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This paper concentrates on harmonic analysis in gaseous helium, including microscopic generation, selective filtration and macroscopic propagation. A coherent method is proposed, with time-dependent Schrödinger equation for harmonic generation and Maxwell’s wave equation for harmonic propagation. By introducing the polarization source based on the microscopic single-atom response, the macroscopic nonlinear propagation can be efficiently solved by a set of linear equations at each harmonic frequency. Using the proposed method, we numerically investigate the propagation effects of selective harmonics in gaseous helium. Our results reveal that specific harmonics allow the synthesis of an isolated attosecond pulse, which presents a high beam quality and an excellent spatial profile with Gaussian-like distribution. Moreover, the generated pulse provides a promising potential on high power defense, quantum radar and communication.

Harmonic Analysis in Gaseous Helium by Coherent Schrödinger-Maxwell Method