Tracking nanoscale perturbation in active disordered media

Disorder-induced feedback makes random lasers very susceptible to any changes in the scattering medium. The sensitivity of the lasing modes to perturbations in the disordered systems has been utilized to map the regions of perturbation. A tracking parameter that takes into account the cumulative effect of changes in the spatial distribution of the lasing modes of the system has been defined to locate the region in which a scatterer is displaced by a few nanometers. We show numerically that the precision of the method increases with the number of modes. The proposed method opens up the possibility of application of random lasers as a tool for monitoring locations of nanoscale displacement, which can be useful for single-particle detection and monitoring.

Figure 1

Emission spectra of the unperturbed system and the system with a single particle perturbed by $10\text{nm}$ at three different locations in the system. Ten peaks considered are marked with arrows. The labeled modes are (1) 607.45 nm, (2) 613.20 nm, (3) 623.01 nm, and (4) 626.13 nm. The inset shows the magnified image of the region marked with a dashed magenta line. It shows the spectral shift of the mode as the perturbation is introduced in the system.

Figure 2

Spatial field distribution of modes marked as 1–4 in Fig. 1, (a–d) before and (e–h) after a single particle is displaced by $10\text{nm}$. The perturbed particle is marked in blue.

Figure 3

Variation of $C_E$ with the spectral shift ($\mathrm{\Delta }\lambda$) in the lasing modes due to perturbation introduced in the system. The solid line represents the linear fit to the data points. The data points marked in red squares correspond to modes 1–4 in Fig. 2.

Figure 4

The maps generated to locate the position of perturbed particle with the help of TP. The TP mapped regions when number of modes (a) $N$= 1, (b) $N$= 2, (c) $N$= 4, (d) $N$= 6, (e) $N$= 8, and (f) $N$= 10 are considered for the particle perturbed by $10\text{nm}$ at location 1 (Fig. 1). The perturbed particle is marked in blue.

Figure 5

(a–d) Maps generated with the help of TP to locate the position of a particle perturbed by $10\text{nm}$ at different locations in the system. The perturbed particle is marked in blue. (e) The proximity parameter $P$ as a function of number of modes ($N$) for systems in (a)–(d) and for the system in Fig. 4 [marked as (e)].

Figure 6

Maps generated with the help of TP to locate the position of a particle perturbed by (a) 20, (b) 30, (c) 40, and (d) $50\text{nm}$ at location 1 in the system. The perturbed particle is marked in blue. (e) The proximity parameter for different values of displacements in (a)–(d).

Figure 7

The 2D disordered system considered for simulation.

Figure 8

Semilogarithmic representation of energy of RL system as a function of time, recorded during the growth of laser emission above the lasing threshold.

Figure 9

Flowchart of the FDTD algorithm.