Introduction
The study of propagation of light pulses in nonlinear optical media is of great technological interest. It also leads to some beautiful and sophisticated mathematics. The interplay of nonlinearity (the index of refraction depends on the intensity of the light) and randomness (the presence of loss and quantum mechanical effects lead to noise, and medium imperfections as well as the random nature of the data stream) leads to nontrivial problems in stochastic partial differential equations.
Computational Methods
ACMS has developed state-of-the-art numerical algorithms for solving 3D time domain and spectral vector Maxwell simulators. The software we develop employs the most advanced and computationaly effcient methods based on adaptive structures mesh refinement FDTD, high order vectorial and discontinuous Galerkin spectral finite element mehods in both frequency and time domain. These methods improve dramatically overall effciency and accuracy in comparison to conventional finite difference and finite element methods. These simulators can model electro-magnetic waves over time (such as light, radiation, etc) and play an important role in developing optical devices as well as many other applications. We focusus on designing efficient parallel supercomputing algorithms for sub-wavelength scale light propagation and intercation throught composite materials, including dispersive materials and metal/dielectric intefaces. 
Nanophotonics
Nanophotonics is a rapidly developing new area of science of great importance for technology and basic science. It is based on new materials incorporating inclusions of nanoscale size. These materials do not exist in nature and they display exotic properties which can be used for design of new optical devices with superb characteristics. Nanophotonics studies the interaction of light with structures formed by nanoparticles.These subjects must be studied using a combination of mathematical analysis, ideas from theoretical physics, quantum mechanics and numerical simulation. .
VECSEL Design
Vertical external cavity surface emitting lasers (VECSEL) can provide high out put powers with excellent beam quality in a rather simple and robust device set-up. The intrinsic gain medium, semiconductor quantum wells can be designed for a wide variety of operating wavelengths that are difficult to access with other laser concepts. VECSEL have already been successfully demonstrated for wavelengths between 670nm and 2.4micron and with output powers from a single chip of over 80W in CW operation and over 360W in pulsed operation. Thanks to the open cavity concept intra- (and external) cavity frequency multiplying allows these devices to reach even wavelengths in the UV. Frequency-selective filters can be inserted for wavelength tuning and single frequency operation. .
Extreme nonlinear optics
The major experimental activity in the ACMS lab involves studies of how beam and pulse shaping affect the formation and dynamics of light-strings in various gaseous and condensed media. Two particular beam shapes that have been extensively investigated so far are Bessel and Airy beams. The diffraction-free propagation of femtosecond Bessel beams allows for the creation of extended plasma channels in air. These extended filaments can be used for the generation of energetic optical pulses with the duration in the few-cycle range.
Computational Electrodynamics
Computational Electrodynamics is the process of modeling the interaction of electromagnetic fields with physical objects and the environment. The ACMS has developed a range of state-of-the-art simulation codes for solving 3D time domain and spectral vector Maxwell equations. The software we develop employs the most advanced and computationaly effcient methods and are used to tackle a diverse set of problems from all areas of electrostatics and electrodynamics. .
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