Law Of Refraction Research Articles

Metal-free flat lens using negative refraction by nonlinear four-wave mixing.

A perfect lens with unlimited resolution has always posed a challenge to both theoretical and experimental physicists. Recent developments in optical metamaterials promise an attractive approach towards perfect lenses using negative refraction to overcome the diffraction limit, improving resolution. However, those artificially engineered metamaterials are usually accompanied by high losses from metals and are extremely difficult to fabricate. An alternative proposal using negative refraction by four-wave mixing has attracted much interest recently, though most existing experiments still require metals and none of them have been implemented for an optical lens. Here, we experimentally demonstrate a metal-free flat lens for the first time using negative refraction by degenerate four-wave mixing with a thin glass slide. We realize an optical lensing effect utilizing a nonlinear refraction law, which may have potential applications in microscopy.

Giving birth to the refined unambiguous statement of Snell's law in ray optics

This paper reports on the ambiguity present in the long-running Snell's law of refraction of light, which is based on the traditional ambiguous definitions of the angles of incidence and refraction in ray optics. To get rid of the said ambiguity, the refined unambiguous definitions of angles of incidence and refraction reported earlier by the author have been employed to give birth to the refined unambiguous statement of Snell's law of refraction. The most interesting physical insights that resulted from the refined unambiguous statement of Snell's law are: (i) in case of refraction of light of a particular colour while passing from one optical medium to another, the ratio of the sine of the angle of incidence and the sine of the angle of refraction is approximately equal to the refractive index of the second optical medium with respect to the first optical medium and (ii) the refractive index of an optical medium ‘b’ with respect to another optical medium ‘a’ is approximately equal to the reciprocal of the refractive index of the optical medium ‘a’ with respect to the optical medium ‘b’, and vice versa. These results are entirely novel and different from those existing in the traditional literature of ray optics.

Study on Design and Mechanism of a New Invisible Cloak for Visible Light

In order to realize the macroscopic objects invisible in the visible region, according to the law of refraction, total internal reflection law and symmetry reduction transformation method, a new type of visible light stealth cloak was designed. The cloak was prepared using the ordinary homogeneous and isotropic glass materials, which can guide the light around the hidden region, and the direction of propagation of light has not changed. Thus the macroscopic object achieve the perfect stealth. The invisible cloak in air environment for arbitrary polarized visible light have stealth features, easy processing, low cost, has potential application value.

The momentum of an electromagnetic wave inside a dielectric derived from the Snell refraction law

Author of the paper [M. Testa, Ann. Physics 336 (2013) 1] has derived a conclusion that there is a connection between the Snell refraction law and the Abraham form of the momentum of light in matter. In other words, author derived the Snell law on assumption that the momentum of light in matter decreases by n times as compared with that in free space. The conclusion is derived under assumption that the forces exerted on an optical medium by an electromagnetic field do not distinguish between polarization and free charges. We show that, on the contrary, the Minkowski form of the momentum of light in matter directly follows from the Snell law. No previous assumption is required for this purpose.

Studies of the reflection, refraction and internal reflection of light

An inexpensive apparatus and associated experiments are described for studying the basic laws of reflection and refraction of light at an air–glass interface, and multiple internal reflections within a glass block. In order to motivate students and encourage their active participation, a novel technique is described for determining the refractive index of a block of glass by observing multiple internal reflections. With a similar intention, the paper also includes a number of guidance notes for instructors.

Refraction into an Isotropic Medium with Negative Permittivity and Permeability

Generalized representations of the refraction law are obtained for electromagnetic waves at the interface of transparent isotropic media with positive and/or negative permittivity and permeability.

Absolute shape measurement of high NA focusing microobjects in digital holographic microscope with arbitrary spherical wave illumination.

In this paper a new high NA shape measurement technique working with an arbitrary spherical wave illumination is presented. The main contribution of this work are formulas, derived from exact reflection and refraction laws for both the reflection and the transmission configurations, which enable accurate shape calculations in systems with an arbitrary location of the illuminating point source. The proposed algorithms permit measurement of multiple samples of arbitrary shapes using a single hologram. An accuracy of this method is confirmed with numerical simulations, which show superiority of this approach over a standard procedure utilizing paraxial approximation. The method is validated experimentally using a reflective measurement of a microlens topography, whose NA in reflection is 0.7. Furthermore, a new measurement configuration is presented that extends the capabilities of transmission systems for characterization of high gradient shapes.

Theoretical study on a broadband, high cross-polarization conversion efficiency metalens based on phase discontinuity

In this paper, a novel unit cell for the metalens in a microwave band based on the principle of phase discontinuity at the interface is suggested and theoretically investigated. It has a broad bandwidth of 25%, in which the cross-polarization conversion efficiency approaches the theoretical limit. The Pancharatnam–Berry phase is adopted to achieve the desired abrupt phase change for the transmitted cross-polarized wave, then an anomalous refraction metalens and a bi-functional metalens are proposed. The simulated results show that the anomalous refraction metalens can bend the transmitted cross-polarized wave with a specific angle predicted by the generalized laws of refraction, and the bi-functional metalens can diverge or converge the circularly polarized incident wave with a focal length of 10λ, determined by the helicity of the incident wave. Our designs provide a promising approach to planarize microwave components.

Babinet's principle in double-refraction systems

Babinet's principle applied to systems with double refraction is shown to involve spatial interchanges between the ordinary and extraordinary patterns observed through two complementary screens. As in the case of metamaterials, the extraordinary beam does not follow the Snell-Descartes refraction law, the superposition principle has to be applied simultaneously at two points. Surprisingly, by contrast to the intuitive impression, in the presence of the screen with an opaque region, we observe that the emerging extraordinary photon pattern, which however has undergone a deviation, remains fixed when a natural birefringent crystal is rotated while the ordinary one rotates with the crystal. The twofold application of Babinet's principle implies intensity and polarization interchanges but also spatial and dynamic interchanges which should occur in birefringent metamaterials.

Grain boundaries in hybrid two-dimensional materials

In two-dimensional (2D) materials, bisector grain boundaries (GBs) are energetically favorable as they allow perfect match of neighbor grains. We demonstrate here a contrasting behavior for GBs in hybrid 2D materials, which tend to be non-bisector and obey a universal law to optimally match the heterogeneous grains: the ratio of cosines of the rotation angles of two neighbor grains equals the ratio of constituent׳s lattice parameters, reminiscent of Snell׳s law for light refraction. Details of the optimal GB structures are further formulated in terms of tilt angle, lattice mismatch strain and deviation angle from the bisector line, in good agreement with comprehensive numerical analyses. The ground state structures of the GBs manifest as a series of laterally misaligned bisector segments, which are verified by intensive first-principle calculations. Our findings not only provide a general guidance for exploring GBs in various hybrid 2D materials but also serve as an important stepping stone for understanding mechanical and electronic behaviors in these 2D nanoscale patchworks.

Vector and matrix methods of computing the direction of a ray refracted by a system of arbitrarily placed flat refracting surfaces

Based on the law of refraction in vector form, an expression is obtained that determines the direction of a ray refracted at two refracting surfaces. As a result of analyzing this expression, represented in matrix form, a form of the expression is proposed that determines the direction of a ray refracted by an arbitrary number of refracting surfaces. The method of mathematical induction is used to prove that the resulting expression is valid for computing the unit vector of a ray refracted by a system of flat, arbitrarily placed refracting surfaces.

Uniaxial epsilon-near-zero metamaterials: from superlensing to double refraction

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.

Deriving the Snel--Descartes law for a single photon

The laws of reflection and refraction are typically derived using a dispersion relation that assumes that the angular frequency stays the same across a vacuum--dielectric interface and that the angular wave number increases. At the single photon level, this means that the total energy of the photon is conserved but the linear momentum is not. Here I derive the laws of reflection and refraction for a single photon using a dispersion relation that is consistent with the conservation of both total energy and linear momentum. To ensure that both conservation laws are upheld, the optical path length must be considered to be more fundamental than the geometrical path length when reckoning optical distances. As long as the medium is transparent, the optical path length traveled by a photon in a given duration of time is constant. By contrast, the geometrical path length traveled in a given duration of time is inversely proportional to the index of refraction. A photon propagating across a vacuum--dielectric interface is considered to be an indivisible package whose total energy (and angular frequency) and linear momentum (and angular wave number) remain constant, but whose velocity decreases with refractive index as a result of unspecified electromagnetic interactions.

On minimum-time paths of bounded curvature with position-dependent constraints

We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with constraints on the minimum turning radius of the particle over multiple regions of the state space. Necessary conditions for optimality of these paths are derived to characterize the nature of optimal paths, both when the particle is inside a region and when it crosses boundaries between neighboring regions. These conditions are used to characterize families of optimal and nonoptimal paths. Among the optimality conditions, we derive a “refraction” law at the boundary of the regions that generalizes the so-called Snell’s law of refraction in optics to the case of paths with bounded curvature. Tools employed to deduce our results include recent principles of optimality for hybrid systems. A numerical example is given to demonstrate the derived results.

Law of refraction for generalised confocal lenslet arrays

We derive the law of generalised refraction for generalised confocal lenslet arrays, which are arrays of misaligned telescopes. We have implemented this law of refraction in TIM, a custom open-source ray tracer.

Wave theory of light leading to the generalized vectorial laws of reflection and refraction

This paper deals with the application of Huygens’ wave theory of light for the derivation of the generalized vectorial laws of reflection and refraction discovered by the author in 2005. The long-running literature falls short of such a theoretical proof of the generalized vectorial laws of reflection and refraction on the basis of wave theory. As such the present work is novel and original. At the same time it also enhances the theoretical foundation of the discovery of the generalized vectorial laws of reflection and refraction there by proving the efficiency and increasing the range of applicability of the wave theory of light as well.

Discovering the generalized vectorial laws of multiple reflection and refraction

This paper reports on the discovery of the generalized vectorial laws of multiple reflection and refraction as an extension of the earlier discovery of the generalized vectorial laws of reflection and refraction reported in 2005. The present discovery is novel and original and interesting from academic point of view. It will enrich the field of optics.

Hydroelastic interaction between obliquely incident waves and a semi-infinite elastic plate on a two-layer fluid

The hydroelastic response of a semi-infinite thin elastic plate floating on a two-layer fluid of finite depth due to obliquely incident waves is investigated. The upper and lower fluids with different densities separated by a sharp and stable interface are assumed to be inviscid and incompressible and the motion to be irrotational. Simply time-harmonic incident waves of the surface and interfacial wave modes with a given angular frequency are considered within the framework of linear potential flow theory. With the aid of the methods of matched eigenfunction expansion and the inner product of the two-layer fluid, a closed system of simultaneous linear equations is derived for the reflection and transmission coefficients of the series solutions. Based on the dispersion relations for the gravity waves and the flexural–gravity waves in a two-layer fluid and Snell’s law for refraction, we obtain a critical angle for the incident waves of the surface wave mode and three critical angles for the incident waves of the interfacial wave mode, which are related to the existence of the propagating waves. Graphical representations of the series solutions show the interaction between the water waves and the plate. The effects of several physical parameters, including the density and depth ratios of the fluid and the thickness of the plate, on the wave scattering and the hydroelastic response of the plate are studied. It is found that the variation of the thickness of the plate may change the wave numbers and the critical angles. The density ratio is the main factor to influence the wave numbers of the interfacial wave modes. Finally, the stress state is considered.

Modeling of the general astigmatic Gaussian beam and its propagation through 3D optical systems

The paper introduces the complete model of the general astigmatic Gaussian beam as the most general case of the Gaussian beam in the fundamental mode. This includes the laws of propagation, reflection, and refraction as well as the equations for extracting from the complex-valued beam description its real-valued parameters, such as the beam spot radii and the radii of curvature of the wavefront. The suggested model is applicable to the case of an oblique incidence of the beam at any 3D surface that can be approximated by the second-order equation at the point of incidence. Thus it can be used in simulations of a large variety of 3D optical systems. The provided experimental validation of the model shows good agreement with simulations.

Thomas Harriot’s optics, between experiment and imagination: the case of Mr Bulkeley’s glass

Some time in the late 1590s, the Welsh amateur mathematician John Bulkeley wrote to Thomas Harriot asking his opinion about the properties of a truly gargantuan (but totally imaginary) plano-spherical convex lens, 48 feet in diameter. While Bulkeley’s original letter is lost, Harriot devoted several pages to the optical properties of “Mr Bulkeley his Glasse” in his optical papers (now in British Library MS Add. 6789), paying particular attention to the place of its burning point. Harriot’s calculational methods in these papers are almost unique in Harriot’s optical remains, in that he uses both the sine law of refraction and interpolation from Witelo’s refraction tables in order to analyze the passage of light through the glass. For this and other reasons, it is very likely that Harriot wrote his papers on Bulkeley’s glass very shortly after his discovery of the law and while still working closely with Witelo’s great Optics; the papers represent, perhaps, his very first application of the law. His and Bulkeley’s interest in this giant glass conform to a long English tradition of curiosity about the optical and burning properties of large glasses, which grew more intense in late sixteenth-century England. In particular, Thomas Digges’s bold and widely known assertions about his father’s glasses that could see things several miles distant and could burn objects a half-mile or further away may have attracted Harriot and Bulkeley’s skeptical attention; for Harriot’s analysis of the burning distance and the intensity of Bulkeley’s fantastic lens, it shows that Digges’s claims could never have been true about any real lens (and this, I propose, was what Bulkeley had asked about in his original letter to Harriot). There was also a deeper, mathematical relevance to the problem that may have caught Harriot’s attention. His most recent source on refraction—Giambattista della Porta’s De refractione of 1593—identified a mathematical flaw in Witelo’s cursory suggestion about the optics of a lens (the only place that lenses appear, however fleetingly, in the writings of the thirteenth-century Perspectivist authors). In his early notes on optics, in a copy of Witelo’s optics, Harriot highlighted Witelo’s remarks on the lens and della Porta’s criticism (which he found unsatisfactory). The most significant problem with Witelo’s theorem would disappear as the radius of curvature of the lens approached infinity. Bulkeley’s gigantic glass, then, may have provided Harriot an opportunity to test out Witelo’s claims about a plano-spherical glass, at a time when he was still intensely concerned with the problems and methods of the Perspectivist school.