Waveguide approach to plasmonic antennas

The thesis aims to investigate select problems of practical interest in plasmonic systems primarily from a viewpoint of guided wave dynamics. After providing theoretical foundation of the fundamental concepts, it re-examines the problem of quasi-static resonance in plasmonic nano-particles and demonstrates its equivalence with the standing wave model. Thereafter, it presents an approach to designing cylindrical metallic antennas tailored to sustain resonances at both fundamental and second harmonics for enhanced nonlinear frequency conversion. Lastly, it visits plasmonic slot waveguides with a view to identify the possibility of phase-matched interaction between fundamental and second harmonic which is necessary for steady nonlinear frequency conversion

Impedance generalization for plasmonic waveguides beyond the lumped circuit model

We analytically derive a rigorous expression for the relative impedance ratio between two photonic structures based on their electromagnetic interaction. Our approach generalizes the physical meaning of the impedance to a measure for the reciprocity-based overlap of eigenmodes. The consistence with known cases in the radiofrequency and optical domain is shown. The analysis reveals where the applicability of simple circuit parameters ends and how the impedance can be interpreted beyond this point. We illustrate our approach by successfully describing a Bragg reflector that terminates an insulator-metal-insulator plasmonic waveguide in the near-infrared by our mpedance concept

Finite-size Scaling of the Density of States in Photonic Band Gap Crystals

The famous vanishing of the density of states (DOS) in a band gap, be it photonic or electronic, pertains to the infinite-crystal limit. In contrast, all experiments and device applications refer to finite crystals, which raises the question: Upon increasing the linear size $L$ of a crystal, how fast does the DOS approach the infinite-crystal limit? We present a theory for finite crystals that includes Bloch-mode broadening due to the presence of crystal boundaries. Our results demonstrate that the DOS for frequencies inside a band gap has a $1/L$ scale dependence for crystals in one, two and three dimensions

Relating localized nanoparticle resonances to an associated antenna problem

We conceptually unify the description of resonances existing at metallic nanoparticles and optical nanowire antennas. To this end the nanoantenna is treated as a Fabry-Perot resonator with arbitrary semi-nanoparticles forming the terminations. We show that the frequencies of the quasi-static dipolar resonances of these nanoparticles coincide with the frequency where the phase of the complex reflection coefficient of the fundamental propagating plasmon polariton mode at the wire termination amounts to $\pi$. The lowest order Fabry-Perot resonance of the optical wire antenna occurs therefore even for a negligible wire length. This approach can be used either to easily calculate resonance frequencies for arbitrarily shaped nanoparticles or for tuning the resonance of nanoantennas by varying their termination.Comment: Submitted to Phys. Rev.

Finite size scaling of the density of states in photonic band gap crystals

Photonic crystals are tailored periodic dielectric media that allow for an unprecedented control in the manipulation of light-matter interactions. One of their outstanding features is the realization of a complete photonic band gap that drastically inhibits light propagation in all directions and for all polarizations. A band gap is associated with a complete vanishing of the density of optical states (DOS) in the crystal. As a necessary corollary, it implies a vanishing of the local DOS (LDOS) too, which leads to a complete inhibition of spontaneous emission everywhere inside such a crystal.In our paper, we will present our approach for the DOS in finite support crystals in both 2D and 3D spatial dimensions. We will show the surprising result that the DOS inside the bandgap decreases linearly with size irrespective of the crystal dimensionality as shown in Fig. 1(b) for the example of inverse woodpile crystals that are being pursued in our group [3]. Our work sets design rules for the sizes of photonic bandgap crystals for practical applications in cavity QED and quantum information processing (vacuum noise shielding). It also has the potential of establishing new methods for engineering finite crystals to enhance the suppression of DOS

Reflectivity calculated for a 3D silicon photonic band gap crystal with finite support

We study numerically the reflectivity of three-dimensional (3D) photonic crystals with a complete 3D photonic band gap, with the aim to interpret recent experiments. We employ the finite element method to study crystals with the cubic diamond-like inverse woodpile structure. The high-index backbone has a dielectric function similar to silicon. We study crystals with a range of thicknesses up to ten unit cells ($L \leq 10 c$). The crystals are surrounded by vacuum, and have a finite support as in experiments. The polarization-resolved reflectivity spectra reveal Fabry-P{\'e}rot fringes related to standing waves in the finite crystal, as well as broad stop bands with nearly $100~\%$ reflectivity, even for thin crystals. From the strong reflectivity peaks, it is inferred that the maximum reflectivity observed in experiments is not limited by finite size. The frequency ranges of the stop bands are in excellent agreement with stop gaps in the photonic band structure, that pertain to infinite and perfect crystals. The frequency ranges of the observed stop bands hardly change with angle of incidence, which is plausible since the stop bands are part of the 3D band gap. Moreover, this result supports the previous assertion that intense reflection peaks measured with a large numerical aperture provide a faithful signature of the 3D photonic band gap. The Bragg attenuation lengths $L_{B}$ exceed the earlier estimates based on the width of the stop band by a factor $6$ to $9$. Hence crystals with a thickness of $12$ unit cells studied in experiments are in the thick crystal limit ($L >> L_{B}$). In our calculations for p-polarized waves, we also observe an intriguing hybridization of the zero reflection of Fabry-P{\'e}rot fringes and the Brewster angle, which has not yet been observed in experiments