Fractal Photonic Crystal Waveguides

We propose a new class of one-dimensional (1D) photonic waveguides: the fractal photonic crystal waveguides (FPCWs). These structures are photonic crystal waveguides (PCWs) etched with fratal distribution of grooves such as Cantor bars. The transmission properties of the FPCWs are investigated and compared with those of the conventional 1D PCWs. It is shown that the FPCW transmission spectrum has self-similarity properties associated with the fractal distribution of grooves. Furthermore, FPCWs exhibit sharp localized transmissions peaks that are approximately equidistant inside the photonic band gap

Visualizing the Doppler Effect

The development of Information and Communication Technologies suggests some spectacular changes in the methods used for teaching scientific subjects. Nowadays, the development of software and hardware makes it possible to simulate processes as close to reality as we want. However, when we are trying to explain some complex physical processes, it is better to simplify the problem under study using simplified pictures of the total process by eliminating some elements that make it difficult to understand this process. In this work we focus our attention on the Doppler effect which requires the space-time visualization that is very difficult to obtain using the traditional teaching resources. We have designed digital simulations as a complement of the theoretical explanation in order to help students understand this phenomenon.Comment: 16 pages, 8 figure

Tunnelling in quantum superlattices with variable lacunarity

Quantum fractal superlattices are microelectronic devices consisting of a series of thin layers of two semiconductor materials deposited alternately on each other over a substrate following the rules of construction of a fractal set, here, a symmetrical polyadic Cantor fractal. The scattering properties of electrons in these superlattices may be modeled by using that of quantum particles in piecewise constant potential wells. The twist plots representing the reflection coefficient as function of the lacunarity parameter show the appearance of black curves with perfectly transparent tunnelling which may be classified as vertical, arc, and striation nulls. Approximate analytical formulae for these reflection-less curves are derived using the transfer matrix method. Comparison with the numerical results show their good accuracy.Comment: 12 pages, 3 figure

Fractal Light Vortices

Vortex lenses produce special wavefronts with zero-axial intensity, and helical phase structure. The variations of the phase and amplitude of the vortex produce a circular flow of energy that allows transmitting orbital angular momentum. This property is especially in optical trapping, because due to the orbital angular momentum of light, they have the ability to set the trapped particles into rotation. Vortex lenses engraved in diffractive optical elements have been proposed in the last few years. These lenses can be described mathematically as a two-dimensional (2D) function, which expressed in polar coordinates are the product of two different separable one-dimensional (1D) functions: One, depends only on the square of radial coordinate, and the other one depends linearly on the azimuthal coordinate and includes the topological charge. The 1D function that depends on the radial coordinate is known as a zone plate. Here, vortex lenses, constructed using different aperiodic zone plates, are reviewed. Their optical properties are studied numerically by computing the intensity distribution along the optical axis and the transverse diffraction patterns along the propagation direction. It is shown that these elements are able to create a chain of optical traps with a tunable separation, strength and transverse section

Testing theoretical models of magnetic damping using an air track

Magnetic braking is a long-established application of Lenz's law. A rigorous analysis of the laws governing this problem involves solving Maxwell's equations in a time-dependent situation. Approximate models have been developed to describe different experiences related to this phenomenon. In this paper we present a new method for the analysis of the magnetic braking using a magnet fixed to the glider of an air track. The forces acting on the glider, a result of the eddy currents, can be easily observed and measured. As a consequence of the air track inclination, the glider accelerates at the beginning, although it asymptotically tends towards a uniform rectilinear movement characterized by a terminal speed. This speed depends on the interaction between the magnetic field and the conductivity properties of the air track. Compared with previous related approaches, in our experimental setup the magnet fixed to the glider produces a magnetic braking force which acts continuously, rather than over a short period of time. The experimental results satisfactorily concur with the theoretical models adapted to this configuration.Comment: 15 pages, 5 figure