platform based on a single magnetic tunnel junction (MTJ) scanning probe and DNA microarrays labeled with magnetic particles has been developed to provide an inexpensive, sensitive and reliable detection of DNA. The biosensing platform was demonstrated on a DNA microarray assay for quantifying bacteria capable of degrading methyl tertiary butyl ether (MTBE), where concentrations as low as 10 pM were detectable. Synthetic probe bacterial DNA was immobilized on a microarray glass slide surface, hybridized with the 48 base pair long biotinylated target DNA and subsequently incubated with streptavidin-coated 2.8 μm diameter magnetic particles. The biosensing platform then makes use of a micron-sized MTJ sensor that was raster scanned across a 3 mm by 5 mm glass slide area to capture the stray magnetic field from the tagged DNA and extract two dimensional magnetic field images of the microarray. The magnetic field output is then averaged over each 100 μm diameter DNA array spot to extract the magnetic spot intensity, analogous to the fluorescence spot intensity used in conventional optical scanners. The magnetic scanning result is compared with results from a commercial laser scanner and particle coverage optical counting to demonstrate the dynamic range and linear sensitivity of the biosensing platform as a potentially inexpensive, sensitive and portable alternative for DNA microarray detection for field applications

Hybrid GMR Sensor Detecting 950 pT/sqrt(Hz) at 1 Hz and Room Temperature.

Advances in the magnetic sensing technology have been driven by the increasing demand for the capability of measuring ultrasensitive magnetic fields. Among other emerging applications, the detection of magnetic fields in the picotesla range is crucial for biomedical applications. In this work Picosense reports a millimeter-scale, low-power hybrid magnetoresistive-piezoelectric magnetometer with subnanotesla sensitivity at low frequency. Through an innovative noise-cancelation mechanism, the 1/f noise in the MR sensors is surpassed by the mechanical modulation of the external magnetic fields in the high frequency regime. A modulation efficiency of 13% was obtained enabling a final device's sensitivity of ~950 pT/Hz1/2 at 1 Hz. This hybrid device proved to be capable of measuring biomagnetic signals generated in the heart in an unshielded environment. This result paves the way for the development of a portable, contactless, low-cost and low-power magnetocardiography device

A MEMS Light Modulator Based on Diffractive Nanohole Gratings

We present the design, fabrication, and testing of a microelectromechanical systems (MEMS) light modulator based on pixels patterned with periodic nanohole arrays. Flexure-suspended silicon pixels are patterned with a two dimensional array of 150 nm diameter nanoholes using nanoimprint lithography. A top glass plate assembled above the pixel array is used to provide a counter electrode for electrostatic actuation. The nanohole pattern is designed so that normally-incident light is coupled into an in-plane grating resonance, resulting in an optical stop-band at a desired wavelength. When the pixel is switched into contact with the top plate, the pixel becomes highly reflective. A 3:1 contrast ratio at the resonant wavelength is demonstrated for gratings patterned on bulk Si substrates. The switching time is 0.08 ms and the switching voltage is less than 15V

High-dimensional spatial mode sorting and optical circuit design using multi-plane light conversion

Multi-plane light converters (MPLCs) are an emerging class of optical device capable of converting a set of input spatial light modes to a new target set of output modes. This operation represents a linear optical transformation - a much sought after capability in photonics. MPLCs have potential applications in both the classical and quantum optics domains, in fields ranging from optical communications, to optical computing and imaging. They consist of a series of diffractive optical elements (the 'planes'), typically separated by free-space. The phase delays imparted by each plane are determined by the process of inverse-design, most often using an adjoint algorithm known as the wavefront matching method (WMM), which optimises the correlation between the target and actual MPLC outputs. In this work we investigate high mode capacity MPLCs to create arbitrary spatial mode sorters and linear optical circuits. We focus on designs possessing low numbers of phase planes to render these MPLCs experimentally feasible. To best control light in this scenario, we develop a new inverse-design algorithm, based on gradient ascent with a specifically tailored objective function, and show how in the low-plane limit it converges to MPLC designs with substantially lower modal cross-talk and higher fidelity than achievable using the WMM. We experimentally demonstrate several prototype few-plane high-dimensional spatial mode sorters, operating on up to 55 modes, capable of sorting photons based on their Zernike mode, orbital angular momentum state, or an arbitrarily randomized spatial mode basis. We discuss the advantages and drawbacks of these proof-of-principle prototypes, and describe future improvements. Our work points to a bright future for high-dimensional MPLC-based technologies

All-optically untangling light propagation through multimode fibres

When light propagates through a complex medium, such as a multimode optical fibre (MMF), the spatial information it carries is scrambled. In this work we experimentally demonstrate an all-optical strategy to unscramble this light again. We first create a digital model capturing the way light has been scattered, and then use this model to inverse-design and build a complementary optical system - which we call an optical inverter - that reverses this scattering process. Our implementation of this concept is based on multi-plane light conversion, and can also be understood as a diffractive artificial neural network or a physical matrix pre-conditioner. We present three design strategies allowing different aspects of device performance to be prioritised. We experimentally demonstrate a prototype optical inverter capable of simultaneously unscrambling up to 30 spatial modes that have propagated through a 1m long MMF, and show how this enables near instantaneous incoherent imaging, without the need for any beam scanning or computational processing. We also demonstrate the reconfigurable nature of this prototype, allowing it to adapt and deliver a new optical transformation if the MMF it is matched to changes configuration. Our work represents a first step towards a new way to see through scattering media. Beyond imaging, this concept may also have applications to the fields of optical communications, optical computing and quantum photonics.Comment: 18 pages, 11 figure

Monolithic ultrasound fingerprint sensor.

This paper presents a 591×438-DPI ultrasonic fingerprint sensor. The sensor is based on a piezoelectric micromachined ultrasonic transducer (PMUT) array that is bonded at wafer-level to complementary metal oxide semiconductor (CMOS) signal processing electronics to produce a pulse-echo ultrasonic imager on a chip. To meet the 500-DPI standard for consumer fingerprint sensors, the PMUT pitch was reduced by approximately a factor of two relative to an earlier design. We conducted a systematic design study of the individual PMUT and array to achieve this scaling while maintaining a high fill-factor. The resulting 110×56-PMUT array, composed of 30×43-μm2 rectangular PMUTs, achieved a 51.7% fill-factor, three times greater than that of the previous design. Together with the custom CMOS ASIC, the sensor achieves 2 mV kPa-1 sensitivity, 15 kPa pressure output, 75 μm lateral resolution, and 150 μm axial resolution in a 4.6 mm×3.2 mm image. To the best of our knowledge, we have demonstrated the first MEMS ultrasonic fingerprint sensor capable of imaging epidermis and sub-surface layer fingerprints

Threading light through dynamic complex media

The scattering of light impacts sensing and communication technologies throughout the electromagnetic spectrum. Overcoming the effects of time-varying scattering media is particularly challenging. In this article we introduce a new way to control the propagation of light through dynamic complex media. Our strategy is based on the observation that many dynamic scattering systems exhibit a range of decorrelation times -- meaning that over a given timescale, some parts of the medium may essentially remain static. We experimentally demonstrate a suite of new techniques to identify and guide light through these networks of static channels -- threading optical fields around multiple dynamic pockets hidden at unknown locations inside opaque media. We first show how a single stable light field propagating through a partially dynamic medium can be found by optimising the wavefront of the incident field. Next, we demonstrate how this procedure can be accelerated by 2 orders of magnitude using a physically realised form of adjoint gradient descent optimisation. Finally, we describe how the search for stable light modes can be posed as an eigenvalue problem: we introduce a new optical matrix operator, the time-averaged transmission matrix, and show how it reveals a basis of fluctuation-eigenchannels that can be used for stable beam shaping through time-varying media. These methods rely only on external camera measurements recording scattered light, require no prior knowledge about the medium, and are independent of the rate at which dynamic regions move. Our work has potential future applications to a wide variety of technologies reliant on general wave phenomena subject to dynamic conditions, from optics to acoustics.Comment: 16 pages, 6 figures. This updated version includes supplementary informatio