Eikonal equation for a general anisotropic or chiral medium: application to a negative-graded index-of-refraction lens with an anisotropic material

Parazzoli, C. G.; Koltenbah, B. E. C.; Greegor, R.B.; Lam, Tai; Tanielian, M.

doi:10.1364/josab.23.000439

Cited by 21 publications

(22 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present work we analyze the ray trajectories in a single LL and subsequently we use this analysis in waveguides build exclusively through LLs. Specifically, in the next section we present analytical approaches for the trajectories traversing a LL [1,2,3,7,8,10,15,16,17,18,19] and derive explicitly a solution expressing the ordinate of the trajectory as a function of the abscissa in Cartesian coordinates. In section 3 we introduce the main point of the present work, viz.…”

Section: Introductionmentioning

confidence: 99%

Luneburg lens waveguide networks

Mattheakis¹,

Tsironis²,

Kovanis³

2012

J. Opt.

View full text Add to dashboard Cite

We investigate certain configurations of Luneburg lenses that form light propagating and guiding networks. We study single Luneburg lens dynamics and apply the single lens ray tracing solution to various arrangements of multiple lenses. The wave propagating features of the Luneburg lens networks are also verified through direct numerical solutions of Maxwell's equations. We find that Luneburg lenses may form efficient waveguides for light propagation and guiding. The additional presence of nonlinearity improves the focusing characteristics of the networks.

show abstract

Section: Introductionmentioning

confidence: 99%

Luneburg lens waveguide networks

Mattheakis¹,

Tsironis²,

Kovanis³

2012

J. Opt.

View full text Add to dashboard Cite

show abstract

“…An iterative ray-tracing routine based on the eikonal approximation [22] is used to determine the optimal value of β that minimizes the lens aberration. The isotropic refraction gradient in Eq.…”

Section: Lens Designmentioning

confidence: 99%

“…(1) prescribesc avg ðyÞ and hence the lattice geometry a y =a x for a given value of β; however, to optimize β, an eikonal approximation that accounts for the anisotropic sound speeds in the lattice is employed to more accurately predict the ray trajectories on the focal plane and hence the degree of aberration. The differential equation governing the eikonal function ξðxÞ in the presence of anisotropy can be derived for acoustic metafluids in a similar manner to the electromagnetic case [22]:…”

Section: Lens Designmentioning

confidence: 99%

Transparent Gradient-Index Lens for Underwater Sound Based on Phase Advance

et al. 2015

View full text Add to dashboard Cite

Spatial gradients in a refractive index are used extensively in acoustic metamaterial applications to control wave propagation through phase delay. This study reports the design and experimental realization of an acoustic gradient-index lens using a sonic crystal lattice that is impedance matched to water over a broad bandwidth. In contrast to previous designs, the underlying lattice features refractive indices that are lower than the water background, which facilitates propagation control based on a phase advance as opposed to a delay. The index gradient is achieved by varying the filling fraction of hollow, air-filled aluminum tubes that individually exhibit a higher sound speed than water and matched impedance. Acoustic focusing is observed over a broad bandwidth of frequencies in the homogenization limit of the lattice, with intensity magnifications in excess of 7 dB. An anisotropic lattice design facilitates a flatfaceted geometry with low backscattering at 18 dB below the incident sound-pressure level. A threedimensional Rayleigh-Sommerfeld integration that accounts for the anisotropic refraction is used to accurately predict the experimentally measured focal patterns.

show abstract

“…Concerning focusing property of GRIN PC, Parazzoli and co‐authors derived a general form of eikonal equation and developed a numerical procedure to simulate the GRIN PC lens . The performances of a GRIN lens have been evaluated first using the eikonal equation and then with a FDTD code.…”

Section: Applications Of Grin Pc and Future Prospectsmentioning

confidence: 99%

Graded index photonic crystals: A review

Zhu

Liu

2015

Annalen der Physik

View full text Add to dashboard Cite

A new type of photonic crystal (PC) named graded index (GRIN) PC was proposed by E. Centeno in 2005. It is obtained by appropriately modifying the parameters of a regular PC, thus resulting in gradual index variation. Many applications are inspired by this notion. This review will introduce different ways of designing GRIN PCs from both theoretical and experimental point of views. Some typical applications based on GRIN PCs are presented, followed by the focusing mechanism of GRIN PC.

show abstract

Eikonal equation for a general anisotropic or chiral medium: application to a negative-graded index-of-refraction lens with an anisotropic material

Cited by 21 publications

References 11 publications

Luneburg lens waveguide networks

Luneburg lens waveguide networks

Transparent Gradient-Index Lens for Underwater Sound Based on Phase Advance

Graded index photonic crystals: A review

Contact Info

Product

Resources

About