New publication of one of our researchers in Physical Review Letters

The article “Surface bound states in the continuum”, has been accepted in the prestigious journal Physical Review Letters, and was published officially during February [Molina et al., Phys. Rev. Lett. 108, 070401 (2012), ver aquí]. One of the authors of the paper is Dr. Mario Molina, Responsible Researcher for the “Nonlinear Optics” Division of CEFOP. The work, carried out by Dr. Mario Molina, along with researchers Andrey Miroshnichenko and Yuri Kivshar of the Center of Nonlinear Physics at the National University of Australia, is a general result of wave mechanics, that can be applied to many different systems – quantum and/or classic – but that shares certain characteristics, such as space periodicity and, ideally, a certain degree of nonlinear response.

According to Dr. Molina, in the article “what we did it was to start off with a system where the refractive index is periodic in space, and we proceeded to modulate it smoothly to obtain that one of the colors belonging to the extended band, that is to say, extended in the space, would concentrate itself at the end of the sample, as a result of this modulation.

With this process, one obtains the spatial localization of one of the many colors within the band,” indicates the researcher. This modulation mainly does not affect the other colors, only one of them. The article shows how such modulation of the refractive index is constructed and the space profile (localized) of the optical mode. In a uniform optical medium, a light beam propagates without problems, with a speed that depends only on its color. When this refractive index is replaced by one which is periodic in space, the colors which can propagate in this medium are grouped in bands, separated from each other by “gaps”. However, the waves whose colors fall within any of these bands can propagate in all space with a more or less uniform electrical field strength in space. However, those waves whose colors fall within “gaps” (prohibited regions) cannot propagate. The researcher adds that another interesting case is when the refractive index is random, and changes in space in an unpredictable way. In this case, waves of any color cannot propagate. “If one measured the associate electric field to one of these waves, this field would be located around a certain point in space, decaying quickly. In this case it is said that the waves are all localized,” he indicates. In the work we did, we managed to concentrate the wave corresponding to a specific color at the edge of the sample, leaving the rest untouched.

But there is more. “If one adds a little nonlinear response to the optical medium, then, as the nonlinearity mainly affects those waves that are localized, our state located at the edge of the sample is the most affected and its “effective color” changes, depending on the strength of the nonlinearity,” the author of the publication adds. In optics, the nonlinearity is controlled by means of the power of the light. Therefore, it is possible to change the color of this localized mode within the band, without altering the rest of the modes. Thus, only one of the many colors in the allowed band gets localized, while the others continue behaving like normal light (extended). Also, the work carried out demonstrated that this method is structurally stable, that is to say, if somebody constructs this modulation and small errors in this construction are made, the effect still holds, and only the form of the localized wave changes a bit.

The results of the paper can be used in several fields, like solid physics (tight-binding model), in optics as described above, in systems of weakly connected split-ring resonators (metamaterials), and in any system described by a paraxial wave equation, that can be reduced to a set of coupled discrete equations. Systems of this type occur very frequently in diverse fields of physics. A natural consequence in the context of optics is that the method in principle allows the construction of a super-selective filter: all the colors can travel, except one of them. And “the prohibited” color can be chosen by means of the increase or decrease of the light intensity.

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