Desing and Analysis of Metallo-Dielectric Photonic Crystalls

Identificador:  TDX:1904

Handle: https://hdl.handle.net/20.500.11797/TDX1904

Autors:  Ustyantsev, Mykhaylo

Resum:
We are living in the information age with an over-abundance of information everywhere we turn. The increasing traffic of data in the telecommunication networks (audio video in the Internet) leads to the development of new devices with greater bandwidth and velocity by substituting electronic devices by optical ones. Such devices can be achieved by using the photonic crystal technology that is one of the most important scientific areas with a huge industrial potential.<br/><br/> Photonic crystals are artificial structures with periodic modulation of refractive index. It is common to distinguish one-, two- and three-dimensional photonic crystals by the number of dimensions within which the periodicity has been introduced into the structure. The most important properties are: 1) the existence of the photonic band gap (PBG), where the electromagnetic radiation is not allowed and also permits the existence of localized modes by introducing point or linear defects; 2) the Bloch's mode propagation without losses due to the photonic band gap effect. Such exceptional properties of photonic crystals convert them into principal candidates for future design of nanophotonics circuits that will substitute electronic ones.<br/><br/><br/> In this thesis we have studied optical properties of two-dimensional metallo-dielectric photonic crystals. We have proposed two numerical approximations for calculating such properties <br/><br/>a) calculation of dispersion characteristics gaps by plane-wave expansion method. The dispersion characteristics are relations between frequency and wavevector of the eigenmodes of the infinite photonic crystal and they are very important to study the optical properties of such structures. Also, with this method it is possible to obtain field distribution of eigenmodes.<br/><br/>b) simulation of finite structures by finite-difference time domain method. By this method it is possible to obtain transmission and reflection coefficients. Also, this method permits to study the quality factors of such structures.<br/><br/><br/><br/>General conclusions of the thesis:<br/><br/>Due to the high-level of integration and low cost fabrication metallo-dielectric photonic crystals have very interesting properties for using as passive optical devices. Some of these properties were studied in this thesis.<br/><br/>a) We have analyzed the effect of the variation of the background dielectric constant on the photonic band structure for a two-dimensional square lattice of circular metallic rods and triangular lattice wit square rods. Increasing the background dielectric constant leads to the creation of a new gap, to the shift of the bands towards the low frequencies and to the flattening of the bands which means the reduction on the group velocity. We demonstrated that, for square lattice, increasing dielectric constant of background (&#949;b) can be used to tailor the PBG frequencies to achieve a relative band gap as large as 42.3% for TM1-2 and 13.8% for TM3-4. By studying the field distributions and how they change with increasing background we have shown that the new band gap appears because some photonic bands have a larger shift to lower frequencies than others, and this difference in the shift is explained by the different amount of electromagnetic energy within the metal region for the different bands. We have shown that 2D metallo-dielectric photonic crystals consisting of a triangular lattice of square rods embedded into background materials with different dielectric constants can have absolute Photonic Band Gaps in TM polarization. We have found out that in order to have such a PBG the dielectric constant of the background must be at least 1.6. We have also shown that the PBG widths can be tuned by using background materials with different &#949;b or by changing the filling fraction. In this way, relative band gaps larger than 10% can be achieved for filling fractions away from the close packed condition. These results show that large relative band gap widths can be achieved by a careful selection of the background dielectric and of the metal composing the metallo-dielectric photonic crystal. <br/><br/>b) We have studied the influence of the background dielectric constant on the resonant frequencies and quality factors (Q) of two-dimensional metallo-dielectric photonic crystals with defect sites. We have also analyzed the dependence of these resonant frequencies and Q factors with the defect radius. We have found that, as it happens with the Photonic Band Gap edge frequencies, the resonant frequencies shift to lower values with increasing background dielectric constant, and that the relative position of the resonant frequencies within the PBG is not affected by the change in the host material. In general, the Q factor increases with increasing background dielectric constant. Thus, high values of quality factor can be obtained using host materials with bigger &#949;b. We have also found that the quality factor can be tuned also by changing the defect radius (rd), although the behaviour of the Q with rd is different for the different modes considered. We have shown that high Q factors can be obtained by using resonant structures based on metallo-dielectric photonic crystals with a defect on one of the lattice positions. This opens a wide field of application, since the Q factors demonstrated in this work can be further enlarged by the consideration of more complex defects<br/><br/>c) We studied the influence of the losses on the resonant frequencies and the quality factors of two-dimensional silver metallo-dielectric photonic crystals. The photonic crystal with lattice constant 300 nm is composed of silver nanorods with radius equal to 142 nm. We used fitted parameters of Drude model to adequately describe the frequency-dependent experimental dielectric constant of silver from 300 nm to 900 nm wavelength range. We have shown that the quality factors of different modes of silver metallo-dielectric photonic crystals behave different. The quality factors of monopole mode are monotonically decreasing function of the &#949;b. However, the quality factors of dipole reach their maximum for &#949;b = 2, and for the 2nd order monopole and quadrupole the maximum quality factors found for &#949;b = 3. Further increasing of dielectric constant of background leads to decreasing in the quality factors. Also, we have shown how the quality factors are affected by losses introduced by metals at optical frequencies. Obtained results show that larger quality factors can be achieved by carefully selecting the host materials and the radiuses of the nanorods.