Topology of phase and polarisation singularities in focal regions

Andrejić, Petar; Lekner, John

doi:10.1088/2040-8986/aa895d

Cited by 16 publications

(10 citation statements)

References 17 publications

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“…The qualitative features of the class of beams presented here will be found in other beams with strong focusing. For example, the occurrence of vortices in focused waves has been found to be quite generic [11,4,37,38,25]. This is one reason why the class of beams discussed here is worth studying, even though it corresponds to an experimentally unrealistic case of maximal focusing.…”

Section: Discussionmentioning

confidence: 99%

“…We will discuss examples based on the basic beam solution (12) and derivatives thereof, but none of our examples will have a z-derivative of (12) and so they will not be in Lekner's class of solutions. We refer the reader to [22,24,25] for many interesting details of the proto-beam and electromagnetic beams built from it. Lekner [22] also points out that further solutions can be generated by the method of displacing z by a complex constant, which was used to generate the "complex-sources" waves described in the Introduction.…”

Section: Beams From a Spherical Standing Wavementioning

confidence: 99%

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Some exact solutions for light beams

Philbin

2018

J. Opt.

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We give an infinite class of exact analytical solutions for monochromatic light beams with strong focusing. As the solutions do not contain integrals, they are easy to explore compared with diffraction-theory results for strongly focused light. All monochromatic beams can be decomposed into two standing waves, each proportional to a Hilbert transform of the other. This means a beam can be built from any standing wave and our class is derived using this procedure. We give a visual overview of some of the beams, which reveals many interesting energy and field structures, including vortices in the energy flow, angular momentum in the propagation direction, and knotted field lines. We also show how the method can be used to design beams with an arbitrary focal shape.

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Section: Discussionmentioning

confidence: 99%

Section: Beams From a Spherical Standing Wavementioning

confidence: 99%

Some exact solutions for light beams

Philbin

2018

J. Opt.

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“…These families approximate the Gaussian beam along the beam axis, and radially, respectively, for large kb 15,16 . The limit of tightest focus for both of these families is the proto-beam.…”

Section: Highest Peak For a Given Intensitymentioning

confidence: 99%

Convergent measure of focal extent, and largest peak intensity for non-paraxial beams

Andrejić

2018

J. Opt.

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Second moment beam widths are commonly used in paraxial optics to define the focal extent of beams. However, second moments of arbitrary beams are not guaranteed to be finite. I propose the focal concentration area as a measure of beam focal area, defined to be the ratio of total radial intensity to radial intensity regulated by a unit area Gaussian distribution. I use the Dirac delta limit of this distribution to establish a rigorous upper bound on the peak intensity of non-paraxial beams of a given total intensity, and show that this is achieved by the recently proposed 'protobeam' solution. I discuss the generalisation to electromagnetic beams, and find the same lower bound as the scalar case. This bound cannot be achieved for any physical beam, and as such the physical lower bound must be higher.

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“…Chapters 3 and 4 reproduce verbatim two papers that I have co-authored with John Lekner during the course of this thesis. These have been published in Optics Communications [22] and Journal of Optics [23] respectively.…”

Section: Academic Contributionsmentioning

confidence: 99%

Localised Waves: Tightest Focus, Lorentz Transformation, and Polarization Singularities of Non-Paraxial Beams

Andrejić¹

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<p>I explore the limits of how tightly a beam can be focused, and derive a focal parameter for scalar beams that can be symbolically evaluated for most beams, and is guaranteed to be convergent for physical beams, that compares peak in- tensity to the total intensity in the beam profile. I argue that this parameter is superior to spot size, and use this to derive a rigorous limit of focusing for scalar beams. A particular beam known as the proto-beam achieves this tight- est focus possible. I show the generalisation of this measure to electromagnetic beams, and place a lower bound on the focal extent of electromagnetic beams. I also propose the use of exponential regulators as alternatives to moment based measures, as a solution to the convergence issues created by the power law decay of exact solutions. I explore the Doppler shift for finite beams, and how monochromatic beams become polychromatic under a Lorentz boost. The local frequency is also explored, and I show that a deviation of the local frequency from the Doppler frequency will occur due to wavelength broadening near the focus. Lekner and I examine a beam that closely approximates a paraxial Gaussian beam radially, and examine the phase singularities for optical beams that occur near the zeros of the beams wavefunction. We also investigate attempts to find exact solutions with Gaussian profiles, and show that this is impossible; any such beam will be evanescent and exponentially grow. Finally, I investigate the property of finite classical electromagnetic pulses having a zero momentum frame, and show that for quantum single photon pulses this property holds for the expectation value. I show that any individual measurement however, still measures a light-like four-momentum for the photon.</p>

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Topology of phase and polarisation singularities in focal regions

Cited by 16 publications

References 17 publications

Some exact solutions for light beams

Some exact solutions for light beams

Convergent measure of focal extent, and largest peak intensity for non-paraxial beams

Localised Waves: Tightest Focus, Lorentz Transformation, and Polarization Singularities of Non-Paraxial Beams

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