9 Russells Crescent

Horley, United Kingdom

9 Russells Crescent

Horley, United Kingdom
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Laven P.,9 Russells Crescent
Applied Optics | Year: 2017

Supernumerary arcs on rainbows are historically important because in the early 1800s they provided evidence in favor of the wave theory of light. The success of Airy's rainbow integral has overshadowed the earlier contribution from Young, who proposed that supernumerary arcs were caused by interference between two geometrical rays that emerge from the raindrop at the same scattering angle. Airy dismissed Young's idea as "the imperfect theory of interference" because it predicted supernumerary arcs at the wrong angles. Young was unaware that a light ray encountering a focal line can suffer a phase shift of 90. If these phase shifts are taken into account, the theory of interference becomes surprisingly accurate. © 2017 Optical Society of America.


Laven P.,9 Russells Crescent
Applied Optics | Year: 2017

Near-forward scattering of sunlight generates coronas and iridescence on clouds. Coronas are caused by diffraction, whereas iridescence is less easily explained. Iridescence often appears as bands of color aligned with the edges of clouds or as apparently random patches of color on clouds. This paper suggests that iridescence is due to interference between light that has been diffracted by a spherical droplet of water and light that has been transmitted through the same droplet. © 2017 Optical Society of America.


Lock J.A.,Cleveland State University | Laven P.,9 Russells Crescent
Applied Optics | Year: 2017

We consider transmission scattering of a plane wave by a radially inhomogeneous sphere containing a localized region of refractive index decrease. In ray theory, the boundary conditions on the deflection angle at axial and grazing incidence determine that transmission scattering gives rise to an even number of bows, half of them being relative maximum bows and half being relative minimum bows. For a model refractive index profile, we determine the conditions under which different numbers of bows occur, and we suggest physical mechanisms responsible for producing them. We also verify that these bows occur in wave scattering in the short wavelength limit, both in the frequency domain and time domain. © 2017 Optical Society of America.


Lock J.A.,Cleveland State University | Laven P.,9 Russells Crescent
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2011

We computed the Debye series p = 1 and p = 2 terms of the Mie scattered intensity as a function of scattering angle and delay time for a linearly polarized plane wave pulse incident on a spherical dielectric particle and physically interpreted the resulting numerical data. Radiation shed by electromagnetic surface waves plays a prominent role in the scattered intensity. We determined the surface wave phase and damping rate and studied the structure of the p = 1; 2 surface wave glory in the time domain. © 2011 Optical Society of America.


Lock J.A.,Cleveland State University | Laven P.,9 Russells Crescent
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2011

The p = 0 term of the Mie-Debye scattering amplitude contains the effects of external reflection and diffraction. We computed the reflected intensity in the time domain as a function of the scattering angle and delay time for a short electromagnetic pulse incident on a spherical particle and compared it to the predicted behavior in the forward-focusing region, the specular reflection region, and the glory region. We examined the physical consequences of three different approaches to the exact diffraction amplitude, and determined the signature of diffraction in the time domain. The external reflection surface wave amplitude gradually replaces the diffraction amplitude in the angular transition region between forward-focusing and the region of specular reflection. The details of this replacement were studied in the time domain. © 2011 Optical Society of America.


Lock J.A.,Cleveland State University | Laven P.,9 Russells Crescent
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2012

Although scattering of light by a coated sphere is much more complicated than scattering by a homogeneous sphere, each of the partial wave amplitudes for scattering of a plane wave by a coated sphere can be expanded in a Debye series. The Debye series can then be rearranged in terms of the various reflections that each partial wave undergoes inside the coated sphere. For a given number of internal reflections, it is found that many different Debye terms produce the same scattered intensity as a function of scattering angle. This is called path degeneracy. In addition, some of the ray trajectories are repeats of those occurring for a smaller number of internal reflections in the sense that they produce identical time delays as a function of scattering angle. These repeated paths, however, have a different intensity as a function of scattering angle than their predecessors. The degenerate paths and repeated paths considerably simplify the interpretation of scattering within the coated sphere, thus making it possible to catalog the contributions of the various paths. © 2012 Optical Society of America.


Laven P.,9 Russells Crescent | Lock J.A.,Cleveland State University
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2012

Numerical computations were made of scattering of an incident electromagnetic pulse by a coated sphere that is large compared to the dominant wavelength of the incident light. The scattered intensity was plotted as a function of the scattering angle and delay time of the scattered pulse. For fixed core and coating radii, the Debye series terms that most strongly contribute to the scattered intensity in different regions of scattering angle-delay time space were identified and analyzed. For a fixed overall radius and an increasing core radius, the first-order rainbow was observed to evolve into three separate components. The original component faded away, while the two new components eventually merged together. The behavior of surface waves generated by grazing incidence at the core/coating and coating/exterior interfaces was also examined and discussed. © 2012 Optical Society of America.


Lee Jr. R.L.,U.S. Naval Academy | Laven P.,9 Russells Crescent
Applied Optics | Year: 2011

Naturally occurring tertiary rainbows are extraordinarily rare and only a handful of reliable sightings and photographs have been published. Indeed, tertiaries are sometimes assumed to be inherently invisible because of sun glare and strong forward scattering by raindrops. To analyze the natural tertiary's visibility, we use Lorenz-Mie theory, the Debye series, and a modified geometrical optics model (including both interference and nonspherical drops) to calculate the tertiary's (1) chromaticity gamuts, (2) luminance contrasts, and (3) color contrasts as seen against dark cloud backgrounds. Results from each model show that natural tertiaries are just visible for some unusual combinations of lighting conditions and raindrop size distributions. © 2011 Optical Society of America.


Laven P.,9 Russells Crescent
Journal of Nanophotonics | Year: 2010

Craig Bohren has offered a million-dollar prize to anyone who can devise a detector that accepts scattered light but rejects diffracted light. This challenge was examined from a theoretical perspective by considering the scattering of red light by a spherical droplet of water with diameter 20 μm. Illumination of the droplet by short pulses (e.g. a duration of 5 fs) could allow a detector to distinguish between light scattered by various mechanisms, such as diffraction, transmission, reflections and surface waves. Although such techniques would not satisfy the precise terms of the challenge, the time domain approach can deliver remarkable insights into the details of the scattering processes. © 2010 Society of Photo-Optical Instrumentation Engineers.


Laven P.,9 Russells Crescent
Applied Optics | Year: 2015

The atmospheric corona is a well-known diffraction phenomenon, typically seen as colored rings surrounding the Sun or Moon. In many respects, Fraunhofer diffraction provides a good explanation of the corona. As the angular sizes of the corona's rings are inversely proportional to the radius, r, of the spherical particles causing the corona, it should be easy to estimate the particle size from observations and photographs. Noting that some of the techniques commonly used for particle sizing based on diffraction theory can give misleading results for coronas caused by the scattering of sunlight, this paper uses Mie theory simulations to demonstrate that the inner 3 red rings of the corona have angular radii of θ ≈ 16/r, 31/r, and 47/r, when θ is measured in degrees and r is measured in μm. © 2014 Optical Society of America.

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