Experimental Detection of the Optical Pendellösung Effect

Abstract

We report observations of periodic oscillatory behavior of the angular selectivity, near the Bragg angle, in volume holographic gratings recorded in a new photopolymerizable glass with high refractive index modulation. We have detected the presence of overmodulation in the intensity distribution of the first diffraction order. The results reported here were achieved by incorporating in the photopolymerizable solgel glass zirconium-based high refractive index species at the molecular level. This is the first time that this effect is observed for light diffraction in an amorphous material. Introduction.-The Pendellösung effect was first observed by Shull in 1968 for the interference formed by the diffraction of slow neutron beams by thick perfect crystals of silicon with a thickness ranging from 0.33 to 1 cm [1]. The oscillatory behavior of the diffracted intensity was caused by the coherent transfer of neutron flux between the transmitted and internally Bragg-reflected beams by the periodic crystalline structure producing amplitude overmodulation. The Laue diffraction formalism provides the theoretical explanation of this phenomenon [2].The Pendellösung fringe structure appears as a consequence of the interference between two branches of the wave function that result as solutions of the wave (Schrödinger) equation within the framework of the dynamical theory of diffraction. This phenomenon is formally analogous to the transfer of energy between two coupled pendulums, hence its name. One actual application of this effect was the experimental determination of the unit cell of the crystal structure and the scattering amplitude. The defects in the crystal structures (e.g., lattice dislocations) can hinder observation of the Pendellösung phenomenon since the presence of such defects can disturb the interference and the resulting energy transfer process. Similar experiments were later carried out on crystals other than silicon (e.g., Ge, FeBO 3 , and Fe 2 O 3 ) and polarized neutron beams [3]. The Pendellösung effect has also been predicted and observed in second-order Bragg scattering of matter waves from a standing light wave acting as a thick grating [4]. Further experiments showed that a quasiPendellösung effect can be observed in the Raman-Nath regime for diffraction of atomic beams from standing light waves [5].The dynamical theory of x-ray diffraction formulated by Ewald [6] accounts for the Pendellösung effect. The coherent splitting of the incident beam will result in radiation periodically beating at different depths of the grating. The experimental observation of this effect is not trivial since it requires thick almost perfect crystal structures, or amor-

Polarization and phase-shift properties of high spatial frequency holographic gratings in a photopolymerizable glass

“…This mechanism results in a self-developed hologram with a permanent phase grating with an increased dynamic range along with low coherent and incoherent scattering noise, high optical quality, high diffraction efficiency, and negligible shrinkage [8]. The optical Pendellö-sung effect was reported in the visible domain using this material [11].We holographically recorded transmission volume gratings in a 90°recording geometry by the interference of two collimated mutually coherent s-polarized beams of 532 nm in wavelength and 50 mW of power. To achieve a 90°recording geometry inside the holographic material (HM), Fig.…”

“…This mechanism results in a self-developed hologram with a permanent phase grating with an increased dynamic range along with low coherent and incoherent scattering noise, high optical quality, high diffraction efficiency, and negligible shrinkage [8]. The optical Pendellö-sung effect was reported in the visible domain using this material [11].…”

Photopolymerizable glasses incorporating high refractive index species and ionic liquid: A comparative study

“…In particular, the applications for the implementation of transmission volume phase holographic gratings (VPHG) with the aim to operate as holographic optical elements (HOE) for various purposes and experiments, have demonstrated their flexibility for maintaining the high performance under a wide range of spatial frequencies and laser sources conditions for the recording and readout. [23][24][25][26] However, in order to perform the comparative study with the photopolymerizable glasses incorporating IL, these analyses were revisited by using in the subsequent characterization samples synthesized at the same time than those with IL, and thus ensuring the same synthesis conditions for all the photopolymerizable glasses of the present study.…”

“…In this paper, and encouraged by the previous mentioned results, we present a comparative study among three alternative formula for the composition of a photopolymerizable glass: (1) the formula that contains HRIS, already studied by us, [23][24][25][26] (2) incorporation of IL to the previous formula, and (3) exclusion of the HRIS in the composition while maintaining the IL as a component. A comparative study of the various physical performances obtained is presented.…”

Diffusion study in tailored gratings recorded in photopolymer glass with high refractive index species

“…The exposure time was chosen in all samples such that the maximum diffraction efficiency is obtained. Longer exposure intervals result in the overmodulation effect and a corresponding decrease in the reconstruction fidelity ͑Pendellösung effect͒ 6 and diffraction efficiency. In all the studied cases, we found excellent agreement between the experimental and the theoretical angular selectivity results, including the three first secondary maxima and minima of the angular selectivity curves.…”