Figure 4

Probability distributions of the field quadratures, amplitude, and phase in ring lattices with off-diagonal disorder. (a–d) Probability distributions of the (a) real quadrature, (b) imaginary quadrature, (c) amplitude, and (d) phase of the complex optical field at different output sites x after propagating through an even-sited ring lattice. The real (imaginary) quadrature vanishes on the odd (even) sites, and the phase takes binary values with equal probability: 0 or π \((\pm \pi \mathrm{/2})\) at even (odd) positions. (e–h) Same as in (a–d) for an odd-sited ring lattice. (g) Amplitudes of the fields take Rayleigh-like distributions. (h) Phase distributions reflect an intermediate stage between discrete and uniform probability distributions.