Non-Hermitian Engineering of Synthetic Saturable Absorbers for Applications in Photonics

We explore a type of synthetic saturable absorber based on quantum-inspired photonic arrays. We demonstrate that the interplay between optical Kerr nonlinearity, interference effects, and non-Hermiticity through radiation loss leads to a nonlinear optical filtering response with two distinct regimes of small and large optical transmissions. More interestingly, we show that the boundary between these two regimes can be very sharp. The threshold optical intensity that marks this abrupt “phase transition” and its steepness can be engineered by varying the number of the guiding elements. The practical feasibility of these structures as well as their potential applications in laser systems and optical signal processing are also discussed.

Figure 1

Schematic of a nonlinear $J_x$ array made of seven waveguide elements. The coupling profile is symmetric around the central channel and values of the coupling coefficients are indicated. The array length $\xi =L\equiv \pi /2$ is chosen to provide coherent perfect transfer under linear conditions. The Kerr nonlinear coefficient in these arrangements is a function of the material properties and the mode confinement inside the waveguide. In our proposed saturable absorber scheme, light is launched in and collected from in the leftmost port. The other additional ports serve as a mean to introduce optical loss either by direct radiation into free space or by introducing physical loss as explained in the text.

Figure 2

(a) Transmission coefficient between the input and output ports as defined in Fig. 1 as a function of the nonlinear parameters (or input light intensity) for $J_x$ arrays made of three, seven, and eleven waveguides, respectively. (b) A comparison with the performance of a uniform array as described in the text. Evidently, $J_x$ arrays provide an abrupt transition between the off and on regimes—an effect that is not observed in uniform arrays. Note that the nonlinear response of the uniform array for $M=7$ and 11 is almost identical. The black arrows in (a) indicate roughly the location of ${\alpha }_{\mathrm{TH}}$ on each curve. The transition region is indicated on the $M=11$ curve by the black and red arrows. (c) Nonlinear response under edge excitations in a simple directional coupler with coupling coefficient ${\kappa }_u=1$ (curve $C$) and uniform arrays with seven waveguide channels when the coupling is ${\kappa }_u=1$ ($S_1$), ${\kappa }_u=2$ ($S_2$), and ${\kappa }_u=3$ ($S_3$), respectively. In the directional coupler case, we observe smooth but not very abrupt (compared to the $J_x$ array) transition. For larger uniform arrays, we observe a smooth transition for small coupling coefficients. As the coupling increases, the transition becomes sharper and is accompanied with fast oscillatory behavior.

Figure 3

Light-transport dynamics in a nonlinear $J_x$ array made of seven waveguides under different input light intensities as quantified by the value of the nonlinear parameter: (a) $\alpha =0$, (b) $\alpha =10$, (c) $\alpha =11.3$, and (d) $\alpha =12$. For a wide range of $\alpha$, the self-trapping effects are not strong enough to prevent light diffraction and force the optical intensities to be confined in the same input channel. However, at a certain light-intensity threshold (defined in the text by ${\alpha }_{\mathrm{TH}}$), strong spatial soliton effects emerge, leading to a sudden and sharp increase in the transmission coefficient.

Figure 4

The dependence of the threshold intensity characterized by ${\alpha }_{\mathrm{TH}}$ and transition steepness defined by ${(dT/d\alpha )}_{{\alpha }_{\mathrm{TH}}}$ on the array size. Our numerical results indicate that ${\alpha }_{\mathrm{TH}}$ scales with the coupling between the edge waveguide and its neighbor channel $g_{\text{edge}}=\sqrt{2N}$. We also find that the slope ${(dT/d\alpha )}_{\mathrm{TR}}$ follows a quadratic function with the array size to within 7%.

Figure 5

Transmission dynamics in a $J_x$ array made of seven waveguides as a function of the input light intensity when light is launched and collected from the same channel for waveguides number two, three, and four, respectively, after a normalized propagation distance of $\xi =L\equiv \pi /2$. Note that interference effects play an important role in these cases, leading to oscillatory behavior. When light is launched in the central channel, a low-transmission band (defined by intensity range rather than frequency range) exists between high-transmission bands—a feature that might find applications in laser systems.

Figure 6

Nonlinear wave propagation in the $J_x$ array studied in Fig. 5 when light is excited at the central waveguide for $\alpha =0$, 9, 12, 14.5, 16.5, and 18, respectively are depicted in (a)–(f). From the plots, we can see that the interplay between nonlinear self-localization effects, reflection from the array edges, and interference lead to the oscillatory transmission behavior observed in Fig. 5.