Abstract
We consider the optimization problem of least energy-cost path in open systems that are described by non-Hermitian Hamiltonians. We apply it to find the optimal gain-loss profile for a non-uniform PT-symmetric coupler performing a binary transfer function. We bring evidence that the gain-loss profile fulfilling this requirement corresponds to a non-conventional situation where light intensity is conserved at every point along the PT-symmetric system. Besides, we find that the optimal profile corresponds to a practically important case of optical switching operation achieved with minimal amount of aggregate amplification level. We show that switching architectures using such type of gain-loss profiles are much more advantageous than conventional uniform PT-symmetric couplers in terms of gain and energy. Furthermore, this type of optimal profile turns out to be robust against fabrication imperfections. This opens new prospects for functional applications of PT-symmetric devices in photonics.
Highlights
We consider the optimization problem of least energy-cost path in open systems that are described by non-Hermitian Hamiltonians
It offered the systems of choice to emulate the equivalent of the complex-valued potential thanks to optical gain and losses of macroscopic photonic systems: balanced gain and loss can realize PT -symmetry, as was first suggested in[5] and experimentally investigated in the following years[6,7,8]
In classical physics the brachistochrone or shortest-time-delay problem is the well-known example of optimization problems[14]
Summary
We consider the optimization problem of least energy-cost path in open systems that are described by non-Hermitian Hamiltonians. We apply it to find the optimal gain-loss profile for a non-uniform PT-symmetric coupler performing a binary transfer function. We show that switching architectures using such type of gain-loss profiles are much more advantageous than conventional uniform PT-symmetric couplers in terms of gain and energy. This type of optimal profile turns out to be robust against fabrication imperfections. Our cost is the total gain needed to achieve switching, i.e. the integral
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