The noise of ultrashort pulse mode-locked lasers beyond the slowly varying envelope approximation

The zero-point fluctuations in an L–C circuit of finite Q are revisited. The zero-point energy is shown to approach the value of only in the limit of an infinite Q. A Fabry–Perot resonator, on the other hand, has bounded zero-point energies of its modes that are equal to for each resonance. Based on the Fabry–Perot resonator with broadband noise, we analyse the noise of an ultrafast mode-locked laser when the slowly varying envelope approximation (SVEA) is not valid. This is achieved by reinterpreting the quantized form of the master equation of mode locking as an equation of motion for the electric field rather than for the creation operator of a photon. It is found that in this formulation quantum correlations exist that are not present in the SVEA. The correlations become evident in the spectrum of the zero-point fluctuations and therefore in the background noise of the laser. This behaviour can be detected by homodyne detection of the laser output. The linewidth of the frequency comb generated by the mode-locked laser is not affected by these correlations and is given by the Schawlow–Townes linewidth of an equivalent continuous wave taking the additional intracavity loss due to the mode locking process into account.