In photonics and quantum optics, a key challenge facing any technological application has traditionally been the mitigation of optical losses. Recent work has shown that a new class of optical materials, called Parity-Time symmetric materials, that consist of a precisely balanced distribution of loss and gain can be exploited to engineer novel functionalities for propagating and filtering electromagnetic radiation. Here we show a generic property of optical systems that feature an arbitrary distribution of loss and gain, described by non-Hermitian operators, namely that overall lossy optical systems can transiently amplify certain input signals by several orders of magnitude. We present a mathematical framework to analyze the dynamics of wave propagation in media with an arbitrary distribution of loss and gain and construct the initial conditions to engineer such non-Hermitian power amplifiers.
We use the multi-mode lasing equations of Haken to analyze the stationary state lasing patterns of two-dimensional dielectric
microcavity lasers of different shape, including the circle and various smooth deformations of the circle. We find a generic increase
in the power output with deformation which is relatively insensitive
to the specific form of the shape deformation. In addition we find
strong mode selection in favor of librational modes (including but
not solely the bow-tie modes) in the case when the pumping is concentrated near the center of the cavity. These results point towards an explanation of the dramatic results on power increase with deformation obtained by Gmachl et al. in quantum cascade micro-cylinder lasers. The sensitivity of the lasing solutions to the nature of the ray dynamics (chaotic, integrable and mixed) will also be analyzed.
Conference Committee Involvement (1)
Integrated Photonics: Materials, Devices and Applications