David J. T. Liu

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Current optical communication systems rely almost exclusively on multimode fibres for short- and medium-haul transmissions, and are now expanding into the long-haul arena. Ultra-high bandwidth applications are the main drive for this expansion, based on the ability to spatially multiplex data channels in multimode systems. Integrated photonics, on the other(More)
We present a new technique for the design of transformation-optics devices based on large-scale optimization to achieve the optimal effective isotropic dielectric materials within prescribed index bounds, which is computationally cheap because transformation optics circumvents the need to solve Maxwell's equations at each step. We apply this technique to(More)
We demonstrate that due to strong modal interactions through cross-gain saturation, the onset of a new lasing mode can switch off an existing mode via a negative power slope. In this process of interaction-induced mode switching (IMS) the two involved modes maintain their identities, i.e. they do not change their spatial field patterns or lasing(More)
David Liu,1, 2, ∗ Bo Zhen,2 Li Ge,3 Felipe Hernandez,1 Adi Pick,4 Stephan Burkhardt,5 Matthias Liertzer,5 Stefan Rotter,5 and Steven G. Johnson1, 2, † Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA(More)
While two-dimensional triangles are always subdivision invariant, the same does not always hold for their three-dimensional counterparts. We consider several interesting properties of those three-dimensional tetrahedra that are subdivision invariant and offer them a new classification. Moreover, we study the optimization of these tetrahedra, arguing that(More)
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