Control of interacting spin-pulse waveforms in an oscillator-less photonic Ising machine and its similarity to the AM...

We describe the operating mechanism of a photonic Ising machine (PIM) using ultrahigh-speed optical pulse transmission technology in an optical fiber loop from the perspective of the AM mode-locking of lasers. Although this PIM does not generate pulses like a conventional mode-locked laser, the theory of the AM mode-locking of a laser can be used to explain the operating principle of the present PIM when the feedback of coherent pulses is considered as equivalent gain. Specifically, we describe the existence of Gaussian-like steady-state pulses in the fiber loop of the PIM, the relationship between the recirculating pulse width and the spectrum, and the consistency with AM mode-locking theory as regards the optical filter width and pulse width. The time-bandwidth product of the pulses in the loop is approximately 0.44, and the waveform in the time domain closely matches that of a Gaussian pulse. Furthermore, the calculation of (Δf)^1/2Δτ, where Δf is the full width at half maximum (FWHM) of the optical filter, and Δτ is the FWHM of the recirculating pulse width in intensity, revealed that it remains nearly constant, indicating that the pulses in the loop satisfy the relationship predicted by the AM mode-locking theory. In addition, an investigation of the bandwidth dependence of bifurcation switching showed that narrowing the bandwidth results in broader pulses, thereby reducing the peak value of the pulses and hence suppressing bifurcation switching caused by the Kerr effect. Finally, we investigated the auto stabilization effect of the pulse width and pulse amplitude caused by the gain saturation of the erbium-doped fiber amplifier (EDFA) and showed that a very stable bifurcation can be achieved.