Spectrometer based on a compact disordered multi-mode interferometer.

We present a compact, CMOS compatible, photonic integrated circuit (PIC) based spectrometer that combines a dispersive array element of SiO2-filled scattering holes within a multimode interferometer (MMI) fabricated on the silicon-on-insulator (SOI) platform. The spectrometer has a bandwidth of 67 nm, a lower bandwidth limit of 1 nm, and a peak-to-peak resolution of 3 nm for wavelengths around 1310 nm.

Non-diffracting beam generated from a photonic integrated circuit based axicon-like lens.

We demonstrate an on-chip silicon-on-insulator (SOI) device to generate a non-diffracting beam of ≈850 µm length from a diffractive axicon-like lens etched using a low resolution (200 nm feature size, 250 nm gap) deep-ultraviolet lithographic fabrication. The device consists of circular gratings with seven stages of 1x2 multimode interferometers. We present a technique to apodize the gratings azimuthally by breaking up the circles into arcs which successfully increased the penetration depth in the gratings from ≈5 µm to ≈60 µm. We characterize the device's performance by coupling 1300±50 nm swept source laser in to the chip from the axicon and measuring the out-coupled light from a grating coupler. Further, we also present the implementation of balanced homodyne detection method for the spectral characterization of the device and show that the position of the output lobe of the axicon does not change significantly with wavelength.

Relation between dilation and stress fluctuations in discontinuous shear thickening suspensions.

We investigate dilation-induced surface deformations in a discontinuous shear thickening (DST) suspension to determine the relationship between dilation and stresses in DST. Video is taken at two observation points on the surface of the suspension in a rheometer while shear and normal stresses are measured. A roughened surface of the suspension is observed as particles poke through the liquid-air interface, an indication of dilation in a suspension. These surface roughening events are found to be intermittent and localized spatially. Shear and normal stresses also fluctuate between high- and low-stress states, and surface roughening is observed frequently in the high-stress state. On the other hand, a complete lack of surface roughening is observed when the stresses remain at low values for several seconds. Surface roughening is most prominent while the stresses grow from the low-stress state to the high-stress state, and the roughened surface tends to span the entire surface by the end of the stress growth period. Surface roughening is found only at stresses and shear rates in and above the shear thickening range. These observed relations between surface roughening and stresses confirm that dilation and stresses are coupled in the high-stress state of DST.

Effective packing fraction for better resolution near the critical point of shear thickening suspensions.

We present a technique for obtaining an effective packing fraction for discontinuous shear thickening suspensions near a critical point. It uses a measurable quantity that diverges at the critical point-in this case the inverse of the shear rate γ[over ̇]_{c}^{-1} at the onset of discontinuous shear thickening-as a proxy for packing fraction ϕ. We obtain an effective packing fraction for cornstarch and water by fitting γ[over ̇]_{c}^{-1}(ϕ) and then invert the function to obtain ϕ_{eff}(γ[over ̇]_{c}). We further include the dependence of γ[over ̇]_{c}^{-1} on the rheometer gap d to obtain the function ϕ_{eff}(γ[over ̇]_{c},d). This effective packing fraction ϕ_{eff} has better resolution near the critical point than the raw measured packing fraction ϕ by as much as an order of magnitude. Furthermore, ϕ_{eff} normalized by the critical packing fraction ϕ_{c} can be used to compare rheology data for cornstarch and water suspensions from different laboratory environments with different temperature and humidity. This technique can be straightforwardly generalized to improve resolution in any system with a diverging quantity near a critical point.

System-spanning dynamically jammed region in response to impact of cornstarch and water suspensions.

We experimentally characterize the structure of concentrated suspensions of cornstarch and water in response to impact. Using surface imaging and particle tracking at the boundary opposite the impactor, we observed that a visible structure and particle flow at the boundary occur with a delay after impact. We show the delay time is about the same time as the strong stress response, confirming that the strong stress response results from deformation of the dynamically jammed structure once it spans between the impactor and a solid boundary. A characterization of this strong stress response is reported in a companion paper [Maharjan, Mukhopadhyay, Allen, Storz, and Brown, Phys. Rev. E 97, 052602 (2018)10.1103/PhysRevE.97.052602]. We observed particle flow in the outer part of the dynamically jammed region at the bottom boundary, with a net transverse displacement of up to about 5% of the impactor displacement, indicating shear at the boundary. Direct imaging of the surface of the outer part of the dynamically jammed region reveals a change in surface structure that appears the same as the result of dilation in other cornstarch suspensions. Imaging also reveals cracks, like a brittle solid. These observations suggest the dynamically jammed structure can temporarily support stress according to an effective modulus, like a soil or dense granular material, along a network of frictional contacts between the impactor and solid boundary.

Constitutive relation for the system-spanning dynamically jammed region in response to impact of cornstarch and water suspensions.

We experimentally characterize the impact response of concentrated suspensions consisting of cornstarch and water. We observe that the suspensions support a large normal stress-on the order of MPa-with a delay after the impactor hits the suspension surface. We show that neither the delay nor the magnitude of the stress can yet be explained by either standard rheological models of shear thickening in terms of steady-state viscosities, or impact models based on added mass or other inertial effects. The stress increase occurs when a dynamically jammed region of the suspension in front of the impactor propagates to the opposite boundary of the container, which can support large stresses when it spans between solid boundaries. We present a constitutive relation for impact rheology to relate the force on the impactor to its displacement. This can be described in terms of an effective modulus but only after the delay required for the dynamically jammed region to span between solid boundaries. Both the modulus and the delay are reported as a function of impact velocity, fluid height, and weight fraction. We report in a companion paper the structure of the dynamically jammed region when it spans between the impactor and the opposite boundary [Allen et al., Phys. Rev. E 97, 052603 (2018)10.1103/PhysRevE.97.052603]. In a direct follow-up paper, we show that this constitutive model can be used to quantitatively predict, for example, the trajectory and penetration depth of the foot of a person walking or running on cornstarch and water [Mukhopadhyay et al., Phys. Rev. E 97, 052604 (2018)10.1103/PhysRevE.97.052604].