Resonant and Secular Orbital Interations

In stable solar systems, planets remain in nearly elliptical orbits around their stars. Over longer timescales, however, their orbital shapes and sizes change due to mutual gravitational perturbations. Orbits of satellites around a planet vary for the same reason. Because of their interactions, the orbits of planets and satellites today are different from what they were earlier. In order to determine their original orbits, which are critical constraints on formation theories, it is crucial to understand how orbits evolve over the age of the Solar System. Depending on their timescale, we classify orbital interactions as either short-term (orbital resonances) or long-term (secular evolution). My work involves examples of both interaction types. Resonant history of the small Neptunian satellites In satellite systems, tidal migration brings satellite orbits in and out of resonances. During a resonance passage, satellite orbits change dramatically in a very short period of time. We investigate the resonant history of the six small Neptunian moons. In this unique system, the exotic orbit of the large captured Triton (with a circular, retrograde, and highly tilted orbit) influences the resonances among the small satellites very strongly. We derive an analytical framework which can be applied to Neptune's satellites and to similar systems. Our numerical simulations explain the current orbital tilts of the small satellites as well as constrain key physical parameters of both Neptune and its moons. Secular orbital interactions during eccentricity damping Long-term periodic changes of orbital shape and orientation occur when two or more planets orbit the same star. The variations of orbital elements are superpositions of the same number of fundamental modes as the number of planets in the system. We investigate how this effect interacts with other perturbations imposed by external disturbances, such as the tides and relativistic effects. Through analytical studies of a system consisting of two planets, we find that an external perturbation exerted on one planet affects the other indirectly. We formulate a general theory for how both orbits evolve in response to an arbitrary externally-imposed slow change in eccentricity.

MICROSCALE DIELECTRIC ANTI-REFLECTION COATINGS FOR PHOTOVOLTAICS

In order to power our planet for the next century, clean energy technologies need to be developed and deployed. Photovoltaic solar cells, which convert sunlight into electricity, are a clear option; however, they currently supply 0.1% of the US electricity due to the relatively high cost per Watt of generation. Thus, our goal is to create more power from a photovoltaic device, while simultaneously reducing its price. To accomplish this goal, we are creating new high efficiency anti-reflection coatings that allow more of the incident sunlight to be converted to electricity, using simple and inexpensive coating techniques that enable reduced manufacturing costs. Traditional anti-reflection coatings (consisting of thin layers of non-absorbing materials) rely on the destructive interference of the reflected light, causing more light to enter the device and subsequently get absorbed. While these coatings are used on nearly all commercial cells, they are wavelength dependent and are deposited using expensive processes that require elevated temperatures, which increase production cost and can be detrimental to some temperature sensitive solar cell materials. We are developing two new classes of anti-reflection coatings (ARCs) based on textured dielectric materials: (i) a transparent, flexible paper technology that relies on optical scattering and reduced refractive index contrast between the air and semiconductor and (ii) silicon dioxide (SiO2) nanosphere arrays that rely on collective optical resonances. Both techniques improve solar cell absorption and ultimately yield high efficiency, low cost devices. For the transparent paper-based ARCs, we have recently shown that they improve solar cell efficiencies for all angles of incident illumination reducing the need for costly tracking of the sun’s position. For a GaAs solar cell, we achieved a 24% improvement in the power conversion efficiency using this simple coating. Because the transparent paper is made from an earth abundant material (wood pulp) using an easy, inexpensive and scalable process, this type of ARC is an excellent candidate for future solar technologies. The coatings based on arrays of dielectric nanospheres also show excellent potential for inexpensive, high efficiency solar cells. The fabrication process is based on a Meyer rod rolling technique, which can be performed at room-temperature and applied to mass production, yielding a scalable and inexpensive manufacturing process. The deposited monolayer of SiO2 nanospheres, having a diameter of 500 nm on a bare Si wafer, leads to a significant increase in light absorption and a higher expected current density based on initial simulations, on the order of 15-20%. With application on a Si solar cell containing a traditional anti-reflection coating (Si3N4 thin-film), an additional increase in the spectral current density is observed, 5% beyond what a typical commercial device would achieve. Due to the coupling between the spheres originated from Whispering Gallery Modes (WGMs) inside each nanosphere, the incident light is strongly coupled into the high-index absorbing material, leading to increased light absorption. Furthermore, the SiO2 nanospheres scatter and diffract light in such a way that both the optical and electrical properties of the device have little dependence on incident angle, eliminating the need for solar tracking. Because the layer can be made with an easy, inexpensive, and scalable process, this anti-reflection coating is also an excellent candidate for replacing conventional technologies relying on complicated and expensive processes.

Design of Nanophotonic Antireflection Coatings for III-V Thin-Film Photovoltaics

Thin-film photovoltaics have provided a critical design avenue to help decrease the overall cost of solar power. However, a major drawback of thin-film solar cell technology is decreased optical absorption, making compact, high-quality antireflection coatings of critical importance to ensure that all available light enters the cell. In this thesis, we describe high efficiency thin-film InP and GaAs solar cells that utilize a periodic array of nanocylinders as antireflection coatings. We use coupled optical and electrical simulations to find that these nanophotonic structures reduce the solar-weighted average reflectivity of InP and GaAs solar cells to around 1.3 %, outperforming the best double-layer antireflection coatings. The coupling between Mie scattering resonances and thin-film interference effects accurately describes the optical enhancement provided by the nanocylinders. The spectrally resolved reflectivity and J-V characteristics of the devices under AM1.5G solar illumination are determined via the coupled optical and electrical simulations, resulting in predicted power conversion efficiencies > 23 %. We conclude that the nanostructured coatings reduce reflection without negatively affecting the electronic properties of the InP and GaAs solar cells by separating the nanostructured optical components from the active layer of the device.