Our effort is directed at studying the transport of optical waves through media which have a variation in the refractive index over length scales comparable to the wavelength. These experiments mostly deal with radiation at or near visible wavelengths. The structure can be ordered, or disordered, or even a combination of both. While some parallels can be drawn with the propagation of electrons in crystals, there also exist significant differences. For example, light can experience amplification which leads to fascinating phenomena hitherto unpredicted by theoretical studies. The existence of sophisticated laser sources, light detectors, and nanofabrication techniques makes it possible to experimentally study even the most elusive of phenomena. We aim to study light propagation through such nanostructured media in a passive, active, dielectric or a metallic environment. In this website, we broadly summarize the focus areas of this laboratory. To know more details of our studies, email us!
Transition from sub-threshold emission to diffusive random laser to coherent random laser.
When optical gain is added to a medium with a random variation in its refractive index, a fascinating synergy of coherent amplification and multiple scattering occurs within the medium. The result is a drastic change in the emission characteristics of the system, which originates from the novel gain dynamics realized by the inhomogeneous structure. Ballistic propagation of light within the medium (that would occur in absence of the structure) is completely inhibited by the varying refractive index, and the light is made to undergo a Gaussian random walk that approximates a diffusion-like propagation while concomitantly undergoing optical amplification. Unlike a regular laser, the mode that eventually supersedes the emission is not chosen by any geometric resonance, but rather by the gain profile. The spectral profile narrows by roughly an order of magnitude. Refer to the figure, which shows the green profile collapsing in bandwidth to yield the blue profile.
Further to this behaviour, a dependence on two parameters is observed, namely, the degree of disorder, and the gain cross-section. When the two parameters are just right, the emission undergoes a transition from incoherent to coherent, and the spectrum further narrows by another order of magnitude, creating ultranarrow lasing modes. This is the critical regime of random lasing, which is realised by a combination of several factors occurring simultaneously, namely, mode competition, local pockets of ultrahigh gain, finite size effects and so on. All these factors, in turn, are realized solely by the disorder. Refer once again to the figure wherein the red profile depicts the ultranarrow modes.
At a critical degree of disorder, the diffusive modes of light are also inhibited by mesoscopic interferences within the system, and the transport comes to a halt. This manifests as closed-loop random paths inside the medium within regions that harbour exponentially decaying optical wavefunctions, known as Anderson localized modes, at the resonant frequencies. Again, these resonances are strictly mesoscopic, and not geometric. When gain is introduced over such a loop, it excessively amplifies the resonant frequency, which results in the occurrence of ultranarrow modes.
Light amplification in random media is a rich field of physics, wherein the above-mentioned and more phenomena have been observed. The physics is of interest to optics specialists, condensed-matter physicists, statistical physicists alike. We study this field through sophisticated experiments, coupled with advanced modelling techniques based on Monte Carlo methods of photon propagation, and finite difference time domain simulations. In fact, we were the first ones to apply a three-dimensional Gaussian random walk model to random lasing, which explained a few of the spectral features. We subsequently improvised this model to explain the ultranarrow lasing modes.
The samples used for study in our laboratory are often structured over few tens of nanometers, which is an order of magnitude smaller than the wavelength of light.
In such cases, imaging of the sample is impossible using conventional techniques because of the diffraction limit. A scanning probe method needs to be used in such cases.
A scanning probe microscope uses an ultrasmall probe, the size of which is maintained to be of the desired resolution. The probe interacts with the sample at very close distances (5-10 nm) in such a manner that as it scans the surface,
it gives the information of the topography of the surface. The advantage with the near-field scanning optical microscope (NSOM) is that simultaneous to the topography map, it provides a direct image of the light field within
the resonator. This measurement is crucial in inferring about the correlations in structure and field distribution.
SEM of a sharp tip, size about 80 nm.
We are in the final stages of constructing a near-field microscope. We have succeeded in fabricating ultra-fine silica tips of dimensions upto 50 nm, by pulling an optical fiber under the heat
of a CO2 laser. The neighbouring image shows the scanning electron micrograph of a tip with 80 nm tip size.
Topography scan of a test sample.
Topography measurements are based on the vibrating tuning fork technique. The sharp tip is glued to a quartz tuning fork, and is oscillated in the vicinity of a surface. The amplitude of tip
scillations is sensitive to the shear force subtended by the surface of the tip, and can be calibrated and used to maintain the tip at a fixed distance of a few nanometers from the surface.
A raster scan of the surface then creates a virtual image of the topography. The neighbouring image shows the topography of a test sample. Subsequently, the light scattered from the surface is
guided by the optical fiber to a photodetector to create an optical image.
Probability density distribution of Anderson localized modes.
Generally, when radiation is transported through matter, it suffers from dissipation due to the natural absorptive properties of the material. In a scattering medium, some very exotic behaviour can be expected
due to the interplay of scattering of waves and their interference. However, the presence of absorption inhibits the observation of this behaviour. So when samples are created such that they are smaller than
the absorption length-scales, and yet scattering, then we can see the manifestation of interference. Such small scales are the mesoscopic scales, and the phenomena are called mesoscopic.
With light, we have an advantage of designing our media such that absorption length-scales become rather large, and such phenomena become measurable. As examples, conductance fluctuations, coherent
backscattering of light, or Anderson localization of light are direct consequences of interference of waves in disorder. Experiments in the lab are aimed to observe these, and similar, mesoscopic effects.
The figure shows calculated intensity distribution of light in a two-dimensional localizing medium. Two localized states are observed, that are spatially separated from each other.
The intensity decays exponentially outwards from the maximum. Localization occurs only after a critical disorder in three dimensional systems, while in lower dimensional systems,
all states are localized, and the size of the sample determines the probability of observing them.
Photonic crystals involve a periodic lattice of two constituent materials which create a bandgap for light which forbids propagation for the relevant frequencies.
They are the proven mechanism of controlling and manipulating light over small distances. Defects introduced in the lattice lift the bandgap at small, local regions thus allowing propagation,
leading to formation of devices such as waveguides and resonators, that guide light, bend it sharply, or store it in small regions.
Intensity distribution in the line defect resonator.
Our object of interest is the line defect heterostructure resonator, which confines light on the virtue of waveguide-mode gaps, unlike conventional resonators that rely on photonic band gaps.
We have studied field distributions of such resonators, and furthermore, we have observed a shift in the resonant frequency of the resonator when it interacts in the near-field with an NSOM tip.
Tunability range as a function of tip-sample distance, for various parameters.
The architecture of the line defect resonator offers a few physical parameters that can be tuned to actively control the resonant frequency of the resonator in real-time using the NSOM tip. We have recently
numerically analyzed this shift by varying the parameters. These studies suggest that such real-time tuning using the NSOM tip is an attractive method to achieve control on active photonic devices.
Our recent publications
Discrepant transport characteristics under Anderson localization at the two limits of disorder.
Randhir Kumar, Sandip Mondal, M. Balasubrahmaniyam, Martin Kamp and Sushil Mujumdar
Prof. Mujumdar completed his PhD in 2001 from the Raman Research Institute, Bangalore in the field of light propagation in passive and active random media.
He followed up with postdoctoral research in coherent random lasing and near-field optics in LENS, Florence, University of Alberta, Canada, and ETH, Zurich.
He joined TIFR, Mumbai in 2006 and set up a programme on Nano-Optics and Mesoscopic Optics
Anderson localization of light in 2-D disordered photonic crystal with kerr-nonlinearity. Machine Learning in complex photonic systems Contact
email: sandip . mondal @ tifr . res . in
Vikas joined TIFR in August 2019 as an Int. PhD student. He finished his 4-years B.Sc degree in Physics from Shiv Nadar Univisity, Greater Noida in 2019. From January 2021, he has started Departmental Project-I in our lab.
Research Interests Contact
email: vikas . bhat @ tifr . res . in
Rounak joined TIFR in August 2019 as an Int. PhD student. He gratuated with honours in Physics from St. Xavier's College (Autonomous), Kolkata in 2019. From January 2021, he has started Departmental Project-I in our lab.
Research interests: Contact
email: rounak . chatterjee @ tifr . res . in