Left-handed materials

Left-handed materials (LHM) are composite materials whose properties are not determined by the fundamental physical properties of their constituents but by the shape and distribution of specific patterns included in them. LHM have the unique property of having both the effective permittivity and the effective permeability negative. The aim of the research is the theoretical understanding, analysis, development, fabrication and testing of left-handed materials (LHM), and also the investigation of their feasibility for applications.

The recent demonstration of a Left-Handed (LH) material, following the work by Pendy et al, underscores the relevance of utilizing structured materials to create electromagnetic response not available in naturally occurring materials. This LH material made use of an array of conducting, nonmagnetic elements to achieve a negative effective permeability &mu(&omega) and an array of conducting wires to achieve a negative effective permittivity &epsilon(&omega), the simultaneous combination of which has never before been observed in any previously known material. Since the product of (-&epsilon)(-&mu) is a positive number, Maxwell’s equations permit propagation, and thus the LH material offers exciting new opportunities for controlling and modifying the flow of electromagnetic radiation.

 

E, H, k form a right set of vectors	E, H, k form a left set of vectors

LH materials will display unique “reversed” electromagnetic properties, as discussed by Veselago [6] long before such materials existed. In LH materials, the phase and group velocities of an electromagnetic wave propagate in opposite directions, giving rise to a number of novel properties. In particular, Veselago predicted that Cerenkov radiation, Doppler shift, radiation pressure, and even Snell’s law would be reversed in LH materials. All of these reversals stem from the fact that a LH material is characterized by a negative refractive index, a property that does not exist in any known material, and represents a new regime of physics. Thus, for the first time, we have the possibility of engineering a composite structure that can, for example, have a low reflectivity for electromagnetic waves incident at any angle! While we must continue to explore to what extent these conditions can be achieved under the constraints of losses and frequency dispersion inherent to LH media, nevertheless, the discovery of negative refractive index materials is very exciting, and we are certain that this property will be exploited in future applications. One potential application suggested by Pendry is a flat perfect lens! On the right panel is a meta-material with n=-1, which gives focusing for a flat lens. A similar lens with n=2.3 (left) no focusing is observed.
A very interesting question is whether the negative index of refraction property can be implemented at optical frequencies. The phenomenon of negative refraction has recently been predicted by numerical simulations on dielectric, photonic crystals, at certain frequencies near negative group-velocity bands. Although the refracted beam may bend toward a negative angle in these systems, it is difficult to define an equivalent index of refraction with the same generality as we find in LHM materials, because these effects cab be interpreted as higher order Bragg reflection peaks. Furthermore, surface waves at the interface between photonic crystals and other uniform media complicate the surface matching problem, making design considerations more difficult. Nevertheless, the use of photonic crystals as negative refractive materials is intriguing and may offer the means of extending the phenomenon of negative refractive index to optical wavelengths. Any material that exhibits the property of negative refractive index, a property not observed in naturally occurring materials, will have a variety of practical applications.
  (Left) The first LH structure fabricated by the UCSD.The medium consists of Split Ring Resonators (SRR), created lithographically on circuit board material, and metallic posts. (Right) A split ring structure etched into copper circuit board plus copper wires to give negative mu and negative epsilon.   Measured power distribution (solid point) and calculated average intensity (solid line) at 0.7 mm away from the second interface for two incoherent sources at a distance l/3. So sub-wavelength resolution was achieved. Calculated average intensities at these points with dielectric slabs are also shown (dashed line).

We therefore plan to continue the exploration that has been recently initiated worldwide – including analysis, development, and testing – of novel fabricated structures, with the ultimate goal of developing LH materials with unique electromagnetic functionality.

In summary, the targets of our research efforts are:
(a) A better understanding of the physics of left-handed (LH) materials.
(b) Improvement of the existing tools for modeling and simulating more complicated structures than can be done today.
(c) Fabrication of LH-materials, using various approaches, materials and processes.
(d) Testing the electromagnetic behavior of these materials.
(e) Identifying several different applications where such materials can make a big contribution.

 

Photonic crystals (Electromagnetic wave band gap materials)

Photonic crystals are a class of artificial periodic composite materials which exhibit electromagnetic band gaps (i.e. frequency regimes where the EM waves can not propagate). This band gap property makes the PCs very important for the manipulation of EM waves; they can act for the EM waves in the same way as the semiconductors for the propagation of electrons; e.g., formation of proper defects leads to localized light modes with desired properties, like guiding of light (by creating linear defects in PCs – see next figure), storing light in point-like defects etc. All this ability for light manipulation can be used to improve the functionality of existing light emitting, receiving and propagating devices, to produce novel, optimum devices, making even possible the creation of integrated circuits fully photonic.

 

Guiding and bending of light through a two-dimensional photonic crystal waveguide with a bend.  

Our tasks in the PC research include study of various PC-based structures and identification of structures that can be used as components for the creation of PC integrated circuits; also, exploration of the interaction of sources with finite PCs, study of defects in PCs, left-handed behaviour of PCs etc.

 

 

Phononic crystals (elastic wave band gap materials)

Phononic crystals are the acoustic analogue of photonic crystals. It is going for periodic composite media with spectral regions where the propagation of the acoustic   and elastic waves is forbidden (phononic band gaps). Phononic crystals have for the acoustic and elastic waves all the manipulation capabilities that photonic crystals have for light. Their most important application is in the creation of acoustic filters, as the richness in parameters of the acoustic systems gives the ability for very wide band gaps.

Our current topics on the phononic crystal research include combination of phononic and photonic band gaps in the same system for the creation of opto-acoustic devices, characterization of self-assembled colloidal crystals made of core-shell particles (which can give band gap in sub-wavelength regimes) and optimization of their properties, negative refraction effects in phononic crystals etc.

 
Negative refraction in a phononic crystal. The crystal has the shape of the triangle.

 

 

 

Waves in random media

The aim of the present research is the theoretical understanding of the properties of disordered systems, with emphasis on light localization and random lasers.

 

Random Lasers

Random lasers are a combination of strongly scattering media and an optical gain medium.   These systems have many features in common with conventional lasers based on an optical gain medium enclosed in a cavity with two mirrors to enhance stimulated emission.   In random lasers, multiple scattering plays the role of the mirrors (see the figure in the beginning).   For example, threshold behavior for lasing action and frequency narrowing has been observed in random lasers.   Evidently, the optical properties of random lasers are quite different from conventional lasers; the propagation of pump and fluorescence light is diffusive, and the absence of a well-defined cavity with modes along its axis, there is no “preferred direction” in feedback and loss processes.   The ambiguity as to what exactly constitutes the loss of a random laser, how optical feedback works if it is “omni-directional,” and the theoretical prediction of an intensity divergence have led a continuous debate about what happens at, and above, the laser threshold.   We have developed a dynamical approach for understanding the properties of random lasers, especially above the laser threshold. We plan to collaborate with experimental groups at Amsterdam and IESL-FORTH (Laser group) to understand the dynamical behavior of the random laser systems and check our recent predictions about the shape of the wavefunctions of random lasers and low threshold lasing in periodic and/or random materials. It is expected that in the case of a 3d PBG material, the random feedback effects will be considerably stronger, and can give lasing with a much lower threshold. We plan to use the inverse opal structures fabricated at the University of Amsterdam to check these ideas. We plan to investigate the emission spectra of dopants (such as Erbium) inside 3d photonic crystals.   The situation is reminiscent of atoms or molecules in 1d Fabry-Perot cavities.   The main difference between Fabry-Perot cavities and photonic crystals is that PC acts as 3d cavities, thereby promising complete control over emission. These studies will help us develop low threshold lasers and light-emitting diodes using photonic crystals.

One of the current challenges in laser optics is to take advantage of the resonant modes within particles to obtain high quality micro-cavities with low threshold. We have presented a study of the effect that the internal resonances of individual particles play on the emitted intensity, and demonstrated how optimal tuning of the size and distances between the particles can enhance the quality factor by more than 4 orders of magnitude. The potential applications of this work on the design of an optimal mirco-cavity and on a random laser are essential.

Light Localization

The analogy between the propagation of electron waves and classical waves has led to a revival in the research of the transport of light in disordered scattering systems. The final goal of many of these studies has been to observe the optical analogue of Anderson localization in electronic systems.   Experimental difficulties in realizing a random medium where the optical absorption is low enough and the light scattering is efficient enough to induce localization has been the reason why, for a long time, only microwave localization was realized.   In light localization experiments, the absorption is large and, therefore, complicates the interpretation of results. We plan to carry out new experiments at the University of Amsterdam in very strong scattering media to clearly distinguish between the effects of optical absorption and multiple scattering.   The effects of finite size and internal reflection at the boundary of the sample should be also included appropriately. Currently, experiments are in progress with powders of semiconducting materials such as Si, Ge and GaP at frequencies near and below the semiconductor gap of these materials. In addition, a unique porous form of GaP has recently been developed as well-defined random sample with a connected network topology. The difference in topology of powders and network structures and its consequences in localization behavior are still under study both experimentally and theoretically. To characterize the wave propagation of light in random media, a variety of optical techniques have been developed.   In particular, the dependence of scattering properties such as the mean free path as a function of sample thickness, the enhanced backscattering profiles and speckle correlation techniques have proven to be essential to augment the static measurements with time dependent techniques to determine the dynamical transport properties.   For example, short optical pulse transmission measurements are able to determine the dynamical diffusion constant and properties such as the effective energy and phase velocity in the medium. We will use the Energy Density Coherent Potential Approximation developed by K. Busch, E. N. Economou, Maria Kafesaki and C. M. Soukoulis, to obtain better estimates for the optimum topology and scatter characteristics. We also plan to develop the theory of pulse transport in disordered systems and will be in close contact with the group of Professor Ad Lagendijk at the University of Amsterdam, which recently moved to University of Twente.

Nonlinearities

Nonlinear dielectric materials exhibiting a bistable response to intense radiation are key elements for an all-optical digital technology. We have used our FDTD methods to study the time-dependent switching properties of nonlinear systems for constant wave illumination. The conditions for a fully controlled and reproducible switching were obtained. Our FDTD methods were also used to study the effects of disorder on the width of the photonic gaps. It is found that the gaps can survive a strong amount of disorder. It looks like that short-range order is needed to have a gap in a photonic crystal.

In summary, fascinating novel science and technology can be expected from the synergy of the fields of light localization, photonic band gap materials, and random lasers. Photonic crystals offer innovative ways to manipulate light not possible in any previously known photonic material. They represent the “semiconductors of the future,” and may become the focus of the photonics revolution of the twenty-first century.