Quantum phase amplification for temporal pulse shaping and super-resolution in remote sensing

The use of nonlinear optical interactions to perform nonclassical transformations of electromagnetic field is an area of considerable interest. Quantum phase amplification (QPA) has been previously proposed as a method to perform nonclassical manipulation of coherent light, which can be experimentally realized by use of nonlinear optical mixing processes, of which phase-sensitive three-wave mixing (PSTWM) is one convenient choice. QPA occurs when PSTWM is operated in the photon number deamplification mode, i.e., when the energy is coherently transferred among the low-frequency signal and idler waves and the high-frequency pump wave. The final state is nonclassical, with the field amplitude squeezed and the phase anti-squeezed.;In the temporal domain, the use of QPA has been studied to facilitate nonlinear pulse shaping. This novel method directly shapes the temporal electric field amplitude and phase using the PSTWM in a degenerate and collinear configuration, which has been analyzed using a numerical model. Several representative pulse shaping capabilities of this technique have been identified, which can augment the performance of common passive pulse shaping methods operating in the Fourier domain. The analysis indicates that a simple quadratic variation of temporal phase facilitates pulse compression and self-steepening, with features significantly shorter than the original transform-limited pulse. Thus, PSTWM can act as a direct pulse compressor based on the combined effects of phase amplification and group velocity mismatch, even without the subsequent linear phase compensation. Furthermore, it is shown numerically that pulse doublets and pulse trains can be produced at the pump frequency by utilizing the residual linear phase of the signal. Such pulse shaping capabilities are found to be within reach of this technique in common nonlinear optical crystals pumped by pulses available from compact femtosecond chirped-pulse amplification laser systems.;The use of QPA in the spatial domain has also been studied as a method to enhance the spatial resolution of imaging systems. A detailed model has been developed for achieving both super-resolution and detection of phase-amplified light. The imaging resolution problem considered here is treated as a binary hypotheses testing problem. Resolution enhancement is achieved by magnification of the angular separation of two targets in the sub-Rayleigh regime. The detection model includes optimization of detector segmentation, detector noise, and detection in both the spatial and the spatial frequency domain, which provide strategies for the optimization of the signal-to-noise ratio that take advantage of both the change of the field distribution and the change of energy of the signal in the QPA process.;Proof-of-principle experiments have been conducted in the spatial domain. For the first time, beam angular amplification has been demonstrated, and the experimental result is in good agreement with simulations. The experimental demonstration has been achieved by observing the correlation of amplitude and angular phase in the phase-sensitive three-wave mixing process using ultrashort laser pulses and utilizing a type I three-wave mixing process. Several diagnostics have been developed and employed in the experimental measurements, including the near-field diagnostic, the far-field diagnostic, and the interferometry diagnostic. They have all been used to confirm the existence and study the properties of the QPA process on a shot-to-shot basis. Specifically, amplitude was measured in the near-field diagnostic, while the angular phase was indirectly measured in the far-field diagnostic by determining the position of the beam centroid. Interferometric measurements have been found to be of insufficient accuracy for this measurement in the way they were implemented.;The demonstration of beam angular amplification by use of QPA lays the foundation for future integrated demonstration of imaging resolution enhancement, while the results of the modeling in the time domain open opportunities for development of flexible pulse shaping benefitting a variety of ultrafast applications.