Efficient first-principles inverse design of nanolasers

Abstract

We develop and demonstrate a first-principles approach, based on the nonlinear Maxwell-Bloch equations and steady-state ab-initio laser theory (SALT), for inverse design of nanostructured lasers, incorporating spatial hole-burning corrections, threshold effects, out-coupling efficiency, and gain diffusion. The resulting figure of merit exploits the high-$Q$ regime of optimized laser cavities to perturbatively simplify the nonlinear model to a single linear ''reciprocal'' Maxwell solve. The consequences for laser-cavity design, and in particular the strong dependence on the nature of the gain region, are demonstrated using topology optimization of both 2d and full 3d geometries.

Figures (7)

• Figure 1: (a) Schematic nanolaser: pump power $P_\text{pump}$ excites a gain profile $D_0$ and a lasing mode that outputs power $P_\text{out}$ into a channel (waveguide), for a cavity (from Sec. \ref{['sec:benchmark']}) that maximizes efficiency $\sim P_\text{out} / P_\text{pump}$. (b) Lasing amplitude $|a_0|^2$ ($\sim\text{energy}$) vs. pump strength $d$, lasing above a threshold $d_\text{thresh}$. (c) Change $\Im\{\Delta \omega \}$ in modal gain/loss depends nonlinearly on amplitude $|a|^2$, and stabilizes at $|a_0|^2$, where $\Im\{\Delta \omega\}=$ passive cavity loss $\gamma_0$.
• Figure 2: Coupled optical system composed of a waveguide guiding an input field with amplitude $s_\text{in}$ and an output field with amplitude $s_\text{out}$, coupled to a cavity with an amplitude $a_1$ through the decay rate $\tau_\text{wg}$.
• Figure 3: Performance of inverse designed devices for increasing active region sizes $\sigma_{\text{g}}$. (a) Evaluation of the nonlinear FOM normalized by the gain region size-dependent factor $\zeta(\sigma_g)=\max\left\{|\mathbf{E}_\text{in}|^2\right\}\left(\int_\Omega D^*_0(\sigma_g) \mathop{}\!\mathrm{d} \Omega\right)^2$, for designs optimized for the naive FOM (green) and nonlinear FOM (yellow). The gain profile $D_0$ is shown in (b), (c), and (d) in max-normalized units for increasing active region sizes. The standard deviation $\sigma_{\text{g}}$ of the gain profile is marked in a dashed white line. In the gain profile for the nonlinear device in (d), the active region size $\sigma_{\text{g}}$ is explicitly shown for illustration purposes.
• Figure 4: Electric-field norm $|\mathbf{E}(\mathbf{r})|$ in devices optimized for a gain medium of standard deviation $\sigma_{\text{g}} = 500$ nm. The fields are expressed in max-normalized units.
• Figure 5: Spatial profile of the gain medium $D_0(\mathbf{r})$ with a standard deviation $\sigma_{\text{g}}=250$ nm, the diffused gain medium $\mathbb{S}[D_0](\mathbf{r})$, for a diffusion length of $R_0=5\,\upmu\text{m}$, and the electric-field norm $|\mathbf{E}(\mathbf{r})|$ of the cavity mode for the inverse designed cavity not accounting (left) and accounting (right) for diffusion. All fields are expressed in max-normalized units.