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Schematics used to derive the generalized Snell’s law of reflection. The interface between the two media is artificially structured in order to introduce an abrupt phase shift in the light path, which is a function of the position along the interface. and
Source publication
The general reflection and refraction laws at the metasurface with the abrupt
phase shift were derived by two different methods of Fermat's principle and the
boundary conditions respectively. It is found that one or two critical angles
for total internal reflection exist when a light hits on the optical sparse
material from the optical denser mater...
Contexts in source publication
Context 1
... we derived the general reflection law. Considering a plane wave with a incident angle of i , assuming that the two paths ACE and ADE are infinitesimally close to the actual path between the points A and E (See Fig. 1), then the phase difference between them should be ...
Context 2
... numerical simulations were done using the Comsol software to study the propagation behavior of light crossing the ultra-thin interface. In our simulations, the refractive index gradually increased along the x-axis direction (See Fig. 1 impedance matching was employed to minimize the affection of reflection so that to well demonstrate the simulating results. Similar results were obtained for other wavelengths in our ...
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Citations
... incident angle of 45° hitting the NZIM vertically; while in the emergent area, the effect of PCM becomes such that the waves perpendicularly transmit from NZIM can be anomalously refracted at 45°. As shown in Fig. 5(a), the phase profile in one side of square PCM (blue solid curve) can be derived by the generalized laws of refraction 34 , and 32 labyrinth units are used for discretization with the phase shifts induced by each unit represented by red dots. The construction details of 32 labyrinth units are shown in Fig. 5(b). ...
Ultrathin acoustic cloaking of obstacles with arbitrary shape is achieved by a conformal hybrid metasurface, which is composed of an outer layer of phase-control metasurface (PCM) and an inner layer of near-zero-index metasurface (NZIM). Here, the PCM and NZIM are discretized into two types of labyrinth elements. The NZIM is functionally equivalent to an equiphase area and can guide the waves around the obstacle, while the PCM can perpendicularly transfer the incident waves to the NZIM and then control the emergent waves from NZIM to propagate along the original incident direction. The efficient cloaking by hybrid metasurface tightly covered on the edges of the square and circular obstacles is demonstrated, with a total thickness only 0.62 times of operating wavelength.
... For example, in order to control wave trace, the metasurface must provide corresponding phase profile in different positions. This phase profile is usually derived from the generalized laws of diffraction 18 , leading to the inherent dependence on the working frequency. Thus, the phase aberrations make the metasurface only work in a narrow frequency band. ...
Metasurface has recently attracted a lot of attentions for controlling wave fields. Based on the diffraction effects of phase gratings, we demonstrate a broadband acoustic metagrating which can concentrate the diffracted waves in the first (±1) orders and achieve multifunctional wave steering such as broadband anomalous diffraction. In the acoustic metagrating, the subwavelength rectangular waveguides (SRWs) function as the periodic elements to replace the fences in ordinary gratings. Thus, we can achieve a group of phase delay from 0 to 2π independently with frequency just by reconfiguring the relative locations of the effective apertures. With the iterative algorithm, the acoustic metagrating can be used to record the phase profile and then control the output waveform. We further demonstrate that the broadband metagrating can be used to achieve the acoustic Gaussian beam. By rotating the periodic elements into a two-dimensional structure, the Bessel beam is further obtained.
... (1)-(3). The generalized Snell's law for anomalous reflection and refraction are given by [39,41,43], ...
Motivated by recent experimental observation of photonic spin Hall effect at metasurfaces, we study lateral Goos-Hänchen (GH) and transverse Imbert-Fedorov (IF) shifts of an arbitrarily polarized light beam totally reflected from metasurfaces, in terms of stationary phase method and energy flux method. The intriguing phenomenon is that the gradient in phase discontinuity results in anomalous reflection and refraction, and the GH and IF shifts can be thus controlled from negative to positive values by changing the sign of phase discontinuity. The tunable GH and IF shifts have potential applications in nano-optics, with the development of novel functionalities and performances of metasurfaces.
Çoxqatlı dairəvi dalğaötürənlər müxtəlif ifrat yüəsək tezlikli sistemlərin bir hissəsi kimi istifadə olunur. Dalğaötürənin laylı təbəqə ilə doldurulması qurğunun parametrlərinin daha çevik tənzimlənməsinə və optimallaşdırılmasına imkan verir. Qeyri-bircins mühitlə doldurulmuş dalğaötürəndə məxsusi dalğaların kritik tezliyi boş dalğaötürənin kritik tezliyindən fərqlənir. Bu məqalədə çoxqatlı dairəvi dalğaötürənin dispersiya xarakteristikalarını almaq üçün yeni yanaşma edilərək ekvivalent radial ötürmə xətlər metodundan istifadə edilmişdir. Təklif olunan metod çoxqatlı dairəvi dalğaötürənin dispersiya xarakteristikalarının alınmasında daha səmərəlidir. Belə ki, bu metodda sərhəd şərtlər daxilində tənliklər sisteminin birbaşa həlli əvəzinə mikrodalğalı dövrələr nəzəriyyəsindən istifadə edilmişdir.
In this paper, a novel polarization splitter has been designed at the telecommunication wavelength of 1500 nm successfully based on the dielectric metasurface consisting of a silicon nanobrick array, which can generate two different wavefronts for two orthogonal input polarizations with well over 90% transmitted efficiency by exactly selecting the sizes of the used nanobricks. The splitting mechanism is attributed to the fact that the used nanobricks can supply two different incremental transmission phases for the X-linear-polarization (XLP) incidence and Y-linear-polarization (YLP) incidence respectively. A polarization-dependent beam splitter which can effectively deflect the X- and Y-linear-polarization incidences in the opposite direction with 90% transmitted efficiency have been realized based on the same metasurface, where the refracted angle of the co-polarized refracted light can be arbitrarily controlled by changing the lattice constant of the nanobricks. In addition, a polarization-independent beam deflector which can make the linear-polarization (XLP and YLP) incident lights refract in the same direction has also been designed and presented. However, it is very difficult to obtain concrete XLP and YLP compositions in the transmitted fields in real experiments. Thus we have designed a novel metalens to focus the two orthogonal polarization compositions in different positions. The capacities to completely manipulate the phase and wavefronts demonstrate the potential of the designed metasurfaces in realizing most free-space transmissive optical devices such as phase plates, polarizers, as well as vector beam generators and so on.
Snell's law states that the quantity n sin θ is unchanged in refraction of light passing from one medium to another. We inquire whether this is true in the general case where the speed of light varies continuously within a medium. It turns out to be an instructive exercise in application of Snell's law and Fermat's principle. It also provides good pedagogical problems in calculus of variations to deal with the subtleties of a variable domain of integration and inclusion of constraints. The final result of these exercises is that, contrary to an initial expectation, the answer to the question in the title is negative.
