# comparison between nonlinear simulations of different wavelength

In this paper (Link: http://aip.scitation.org/doi/abs/10.1063/1.4886409), the authors simulate third harmonic generation of gold by Lumerical FDTD solution.

They compare the third harmonic emission of different wavelength.

However, in the nonorm setting, the unit of the power after integrating the poynting vectors over the 2D monitor supposes to be W/Hz^2, so what I should do before I can compare the power of harmonic generation of different wavelength, like the case in this paper?

Thanks for any kind of help.

Hi,

Although I have not gone through the paper thoroughly, but I think it might be able to approach this question in a slightly more general way - what is “power” in the nonorm state?

In the nonorm state, we typically work with pulses. Therefore, it makes sense to define the energy (in Joule) carried by the pulse. The energy of a pulse can be found by the integration of power(t), where it is the instantaneous power. It is also not unusual to calculate the power by taking the ratio of total energy to the time it takes to deliver the pulse. I believe this page will give you some insight on how to work with energy and power in the nonorm state.

Thanks for your reply.

In that page, it says energy (in Joule) can be calculated by the area under the power curve in the frequency domain (in Watt/Hz^2). But the area is mainly determined by the peak value since the width is more or less unchanged for different emission wavelength. So, does it mean I can compare the power of different wavelength by simply comparing their peak values of the power curve in the frequency domain, which is obtained by integrating the poynting vectors over an area?

If the width of the peak is fairly constant, then I assume that the height of the peak can give you some idea of the energy it carries. But it should be more accurate to find the area under the curve.

That page is just to give you some general idea of energy calculation in the time and frequency domain. I won’t be surprised that the details can vary from applications to applications.