Recently, it has been shown that if we consider the higher derivative correction, the viscosity bound conjectured to be η/s = 1/4π is violated and so is the causality. In this paper, we consider medium effect and the higher derivative correction simultaneously by adding charge and Gauss-Bonnet terms. We find that the viscosity bound violation is not changed by the charge. However, we find that two effects together create another instability for large momentum regime. We argue the presence of tachyonic modes and show it numerically. We draw a phase diagram relevant to the instability in charge-coupling space. Correspondence. chemical potential in the theory was figured out in [8,9]. Phases of these theories were also discussed in D3/D7 setup [10 -12] as well as in D4D8D8 [9].More recently, it had been conjectured that the viscosity value of theories with gravity dual may give a lower bound for the η/s = 1/4π for all possible liquid [13]. However, the authors of [14] and [15] showed that if we consider the stringy correction to α ′ order, the viscosity bound is violated and causality is also [16] violated as a consequence (See also for more recent paper [17]).The α ′ terms are also related to the (in)stability issues of black holes. The instability of D-dimensional asymptotically flat Einstein-Gauss-Bonnet black holes has been discussed by several authors [18,19]. Their results show that for the gravitational perturbations of Schwarzschild black holes in D = (from 5 to 11) Gauss-Bonnet gravity, the instability occurs only for D = 5 and D = 6 cases at large value of α ′ [19].In this paper, we add charge together with the Gauss-Bonnet term, and calculate η/s and consider the stability issue including the causality violation. We find that the viscosity bound violation is not changed by the charge. However, we find that for large momenta regime, there exists a new instability due to the charge effect. The linearized perturbation has a negative frequency squared signaling an instability. We draw the phase diagram relevant to the instability. We emphasize that the new instability present only if both charge and Gauss-Bonnet term present.

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A compact arrayed-waveguide grating (AWG) using multiple-arrowhead structures has been proposed. Arrowhead structures are useful for achieving low-cost and highly integrated waveguide devices because of their compactness. Therefore, the use of multiple-arrowhead structures enables us to achieve high-resolution AWGs with a channel spacing of less than 10 GHz, and we have already fabricated an 8-channel, 25-GHz-spacing AWG using a single-arrowhead structure, a 16-channel, 100-GHzspacing AWG using a double-arrowhead structure and an 8-channel, 6.25-GHz-spacing AWG using a triple-arrowhead structure. The dimension of the third type of AWG is much smaller than a conventional AWG, with a size ratio of 1 : 6:4. The levels of the losses and adjacent crosstalk are mainly determined by insertion losses in the v-bend waveguides and by phase shifts due to misalignment of the mirror position, respectively.

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