The properties of isofrequency dependences and the laws of geometrical optics

Lock, E. H.

doi:10.3367/ufnr.0178.200804d.0397

Cited by 25 publications

(16 citation statements)

References 21 publications

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“…It follow from formulas (18) and (19), in particular, that at the interface of two left-handed media refraction takes place in the same way as in the case of two right-handed media. This property was already noted earlier in [26].…”

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confidence: 54%

Refraction into an Isotropic Medium with Negative Permittivity and Permeability

Fisanov

2014

Russ Phys J

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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.The phenomenon of reversed (negative) refraction has been well known among physicists for a long time. Sir Horace Lamb [1], responding to the model proposed by Lord Rayleigh (John Strutt) of a device in the form of a clamped wire subjected to tension and torsion [2], conjectured that in a cylindrical wire under certain conditions vibrations can also arise having group velocity that is negative with respect to the phase velocity. He considered the passage of a one-dimensional wave from a segment of the wire with the usual vibrational regime to a segment with the anomalous regime and was the first to observe that the transmitted wave should have a phase velocity oppositely directed relative to the phase velocity of the wave incident on the inhomogeneity. That same year, A. Schuster noticed and graphically elucidated [3, p. 317, Fig. 179] the curious result of the negative angle of the refracted light wave in a medium with opposed phase and group velocities, which was necessary to ensure unidirectional translation of the intersection lines of the wave fronts of the incident and refracted wave with the boundary of the two media. In optics and electrodynamics the simplest isotropic medium, at the boundary with which negative refraction can take place, is a magnetodielectric with negative values of its electric permittivity ( 0   ) and magnetic permeability ( 0   ), which was first pointed out by D. V. Sivukhin [4] and V. G. Veselago [5-7]. Negative refraction is most graphically manifested, for example, for oblique incidence of a plane wave from vacuum ( 0    and 0    ) into anti-vacuum (this term was proposed in [8], 0    and 0    ), where 0 and 0  are the electric and magnetic constants. In this case, reflection of a wave from the interface does not take place, but the initial direction of propagation as the wave propagates into the second medium is changed to the direction of the wave vector of the absent reflected wave. Here the refracted wave, being a backward wave, transfers energy in accordance with the radiation condition from the interface into the periphery of the second medium. References [9][10][11] are dedicated to historical and other aspects of the electrodynamics of media with backward waves and their discussion in the literature. A modification of Snell's refraction law was proposed in [5][6][7] relevant to the interface with a hypothetical lefthanded medium with both  and  negative, presaging the introduction of the new concept of a negative refractive index. After the first experimental confirmation of the phenomenon of negative refraction for microwaves [12] and the appearance of the concept of electromagnetic metamaterials, the English-language version [7] of Veselago's paper [6] acquired some fame and became widely cited and much in demand. Despite some doubts and objections [13][1...

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confidence: 54%

Refraction into an Isotropic Medium with Negative Permittivity and Permeability

Fisanov

2014

Russ Phys J

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“…If a Bloch mode's equifrequency contour is elliptical or hyperbolic, then diagonal and µ tensors can describe it at the fixed frequency [132]. But if the equifrequency contour is not elliptical or hyperbolic, then the PC cannot be characterised at that frequency even by a uniaxial optical crystal [155]. Generally, k x and k y are only related at a given frequency by lattice symmetries.…”

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confidence: 99%

Photonic-crystal surface modes found from impedances

et al. 2010

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We present a rigorous definition of a wave impedance for 2D rectangular and triangular lattice photonic crystals (PCs), in the form of a matrix. Reflection and transmission at an interface between PCs can be represented by matrices that relate the Bloch mode (eigenmode) amplitudes in the two PCs; we show that these matrices, which are multi-mode generalisations of reflection and transmission coefficients, may be calculated from the PCs' impedances that we define.Given the impedances and Bloch factors (propagation constants) of a collection of PCs, the reflection and transmission properties of arbitrary stacks of these PCs may be calculated efficiently using a few matrix operations. Therefore our definition enables PC-based antireflection coatings to be designed efficiently: some computationally expensive simulations are required in an initial step to find a range of PCs' impedances, but then the reflectances of every coating that consists of a stack of these PCs can be calculated without any further simulations.We first define the PC impedance from the transfer matrix of a single PC layer (i.e., a grating). Since transfer matrix methods are not especially widespread, we also present a method and associated source code to extract a PC's propagating and evanescent Bloch modes from a scattering calculation that can be performed by any off-the-shelf field solver, and to calculate impedances from the extracted modal fields.Finally, we put our method to use. We apply it to design antireflection coatings, nearly eliminating reflection at a single frequency for one or both polarisations, or lowering it across a larger bandwidth. We use it to find surface modes at interfaces between PCs and air, and their projected band structures. We use the impedance to define effective parameters for PC homogenisation, and we briefly describe how our definition has been used to dispersion engineer a PC waveguide. Statement of contribution for joint author publicationsLawrence, F. J. et al. "Antireflection coatings for two-dimensional photonic crystals using a rigorous impedance definition". Appl. Phys. Lett. 93, 1114Lett. 93, (2008 This Letter is partially based on work done in FL's Honours year, and partially on work done during his PhD. Most of the software used was provided by KD and LB, and FL extended it in collaboration with them. In FL's PhD he extended the software implementation of the method (with help from KD and LB) to support non-normal incidence and frequencies above the first Wood anomaly. FL wrote the letter, which was heavily edited and proofread by MdS, KD, and LB.Lawrence, F. J. et al. "Impedance of square and triangular lattice photonic crystals". Phys. Rev. A 80, 23826 (2009) The suggestion of generalising the method to triangular lattices was made by FL's supervisors. LB supplied the orthogonality relations, which as noted in the paper are from previous work, and FL worked out how to use these to define the impedance for these structures. LB suggested the final notation used in the paper. Taking the Ma...

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“…A remarkable feature of the isofrequency curves of magnetostatic spin waves is that large segments of the curves are nearly straight. [17][18][19] If, therefore, spin waves with a broad range of wave vectors are excited, e.g., by a point-like source, the straight segments of the isofrequency curves lead to collinearity of the group velocities corresponding to wave vectors on those straight segments. In real space, this causes true spin-wave point-sources to emit tightly focused spin wave beams (commonly referred to as "spin-wave caustics") 20 with a two-fold symmetry.…”

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confidence: 99%