# Previous Research

Below is a sampler of my previous research work

### Nonlinear optics of ultrashort pulses

##### Dynamic X-waves in femtosecond pulses:

For about a decade, the nonlinear optics community has been investigating the phenomenon of ultrashort pulses which can propagate in nonlinear media for distances that are much longer than expected based on their beam diameters. In Phys. Rev. Lett. 92 (2004) 253901, we identified a general mechanism responsible for the long-distance propagation in optical filaments in condensed media. This is based on the notion of dynamic X-waves, which constitute a class of wavepackets that are localized and are resistant to dispersion spreading and diffraction.

##### Turbulent filament formation in high-power beams:

The self-focusing instability in high-power, wide-beam pulses leads to the formation of multiple high-intensity spots, or filaments in the transverse cross-section of the beam. Depending on conditions, filamentation can persist for hundreds of meters. The mechanism that keeps the beam from falling appart is based on continuous energy exchange between the individual filaments and a low-intensity background that plays the role of an energy reservoir. This scenario was for the first time described in our work in Phys. Rev. Lett. 83 (1999) 2938, and it was the simulation that made this result possible. This often cited work was a crucial contribution to the current understanding of high-power optical filamentation (also called light-string formation) in gases.

##### Supercontinuum generation:

Supercontinuum generation is a fascinating nonlinear phenomenon in which the spectrum of a light pulse explosively broadens to span the whole visible spectrum. Because of its many applications, it has been studied for several decades. Yet, new insights continue to appear in the literature. In a series of theoretic and simulation works [e.g. Appl. Phys. B 85 (2006) 531, Phys. Rev. Lett. 91 (2003) 043905, Appl. Phys. B 77 (2003) 185 ], we studied supercontinuum generation in bulk media. In a simulated experiment we demonstrated that “the old explanation” cannot be correct, and have shown that the shape and extent of the supercontinuum spectrum, as well as its dependence on the material band-gap, are all tightly related to the linear chromatic dispersion of the medium.

##### Third harmonic generation and its relation to supercontinuum:

Third harmonic generation by intense light pulses in gases has been creating a lot of interest, both for its applications and the underlying physics. We have published a work [ Appl. Phys. B 85 (2006) 531. ] that for the first time revealed the common principles that govern the production of both the supercontinuum and of the third-harmonic radiation.

##### Remote control of filamentation:

For remote sensing applications, it is desirable to be able to deliver high-intensity light to the target over long distance. Optical filamentation in high-power pulses has already been proven to be a feasible approach. However, since the filamentation is driven by several nonlinear effects, the accurate control remains a problem. Recently, several avenues has been studied for efficient control of filamentation in high-power optical pulses. However, truly long-distance control is so far possible only with very high-power pulses. I have proposed a new approach [ Opt. Lett. 32 (2007) 2753] that allows to control the filamentation, plasma formation, and supercontinuum generation at a precisely chosen distance while using low-energy pulses. This method should open new possibilities in remote sensing applications.

##### Computational methods for nonlinear optics:

A great deal of the work mentioned above was enabled by our Unidirectional Pulse Propagation Equation (UPPE) solver [ Phys. Rev. Lett. 89 (2002) 283902, Phys. Rev. E 70 (2004) 036604 ]. This equation bridges, in a transparent and consistent manner, the gap between the Maxwell`s equations on one hand and various envelope equations widely used in nonlinear pulse simulations on the other. UPPE makes it possible to perform calculations that are not feasible on the Maxwell solver level (due to resolution, memory, and time constraints), and at the same time it consistently solves the problem of corrections to the nonlinear Schroedinger equations. In fact, every pulse propagation equation found in the nonlinear optics literature can be obtained as an approximation from the UPPE. We used the UPPE solver to predict universal structures in the angularly resolved supercontinuum spectra [Phys. Rev. Lett. 92 (2004) 253901 ] before they were observed experimentally, and to improve our understanding of femtosecond pulse filamentation in general.

### Modeling of semiconductor lasers

##### Broad-area high-power semiconductor lasers:

Power scaling in semiconductor lasers by designing the active structure area larger and larger is hampered by the inherent tendency of such lasers to filamentation and temporal instability. Lot of effort goes into understanding the dynamics of semiconductor lasers. From a simulation point of view, this is a class of lasers extremely difficult to model in a realistic way. The origin of this problem is the strong frequency and carrier-density dependence of the real and imaginary parts of the semiconductor gain. I have developed a method capable of truly realistic simulation of broad-area semiconductor lasers [IEEE J. Quantum Electronics, 37 (2001) 936]. The approach, based on the use of multiple digital filters, is highly unconventional from the point of view of numerical solution of partial differential equations. It is fair to say that at present it is the only method available that can both perform simulations over long times and correctly capture the extremely wide bandwidth and the fast dynamics in these lasers.

##### Optically pumped semiconductor lasers:

Vertical external cavity semiconductor lasers (VECSEL) are a relatively new member of the semiconductor laser family. Of special interest is the high-power, high repetition rate, ultrashort pulse generation in VECSELs. It has been investigated intensively both experimentally and theoretically. However, the current models can not be trusted completely because they fail to capture accurately the frequency dependent response of the active structure. I have proposed a new model [ IEEE J. Quantum Electron. 43 (2007) 588. ] for VECSELs that allows to build a simulator for a given active structure design, and captures its properties accurately over wide ranges of wavelength, temperature and carrier density.

##### Fluctuations and universality in broad-area lasers:

Optical damage and degradation in semiconductor lasers is a difficult obstacle for building affordable high-power light sources. This difficulty is related to the filamentation instability in high-power lasers. Using methods developed a few years earlier [IEEE J. Quantum Electronics, 37 (2001) 936], we have characterized the intensity fluctuations in the broad-area semiconductor lasers. It turns out that the semiconductor laser intensity must be viewed as a stochastic quantity since it displays a very broad probability distribution. Quite surprisingly, the fluctuation statistics turns out to be universal, independent of the details of the active laser structure. This has consequences for estimating the threshold for the catastrophic optical damage in high-power semiconductor lasers: Namely, it turns out that a naive estimate would be an order of magnitude too optimistic!

### Statistical mechanics

##### Modeling of interface dynamics:

Because moving interfaces are ubiquitous in nature, their detailed understanding is important for several sciences. In a series of works with Per Rikvold [e.g. PRB 76 (2007) 045422, PRB 73 (2006) 045437, PRE 67 (2003) 066113, J. Phys. A, 35 (2002) L117, PRE 66 (2002) 066116, J. Stat. Phys. 100 (2000), 377 ], we studied a class of moving boundaries subject to microscopic local dynamics of various types. Contrary to the common belief that any local microscopic dynamics satisfying detailed balance ensures not only proper equilibrium but also the correct evolution, we have demonstrated that the interface dynamics is in general not universal with respect to the details of the underlying local dynamics. This result means that a whole class of dynamic Monte Carlo simulations might not give realistic results unless it uses correct, first-principles-derived microscopic dynamics.

##### Magnetization switching in nanoparticles and ultra-thin films:

In collaboration with Mark Novotny and Per Rikvold, we investigated different regimes of magnetization switching in nanoparticles, the role of disorder, boundaries and growth morphology [e.g. Phys. Rev. B 56 (1997) 11791, Phys. Rev. B 55 (1997) 11521 ]. Extremely long-lived states in these systems motivated our introduction of a new dynamic Monte-Carlo based method [Phys. Rev. Lett. 80 (1998) 3384] capable of simulating metastable systems with exceedingly slow decay.