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Random lasing: lasers sans mirrors

[Article posted on 25-February-2011]
Sushil A Mujumdar
©  Sushil A Mujumdar
Schematic of the random laser. Scatterers inside an amplifying medium trap the light within, to create coherent emission. Consequent changes in the spectrum are shown alongside.

To a layperson, the term LASER brings to the mind images of Luke Skywalker battling Darth Vader, with guns emitting resplendent red, green or blue beams of powerful light, which can cut through steel and shoot exactly in the direction the gunner wants. Power and directionality, precisely the two virtues that make the laser a laser, originate from a physical attribute called coherence, which essentially states that all light waves emitted by the laser are made of electromagnetic fields that oscillate in phase. Notwithstanding the Hollywoodish brouhaha, the term "laser" technically comes down to light with coherence; both power and directionality are the consequences thereof. However, to achieve this coherence in the laser device, a sophisticated amount of engineering has to go in, with precise alignments, ultrasmooth mirrors, exactly machined sizes etc required to make the laser. The precision engineering basically aims to create a mirror-based device (technically, a resonator) that can trap light into the material (the amplifier) that is emitting it in the first place. The trapping and amplification together creates the bright beam of laser light.

The term "random laser" elicits a response of disbelief and curiosity in the minds of people. Why random? Where are the mirrors? Where has the precision engineering gone? It turns out that, 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. (Note the sketch of scatterers in an amplifier.) This concoction approximately imitates a laser, but the coherence that it generates is very real. 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 modeling 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 majority of the experimentally observed features from random lasers. We are now working on parametrizing this amazing phenomenon, taking into account the rich statistical behavior it exhibits.

FAQ

Click on the question to see the answers and comments

Sandeep Jain : I'm curious - for a given input power, what is the output power delivered by this laser per square inch of the surface on which the laser is impacting, as a function of the distance of the surface from the laser, and how does this compare with the power delivered by a traditional laser?
  Sushil A Mujumdar : The system is currently known to work in the range of nanojoules energy, with the emission spot of the order of a few tens of micrometers. The temporal dynamics is self-regulated, and we estimate the lasing to last for about few tens of picoseconds. The energy drops rapidly as you go away from the surface, and since the wavefront is not spherical, we cannot estimate the drop as a function of distance. For comparison, the energy of a spherical wave drops as square of the distance. A conventional laser is capable of delivering huge power, mainly because it is able to absorb that much energy due to its structure and the involved medium. The random laser has not yet been constructed for high power emission/absorption, though its close cousin, the modeless laser, was shown to behave comparable to a pulsed dye laser. (Note that this cousin is externally seeded, and the random laser is self-seeded.)


Dr Ajoy Singh : Dear Sir, Can we use this medium to generate 300 femtosecond pulses with 10 micro joules pulse energy and a repitition rate of 1 mega hertz at 1040 nm wavelength ? We require such a laser for a medical application to treat blockages in arteries (to eliminate atherosclerosis from a region of the arterial tree).
  Sushil A Mujumdar : The random laser dynamics are self-regulated, being an interplay of scattering and stimulated emission. The timescales depend upon the lifetime of excited state molecules and the accelerated de-excitation due to stimulated emission. We estimate the pulse time to be few tens of picoseconds. Pulling it down by two orders of magnitude would be hard. Furthermore, there are hitherto no reports on pulse-compression of random laser pulses. Besides, the thrust of this research is to make smaller and smaller sources, so energies are limited by the size of the system. Routine experiments report nanojoules of energy emitted per pulse. The wavelength of 1040 nm is covered by an IR dye, and so should be possible to obtain, though not in every pulse. The repetition rate practically depends upon the excitation repetition rate, and 1 MHz is not out of the ordinary. Still, it is too ambitious to imagine this system to be used for a medical application at this stage.