This web page contains information about our recently published article in Science "Strong Interactions in Multimode Random Lasers".

The image on the left shows a planar realization of a random laser that is pumped with incoherent light from the top and emits coherent light in random directions. In a random laser, light is confined to a gain medium not by conventional mirrors but by random multiple scattering. (Image courtesy of Robert Tandy & Science Magazine)

Please credit Science Magazine & Robert Tandy

Conventional laser versus a diffusive random laser: (a) A conventional laser cavity has highly-reflecting mirrors which trap light long enough for amplification by the gain medium (light blue) to be efficient. The oscillation frequencies are well-defined and are given by "resonance conditions": light has to make an integer number of oscillations upon a roundtrip ("loop") along the length of the cavity. (b) In a random laser, the trapping of light is not achieved by mirrors, but by multiple scattering between sub-wavelength particles (red dots) in this specific realization. In such a random medium the light emitted by an atom (yellow) can make a roundtrip in an infinite number of loops (two of which are indicated). In the special case of a diffusive random laser, the scattering is so weak that without gain most of the light would escape before returning to its starting point. Due to this strong damping (leakage), the oscillation frequencies of such a system are not well-defined. However, when lasing sets in, a number of well-defined, sharp oscillation frequencies appear (see Figure 3) which bear no straightforward relationship to the strongly damped natural oscillations of the system without gain.

Please credit Science Magazine & Li Ge

Diffusive random lasers produce coherent laser light at several frequencies (multi-mode lasing). Strong interactions between modes suppress a large number of possible oscillation frequencies of the system, leading to a well-separated frequency spectrum under the gain curve (black dashed curve) as shown above. While the emission intensities of the individual lasing modes are highly susceptible to spatial fluctuations of the pump source, emission frequencies remain relatively stable (solid lines show intensities for uniform pumping and dashed lines for nonuniform pumping). The circular insets display the field distributions of the lasing modes specific to each lasing frequency (white circles mark the boundary of the gain medium).

Our approach to laser theory is different from all previous approaches we are aware of in that we formulate a time-independent theory of the steady-state of a laser which is "ab initio": given the laser resonator and simple properties of the gain medium we predict the output power as a function of the pump, the number of lasing modes, the lasing frequencies and the spatial dependence of the electric field inside and outside the resonator. Previous theories were based either on time-dependent simulations or on the assumption that passive cavity resonances (often assuming perfectly reflecting mirrors and no leakage) describe the lasing modes. For random lasers, the time-dependent simulations are difficult to do (but there are some) and hard to interpret, and they don't answer the question: what is the nature of the lasing modes in a random laser. The passive cavity approach fails spectacularly. As we show in our paper, the lasing modes have little to do with the passive cavity resonances.

We implemented our analytic formulation in a detailed code, the first of its kind. It solves the self-consistent equation we have derived for the lasing state and outputs all the physical quantities. The results are much easier to obtain and to interpret than those of time-dependent simulations. Ultimately, we hope that such a code could be used as a design tool for micro- and nano-lasers.

We are currently making detailed quantitative tests of our approach, by comparing it to full simulations of the Maxwell-Bloch lasing equations. Initial results are positive and we hope to prove that our approach can replace these simulations in many situations. This will make arbitrarily complex laser systems accessible to theoretical design, whereas up to now the field of microlasers is approached very empirically.

In addition, we have just begun to understand random lasers using our approach and there is a lot of new questions that our findings have spawned. First and foremost, we want to characterize and understand fully the statistical properties of random lasers operating in various regimes, and see how they relate to other disordered photonic or electronic systems. Ultimately, we hope their statistical properties can be predicted fully analytically and further experiments can be done to confirm the theory.

Finally, our theory is an improved version of what is called "semiclassical laser theory" in the textbooks; that means that we do not treat the electromagnetic field quantum-mechanically. All of the noise and coherence properties of lasers require a quantum treatment; it will be fascinating to see if our new insights into the non-linear lasing states can be generalized and used to improve our understanding of the quantum properties of novel and complex lasers.

For many of the proposed applications of random lasers, it is important to know how stable the lasing frequencies are over time and with respect to different pump conditions. Our theory is able to provide answers to such questions. Also the interaction between laser modes ("spatial hole burning") and its consequences on lasing thresholds and output intensities are fully accessible by our theoretical framework. Finally, there is the issue of Anderson localized random lasers versus diffusive random lasers, which makes a distinction between the lasing properties based on the strength of scattering provided by the sub-wavelength particles. The spatial distribution of modes as well as the distribution of frequencies and lifetimes in these two regimes are expected to be drastically different. At least this is the expectation from the linear scattering properties. It remains to be seen how the non-linearity and the resulting interactions modify this expectation in the steady state.

Our approach replaces the passive cavity resonance picture, and works in the highly non-linear regime of lasing well above threshold. Also it treats the openness of the laser cavity system exactly in terms of functions we term “constant flux states”. Therefore, in our most optimistic scenario, this approach would become the standard way to solve and understand the semiclassical laser theory in textbooks. Ultimately it becomes part of the answer to the question: how does a laser work?

Future research in designing novel micro and nanolasers can benefit from this approach, and we are implementing some of these ideas already with experimental collaborators to improve, e.g. power output, directional emission, etc. These applications are in general not related random lasers.

Finally, our results specifically on random lasing may have important general implications e.g. for the physics of disordered and (wave-)chaotic systems in a non-linear medium. It is now clear from our work that a proper description of the statistical properties of random lasing, for instance, has to take into account the strong modal interactions that we find. In some respects, this problem is the analogue of the physics of interacting electrons in a disordered landscape -- a cornerstone problem of condensed matter physics -- for a bosonic field.

A short popular science article by Diederik S. Wiersma on Random Lasers which appeared in Nature.

A review article by Yale Professor Hui Cao on random lasing in Optics & Photonics News.

A newspaper article on the laser work in our group in Yale Scientific.

Postdoctoral Fellow at the Institute of Quantum Electronics, ETH Zurich

8093 Zurich, Switzerland

tureci [at] phys.ethz.ch

Li Ge (top right)

Graduate Student at the Department of Physics, Yale University

CT-06520 New Haven, USA

li.ge [at] yale.edu

Stefan Rotter (bottom left) (previously at Yale)

Staff member at the Institute for Theoretical Physics, TU Vienna

1040 Vienna, Austria, EU

stefan.rotter [at] tuwien.ac.at

A. Douglas Stone (bottom right)

Carl A. Morse Professor at the Department of Applied Physics, Yale University

CT-06520 New Haven, USA

douglas.stone [at] yale.edu