We present a purposeful initiative to open new grounds for teaching Geometrical Optics. It is based on the creation of an innovative education networking involving academic staff from three Spanish universities linked together around Optics. Nowadays, students demand online resources such as innovative multimedia tools for complementing the understanding of their studies. Geometrical Optics relies on basics of light phenomena like reflection and refraction and the use of simple optical elements such as mirrors, prisms, lenses, and fibers. The mathematical treatment is simple and the equations are not too complicated. But from our long time experience in teaching to undergraduate students, we realize that important concepts are missed by these students because they do not work ray tracing as they should do. Moreover, Geometrical Optics laboratory is crucial by providing many short Optics experiments and thus stimulating students interest in the study of such a topic. Multimedia applications help teachers to cover those student demands. In that sense, our educational networking shares and develops online materials based on 1) video-tutorials of laboratory experiences and of ray tracing exercises, 2) different online platforms for student self-examinations and 3) computer assisted geometrical optics exercises. That will result in interesting educational synergies and promote student autonomy for learning Optics.
We investigated optical properties of nanostructured metal-dielectric multilayered lattices under the conditions of epsilon-near-zero (ENZ), a concept derived from the effective-medium approach (EMA). We theoretically found that the periodic array of metallic nanolayers may exhibit either superlensing driven by broadband canalization from point emitters or single-polarization double refraction, and conventional positive as well as negative, even at subwavelength regimes. For the latter case, we formulated a modified EMA, and subsequently a generalized refraction law, that describes both refractive behaviors concurrently. The modal coupling of plasmonic lattice resonances, and nonlocality induced by partial screening across the nanolayer length, are responsible for these distinct effects. Numerical simulations show that deep-subwavelength lensing along the optical axis of Ag-GaAs metamaterial is clearly enhanced at optical wavelengths. On the other hand, transverse-magnetic-polarized radiation that is obliquely incident on the ENZ periodic nanostructures with the same materials in the infrared (around 1.55 μm ) undergoes double refraction neighboring 50/50 beamsplitting.
We investigated surface waves guided by the boundary of a semi-infinite layered metal-dielectric nanostructure cut normally to the layers and a semi-infinite dielectric material. Using the Floquet-Bloch formalism, we found that Dyakonov-like surface waves with hybrid polarization can propagate in dramatically enhanced angular range compared to conventional birefringent materials. Our numerical simulations for an Ag-GaAs stack in contact with glass show a low to moderate influence of losses.
Recent disclosures on subwavelength plasmonic crystals, like the potential excitation of a pair of coexisting wave-fields
with opposite refraction, only can be understood by considering two dispersion branches with completely
different features that characterize the metamaterial. One branch gives elliptic-like dispersion and the other
provides hyperbolic-like dispersion. However the effective medium approximation, also known as Rytov approximation,
is not consistent with both curves simultaneously. We follow an approach leading to a single curve that
allows a complete description of both diffraction behaviors concurrently. Importantly only two parameters of the
closed curve, together with the lattice period, fulfill such a complete picture. In addition, our semi-analytical
approach may include more general situations straightforwardly.
We investigate spatial-dispersion properties of hybrid surface waves propagating in the boundary of a semi-infinite
layered metal-dielectric nanostructure. Electromagnetic fields can be dramatically affected by a nonlocal optical
response of the plasmonic lattice. We demonstrate that the use of the so called effective medium approximation
(EMA) is not justified if the thickness of a metallic layer becomes of the order of the metal skin depth. We
compare the results obtained by means of EMA with computer solutions of Maxwell's equation, including losses
in the metal.
We present recent progress in nondiffracting subwavelength fields propagating in complex plasmonic nanostructures.
In particular, diffraction-free localized solutions of Maxwell's equations in a periodic wire medium are
discussed thoroughly. The Maxwell-Garnett model is used to provide analytical expressions of the electromagnetic
fields for Bessel beams directed along the cylinders axes. Large filling factors of the metallic composite
induce resonant-plasmonic spots with a size that remains far below the limit of diffraction. Some numerical
simulations based on the finite-element method support our analytical approach.
We show that subwavelength diffracted wave fields may be managed inside multilayered plasmonic devices to
achieve ultra-resolving lensing. For that purpose we first transform both homogeneous waves and a broad band
of evanescent waves into propagating Bloch modes by means of a metal/dielectric (MD) superlattice. Beam
spreading is subsequently compensated by means of negative refraction in a plasmon-induced anisotropic effective-medium
that is cemented behind. A precise design of the superlens doublet may lead to nearly aberration-free
images with subwavelength resolution in spite of using optical paths longer than a wavelength.
We identified nanostructured devices sustaining subwavelength diffraction-free beams with grazing propagation.
The components of the optical assembly are a metal-dielectric multilayer stack deposited on a solid transparent
substrate. Launched from the substrate, the nondiffracting beam is resonantly transmitted though the stratiform
medium leading to light confinement and wave amplification around the beam axis near the top end. Potential
applications include optical trapping, biosensing, and nonlinear optics.
Coating lenses are membranes made of materials exhibiting negative index of refraction and deposited on other
media with high dielectric constant ε3. Unfortunately far-field imaging suffers from centrosymmetric aberrations.
We propose a simple procedure to compensate partially deviations from ray-tracing perfect imaging in asymmetric
metamaterial lenses. We also show that, under some circumstances, coating superlens may recover subwavelength
information transmitted in a relative spatial spectrum ranging from 1 to √ε3.
We numerically evaluated the 3D PSF of stratified negative-index superlenses. We determined in terms similar
to the Rayleigh criterion the limit of resolution characterizing these image formers. Under some circumstances,
the limit of resolution may drop approximately one order of magnitude. We investigated this significant increase
of the resolution power in detriment of reducing the depth of field.
The three-dimensional (3D) point spread function (PSF) of multilayered flat lenses was proposed in order to characterize the diffractive behavior of these subwavelength image formers. We computed the polarization-dependent scalar 3D PSF for a wide range of slab widths and for different dissipative metamaterials. In terms similar to the Rayleigh criterion we determined unambiguously the limit of resolution featuring this type of image-forming device. We investigated the significant reduction of the limit of resolution by increasing the number of layers, which may drop nearly 1 order of magnitude. However, this super-resolving effect is obtained in detriment of reducing the depth of field. Limitations exist on the formation of 3D images.
We identified nanostructured devices sustaining out-of-plane nondiffracting beams with near-grazing propagation and a transverse beamwidth clearly surpassing the diffraction limit of half a wavelength. This type of device consists of a planar multilayered metal-dielectric structure with a finite number of films deposited on a solid transparent substrate. We assumed that the nondiffracting beam is launched from the substrate. The construction of the subwavelength diffraction-free beam is attended by plane waves which are resonantly transmitted through the stratified medium. Therefore, light confinement and wave amplification occurs simultaneously. We performed an optimization process concerning the layers width as free parameters in order to reach the most efficient optical resonances with uniform transmission. The value of the propagation constant and the focal placement are initially arbitrary, which can be chosen according to its practical realization. Possible applications include optical trapping, biosensing, and nonlinear optics.
We recognize some photonic-crystal-fiber structures, made up of soft glass, that generate ultrawide (over an octave),
very smooth and highly coherent supercontinuum spectrum when illuminated with femtosecond pulsed light around
1.55 μm. The design of soft-glass microstructured fiber geometry with nearly ultraflattened, positive and low dispersion
is crucial to accomplish the above goals.
In this communication, the authors have determined the longitudinal chromatic aberrations in real eyes. The method that has been used combines real data of corneal morphology, central thickness of crystalline lens and biometric measures of axial length together with numerical calculation of the propagation process. The curvature of the crystalline lens has been adjusted to different curvature models and refractive index distributions. The wavelength dependence of all ocular media has been modelled through the Cauchy formula. Propagation through anterior and posterior chambers has been accomplished through numerical calculation of diffraction integral instead of classical ray-tracing approach. This imposes serous restrictions on the number of samples that are needed for a full propagation process. If we are only interested in amplitude calculations the method consists of evaluating propagation from cornea to crystalline lens with a spectrum propagation method. Propagation from the lens to the best image plane is accomplished by a direct calculation of Fresnel integral. With this model, we have obtained the refraction chromatic difference in diopters for several eyes. Results are compared with real measures of the chromatic aberration, showing a good agreement with numerical calculations. The capabilities of the technique have been demonstrated by applying the method to the study of the chromatic aberration of a keratoconus.
A novel analysis of specially designed photonic crystal fibers accounts for the existence of endlessly single-mode structures with flattened dispersion. Our approach permits to control the fiber dispersion in terms of its geometrical parameters.
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