Search results for "Paraxial approximation"
showing 10 items of 21 documents
Debye representation of dispersive focused waves
2006
We report on a matrix-based diffraction integral that evaluates the focal field of any diffraction-limited 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 matri…
Gaussian imaging transformation for the paraxial Debye formulation of the focal region in a low-Fresnel-number optical system
2000
The Debye formulation of focused fields has been systematically used to evaluate, for example, the point-spread function of an optical imaging system. According to this approximation, the focal wave field exhibits some symmetries about the geometrical focus. However, certain discrepancies arise when the Fresnel number, as viewed from focus, is close to unity. In that case, we should use the Kirchhoff formulation to evaluate accurately the three-dimensional amplitude distribution of the field in the focal region. We make some important remarks regarding both diffraction theories. In the end we demonstrate that, in the paraxial regime, given a defocused transverse pattern in the Debye approxi…
Focal-shift formula in apodized nontelecentric focusing systems
2007
A single analytical formulation for evaluating the focal shift in any apodized nontelecentric focusing setup is reported. The formulation is also useful in the case of imaged paraxial beams. We show explicitly that the magnitude of the focal shift is determined by only one parameter that depends on the effective width of the pupil filter and its axial position. To illustrate our approach we examine different focusing setups.
Filter performance parameters for vectorial high-aperture wave fields.
2008
Performance parameters have been presented that can be used to compare the focusing performance of different optical systems, including the effect of pupil filters. These were originally given for the paraxial case and recently extended to the high-aperture scalar regime. We generalize these parameters to the full vectorial case for an aplanatic optical system illuminated by a plane-polarized wave. The behavior of different optical systems is compared.
Spiral conical approximations to double reflection Wolter optics
2008
The design of a grazing incidence focusing optic obtained from a spiral approximation to multiple nested cones produces an annular image of a point source. The angular size of the annulus depends mainly on the pitch of the winding and the focal length. For a spiral conical approximation to Wolter optics, the effect is magnified by the double reflection. However, if the two conical spirals are wound one clock-wise and the other counter-clock-wise, then the aberration is partially compensated. We use a ray tracing code to evaluate advantages and disadvantages of this optical design for potential applications of a light weight optics technology based on plastic foils that we are currently inve…
Scaling the abruptly autofocusing beams in the direct-space
2017
International audience; We propose a simple technique to scale the abruptly autofocusing beams in the direct space by introducing a scaling factor in the phase. Analytical formulas are deduced based on optical caustics, explicitly revealing how the scaling factor controls location, peak intensity, and size of the focal spot. We demonstrate that the multiplication of a scaling factor on the phase is equivalent to the axial-scaling transformation under the paraxial approximation. Further numerical and experimental results confirm theoretical predictions. In addition, amplitude modulation using phase-only holograms is used to maintain the peak intensity level of the focal spots.
Twisted-Light-Ion Interaction: The Role of Longitudinal Fields.
2017
The propagation of light beams is well described using the paraxial approximation, where field components along the propagation direction are usually neglected. For strongly inhomogeneous or shaped light fields, however, this approximation may fail, leading to intriguing variations of the light-matter interaction. This is the case of twisted light having opposite orbital and spin angular momenta. We compare experimental data for the excitation of a quadrupole transition in a single trapped $^{40}$Ca$^+$ ion by Schmiegelow et al, Nat.\ Comm.\ 7, 12998 (2016), with a complete model where longitudinal components of the electric field are taken into account. Our model matches the experimental d…
Impact of internal curvature gradient on the power and accommodation of the crystalline lens
2017
Human crystalline lens has a layered, shell-like structure with the refractive index increasing from cortex to nucleus (gradient index or GRIN structure). Moreover, every iso-indicial layer has a certain curvature which also varies from cortex to nucleus, with a gradient of curvature (G). In the present manuscript, the role of G on the lens power is investigated along with its implications regarding the lens paradox (change of lens power with age) and intra-capsular accommodation mechanism (larger than expected changes of lens power during accommodation compared to a homogenous lens). To this end, a simplified formulation of paraxial lens power based on thin lens approximation is developed …
Ultrafast diffraction of tightly focused waves with spatiotemporal stabilization
2008
Experimental studies of ultrafast beam shaping have come about from the need to compensate diffraction-induced dispersive effects in femtosecond laser beams. From a theoretical point of view, chromatic matching of diffracted spherical waves in the vicinity of the geometrical focus is attained by applying conveniently dispersive boundary conditions in the far-field zone, a subject thoroughly analyzed in the paraxial regime. For applications demanding high spatial resolution, however, high-numerical-aperture microscope objectives may be employed instead and would lead to nonparaxiality of the focal wavefields. These circumstances have motivated our investigation. Concretely we report on prere…
Considerations on the electromagnetic flow in Airy beams based on the Gouy phase
2012
We reexamine the Gouy phase in ballistic Airy beams (AiBs). A physical interpretation of our analysis is derived in terms of the local phase velocity and the Poynting vector streamlines. Recent experiments employing AiBs are consistent with our results. We provide an approach which potentially applies to any finite-energy paraxial wave field that lacks a beam axis. This research was funded by the Spanish Ministry of Economy and Competitiveness under the project TEC2009-11635.