Abstract thesis Milan Maksimovic

Abstract thesis Milan Maksimovic

We consider the open and finite nature of a specific class of multilayer structures by directly characterizing their resonance properties via an investigation of the quasi-normal mode spectrum. Quasi-normal modes are eigenfunctions that appear as solutions of the eigenvalue problem for open structures. They are field profiles representing damped oscillations of the open optical system after an initial excitation is withdrawn.

We developed and applied QNM expansion method for the solution of the scattering problem in multilayer sructures. We propose a novel and constructive way of connecting a quasi-normal mode description to transmission resonance properties of optical defect microcavities in 1D photonic crystal structures. Our approach is meant specifically for approximations of the defect induced transmission modes existing in the bandgap of otherwise periodical structures. It relies on a variational principle for the field representation of the field profiles in the transmission problem.

Furthermore, a variational principle for QNMs allows approximating the eigenfrequencies and QNMs of composite multiple cavity structures by eigenfrequencies and QNMs of simpler structures. Hence, a form of coupled mode theory for finite, open 1-D PC structures is proposed, that uses directly the most relevant QNMs. Closely related, an expression for a first order perturbation correction of the complex eigenfrequencies is derived by means of variational restriction.

We analyzed a series of characteristic examples of multiple cavity structures and were able to point out characteristic features in the composite structures as originating from simpler structures. Here, the QNM analysis rigged with the variational approximation method offers a resourceful method for the interpretation of complex phenomena associated with the resonance properties in 1-D PC structures. Numerical examples suggest that the method is valid for single and multiple cavity structures in both symmetric and nonsymmetric layer arrangements and both weak and strong couplings between defects.

A second class of problems that we address concerns multilayer structures incorporating negative index metamaterials, which are artificial composites with subwavelength features and negative real part of the refractive index of the homogenized structure. We use the Transfer Matrix Method as a mathematical method for numerical computations and analysis. Novel properties of the bandgap structure and transmission spectra can be obtained by the introduction of NIMs in the construction of the multilayers. Key mechanism responsible for novel properties is the phase compensation, the partial or full removal of the phase shift of the wave propagating through a NIM-containing multilayer. We analyzed transmission spectra of periodic and aperiodic Thue-Morse multilayers composed from alternating layers with positive and negative refractive indices.

Further, we apply passive NIM-containing multilayers to tailor the spectral and angular emittance/absorptance distributions of a thick absorbing substrate. On the basis of the transfer matrix method and of the Kirchhoff's law for thermal radiation, we analyze realistic finite structures that comprise NIM-containing multilayers. Dispersion and losses in the NIM part are taken into account. Our results show that structures containing NIM show large influence to the thermal radiation spectrum. The suppressed region of thermal radiation is wider than in usual all-PIM structures, and the spectral characteristics more flat, i.e. without sharp oscillations typical for the all-dielectric case. It can be also seen that the thermal radiation absorbtance/emittance is less dependent on the angle of the incident radiation. Second, our investigations were dedicated to pre-fractal multilayers of triadic Cantor type containing dispersive and lossy negative index media. As for other NIM- containing multilayers the dependence of the spectral transmission on the spatial angle is much weaker than for conventional non-periodic multilayers, while the sequential splitting gives rise to multiple narrow transmission peaks, which has an applicative potential itself.

The theoretical results suggest that a NIM-containing multilayer on top of an absorbing substrate implements the concept of thermal radiation antenna, i.e. a system that enables both spectral and directional selectivity of the thermal power spectrum emitted by some material object.