Photon has a specific wavelength $\lambda$. Imagine we created a mode-locked pulse, with $80\: \text{MHz}$ repetition rate, i.e. pulse are separated by $13\: \text{ns}$. The pulse duration is $4\: \text{ps}$, I understand that pulse has a very broad frequency range. One can imagine, a pulse is composed of many monochromatic wave with different wavelengths adding up together in phase (in dispersion-less medium). So, if the peak power is $100\: \text{W}$ and I wish to calculate the number of photons in a pulse, How am I supposed to take the weighting of each wavelength? Or Should One simply calculate using the center wavelength? I do think other components play a role in different energy.
The whole idea of this question is that I have to do single photon correlation experiment by combining a single photon (from the weak signal) with a pulse (from the strong pump), However, if one detect the pulse, How could one which wavelength upconverts the single photon? I imagined pulse is composed of many photons adding together.
Update: My friend proposed that If the pump pulse combined with the photon from a weak signal, you have the center wavelength of the pulse combined with the center wavelength of the photon, to get a new frequency, and you could filter out other wavelength components, to do a single photon detection.
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