We characterize the phototransistor internal gain of metamorphic high-electron-mobility transistors ͑mHEMTs͒. When the mHEMT operates as a phototransistor, it has internal gain provided by the photovoltaic effect. To determine this internal gain, photoresponse characteristics dominated by the photoconductive effect as well as the photovoltaic effect are investigated. When the device is turned off, it acts as a photoconductor, and by calculating photoconductor gain, the primary photodetected power can be determined, which indicates the absorbed optical power. The ratio between this and the photodetected power due to the photovoltaic effect represents phototransistor internal gain. It is demonstrated that the phototransistor internal gain is function of optical modulation frequency.

We study the linear stability of the exact deep-water capillary wave solution of Crapper (J. Fluid Mech., vol. 2, 1957, pp. 532–540) subject to two-dimensional perturbations (both subharmonic and superharmonic). By linearizing a set of exact one-dimensional non-local evolution equations, a stability analysis is performed with the aid of Floquet theory. To validate our results, the exact evolution equations are integrated numerically in time and the numerical solutions are compared with the time evolution of linear normal modes. For superharmonic perturbations, contrary to Hogan (J. Fluid Mech., vol. 190, 1988, pp. 165–177), who detected two bubbles of instability for intermediate amplitudes, our results indicate that Crapper’s capillary waves are linearly stable to superharmonic disturbances for all wave amplitudes. For subharmonic perturbations, it is found that Crapper’s capillary waves are unstable, and our results generalize to the highly nonlinear regime the analysis for small amplitudes presented by Chen & Saffman (Stud. Appl. Maths, vol. 72, 1985, pp. 125–147).

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