Dynamics of free-standing smectic-<i>A</i>films

Vp, Romanov; Sv, Ul'yanov

doi:10.1103/physreve.63.031706

Cited by 21 publications

(17 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Similar fine structure of optical diffraction was considered as an important criterion for the quality of a 3D PhC crystal [7]. In our case the avoided crossing behaviour is much more pronounced as compared with published data [6,7]. This indicates a good quality of our opalGaN composite.…”

Section: M 300 Nmsupporting

confidence: 65%

“…Such substantial deviation from simple Bragg's law is associated with the simultaneous Bragg diffraction by (111) and (200) PhC planes [6]. Similar fine structure of optical diffraction was considered as an important criterion for the quality of a 3D PhC crystal [7]. In our case the avoided crossing behaviour is much more pronounced as compared with published data [6,7].…”

Section: M 300 Nmsupporting

confidence: 43%

See 1 more Smart Citation

Three-Dimensional GaN Photonic Crystals

Gajiev

Голубев

Kurdyukov

et al. 2002

phys. stat. sol. (b)

View full text Add to dashboard Cite

Wide bandgap GaN based semiconductor structures are highly attractive because of their great potential for development of stable optoelectronic devices in the visible-ultraviolet region [1]. Up to now main efforts of researchers have been directed towards the use of properties of tzhe electron subsystem in GaN. The main goal of our work is to create a material where optical and electronic properties of the nitride semiconductor could be combined with unique features of photonic crystals (PhC) based on artificial opals. The novel properties of such materials open new possibilities to mould and control emission and propagation of light in visible optoelectronic devices [2]. The present work is aimed at synthesizing GaN PhC, investigating their optical properties and effect of a photonic band gap (PBG) on the Bragg diffraction of light.To create GaN based 3D PhC we used highly ordered synthetic polydomain opals as a 3D template. The opals have the fcc structure formed by closed-packed a À SiO 2 spheres of 245 nm in diameter. The sublattices of interconnected opal voids were impregnated with Ga 2 O 3 precursor and the samples were annealed in an atmosphere of nitrogen hydrides. XRD, TEM, SEM, and Raman measurements confirmed the structural perfection of GaN in the opal-GaN composites [3,4]. Then, the silica template was selectively removed by etching off the a À SiO 2 skeleton with HF. As a result we have prepared so-called inverse opal-GaN which is in fact 3D PhC entirely consisting of GaN (Fig. 1).When characterizing the samples fabricated main attention was paid to measuring reflection spectra. In what follows we will present results obtained for s-polarization of diffracted light. To measure the reflection spectra from a domain the 8-fold magnified image of the sample was focused on the entrance slit of a spectrometer.Investigation of reflection spectra is one of the most simple and direct methods to probe the band structure of PhC [5]. Due to the periodic modulation of the dielectric constant photonic crystals reveal photonic band structures and, in particular, forbidden energy gaps for light (stop bands) appear in the energy spectrum. Light waves with energies within these stop bands are Bragg reflected and cannot propagate inside the crystal. As a result, in reflection spectra maxima arise in the energy regions of the stop bands. Figure 2a shows reflection spectra of the initial phys. stat. sol. (b) 231, No. 1, R7-R9 (2002)

show abstract

Section: M 300 Nmsupporting

confidence: 65%

Section: M 300 Nmsupporting

confidence: 43%

Three-Dimensional GaN Photonic Crystals

Gajiev

Голубев

Kurdyukov

et al. 2002

phys. stat. sol. (b)

View full text Add to dashboard Cite

show abstract

“…A stopgap is also formed when Bragg diffraction occurs on multiple Bragg planes simultaneously, which is called multiple-Bragg diffraction [11], and is fundamental for bandgap formation [2,12,13]. Wave propagation in crystals is described along high-symmetry directions [1].…”

mentioning

confidence: 99%

Observation of Sub-Bragg Diffraction of Waves in Crystals

et al. 2012

View full text Add to dashboard Cite

We investigate the diffraction conditions and associated formation of stopgaps for waves in crystals with different Bravais lattices. We identify a prominent stopgap in high-symmetry directions that occurs at a frequency below the ubiquitous first-order Bragg condition. This sub-Bragg diffraction condition is demonstrated by reflectance spectroscopy on two-dimensional photonic crystals with a centred rectangular lattice, revealing prominent diffraction peaks for both the sub-Bragg and first-order Bragg condition. These results have implications for wave propagation in 2 of the 5 two-dimensional Bravais lattices and 7 out of 14 three-dimensional Bravais lattices, such as centred rectangular, triangular, hexagonal and body-centred cubic.The propagation and scattering of waves such as light, phonons and electrons are strongly affected by the periodicity of the surrounding structure [1,2]. Frequency gaps called stopgaps, emerge for which waves cannot propagate inside crystals due to Bragg diffraction. Bragg diffraction is important for crystallography using X-ray diffraction [3] and neutron scattering [4]. Diffraction determines electronic conduction of semiconductors [1,2] and of graphene [5], and broad gaps are fundamental for acoustic properties of phononic crystals [6,7] and optical properties of photonic metamaterials [9, 10].Bragg diffraction is described in reciprocal space by the Von Laue condition − → Here m is an integer, λ is the wavelength inside the crystal, θ is the angle of incidence with the normal to the lattice planes, and d is the spacing between the lattice planes. A stopgap is also formed when Bragg diffraction occurs on multiple Bragg planes simultaneously, which is called multiple-Bragg diffraction [11], and is fundamental for bandgap formation [2,12,13]. Wave propagation in crystals is described along high-symmetry directions [1]. Multiple-Bragg diffraction has been recognized in highsymmetry directions at frequencies above the first-order simple Bragg diffraction condition: m = 1, λ = 2d orhas not yet been observed at frequencies below simple Bragg diffraction [14].In this Letter we show that for high-symmetry directions multiple-Bragg diffraction can occur at frequencies below the first order simple Bragg condition. As a demonstration we have investigated diffraction conditions for two-dimensional (2D) photonic crystals using reflectance spectroscopy. A broad stopgap is observed below the simple Bragg condition, depending on the symmetry of the lattice. Our findings are not limited to light propagation, but apply for wave propagation in general, and therefore we anticipate similar diffraction for electrons in graphene [5], and sound in phononic crystals [6,7].We have studied light propagation in 2D silicon photonic crystals [17]. Figure 1(a) shows a scanning electron microscope (SEM) image of one of these crystals from the top view. The centred rectangular unit cell has a long side a = 693 ± 10 nm and a short side c = 488 ± 11 nm. The pores have a radius of r = 155 ± 10 nm and are approxima...

show abstract

“…The resulting Bragg scattering, on the other hand, has been intensively examined, both experimentally and theoretically in great detail [2,3,4,5,6,7]. In particular, the multiple Bragg diffraction phenomenon in PhC, which occurs when two narrow Bragg bands demonstrate the avoided crossing effect [7,8,9, 10] has been thoroughly studied. Departing from this phenomenon and with intention to further deepen our understanding of light scattering in PhC, a number of challenging problems can be formulated: What can we expect if a spectrally narrow Bragg band interacts with a broad spectrum originating from certain scattering mechanisms such as Mie or Fabry-Perot scattering?…”

mentioning

confidence: 99%

Fano Resonance between Mie and Bragg Scattering in Photonic Crystals

et al. 2009

View full text Add to dashboard Cite

We report the observation of a Fano resonance between continuum Mie scattering and a narrow Bragg band in synthetic opal photonic crystals. The resonance leads to a transmission spectrum exhibiting a Bragg dip with an asymmetric profile, which can be tunably reversed to a Bragg rise. The Fano asymmetry parameter is linked with the dielectric contrast between the permittivity of the filler and the specific value determined by the opal matrix. The existence of the Fano resonance is directly related to disorder due to non-uniformity of a-SiO2 opal spheres. Proposed theoretical "quasi-3D" model produces results in excellent agreement with the experimental data. PACS numbers: 42.70Qs, 42.25.Fx, 42.79.Fm Mie and Bragg scattering are key optical phenomena in photonic crystals (PhC) composed of spherical or nearly spherical particles. Light scattering by an isolated spherical particle can be described by Mie theory [1]. Considering PhC composed of a periodic array of such spheres, interference of scattered waves results in the transformation of Mie scattering into Bragg scattering and gives rise to formation of the photonic band structure [2]. The underlying Mie scattering is therefore hidden in perfectly ordered PhC and as a result, it has been insufficiently studied so that its role is clear only for the case of perfect structures. The resulting Bragg scattering, on the other hand, has been intensively examined, both experimentally and theoretically in great detail [2,3,4,5,6,7]. In particular, the multiple Bragg diffraction phenomenon in PhC, which occurs when two narrow Bragg bands demonstrate the avoided crossing effect [7,8,9, 10] has been thoroughly studied. Departing from this phenomenon and with intention to further deepen our understanding of light scattering in PhC, a number of challenging problems can be formulated: What can we expect if a spectrally narrow Bragg band interacts with a broad spectrum originating from certain scattering mechanisms such as Mie or Fabry-Perot scattering? Is it possible to observe the consequences of this interaction or simply Mie scattering experimentally? What are the effects of inherent disorder in the structural components of opal-based PhC, beyond the well-known broadening and degradation of stop bands [6,11,12,13,14,15]?If a narrow Bragg band interacts with the continuum spectrum through an interference effect constructively or destructively, we can expect an interaction of Fano-type [16], a phenomenon well-known across many different branches of physics. The Fano resonance between continuum and discrete states manifests as an asymmetric profile of narrow band in the transmission spectrum, which in general has the form:where Ω = (ω − ω B )/(γ B /2), ω B is the frequency, γ B is the width of the narrow band, and q is the Fano asymmetry parameter. It was shown theoretically that Fano-type asymmetric line shapes can be created in the response function of certain PhC. In general these systems consist of a waveguide with forward and backward propagating waves being indirectly...

show abstract

Dynamics of free-standing smectic-Afilms

Cited by 21 publications

References 15 publications

Three-Dimensional GaN Photonic Crystals

Three-Dimensional GaN Photonic Crystals

Observation of Sub-Bragg Diffraction of Waves in Crystals

Fano Resonance between Mie and Bragg Scattering in Photonic Crystals

Contact Info

Product

Resources

About