Figure 1

(a) Minimum value $C_{i=0}^{\mathrm{in}}$ of the quadrature quantum optical noise of the ground intracavity mode versus the disorder potential amplitude $\Delta V$ (normalized to the mode homogeneous broadening $\mathit{\Gamma }$). The dotted line ($C_{i=0}^{\mathrm{in}}=1$) is the standard quantum limit. The solid line is calculated under the condition that only the ground mode is driven coherently, while all the other modes are in the vacuum state. The dashed line is obtained by considering a thermal population $N_{i\ne 0}^{\mathrm{th}}=20$, while only the ground mode is coherently pumped. (b) Minimum value $S_{i=0}^{\mathrm{out}}$ of the quadrature noise of the extracavity field which has the same transverse profile as the ground intracavity mode. (c) Surface plots of the disordered potential (bottom) and of the ground mode photonic wave functions (top) for the different amplitudes (i)–(iii) of the disorder potential, also indicated in (a) and (b). Parameters: $100\mu \mathrm{m}\times 100\mu \mathrm{m}$ system with periodic boundary conditions; disorder potential with correlation length ${\lambda }_c=5\mu \mathrm{m}$; $\hslash {\omega }_{k_z,0}=1.5\mathrm{eV}$; $ϵ=13$; $g=0.01\mathrm{meV}\mu {\mathrm{m}}^2$; $\hslash {\mathit{\Gamma }}^{\mathrm{rad}}=0.095\mathrm{meV}$; $\hslash {\mathit{\Gamma }}^{\mathrm{NR}}=0.005\mathrm{meV}$; ${\omega }_p={\omega }_{i=0}+\mathit{\Gamma }$. Averaging over 100 disorder configurations.Reuse & Permissions

Figure 2

(a) Solid line: Localization length $L_0$ of the ground mode normalized to the system size $L_{\mathrm{plane}}$ versus the normalized disorder amplitude $\Delta V/\mathit{\Gamma }$. Dash-dotted line: Averaged frequency gap $⟨{\omega }_{i=1}-{\omega }_{i=0}⟩$ between the first excited and the ground modes, normalized to the broadening $\mathit{\Gamma }$. (b) Solid line: Effective number $N_{\mathrm{eff}}=\pi \mathit{\Gamma }{W}_{\mathrm{DOS}}({\omega }_0)-1$ of modes weighted by the nonlinearity to the ground mode. Dashed line: Actual number $N_{\mathrm{act}}=\pi \mathit{\Gamma }{\rho }_{\mathrm{DOS}}({\omega }_0)-1$ of modes, by taking into account the normal density of states.Reuse & Permissions