A box shape with constant area is often used to represent the complex geometry in the cochlea, although variation of the fluid chambers areas is known to be more complicated. This variation is accounted for here by an “effective area,” given by the harmonic mean of upper and lower chamber area from previous measurements. The square root of this effective area varies linearly along the cochleae in the investigated mammalian species. This suggests the use of a linearly tapered box model in which the fluid chamber width and height are equal, but decrease linearly along its length. The basilar membrane (BM) width is assumed to increase linearly along the model. An analytic form of the far-field fluid pressure difference due to BM motion is derived for this tapered model. The distributions of the passive BM response are calculated using both the tapered and uniform models and compared with human and mouse measurements. The discrepancy between the models is frequency-dependent and becomes small at low frequencies. The tapered model developed here shows a reasonable fit to experimental measurements, when the cochleae are cadaver or driven at high sound pressure level, and provides a convenient way to incorporate cochlear geometrical variations.

An efficient way of describing the linear micromechanical response of the cochlea is in terms of its poles and zeros. Pole-zero models with local scaling symmetry are derived for both one and two degree-of-freedom micromechanical systems. These elements are then used in a model of the coupled cochlea, which is optimised to minimise the mean square difference between its frequency response and that measured on the basilar membrane inside the mouse cochlea by Lee, Raphael, Xia, Kim, Grillet, Applegate, Ellerbee Bowden, and Oghalai [(2016) J. Neurosci. 36, 8160-8173] and Oghalai Lab [(2015). https://oghalailab.stanford.edu], at different excitation levels. A model with two degree-of-freedom micromechanics generally fits the measurements better than a model with single degree-of-freedom micromechanics, particularly at low excitations where the cochlea is active, except post-mortem conditions, when the cochlea is passive. The model with the best overall fit to the data is found to be one with two degree-of-freedom micromechanics and 3D fluid coupling. Although a unique lumped parameter network cannot be inferred from such a pole-zero description, these fitted results help indicate what properties such a network should have.

Luneburg lenses and Maxwell fisheye lenses possess distinct properties of focusing, well beyond conventional lenses made of uniform materials. In this paper, a planar broadband bifunctional Luneburg-fisheye lens synthesized by gradient anisotropic metasurface is proposed. The proposed anisotropic metasurface is formed by non-resonant anisotropic cells, so that it can independently realize the equivalent gradient refractive indexes of Luneburg lens and Maxwell fisheye lens along orthogonal directions in a broad band, respectively. To verify the performance of the bifunctional lens, a prototype associated with a feeding log-periodic dipole antenna has been fabricated. Experimental results show that the proposed lens functions well over a wide frequency range with high efficiency and low profile, which coincides well with theoretical predictions and simulated results. It is expected that the proposed design will facilitate the applications of multifunctional metadevices in microwave and optical ranges.

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