The ability to resolve molecules individually has many potential applications. These include understanding the local environments of single molecules including details of their interactions with surroundings. The ability to individually address and manipulate the spin states is also required for spin based quantum information processing. Although optical detection techniques, such as optically detected electron spin resonance (ESR) seem very powerful in these contexts, multiple molecules in the focal volume of a diffraction limited confocal microscope spot cannot in general be resolved individually. Here we propose to solve this problem using optically detected ESR imaging based on the use of high field gradients. In the present research, subwavelength single molecule imaging is demonstrated by using the optically detected ESR technique and the optically detected electron spin echo envelope modulation (ESEEM) technique. Ultra fast Rabi nutation experiments are also performed to demonstrate the feasibility of fast spin manipulations at a low microwave power. Micrometer sized gradient coils, together with micrometer sized co-planar microstrip transmission lines, are designed and fabricated by optical lithography in order to produce the necessary high magnetic field gradients. These fabricated devices are used to demonstrate this subwavelength imaging technique by imaging single electron spins of the nitrogen-vacancy (NV) defect in diamond. In this demonstration, multiple NV defects, unresolved in a single focal volume of a diffraction limited microscope are successfully resolved by the optically detected ESR techniques. Specifically, two neighboring NV defects separated by about 170nm are resolved. Ultra Fast electron spin nutation with an oscillation period of 1.33ns is also achieved by the high microwave magnetic field induced by the current flowing through the fabricated co-planar microstrip lines. These optically detected ESR and ESEEM techniques combined with the micrometer sized gradient coil may find many applications, including single molecule imaging and quantum information processing.

The dispersion property of periodic structures is a hot research topic in the last decade. By exploiting dispersion properties, one can manipulate the propagation of electromagnetic waves, and produce effects that do not exist in conventional materials. This thesis is devoted to two important dispersion effects: negative refraction and designed surface plasmons. First, we introduce negative refraction and designed surface plasmons, including a historical perspective, main areas for applications and current trends. Several numerical methods are implemented to analyze electromagnetic effects. We apply the layer-KKR method to calculate the electromagnetic wave through a slab of photonic crystals. By implementing the refraction matrix for semi-infinite photonic crystals, the layer-KKR method is modified to compute the coupling coefficient between plane waves and Bloch modes in photonic crystals. The plane wave method is applied to obtain the band structure and the equal-frequency contours in two-dimensional regular photonic crystals. The finite-difference time-domain method is widely used in our works, but we briefly discuss two calculation recipes in this thesis: how to deal with the surface termination of a perfect conductor and how to calculate the frequency response of high-Q cavities more efficiently using the Pad\`{e} approximation method. We discuss a photonic crystal that exhibits negative refraction characterized by an effective negative index, and systematically analyze the coupling coefficients between plane waves in air and Bloch waves in the photonic crystal. We find and explain that the coupling coefficients are strong-angularly dependent. We first propose an open-cavity structure formed by a negative-refraction photonic crystal. To illuminate the physical mechanism of the subwavelength imaging, we analyze both intensity and phase spectrum of the transmission through a slab of photonic crystals with all-angle negative refraction. It is shown that the focusing properties of the photonic crystal slab are mainly due to the negative refraction effect, rather than the self-collimation effect. As to designed surface plasmons, we design a structured perfectly conducting surface to achieve the negative refraction of surface waves. By the average field method, we obtain the effective permittivity and permeability of a perfectly conducting surface drilled with one-dimensional periodic rectangle holes, and propose this structure as a designed surface plasmon waveguide. By the analogy between designed surface plasmons and surface plasmon polaritons, we show that two different resonances contribute to the enhanced transmission through a metallic film with an array of subwavelength holes, and explain that the shape effect is attributed to localized waveguide resonances. / QC 20100817