Spatial Nonlinear Optics
Our group has an special interest in the study of discrete-symmetry nonlinear photonic
structures. These photonic structures are attracting a lot of interest in recent years for they permit a high
degree of tunability of the properties of propagating light. Current examples are nonlinear photonic crystals
and optically-induced lattices. In both cases, the interplay between nonlinearities and discreteness yields a
wide variety of new complex phenomena.
Most of the approaches to the analysis of these systems are mainly numerically-based.
Our group has started an innovative approach which relies on a general and powerful tool that has proven to
be very succesful in other fields: Group Theory as the mathematical framework unveiling the
role of Symmetry. This new approach permits a systematic classification of all symmetric
solitonic solutions of a nonlinear system with discrete-symmetry. General properties of such solutions can be
derived without resorting to numerical simulations. In a field dominated by numerical analysis, these results
can be considered of special relevance.
We are thus interested in the study of different realistic nonlinear discrete-symmetry
systems such as photonic crystal fibers, 2D photonic crystals or optically-induced lattices of different types.
Our goal is the analysis and understanding of the mechanisms behind the existence and stability of soliton
solutions in these systems. Nonparaxial effects, soliton interactions and other nonlinear effects have their
own characteristics when nonlinearities and discreteness are combined.
Photonic Condensed Matter
An exciting and ambitious project is to analyze all these new phenomena in the light
of Field Theory and Statistical Mechanics. The possibility of characterize light in a similar manner to other
matter systems opens a new world to understand some old and new nonlinear optical phenomena in the light of the
formalism of Condensed Matter Physics. This would help to pave the way to establish a closer link between
nonlinear photonic systems and related fields such as Bose-Einstein condensates, superconductivity or other
condensed matter systems. We call this new approach Photonic Condensed Matter.
Temporal Nonlinear Optics
Another hot topic in photonics in which our group shows a great interest is that of
highly-nonlinear temporal effects in pulse propagation in optical systems. That is, those corresponding to
physical situations for which the standard approaches based on the Nonlinear Schrödinger and related equations
are known to fail.
We have developed a general formalism that permits the description of the nonlinear
propagation in optical systems with minimum assumptions and that includes the usual equations in the literature
as particular cases. This generality opens the door to study a wide variety of unsolved problems beyond the
current approaches. Nonparaxial effects and backward radiation, different supercontinuum
scenarios and other high-nonlinearity effects, the role of polarization and soliton
interaction in highly-nonlinear systems are some of the open questions that can be faced with generality using this approach.
The generality of the fomalism also permits to face the problem of Light Quantization
in a standard Quantum Field Theory manner. Due to the low dimensionality of the effective pulse propagation
action, it is expected that many nonperturbative effects such as quantum phase transitions or critical phenomena
appearing in other low dimensional systems can play a role in the photonic framework.
The topic of spatial-temporal effects is one of the most promising areas of research in
photonics since it is still in an incipient exploration phase. The formalism previously mentioned has allowed
us to present an unified description of spatiotemporal propagation in optical nonlinear media. This includes
intermodal effective equations and the possibility of searching new nonlinear solutions such as spatial-temporal
Electromagnetic Propagation in 2D and 3D Photonic Structures
Our group has an extensive experience in the modeling, simulation and design of 2D and
3D photonic structures also in the linear regime. This background turns out to be important for the understanding
and simulation of similar structures where the role played by nonlinearities considerably complicates the physical
scenario. In this way, our group is interested in the linear analysis of 2D and 3D photonic structures with potential
applications. Photonic crystal fibers, 2D and 3D photonic crystals, nonperiodic media with particular features -such
as fractal structures- and microwave guides and cavities are some of the systems in which our group is interested in.
Our group is starting a new line of research devoted to the study of photonic structures of nanometric
scale. The experience accumulated by our group in the simulation of photonic structures both in the linear and nonlinear regime
naturally leads us to face this promising technological challenge. We are interested, for example, in the interplay between
nonlinear and linear light structures such as solitons and surface plasmon polaritons or in light propagation in nonlinear