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.

Limits of spherical blur determined with an adaptive optics mirror

We extended an earlier study (Vision Research, 45, 1967–1974, 2005) in which we investigated limits at which induced blur of letter targets becomes noticeable, troublesome and objectionable. Here we used a deformable adaptive optics mirror to vary spherical defocus for conditions of a white background with correction of astigmatism; a white background with reduction of all aberrations other than defocus; and a monochromatic background with reduction of all aberrations other than defocus. We used seven cyclopleged subjects, lines of three high-contrast letters as targets, 3–6 mm artificial pupils, and 0.1–0.6 logMAR letter sizes. Subjects used a method of adjustment to control the defocus component of the mirror to set the 'just noticeable', 'just troublesome' and 'just objectionable' defocus levels. For the white-no adaptive optics condition combined with 0.1 logMAR letter size, mean 'noticeable' blur limits were ±0.30, ±0.24 and ±0.23 D at 3, 4 and 6 mm pupils, respectively. White-adaptive optics and monochromatic-adaptive optics conditions reduced blur limits by 8% and 20%, respectively. Increasing pupil size from 3–6 mm decreased blur limits by 29%, and increasing letter size increased blur limits by 79%. Ratios of troublesome to noticeable, and of objectionable to noticeable, blur limits were 1.9 and 2.7 times, respectively. The study shows that the deformable mirror can be used to vary defocus in vision experiments. Overall, the results of noticeable, troublesome and objectionable blur agreed well with those of the previous study. Attempting to reduce higher-order aberrations or chromatic aberrations, reduced blur limits to only a small extent.

Selection and optimization of piezoelectric polyvinylidene fluoride polymers for adaptive optics in space environments

Various piezoelectric polymers based on polyvinylidene fluoride (PVDF) are of interest for large aperture space-based telescopes. Dimensional adjustments of adaptive polymer films depend on charge deposition and require a detailed understanding of the piezoelectric material responses which are expected to deteriorate owing to strong vacuum UV, � -, X-ray, energetic particles and atomic oxygen exposure. We have investigated the degradation of PVDF and its copolymers under various stress environments detrimental to reliable operation in space. Initial radiation aging studies have shown complex material changes with lowered Curie temperatures, complex material changes with lowered melting points, morphological transformations and significant crosslinking, but little influence on piezoelectric d33 constants. Complex aging processes have also been observed in accelerated temperature environments inducing annealing phenomena and cyclic stresses. The results suggest that poling and chain orientation are negatively affected by radiation and temperature exposure. A framework for dealing with these complex material qualification issues and overall system survivability predictions in low earth orbit conditions has been established. It allows for improved material selection, feedback for manufacturing and processing, material optimization/stabilization strategies and provides guidance on any alternative materials.

Thomas Young's contribution to visual optics : the Bakerian lecture "On the mechanism of the eye"

Thomas Young (1773-1829) carried out major pioneering work in many different subjects. In 1800 he gave the Bakerian Lecture of the Royal Society on the topic of the “mechanism of the eye”: this was published in the following year (Young, 1801). Young used his own design of optometer to measure refraction and accommodation, and discovered his own astigmatism. He considered the different possible origins of accommodation and confirmed that it was due to change in shape of the lens rather than to change in shape of the cornea or an increase in axial length. However, the paper also dealt with many other aspects of visual and ophthalmic optics, such as biometric parameters, peripheral refraction, longitudinal chromatic aberration, depth-of-focus and instrument myopia. These aspects of the paper have previously received little attention. We now give detailed consideration to these and other less-familiar features of Young’s work and conclude that his studies remain relevant to many of the topics which currently engage visual scientists.

Deterministic diffraction loss modelling for novel broadband communication in rural environments

This paper presents a deterministic modelling approach to predict diffraction loss for an innovative Multi-User-Single-Antenna (MUSA) MIMO technology, proposed for rural Australian environments. In order to calculate diffraction loss, six receivers have been considered around an access point in a selected rural environment. Generated terrain profiles for six receivers are presented in this paper. Simulation results using classical diffraction models and diffraction theory are also presented by accounting the rural Australian terrain data. Results show that in an area of 900 m by 900 m surrounding the receivers, path loss due to diffraction can range between 5 dB and 35 dB. Diffraction loss maps can contribute to determine the optimal location for receivers of MUSA-MIMO systems in rural areas.

Thomas Young’s contributions to geometrical optics

In addition to his work on physical optics, Thomas Young (1773-1829) made several contributions to geometrical optics, most of which received little recognition in his time or since. We describe and assess some of these contributions: Young’s construction (the basis for much of his geometric work), paraxial refraction equations, oblique astigmatism and field curvature, and gradient-index optics.

Thomas Young’s investigations in gradient-index optics

Purpose: James Clerk Maxwell is usually recognized as being the first, in 1854, to consider using inhomogeneous media in optical systems. However, some fifty years earlier Thomas Young, stimulated by his interest in the optics of the eye and accommodation, had already modeled some applications of gradient-index optics. These applications included using an axial gradient to provide spherical aberration-free optics and a spherical gradient to describe the optics of the atmosphere and the eye lens. We evaluated Young’s contributions. Method: We attempted to derive Young’s equations for axial and spherical refractive index gradients. Raytracing was used to confirm accuracy of formula. Results: We did not confirm Young’s equation for the axial gradient to provide aberration-free optics, but derived a slightly different equation. We confirmed the correctness of his equations for deviation of rays in a spherical gradient index and for the focal length of a lens with a nucleus of fixed index surrounded by a cortex of reducing index towards the edge. Young claimed that the equation for focal length applied to a lens with part of the constant index nucleus of the sphere removed, such that the loss of focal length was a quarter of the thickness removed, but this is not strictly correct. Conclusion: Young’s theoretical work in gradient-index optics received no acknowledgement from either his contemporaries or later authors. While his model of the eye lens is not an accurate physiological description of the human lens, with the index reducing least quickly at the edge, it represented a bold attempt to approximate the characteristics of the lens. Thomas Young’s work deserves wider recognition.

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.

The Glenn A. Fry award lecture 2011 : peripheral optics of the human eye

There has been a low level of interest in peripheral aberrations and corresponding image quality for over 200 years. Most work has been concerned with the second-order aberrations of defocus and astigmatism that can be corrected with conventional lenses. Studies have found high levels of aberration, often amounting to several dioptres, even in eyes with only small central defocus and astigmatism. My investigations have contributed to understanding shape changes in the eye with increases in myopia, changes in eye optics with ageing, and how surgical interventions intended to correct central refractive errors have unintended effects on peripheral optics. My research group has measured peripheral second- and higher-order aberrations over a 42° horizontal × 32° vertical diameter visual field. There is substantial variation in individual aberrations with age and pathology. While the higher-order aberrations in the periphery are usually small compared with second-order aberrations, they can be substantial and change considerably after refractive surgery. The thrust of my research in the next few years is to understand more about the peripheral aberrations of the human eye, to measure visual performance in the periphery and determine whether this can be improved by adaptive optics correction, to use measurements of peripheral aberrations to learn more about the optics of the eye and in particular the gradient index structure of the lens, and to investigate ways of increasing the size of the field of good retinal image quality.

Measurement of the first neutron diffraction peak of D2O flowing in a 2 mm diameter aluminium tube as a function of temperature

A pilot experiment was performed using the WOMBAT powder diffraction instrument at ANSTO in which the first neutron diffraction peak (Q0) was measured for D2O flowing in a 2 mm internal diameter aluminium tube. Measurements of Q0 were made at -9, 4.3, 6.9, 12, 18.2 and 21.5 °C. The D2O was circulated using a siphon with water in the lower reservoir returned to the upper reservoir using a small pump. This enabled stable flow to be maintained for several hours. For example, if the pump flow increased slightly, the upper reservoir level rose, increasing the siphon flow until it matched the return flow. A neutron wavelength of 2.4 Å was used and data integrated over 60 minutes for each temperature. A jet of nitrogen from a liquid N2 Dewar was directed over the aluminium tube to vary water temperature. After collection of the data, the d spacing of the aluminium peaks was used to calculate the temperature of the aluminium within the neutron beam and therefore was considered to be an accurate measure of water temperature within the beam. Sigmaplot version 12.3 was used to fit a Weibull five parameter peak fit to the first neutron diffraction peak. The values of Q0 obtained in this experiment showed an increase with temperature consistent with data in the literature [1] but were consistently higher than published values for bulk D20. For example at 21.5 °C we obtained a value of 2.008 Å-1 for Q0 compared to a literature value of 1.988 Å-1 for bulk D2O at 20 °C, a difference of 1%. Further experiments are required to see if this difference is real or artifactual.