Dimensionality effects on the optical diffraction from opal-based photonic structures

M. V. Rybin, I. S. Sinev, A. K. Samusev, K. B. Samusev, E. Yu. Trofimova, D. A. Kurdyukov, V. G. Golubev, and M. F. Limonov

Phys. Rev. B 87, 125131 – Published 19 March 2013

Abstract

We present a comprehensive experimental and theoretical study of visible light diffraction from opal-based photonic structures of different dimensions. We also developed new methodological approaches to collection, processing, and interpretation of experimental diffraction data. The key idea is to analyze the light diffraction data represented in the “incident angle-registration angle” coordinates instead of the widely used “incident angle-registration intensity” coordinates. In such coordinates, a 2D diffraction pattern consists of ovals, while a 3D Bragg diffraction pattern consists of parallel stripes owing to the specular reflection law. Therefore this representation allows one to distinguish easily the patterns originating from 2D diffraction from the ones governed by 3D diffraction. In addition, different types of structural disorder including twinning of the face-centered cubic structure become apparent in the angle coordinates.

Received 26 November 2012

DOI:https://doi.org/10.1103/PhysRevB.87.125131

Authors & Affiliations

M. V. Rybin^1,2,*, I. S. Sinev^1,2, A. K. Samusev^1,2, K. B. Samusev^1,2, E. Yu. Trofimova¹, D. A. Kurdyukov¹, V. G. Golubev¹, and M. F. Limonov^1,2

¹Ioffe Physical-Technical Institute of the Russian Academy of Sciences, St. Petersburg 194021, Russian Federation
²National Research University for Information Technology, Mechanics and Optics (ITMO), St. Petersburg 197101, Russian Federation

^*m.rybin@mail.ioffe.ru

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 87, Iss. 12 — 15 March 2013

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Schematic representation of the experimental setup designed to observe light diffraction in the $X Y$ plane on a cylindrical screen. Six diffracted beams are shown. Three of them are scattered forward with respect to the incident beam, whereas the other three are scattered backward. The angle of incidence $θ$ and the angle of scattered light registration are indicated. Oblique incidence is demonstrated: $θ = 5^{\circ}$ . (b) A development of a white light diffraction pattern obtained on opal film and recorded on a cylindrical screen at normal incidence: $θ$ $=$ 0. (c) The combined experimental pattern of light diffraction in the $X Y$ plane for the angle of light incidence varying within the range $- 90^{\circ} < θ < 90^{\circ}$ . (d) The numerical simulation of the 2D diffraction pattern in the Born approximation. (e) The calculation of the positions of the zeroth, first, and second-order 2D diffraction reflections obtained from Eq. (11) for three different wavelengths: 415, 500, and 585 nm.Reuse & Permissions
Figure 2
Scheme of the scattering geometry. Wave vectors $k_{i}$ of the incident wave, $k_{s}$ of the scattered wave, the scattering vector $q = k_{s} - k_{i}$ and its projection $q_{| |}$ on the sample surface are shown with black lines. The sample and its surface normal $n$ are shown with grey lines. The incident angle $θ$ and the registration angle $Θ$ are also marked.Reuse & Permissions
Figure 3
(a) Calculated intensity of the visible light diffraction from the twinned fcc opal structure with $D = 330$ nm. (b) The experimental pattern of white light diffraction from the synthetic opal sample immersed in water with dielectric permittivity $ɛ_{f} = 1.78$ . The sample thickness is 34 layers. For convenience, diffraction reflections are marked by white boxes.Reuse & Permissions
Figure 4
Calculated intensity of the visible (400–700 nm) light diffraction from one layer of ${SiO}_{2}$ particles and from the fcc opal structure. (a)–(d) Dependence on the number of layers for structures consisting of two equivalent twins: $N_{3} = 1$ (a), $N_{3} = 10$ (b), $N_{3} = 20$ (c), $N_{3} = 100$ (d). (e)–(h) Dependence on the stacking fault probability $p$ for structures with $N_{3} = 100$ : (e) $p = 1$ , (f) 0.95, (g) 0.8, and (h) 0.65. The calculations (a)–(h) were performed for the structures with ${SiO}_{2}$ particle diameter of 330 nm. The opal filler is water ( $ɛ_{f} = 1.78$ ). $θ$ is the angle of incidence, and $Θ$ is the angle of scattered light registration.Reuse & Permissions
Figure 5
(a) Calculated intensity of the visible (400–700 nm) light diffraction from the twinned fcc opal structure with $N_{3} = 35$ and ${SiO}_{2}$ particle diameter $D = 600$ nm. (b) Experimentally measured white light diffraction pattern obtained on an opal film with the same parameters. The opal filler is propylene glycol ( $ɛ_{p g} = 2.05$ ).Reuse & Permissions
Figure 6
Calculated angular FWHM of different diffraction spots for samples with (a) different thicknesses $N_{3}$ and (b) different stacking disorder degree $p$ , $N_{3} = 100$ . The opal filler is water ( $ɛ_{f} = 1.78$ ) and the ${SiO}_{2}$ particle diameter is $D = 330$ nm. The angular width was evaluated at $θ = - 45^{\circ}$ , as shown on the inset in (a).Reuse & Permissions

Physical Review B

covering condensed matter and materials physics