There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

1. Introduction 2. Theoretical foundations 3. Propagation and focusing of optical fields 4. Spatial resolution and position accuracy 5. Nanoscale optical microscopy 6. Near-field optical probes 7. Probe-sample distance control 8. Light emission and optical interaction in nanoscale environments 9. Quantum emitters 10. Dipole emission near planar interfaces 11. Photonic crystals and resonators 12. Surface plasmons 13. Forces in confined fields 14. Fluctuation-induced phenomena 15. Theoretical methods in nano-optics Appendices Index.

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Principles of nano-optics

An overview of the recent developments in the field of cylindrical vector beams is
provided. As one class of spatially variant polarization, cylindrical vector beams
are the axially symmetric beam solution to the full vector electromagnetic wave
equation. These beams can be generated via different active and passive methods.
Techniques for manipulating these beams while maintaining the polarization symmetry
have also been developed. Their special polarization symmetry gives rise to unique
high-numerical-aperture focusing properties that find important applications in
nanoscale optical imaging and manipulation. The prospects for cylindrical vector
beams and their applications in other fields are also briefly discussed.

Cylindrical vector beams: from mathematical concepts to applications

Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

Cylindrical-vector beams are of increasing recent interest for their role in novel laser resonators and their applications to electron acceleration and scanning microscopy. In this paper, we calculate cylindrical-vector fields, near the focal region of an aplanatic lens, and briefly discuss some applications. We show that, in the particular case of a tightly focused, radially polarized beam, the polarization shows large inhomogeneities in the focal region, while the azimuthally polarized beam is purely transverse even at very high numerical apertures.

Focusing of high numerical aperture cylindrical-vector beams.

Two interferometric techniques for converting a linearly polarized laser beam into a radially polarized beam with uniform azimuthal intensity are described. The techniques are based on the linear combination of orthogonally polarized beams, which have tailored intensity and phase profiles. Linearly polarized beams with intensity profiles tailored using a modified laser or an apodization filter are combined in separate experiments to produce radially polarized light. A beam with an extinction ratio of −21.7 dB and azimuthal intensity variations of less than ±12% is produced using the modified laser output. The second technique uses circularly polarized light and a unique spiral phase delay plate to produce the required phase profile. When focused, a radially polarized beam has a net longitudinal field useful for particle acceleration and, perhaps, other unique applications.

Generating radially polarized beams interferometrically.

Conversion of a linearly polarized CO2 laser beam into a radially polarized beam is demonstrated with a novel double-interferometer system. The first Mach–Zehnder interferometer converts the linearly polarized input beam into two beams with sin2 θ and cos2 θ intensity profiles, where θ is the azimuthal angle. This is accomplished by using two spiral-phase-delay plates with opposite handedness in the two legs of the interferometer to impart a one-wave phase delay azimuthally across the face of the beams. After these beams are interfered with, the resulting beams are sent directly into the second Mach–Zehnder interferometer, where the polarization direction of one beam is rotated by 90°. The beams are then recombined at the output of the second interferometer with a polarization-sensitive beam splitter to generate a radially polarized beam. The output beam is ≈ 92% radially polarized and contains ≈ 85% of the input power. This system will be used in upcoming laser particle acceleration experiments.

Efficient radially polarized laser beam generation with a double interferometer.

A 580-MW peak power, radially polarized CO[sub 2] laser beam ([lambda]=10.6[mu]m) focused by an axicon accelerated 40-MeV electrons by [le]3.7 MeV over a 12-cm interaction length (31 MeV/m), using the inverse Cherenkov effect in which a gas is used to slow the light wave. This represents the first direct observation of acceleration using this effect and demonstrates the effectiveness of the radially-polarized--axicon-focused geometry. The observed energy gain agrees with model predictions.

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Laser Acceleration of Relativistic Electrons Using the Inverse Cherenkov Effect.

Acceleration of free electrons by the inverse \ifmmode \check{C}\else \v{C}\fi{}erenkov effect using radially polarized laser light focused through an axicon [J. P. Fontana and R. H. Pantell, J. Appl. Phys. 54, 4285 (1983)] has been studied utilizing a Monte Carlo computer simulation and further theoretical analysis. The model includes effects, such as scattering of the electrons by the gas, and diffraction and interference effects of the axicon laser beam, that were not included in the original analysis of Fontana and Pantell. Its accuracy is validated using available experimental data. The model results show that effective acceleration is possible even with the effects of scattering. Sample results are given. The analysis includes examining the issues of axicon focusing, phase errors, energy gain, phase slippage, focusing of the $e$ beam, and emittance growth.

Modeling of inverse Čerenkov laser acceleration with axicon laser-beam focusing

In the use of spark gaps as switching devices, it is desirable to maximize the power delivered to the load and to minimize the power deposited in the switch; that is, it is desirable for the resistance of the switch to be negligible as compared to the load. The hydrodynamic time scale for expansion of the arc in a spark gap and hence for the reduction in its resistance to a small value is tens to hundreds of nanoseconds. Therefore, with current pulses of duration of a few hundred nanoseconds or less, the resistance of the spark gap may be a significant fraction of that of the load. In this paper, we report on measurements that determine the resistance of the arc in a fully diagnosed laser‐triggered spark gap. The spark gap switches a 100‐ns, 1.5‐Ω waterline into a 1.5‐Ω load resistor. A capacitive voltage divider housed within the switch enclosure measures the voltage drop across the switch, a current‐viewing resistor measures the current, and an interferometer measures the diameter of the plasma column, ...

Wayne D. Kimura

Papers

Generating radially polarized beams interferometrically.

Efficient radially polarized laser beam generation with a double interferometer.

Laser Acceleration of Relativistic Electrons Using the Inverse Cherenkov Effect.

Modeling of inverse Čerenkov laser acceleration with axicon laser-beam focusing

Arc resistance of laser‐triggered spark gaps