Defining the Fresnel zone for broadband radiation

Pearce, Jeremy; Mittleman, Daniel M.

doi:10.1103/physreve.66.056602

Cited by 33 publications

(17 citation statements)

References 17 publications

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“…The gray area is the envelope of Fresnel zones of all SKS analyzed. The Fresnel zones at depth h are calculated following Pearce and Mittleman []: R f = 1 / 2sqrt ( Tvh ) where R f is the radius of the Fresnel zone expressed in km, T is the dominant period of the wave, and ν is the wave velocity. We choose 10 s for the dominant period from waveform observations and the shear wave velocity of the S phases from IASP91 model (4.45 km/s at 150 km depth).…”

Section: Results Of Shear Wave Splitting Analysismentioning

confidence: 99%

Hints on the deformation penetration induced by subductions and collision processes: Seismic anisotropy beneath the Adria region (Central Mediterranean)

2013

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[1] Adria is a small region surrounded by three mountain belts: the Alps, the Apennines, and the Dinarides, built up by long evolution of subduction and collisional systems. We present 253 shear wave splitting measurements obtained by studying more than 100 teleseismic events for 12 stations. SKS splitting measurements show 3-D complexity and quite strong upper mantle deformation. We carefully analyzed results in terms of back azimuthal coverage and interpret measurements as related to Adria rotation and to subductions evolution. In the northern part of Adria, the anisotropy pattern follows the arcuate shape of the Alps; the same pattern, parallel to the mountains, occurs along the Apennines, but fast directions show a sudden change in the Adria foreland. This lateral variation has been analyzed to isolate a distinct Adria mantle anisotropic pattern, which is identified as NE-SW fast direction along the western microplate boundary and as N-S fast direction at Trieste. This pattern might be induced by drag effect of the counterclockwise rotation of Adria lithosphere that behaves as an independent microplate as identified by GPS data. Our measurements suggest that the geodynamic process that generated the Alps is more efficient deforming a larger volume of mantle than its Apennine counterpart. Moreover, the mantle circulation we hypothesize looking at the regional-scale patterns of anisotropy requires the existence of an escape route beneath the Alps-Apennines transition, through which the mantle flows and feed circulation in the Tyrrhenian mantle system as suggested by previous geodynamic models and as seen by some tomographic studies.

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Section: Results Of Shear Wave Splitting Analysismentioning

confidence: 99%

Hints on the deformation penetration induced by subductions and collision processes: Seismic anisotropy beneath the Adria region (Central Mediterranean)

2013

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“…over the bandwidth of the pulse, spatial broadening effects in the irradiance pattern can be also investigated [14,15]. Therefore, Eq.…”

Section: Analytical Approachmentioning

confidence: 99%

“…In this context, there has been a growing interest in studying diffraction-induced effects due to propagating ultrashort laser pulses through binary amplitude DOEs. Several recent works have addressed the study of the spectral and temporal characteristics of ultrashort laser pulses diffracted by a circular aperture [1][2][3][4][5][6][7], serrated apertures [8], single and double slits [9,10], Fresnel zone plates [11][12][13][14], or DOEs having multiple rings [15,16]. Because in most cases the analysis was performed within the spectral or the temporal domain separately, the diffraction effects on the incident ultrashort pulse were understood independently.…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal characterization of ultrashort pulses diffracted by circularly symmetric hard-edge apertures: theory and experiment

Mendoza-Yero¹,

Alonso²,

Varela³

et al. 2010

Opt. Express

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We carry out a complete spatio-temporal characterization of the electric field of an ultrashort laser pulse after passing through a diffractive optical element composed of several binary amplitude concentric rings. Analytical expressions for the total diffraction field in the time and spectral domain are provided, using the Rayleigh-Sommerfeld formulation of the diffraction. These expressions are experimentally validated. The spatio-temporal amplitude and phase structure of the pulse are measured at different planes beyond the diffractive optical element using spatially-resolved spectral interferometry assisted by an optical fiber coupler (STARFISH). Our results allow corroborating theoretical predictions on the presence of multiple pulses or complex spectral distributions due to the diffraction-induced effects by the hard-edge ring apertures.

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“…Diffractive singlets are zone plates which may achieve a high-efficiency performance with phase-only multilevels [35]. Recently, some authors have addressed special attention to investigate the spatio-temporal response of broadband ultra-short pulses focused with zone plates [23,36,37]. Here we are giving a simplified formalism to evaluate the focal field in the frame of the Debye representation.…”

Section: Examples a Apertured Thin Lensmentioning

confidence: 99%

“…However, when the Fresnel number is much higher than unity, some spatial symmetries in the vicinity of focus are found, and the Debye approximation holds [21,22]. By the way, the concept of Fresnel number has recently been interpreted for broadband coherent radiation [23]. However, roughly speaking, the Debye diffraction formulation has been ignored in the evaluation of the focal field of polychromatic (both ultrashort pulsed and temporally incoherent) spherical waves.…”

Section: Introductionmentioning

confidence: 99%

Debye representation of dispersive focused waves

Zapata–Rodríguez

2007

J. Opt. Soc. Am. A

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We report on a matrix-based diffraction integral that evaluates the focal field of any diffractionlimited axisymmetric complex system. This diffraction formula is a generalization of the Debye integral applied to apertured focused beams, which may be accommodated to broadband problems. Longitudinal chromatic aberration may limit the convenience of the Debye formulation and, additionally, spatial boundaries of validity around the focal point are provided. Fresnel number is reformulated in order to guarantee that the focal region is entirely into the region of validity of the Debye approximation when the Fresnel number of the focusing geometry largely exceeds unity. We have applied the matrix-based Debye integral to several examples. Concretely, we present an optical system for beam focusing with strong angular dispersion and free of longitudinal chromatic aberration. This simple formalism leaves an open door for analysis and design of focused beams with arbitrary angular dispersion. Our results are valid for ultrashort pulsed and polychromatic incoherent sources.

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Defining the Fresnel zone for broadband radiation

Cited by 33 publications

References 17 publications

Hints on the deformation penetration induced by subductions and collision processes: Seismic anisotropy beneath the Adria region (Central Mediterranean)

Hints on the deformation penetration induced by subductions and collision processes: Seismic anisotropy beneath the Adria region (Central Mediterranean)

Spatio-temporal characterization of ultrashort pulses diffracted by circularly symmetric hard-edge apertures: theory and experiment

Debye representation of dispersive focused waves

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