Kerr-resonanced bifurcation switching in a photonic Ising machine with a long lossless optical fiber loop

We describe in detail the optical Kerr nonlinearity in our photonic Ising machine (PIM), which employs ultrahigh-speed optical pulse propagation in a lossless fiber loop. Although the peak power of the pulses in the fiber loop is set as low as ∼1 mW, the present PIM requires ultralong-distance pulse propagation of the order of 100,000 km (e.g., ∼2,000 circulations in a 50 km loop) to calculate large-scale optimization problems. As a result, a nonlinear phase rotation of greater than π/2 is accumulated due to the Kerr effect. This nonlinear phase rotation makes it possible to couple between the real (<i>I</i>) and imaginary (<i>Q</i>) parts of the recirculating optical pulse. Thus, as the amplitude of the <i>I</i>-channel changes due to the nonlinear phase rotation, the <i>Q</i>-channel also varies accordingly, and vice versa. We show that this mutual coupling gives rise to a new phenomenon, which we name Kerr-resonanced bifurcation switching, where the accumulated nonlinear phase rotation results in a periodic dip in the cut value of a max-cut problem. This dip phenomenon can be understood as a consequence of optical power peaking in a nonlinear optical fiber loop resonator with Kerr phase rotation. Finally, we propose a method for preventing dip generation by combining a large core fiber and a chirped fiber Bragg grating (CFBG) over a short length, which can reduce the Kerr-induced nonlinear phase rotation.