Applications of space-time duality

Thesis (Ph. D.)--University of Rochester. Institute of Optics, 2017.The concept of space-time duality is based on a mathematical analogy between paraxial diffraction and narrowband dispersion, and has led to the development of temporal imaging systems. The first part of this thesis focuses on the development of a temporal imaging system for the Laboratory for Laser Energetics. Using an electro-optic phase modulator as a time lens, a time-to-frequency converter is constructed capable of imaging pulses between 3 and 12 ps. Numerical simulations show how this system can be improved to image the 1-30 ps range used in OMEGA-EP. By adjusting the timing between the pulse and the sinusoidal clock of the phase modulator, the pulse spectrum can be selectively narrowed, broadened, or shifted. An experimental demonstration of this effect achieved spectral narrowing and broadening by a factor of 2. Numerical simulations show narrowing by a factor of 8 is possible with modern phase modulators. The second part of this thesis explores the space-time analog of reflection and refraction from a moving refractive index boundary. From a physics perspective, a temporal boundary breaks translational symmetry in time, requiring the momentum of the photon to remain unchanged while its energy may change. This leads to a shifting and splitting of the pulse spectrum as the boundary is crossed. Equations for the reflected and transmitted frequencies and a condition for total internal reflection are found. Two of these boundaries form a temporal waveguide, which confines the pulse to a narrow temporal window. These waveguides have a finite number of modes, which do not change during propagation. A single-mode waveguide can be created, allowing only a single pulse shape to form within the waveguide. Temporal reflection and refraction produce a frequency dependent phase shift on the incident pulse, leading to interference fringes between the incident light and the reflected light. In a waveguide, this leads to self-imaging, where the pulse shape reforms periodically at finite propagation lengths. Numerical simulations are performed for the specific case where the moving boundary is produced through cross-phase modulation. In this case, the Kerr nonlinearity causes the boundary to change during propagation, leading to unique temporal and spectral behavior