high harmonic generation is a useful tool for the generation of short, intense attosecond pulses. In order to simulate high harmonic generation, we performed a numerical solution to the time dependent Schrödinger equation. by considering dipole approximation, we predicted generation of a 53 attosecond pulse. In order to see the time and frequency of emission of attosecond pulse, we exploit time frequency analysis. On the other hand, because of uncertainty between time and frequency, it would be of high importance whether which analysis is been applied. our studies show that Gabor analysis exhibits the least uncertainty between time and frequency components. And at least, we set the balance between time and frequency distribution by altering the window size.

Our work is based on high harmonic generation in a gaseous medium (helium ion), by exploiting gold bowtie nanostructures as laser field amplifiers. As the result of emission of a laser pulse, the wave function of the atom varies with time; so, it is necessary to solve 1D time-dependent Schrödinger equation by means of split operator method. By illumination of a short duration, long wavelength three color laser pulse inside the gap, the enhanced field not only changes with time, but also varies in space. In this work we considered this space inhomogeneity in linear and nonlinear schemes. We show that in nonlinear case, the plateau region is more extended. We also show that in larger gaps, cutoff occurs on higher frequencies. But limitation of electron motion in bowtie nanostructures leads to the choice of an optimum 16 nm gap size in our case. We predict that, by the superposition of supercontinuum harmonics, a 26 attosecond pulse can be generated.