Photonics in Random Media

In recent years, random lasing materials (e.g. powders, porous media, precipitates in solution, or photonic crystals with impurities) have been extensively studied experimentally. Pumping energy into these systems causes them to re-emit multi-mode coherent light, with a spectrum displaying randomly arranged peaks in frequency. Starting from the structure and geometry of the atoms and molecules that scatter the light waves, one would eventually want a theory that predicts the onset, the nature and the features of the light modes and answering the following questions.

  1. What shape and size do light modes display in space ?
  2. In which dimension and under which conditions do they localize because of disorder?
  3. On which frequencies do light modes emit in cavity-less media?
  4. Can there be a random laser pulse in time?
  5. Do competing random laser modes phase-lock as in multimode standard lasers?
  6. How strong is the coupling magnitude and how is it related to the coupling modes spatial overlap and the etherogeneous optical susceptibility?

The latter two questions are connected to the coupling property of depending on the spatial overlap of the electromagnetic fields of the interacting modes. This feature ascribes to the problem of assessing the structure of an interacting network of light-modes in a statistical mechanics representation. Indeed, a set of modes can interact only if their electromagnetic fields overlap in space and, in the lasing regime, non-linear amplification occurs only if the frequencies of the modes satisfy some kind of mode-locking condition. These rules strongly influence the set of feasible interactions in which each mode is viewed as a network node. A key challenge that we address is the characterization of the structure of this network of wave-modes, including the strengths and signs of the relevant random interactions, as is required, e.g., in order to distinguish apart physical regimes of laser stationary behaviour. To this aim a Hamiltonian theory has been derived and investigated in systems with different kinds of bond-disorder, ranging from standard ordered multimode mode-locking lasers to recently introduced glassy random lasers.

Glassy Random Laser and Experimental Measurement of Replica Symmetry Breaking

The investigation of the glassy behaviour of light in the framework of our theory is made possible by means of a newly introduced overlap parameter, the Intensity Fluctuation Overlap (IFO) measuring the correlation between intensity fluctuations of waves in random media. This order parameter allows to identify the laser transition in arbitrary physical regimes, with varying amount of disorder and non-linearity. In particular, in random media it allows for the identification of the glassy nature of some kind of random laser, in terms of emission spectra data, the only data so far accessible in random laser measurements. The model devised from first principles in whose framework the parameter is defined is the nonlinear phasor statistical mechanical model. This is a generalised complex spherical spin-glass model solvable in the mean-field approximation by Replica Symmetry Breaking theory. IFO measurements are possible in real experiments, recently leading to a validation of the RSB theory and a new characterisation of lasers in terms of spectral intensity fluctuations.

Interference of Coupling of Waves in Random Media

The light modes interaction network has to be inferred starting from data acquired in measurements, of spectra and correlations of phases and amplitudes of the light modes, and this inference problem is closely analogous to those in our other areas of application of statistical inference. Starting with the analysis of the inverse problem in statistical mechanical systems with continuous variables, like XY and complex phasors, our inference project is concerned with the bottom-up approach for studying statistical models for application to wave and optics. The parameters describing a given model system, like active links in the network system and external field affecting the system, are inferred using the data set which is made available by experimental or numerical measurements.

We adopt various inference techniques to reconstruct the interaction networks and to estimate the coupling values: mean-field approach, Pseudo Likelihood Maximization (PLM) with L1 and L2 regularizations and PLM with decimation. Such inverse problems for network reconstruction are considered on graphs of different kinds, from 2D and 3D nearest-neighbour lattices, Bethe and Erdos-Renyi sparse random graph to dense random graphs.

Facilities and Labs

S.Li.M. Lab @ Roma




CNR Researcher



Associate PostDoc



Associate PostDoc



Associate PostDoc


  1. F Antenucci, Statistical Physics of Wave Interactions,  Springer (2016).
  2. P Tyagi, A Marruzzo, A Pagnani, F Antenucci, L Leuzzi, Regularization and decimation pseudolikelihood approaches to statistical inference in XY-spin models,  Physical Review B 94, 024203 (2016) Doi: 10.1103/PhysRevB.94.024203.
  3. F Antenucci, A Crisanti, M Ibáñez-Berganza, A Marruzzo, L Leuzzi, Statistical mechanics models for multimode lasers and random lasers.  Philosophical Magazine 96, 704-731 (2016) Doi: 10.1080/14786435.2016.1145359.
  4. F Antenucci, MI Berganza, L Leuzzi, Statistical physics of nonlinear wave interaction,  Physical Review B 92, 014204 (2015) Doi: 10.1103/PhysRevB.92.014204 .
  5. P Tyagi, A Pagnani, F Antenucci, M Ibanez Berganza, L Leuzzi, Inference for interacting linear waves in ordered and random media,  Journal of Statistical Mechanics: Theory and Experiment 2015 (5), Doi: 10.1088/1742-5468/2015/05/P05031
  6. F Antenucci, A Crisanti, L Leuzzi, Complex spherical 2+ 4 spin glass: A model for nonlinear optics in random media,  Physical Review A 91, 053816 (2015) Doi: 10.1103/PhysRevA.91.053816.
  7. F Antenucci, MI Berganza, L Leuzzi, Statistical physical theory of mode-locking laser generation with a frequency comb.  Physical Review A 91, 043811 (2015) Doi: 10.1103/PhysRevA.91.043811  .
  8. A Marruzzo, L Leuzzi, Nonlinear XY and p-clock models on sparse random graphs: Mode-locking transition of localized waves,  Physical Review B 91, 054201 (2015) Doi:10.1103/PhysRevB.91.054201 .
  9. F Antenucci, C Conti, A Crisanti, L Leuzzi, General phase diagram of multimodal ordered and disordered lasers in closed and open cavities.  Physical Review Letters 114, 043901 (2015) Doi: 10.1103/PhysRevLett.114.043901 .
  10. N Ghofraniha, I Viola, F Di Maria, G Barbarella, G Gigli, L Leuzzi, C Conti, Experimental evidence of replica symmetry breaking in random lasers,  Nature communications 6, 5 (2015) Doi:10.1038/ncomms7058 .
  11. F Antenucci, A Crisanti, L Leuzzi, The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra,  Scientific reports 5, 16792 (2015) Doi:10.1038/srep16792 .
  12. F Antenucci, M Ibanez Berganza, L Leuzzi, Statistical mechanical theory of mode-locked multimode lasers in closed cavity: determination of thresholds, spectra, pulse phase delays and pulse correlations.  Phys. Rev. A 91, 043811 (2014) Doi: 10.1103/PhysRevA.91.043811.

Other Selected Publications

  1. V Folli, A Puglisi, L Leuzzi, C Conti, Shaken Granular Lasers,  Physical Review Letters 108, 248002   (2012) Doi: 10.1103/PhysRevLett.108.248002.
  2. L Leuzzi, C Conti, V Folli, L Angelani, G Ruocco, Phase Diagram and Complexity of Mode-Locked Lasers: From Order to Disorder,  Physical Review Letters 102, 083901 (2009) Doi:10.1103/PhysRevLett.102.083901 .



Statistical mechanics of disordered granular laser systems: theory and experiment,” funded by the Italian Ministry of Research (MIUR) program futuro in ricerca. (2010-2015),

NETADIS: Networks across disciplines, FP7-PEOPLE-2011-ITN Project (2011-2015).

Latest News

Technology Trasfer in Nanotechnology

Technology Transfer in Nanotechnology: Challenges and Opportunity

Lecce, 18/19 ottobre 2018

CNR NANOTEC c/o Campus Ecotekne

JRC in collaboration with the National Research Council (Cnr) is organising a workshop on Technology Transfer in Nanotechnology,

which will take place in CNR Nanotec (Lecce, Italy) on 18 and 19 October. This workshop is organised in the framework of the TTO-CIRCLE initiatives.   The aim of this event is to explore how technology transfer activities can be used as a mechanism to help EU industry, particularly Start-ups and SMEs, and Government in deploying and adopting Nano-technology. Practical examples will be presented to illustrate the potential of technology transfer in this area.   The workshop will gather technology providers, industry executives, technology transfer officers, policy makers and financial intermediaries to share experiences and lessons learned. One of the key objectives is to discuss policy implications at all levels that could help accelerating the adoption of Nanotechnology by the European manufacturing industry. More informations: Download Locandina

Nanotechnology Transfer Day

26 Luglio 2018 - Lecce

CNR NANOTEC c/o Campus Ecotekne Siglato l’accordo lo scorso maggio tra CNR NANOTEC e Pairstech Capital Management, ha preso il via la collaborazione con PhD TT per la valutazione della ricerca

E’partita la collaborazione con PhD TT per la valorizzazione della ricerca sulla base dell’accordo siglato lo scorso Maggio tra CNR NANOTEC e Pairstech Capital Management, società di gestione patrimoniale che fornisce agli investitori istituzionali e privati un insieme di veicoli di investimento, al fine di valorizzare i risultati della ricerca svolta all'interno dell'Istituto.

Giovedì 19 Luglio dalle ore 11 alle ore 14 nella sede del CNR Nanotec di Lecce si è tenuto un incontro sul trasferimento tecnologico nel settore delle nanotecnologie applicate al settore biomedicale.

L’evento è stato organizzato dall’ufficio di Trasferimento Tecnologico del CNR Nanotec che ha inaugurato con questa giornata un ciclo di eventi mirato a presentare agli attori dell’ecosistema dell’innovazione nel settore delle nanotecnologie i vari modelli e alcune best practice di trasferimento tecnologico. In questa prima giornata il dott. Heber Verri e la dott.ssa Paola Urbani hanno presentato il nuovo modello di trasferimento tecnologico PhD TTãIndex Model.

PhD TT è una realtà italiana completamente indipendente specializzata in trasferimento tecnologico, è un acceleratore organizzato per il Go to Venture Practice, orientata al mondo delle Lifes Sciences.

PhD TT ha sviluppato un nuovo modello di trasferimento tecnologico: il PhD TT©INDEX MODEL dedicato alla generazione di valore dell'innovazione, focalizzato alla riduzione dei rischi delle opportunità di investimento a sostegno della ricerca.

I ricercatori intervengono attivamente nell'analisi iniziale di fattibilità e nella costituzione della futura società (start-up), con l'obiettivo di attrarre capitale di rischio utile a sostenere la fase del trasferimento tecnologico nella visione della "Research for go-to-market".

Il modello PhD TT nasce da un bisogno del mercato, quello di far dialogare due mondi estremamente diversi tra loro: il mondo della ricerca e il mondo degli investimenti.

PhD TT supporta tutte le attività in collaborazione con il TTO - CNR Nanotec con un team di lavoro esperto e grazie a un comitato scientifico-economico qualificato.

In occasione dell'evento del 19/7 u.s. al CNR Nanotec di Lecce, PHD TT ha presentato il proprio track record, dove si sono potuti valutare in dettaglio i casi di successo di intervento del PhD TT©INDEX MODEL.

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Disordered serendipity: a glassy path to discovery

A workshop in honour of Giorgio Parisi’s 70th birthday

September 19-21, 2018 - Roma

Sapienza University

With the occasion of celebrating Giorgio Parisi 70th birthday, the conference "Disordered serendipity: a glassy path to discovery" brings to Rome many among the world-leading experts in the field of complex systems. In order to properly represent the many fields of research where Giorgio Parisi gave a relevant contribution in his studies of disordered systems, the conference covers a broad spectrum of topics: from  fundamental and rigorous analysis of the statistical mechanics of disorder systems to applications in biology and computer science. These subjects are deeply interconnected since they are characterized by the presence of glassy behavior.