Mathematical Analysis of Novel Nonlinear Waves in Dissipative Optical Systems

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This project theoretically investigates dissipative nonlinear wave systems in optics, which exhibit novel and counter-intuitive properties such as conservative-like behaviors and unidirectional wave propagation. Examples of such optical systems include certain advanced lasers supporting unidirectional light propagation along the edges of the laser cavity immune to scattering and disorder, which holds promise as an optical diode in the design of optical computers. Other examples include certain dissipative second-harmonic-generation systems featuring soliton families with continuous ranges of powers, which may be exploited for signal processing devices. Properties manifested in such systems are intriguing, and they will be investigated comprehensively in this project. Through advanced mathematical techniques and sophisticated numerical computations, new insight will be gained on the operation of these optical systems, so that their applications for optical diodes and nonlinear data processing can be assessed and optimized. The problems undertaken in this project are at the cutting edge of applied mathematics and optics. Mathematically, this project ventures into the unchartered territory of dissipative systems behaving like conservative systems, which opens new research directions in the study of nonlinear waves. On the physical side, these studies will lead to better understanding of next-generation laser devices, which will have direct applications to many branches of optics and photonics. Educationally, graduate students will be trained, and undergraduate honors thesis and undergraduate summer research will be supervised, so that this project will help train young talents in the STEM fields.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.