Theoretical and numerical investigation of plasmon nanofocusing in metallic tapered rods and grooves

Effective focusing of electromagnetic (EM) energy to nanoscale regions is one of the major challenges in nano-photonics and plasmonics. The strong localization of the optical energy into regions much smaller than allowed by the diffraction limit, also called nanofocusing, offers promising applications in nano-sensor technology, nanofabrication, near-field optics or spectroscopy. One of the most promising solutions to the problem of efficient nanofocusing is related to surface plasmon propagation in metallic structures. Metallic tapered rods, commonly used as probes in near field microscopy and spectroscopy, are of a particular interest. They can provide very strong EM field enhancement at the tip due to surface plasmons (SP’s) propagating towards the tip of the tapered metal rod. A large number of studies have been devoted to the manufacturing process of tapered rods or tapered fibers coated by a metal film. On the other hand, structures such as metallic V-grooves or metal wedges can also provide strong electric field enhancements but manufacturing of these structures is still a challenge. It has been shown, however, that the attainable electric field enhancement at the apex in the V-groove is higher than at the tip of a metal tapered rod when the dissipation level in the metal is strong. Metallic V-grooves also have very promising characteristics as plasmonic waveguides. This thesis will present a thorough theoretical and numerical investigation of nanofocusing during plasmon propagation along a metal tapered rod and into a metallic V-groove. Optimal structural parameters including optimal taper angle, taper length and shape of the taper are determined in order to achieve maximum field enhancement factors at the tip of the nanofocusing structure. An analytical investigation of plasmon nanofocusing by metal tapered rods is carried out by means of the geometric optics approximation (GOA), which is also called adiabatic nanofocusing. However, GOA is applicable only for analysing tapered structures with small taper angles and without considering a terminating tip structure in order to neglect reflections. Rigorous numerical methods are employed for analysing non-adiabatic nanofocusing, by tapered rod and V-grooves with larger taper angles and with a rounded tip. These structures cannot be studied by analytical methods due to the presence of reflected waves from the taper section, the tip and also from (artificial) computational boundaries. A new method is introduced to combine the advantages of GOA and rigorous numerical methods in order to reduce significantly the use of computational resources and yet achieve accurate results for the analysis of large tapered structures, within reasonable calculation time. Detailed comparison between GOA and rigorous numerical methods will be carried out in order to find the critical taper angle of the tapered structures at which GOA is still applicable. It will be demonstrated that optimal taper angles, at which maximum field enhancements occur, coincide with the critical angles, at which GOA is still applicable. It will be shown that the applicability of GOA can be substantially expanded to include structures which could be analysed previously by numerical methods only. The influence of the rounded tip, the taper angle and the role of dissipation onto the plasmon field distribution along the tapered rod and near the tip will be analysed analytically and numerically in detail. It will be demonstrated that electric field enhancement factors of up to ~ 2500 within nanoscale regions are predicted. These are sufficient, for instance, to detect single molecules using surface enhanced Raman spectroscopy (SERS) with the tip of a tapered rod, an approach also known as tip enhanced Raman spectroscopy or TERS. The results obtained in this project will be important for applications for which strong local field enhancement factors are crucial for the performance of devices such as near field microscopes or spectroscopy. The optimal design of nanofocusing structures, at which the delivery of electromagnetic energy to the nanometer region is most efficient, will lead to new applications in near field sensors, near field measuring technology, or generation of nanometer sized energy sources. This includes: applications in tip enhanced Raman spectroscopy (TERS); manipulation of nanoparticles and molecules; efficient coupling of optical energy into and out of plasmonic circuits; second harmonic generation in non-linear optics; or delivery of energy to quantum dots, for instance, for quantum computations.

A proposed qualitative framework for heterogeneous burning of metallic materials : the 'melting rate triangle'

This paper presents a proposed qualitative framework to discuss the heterogeneous burning of metallic materials, through parameters and factors that influence the melting rate of the solid metallic fuel (either in a standard test or in service). During burning, the melting rate is related to the burning rate and is therefore an important parameter for describing and understanding the burning process, especially since the melting rate is commonly recorded during standard flammability testing for metallic materials and is incorporated into many relative flammability ranking schemes. However, whilst the factors that influence melting rate (such as oxygen pressure or specimen diameter) have been well characterized, there is a need for an improved understanding of how these parameters interact as part of the overall melting and burning of the system. Proposed here is the ‘Melting Rate Triangle’, which aims to provide this focus through a conceptual framework for understanding how the melting rate (of solid fuel) is determined and regulated during heterogeneous burning. In the paper, the proposed conceptual model is shown to be both (a) consistent with known trends and previously observed results, and (b)capable of being expanded to incorporate new data. Also shown are examples of how the Melting Rate Triangle can improve the interpretation of flammability test results. Slusser and Miller previously published an ‘Extended Fire Triangle’ as a useful conceptual model of ignition and the factors affecting ignition, providing industry with a framework for discussion. In this paper it is shown that a ‘Melting Rate Triangle’ provides a similar qualitative framework for burning, leading to an improved understanding of the factors affecting fire propagation and extinguishment.

The increased flammability of metallic materials burning in reduced gravity

Data generated in a normal gravity environment is often used in design and risk assessment for reduced gravity applications. It has been clearly demonstrated that this is a conservative approach for non-metallic materials which have been repeatedly shown to be less flammable in a reduced gravity environment. However, recent work has demonstrated this is not true for metallic materials. This work, conducted in a newly completed drop tower observed a significant increase in both lowest burn pressure and burn rate in reduced gravity. Hence the normal gravity qualification of a metallic materials’ lowest burn pressure or burn rate for reduced-gravity or space-based systems is clearly not conservative. This paper presents a summary of this work and the results obtained for several metallic materials showing an increased flammability and burn rate for a range of oxygen pressures, and discusses the implications of this work on the fire-safety of space-based systems.

Metallic glass fiber-reinforced Zr-based bulk metallic glass

A novel Zr-based bulk metallic glass composite was fabricated using stainless steel capillaries as the reinforcement. Large plasticity (14%) was achieved in the composite with a reinforcement volume fraction of 38%. The high plasticity observed can be attributed to the formation of small glass fibers encapsulated by the steel capillaries, which promotes multiple shear bands in both metallic glass matrix and the fibers themselves. A new parameter was also proposed to approximately evaluate the reinforcement efficiency.

The flammability of metallic materials in normal and reduced gravity

Metallic materials exposed to oxygen-enriched atmospheres – as commonly used in the medical, aerospace, aviation and numerous chemical processing industries – represent a significant fire hazard which must be addressed during design, maintenance and operation. Hence, accurate knowledge of metallic materials flammability is required. Reduced gravity (i.e. space-based) operations present additional unique concerns, where the absence of gravity must also be taken into account. The flammability of metallic materials has historically been quantified using three standardised test methods developed by NASA, ASTM and ISO. These tests typically involve the forceful (promoted) ignition of a test sample (typically a 3.2 mm diameter cylindrical rod) in pressurised oxygen. A test sample is defined as flammable when it undergoes burning that is independent of the ignition process utilised. In the standardised tests, this is indicated by the propagation of burning further than a defined amount, or „burn criterion.. The burn criterion in use at the onset of this project was arbitrarily selected, and did not accurately reflect the length a sample must burn in order to be burning independent of the ignition event and, in some cases, required complete consumption of the test sample for a metallic material to be considered flammable. It has been demonstrated that a) a metallic material.s propensity to support burning is altered by any increase in test sample temperature greater than ~250-300 oC and b) promoted ignition causes an increase in temperature of the test sample in the region closest to the igniter, a region referred to as the Heat Affected Zone (HAZ). If a test sample continues to burn past the HAZ (where the HAZ is defined as the region of the test sample above the igniter that undergoes an increase in temperature of greater than or equal to 250 oC by the end of the ignition event), it is burning independent of the igniter, and should be considered flammable. The extent of the HAZ, therefore, can be used to justify the selection of the burn criterion. A two dimensional mathematical model was developed in order to predict the extent of the HAZ created in a standard test sample by a typical igniter. The model was validated against previous theoretical and experimental work performed in collaboration with NASA, and then used to predict the extent of the HAZ for different metallic materials in several configurations. The extent of HAZ predicted varied significantly, ranging from ~2-27 mm depending on the test sample thermal properties and test conditions (i.e. pressure). The magnitude of the HAZ was found to increase with increasing thermal diffusivity, and decreasing pressure (due to slower ignition times). Based upon the findings of this work, a new burn criterion requiring 30 mm of the test sample to be consumed (from the top of the ignition promoter) was recommended and validated. This new burn criterion was subsequently included in the latest revision of the ASTM G124 and NASA 6001B international test standards that are used to evaluate metallic material flammability in oxygen. These revisions also have the added benefit of enabling the conduct of reduced gravity metallic material flammability testing in strict accordance with the ASTM G124 standard, allowing measurement and comparison of the relative flammability (i.e. Lowest Burn Pressure (LBP), Highest No-Burn Pressure (HNBP) and average Regression Rate of the Melting Interface(RRMI)) of metallic materials in normal and reduced gravity, as well as determination of the applicability of normal gravity test results to reduced gravity use environments. This is important, as currently most space-based applications will typically use normal gravity information in order to qualify systems and/or components for reduced gravity use. This is shown here to be non-conservative for metallic materials which are more flammable in reduced gravity. The flammability of two metallic materials, Inconel® 718 and 316 stainless steel (both commonly used to manufacture components for oxygen service in both terrestrial and space-based systems) was evaluated in normal and reduced gravity using the new ASTM G124-10 test standard. This allowed direct comparison of the flammability of the two metallic materials in normal gravity and reduced gravity respectively. The results of this work clearly show, for the first time, that metallic materials are more flammable in reduced gravity than in normal gravity when testing is conducted as described in the ASTM G124-10 test standard. This was shown to be the case in terms of both higher regression rates (i.e. faster consumption of the test sample – fuel), and burning at lower pressures in reduced gravity. Specifically, it was found that the LBP for 3.2 mm diameter Inconel® 718 and 316 stainless steel test samples decreased by 50% from 3.45 MPa (500 psia) in normal gravity to 1.72 MPa (250 psia) in reduced gravity for the Inconel® 718, and 25% from 3.45 MPa (500 psia) in normal gravity to 2.76 MPa (400 psia) in reduced gravity for the 316 stainless steel. The average RRMI increased by factors of 2.2 (27.2 mm/s in 2.24 MPa (325 psia) oxygen in reduced gravity compared to 12.8 mm/s in 4.48 MPa (650 psia) oxygen in normal gravity) for the Inconel® 718 and 1.6 (15.0 mm/s in 2.76 MPa (400 psia) oxygen in reduced gravity compared to 9.5 mm/s in 5.17 MPa (750 psia) oxygen in normal gravity) for the 316 stainless steel. Reasons for the increased flammability of metallic materials in reduced gravity compared to normal gravity are discussed, based upon the observations made during reduced gravity testing and previous work. Finally, the implications (for fire safety and engineering applications) of these results are presented and discussed, in particular, examining methods for mitigating the risk of a fire in reduced gravity.

Linear and nonlinear propagation of localised plasmon in metallic nanostructures

A major challenge in modern photonics and nano-optics is the diffraction limit of light which does not allow field localisation into regions with dimensions smaller than half the wavelength. Localisation of light into nanoscale regions (beyond its diffraction limit) has applications ranging from the design of optical sensors and measurement techniques with resolutions as high as a few nanometres, to the effective delivery of optical energy into targeted nanoscale regions such as quantum dots, nano-electronic and nano-optical devices. This field has become a major research direction over the last decade. The use of strongly localised surface plasmons in metallic nanostructures is one of the most promising approaches to overcome this problem. Therefore, the aim of this thesis is to investigate the linear and non-linear propagation of surface plasmons in metallic nanostructures. This thesis will focus on two main areas of plasmonic research –– plasmon nanofocusing and plasmon nanoguiding. Plasmon nanofocusing – The main aim of plasmon nanofocusing research is to focus plasmon energy into nanoscale regions using metallic nanostructures and at the same time achieve strong local field enhancement. Various structures for nanofocusing purposes have been proposed and analysed such as sharp metal wedges, tapered metal films on dielectric substrates, tapered metal rods, and dielectric V-grooves in metals. However, a number of important practical issues related to nanofocusing in these structures still remain unclear. Therefore, one of the main aims of this thesis is to address two of the most important of issues which are the coupling efficiency and heating effects of surface plasmons in metallic nanostructures. The method of analysis developed throughout this thesis is a general treatment that can be applied to a diversity of nanofocusing structures, with results shown here for the specific case of sharp metal wedges. Based on the geometrical optics approximation, it is demonstrated that the coupling efficiency from plasmons generated with a metal grating into the nanofocused symmetric or quasi-symmetric modes may vary between ~50% to ~100% depending on the structural parameters. Optimal conditions for nanofocusing with the view to minimise coupling and dissipative losses are also determined and discussed. It is shown that the temperature near the tip of a metal wedge heated by nanosecond plasmonic pulses can increase by several hundred degrees Celsius. This temperature increase is expected to lead to nonlinear effects, self-influence of the focused plasmon, and ultimately self-destruction of the metal tip. This thesis also investigates a different type of nanofocusing structure which consists of a tapered high-index dielectric layer resting on a metal surface. It is shown that the nanofocusing mechanism that occurs in this structure is somewhat different from other structures that have been considered thus far. For example, the surface plasmon experiences significant backreflection and mode transformation at a cut-off thickness. In addition, the reflected plasmon shows negative refraction properties that have not been observed in other nanofocusing structures considered to date. Plasmon nanoguiding – Guiding surface plasmons using metallic nanostructures is important for the development of highly integrated optical components and circuits which are expected to have a superior performance compared to their electronicbased counterparts. A number of different plasmonic waveguides have been considered over the last decade including the recently considered gap and trench plasmon waveguides. The gap and trench plasmon waveguides have proven to be difficult to fabricate. Therefore, this thesis will propose and analyse four different modified gap and trench plasmon waveguides that are expected to be easier to fabricate, and at the same time acquire improved propagation characteristics of the guided mode. In particular, it is demonstrated that the guided modes are significantly screened by the extended metal at the bottom of the structure. This is important for the design of highly integrated optics as it provides the opportunity to place two waveguides close together without significant cross-talk. This thesis also investigates the use of plasmonic nanowires to construct a Fabry-Pérot resonator/interferometer. It is shown that the resonance effect can be achieved with the appropriate resonator length and gap width. Typical quality factors of the Fabry- Pérot cavity are determined and explained in terms of radiative and dissipative losses. The possibility of using a nanowire resonator for the design of plasmonic filters with close to ~100% transmission is also demonstrated. It is expected that the results obtained in this thesis will play a vital role in the development of high resolution near field microscopy and spectroscopy, new measurement techniques and devices for single molecule detection, highly integrated optical devices, and nanobiotechnology devices for diagnostics of living cells.

Grain size distributions of Magneli phases and metallic titanium in chondritic porous interplanetary dust particles

A mineralogical survey of chondritic interplanetary dust particles (IDPs)showed that these micrometeorites differ significantly in form and texture from components of carbonaceous chondrites and contain some mineral assemblages which do not occur in any meteorite class1. Models of chondritic IDP mineral evolution generally ignore the typical (ultra-) fine grain size of consituent minerals which range between 0.002-0.1µm in size2. The chondritic porous (CP) subset of chondritic IDPs is probably debris from short period comets although evidence for a cometary origin is still circumstantial3. If CP IDPs represent dust from regions of the Solar System in which comet accretion occurred, it can be argued that pervasive mineralogical evolution of IDP dust has been arrested due to cryogenic storage in comet nuclei. Thus, preservation in CP IDPs of "unusual meteorite minerals", such as oxides of tin, bismuth and titanium4, should not be dismissed casually. These minerals may contain specific information about processes that occurred in regions of the solar nebula, and early Solar System, which spawned the IDP parent bodies such as comets and C, P and D asteroids6. It is not fully appreciated that the apparent disparity between the mineralogy of CP IDPs and carbonaceous chondrite matrix may also be caused by the choice of electron-beam techniques with different analytical resolution. For example, Mg-Si-Fe distributions of Cl matrix obtained by "defocussed beam" microprobe analyses are displaced towards lower Fe-values when using analytical electron microscope (AEM)data which resolve individual mineral grains of various layer silicates and magnetite in the same matrix6,7. In general, "unusual meteorite minerals" in chondritic IDPs, such as metallic titanium, Tin01-n(Magneli phases) and anatase8 add to the mineral data base of fine-grained Solar System materials and provide constraints on processes that occurred in the early Solar System.