Tracking nanoscale perturbation in active disordered media Renu Yadav1 Patrick Sebbah2 Maruthi M. Brundavanam1 and Shivakiran Bhaktha B. N.1 1Department of Physics Indian Institute of Technology Kharagpur Kharagpur-721302 India

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Tracking nanoscale perturbation in active disordered media

Renu Yadav1, Patrick Sebbah2, Maruthi M. Brundavanam1, and Shivakiran Bhaktha B. N. 1∗

1Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India

2Department of Physics, The Jack and Pearl Resnick Institute for Advanced Technology,

Bar-Ilan University, Ramat-Gan, 5290002 Israel

The disorder induced feedback makes random lasers very susceptible to any changes in the scat-

tering medium. The sensitivity of the lasing modes to perturbations in the disordered systems have

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.

I. INTRODUCTION

A random laser (RL) is an optical device that utilizes

the disorder in the system for the optical feedback. Unlike

conventional lasers, no well-deﬁned cavities are present in

RLs. The idea of feedback by multiple scattering was ﬁrst

proposed by Letokhov [1] and has been extensively used

to realize random lasing in a variety of disordered sys-

tems [2–8]. Two types of RLs have been reported namely,

coherent RLs and incoherent RLs, depending on whether

the scattering induces the feedback in the ﬁeld or the

intensity, respectively [9]. The scattering strength deter-

mines the lasing characteristics such as the lasing thresh-

old of the system, spatial conﬁnement of the modes, etc.

Based on the scattering strength, disordered systems can

be broadly divided into two categories, namely, strongly

scattering and weakly scattering systems. In the strongly

scattering systems the lasing modes are localized well

within the system and are identical to the quasi-bound

(QB) states of the passive system [10–12], whereas, in

weakly scattering systems the lasing modes extend all over

the system [12, 13].

Unlike conventional lasers, RL emission is random in

wavelength, omnidirectional [4] and has low spatial and

temporal coherence [14–16]. These properties make them

suitable for diﬀerent applications like, imaging [17], dis-

plays and lighting [18], holography [19], etc., but it lim-

its their use where speciﬁc wavelength or unidirectional

emission is required. Spatial light modulators (SLMs)

have been used to shape the pump intensity proﬁle to

control the emission and directionality of RLs making

them useful for diﬀerent applications [20–26]. As the

∗Correspondence email address: kiranbhaktha@phy.iitkgp.ac.in

feedback in RLs is provided by disorder-induced scatter-

ing, the lasing modes are very sensitive to any changes in

the scattering medium. This makes RLs a natural candi-

date for designing sensors for various applications. The

strong dependence of emission characteristics of RLs on

the scattering properties of the medium have been uti-

lized to assess nanoscale perturbations [27]. The moni-

toring of single nanoparticle perturbation enables to de-

tect single virus, bacterium and biolmolecule. Random

lasers have been used as a diagnostic tool for bio-imaging

and bio sensing in various biological structures inﬁltrated

with dye [5, 28, 29]. The nanoscale deformation and pre-

failure damage in bones can be detected by monitoring

the shifts in the random lasing peaks [30]. In ex-vivo

dye inﬁltrated human tissues, the changes in the emis-

sion spectrum have been observed in malignant tissues as

compared to the healthy ones [31]. The cancerous tissues

of diﬀerent grades of malignancy can be diﬀerentiated as

they exhibit diﬀerent lasing spectra for same pump en-

ergy [32]. RLs have been proposed as an in-vivo tool to

diﬀerentiate between skin, fat, muscle and nerve tissues

during laser surgery [33].

In this work, RLs have been proposed as a tool to map

the regions of nanoscale perturbation in several random

media. A two dimensional (2D) active disordered system

has been considered and nanoscale perturbations have

been introduced in the medium. Using ﬁnite diﬀerence

time domain (FDTD) method [34] the modes and the

corresponding spatial ﬁeld distributions for the system

before and after the perturbation have been computed.

In the past, RLs have been used to detect changes in

the scattering medium [27]. In this work we go a step

further and show numerically that it is also possible to

identify the position of the perturbation with good preci-

sion. A small perturbation in the system leads to minute

changes in the spectral position of the modes and their

arXiv:2210.02743v1 [physics.optics] 6 Oct 2022

corresponding spatial ﬁeld distributions, but the individ-

ual modes do not provide any information about the lo-

cation of the perturbation. So, a tracking parameter is

deﬁned which takes into account the cumulative eﬀect of

changes in the modes, to map the region of perturbation.

We ﬁnd that its mapping converges to the defect location

when the number of modes increases. This ﬁnding paves

the way to single particle tracking in disordered systems.

The theoretical explorations in this work provide an ini-

tial framework to utilize RLs in the ﬁeld of diagnostics

to monitor and track the growth of tumors in disordered

biological systems.

II. NUMERICAL METHOD AND

COMPUTATIONAL DETAILS

A 2D disordered system of size, L2= 5 ×5µm2has

been considered. It consists of circular particles with

radius, r= 60 nm and refractive index, n2= 2.54,

randomly distributed in a background medium of re-

fractive index, n1= 1.53. The values of the refrac-

tive index have been chosen to mimic the presence of

T iO2particles in 4-(Dicyanomethylene)-2-methyl-6-(4-

dimethylaminostyryl)-4H-pyran (DCM) doped polyvinyl

alcohol (PVA) thin ﬁlms [35–37]. The background

medium has been chosen as the active part of the sys-

tem and modeled as a four level atomic system. The

surface ﬁlling fraction of the scatterers is 28%. In this

study, 2D FDTD computation has been carried out us-

ing transverse magnetic ﬁelds with a grid resolution of

∆x= ∆y= 10 nm, along xand ydirections, respectively.

In order to ensure the stability of the simulation, the time

step chosen is, ∆t= 2.37 ×10−17 s[38]. The parameters

used for the active medium are mentioned in Ref. [10].

The system is pumped uniformly with a Gaussian pulse

of central wavelength 532 nm and pulse duration ∼10−15

s at a pump level above the lasing threshold of system.

III. RESULTS AND DISCUSSION

The 2D active, random system was pumped above the

lasing threshold. The energy in the system was observed

to grow exponentially, and after some strong relaxation

oscillations, it eventually reaches a steady-state. The las-

ing modes of the system are calculated by the Fourier

transform of the time records of the ﬁeld after the system

has reached the stationary state. Several distinct peaks

are observed as shown in Fig. 1. The ten modes con-

sidered for further analysis are marked with arrows. The

discrete peaks in the emission spectrum indicate lasing

action with resonant feedback. The spatial ﬁeld distri-

bution of the modes is computed by taking the Fourier

transform of the ﬁeld recorded at each grid point. The

spatial ﬁeld distribution of the modes marked as (1-4)

in Fig. 1 is shown in Figs. 2(a-d). It is observed that

the modes are conﬁned well within the system, indicating

that the system is strongly scattering. The numerically

computed scattering mean free path for the system using

Mie scattering theory is, ls≈0.3µm [39]. The local-

ization length for the system is calculated by considering

the ﬁeld intensity proﬁles of modes averaged along xor y

directions. The averaged intensity proﬁle exhibits strong

local ﬂuctuations but its envelope decays exponentially

whose characteristic length, gives the localization length

of the modes. The average localization length calculated

for the system is, ξ≈2.6µm. The scattering mean free

path and the localization length also indicate that system

is strongly scattering and the modes are conﬁned well

within the system, respectively.

FIG. 1: Emission spectra of the unperturbed system and

the system with a single particle perturbed by 10 nm at

three diﬀerent locations in the system. Ten peaks

considered are marked with arrows. The labeled modes

are 607.45 nm (1), 613.20 nm (2), 623.01 nm (3), and

626.13 nm (4). The inset shows the magniﬁed image of

the region marked with dashed magenta line. It shows

the spectral shift of the mode as the perturbation is

introduced in the system.

Next, in order to introduce a single nanoscale pertur-

bation in the system, a randomly chosen scatterer was

displaced by 10 nm along an arbitrary direction. The

numerical parameters limit the minimum and the maxi-

mum perturbation that can be introduced in the system.

The minimum displacement cannot be smaller than the

grid resolution and maximum displacement possible is de-

pendent on the surface ﬁlling fraction of the system. In

realistic systems, such limitations don’t exist and hence

it is expected that even smaller perturbations can be de-

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TrackingnanoscaleperturbationinactivedisorderedmediaRenuYadav1,PatrickSebbah2,MaruthiM.Brundavanam1,andShivakiranBhakthaB.N.11DepartmentofPhysics,IndianInstituteofTechnologyKharagpur,Kharagpur-721302,India2DepartmentofPhysics,TheJackandPearlResnickInstituteforAdvancedTechnology,Bar-IlanUniversity,R...

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Tracking nanoscale perturbation in active disordered media Renu Yadav1 Patrick Sebbah2 Maruthi M. Brundavanam1 and Shivakiran Bhaktha B. N.1 1Department of Physics Indian Institute of Technology Kharagpur Kharagpur-721302 India.pdf

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Tracking nanoscale perturbation in active disordered media Renu Yadav1 Patrick Sebbah2 Maruthi M. Brundavanam1 and Shivakiran Bhaktha B. N.1 1Department of Physics Indian Institute of Technology Kharagpur Kharagpur-721302 India

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