Signatures of light-beam spatial filtering in a three-dimensional photonic crystal

Abstract

We report experimental evidence of spatial filtering of light beams by three-dimensional, low-refraction-indexcontrast photonic crystals. The photonic crystals were fabricated in a glass bulk, where the refraction index has been periodically modulated using tightly focused femtosecond laser pulses. We observe filtered areas in the angular distributions of the transmitted radiation, and we interpret the observations by theoretical and numerical study of light propagation in index-modulated material in paraxial model.

Femtosecond direct laser writing of photonic spatial filters in soda–lime glass

“…The gapless spatial filtering can be obtained for substantially larger longitudinal periods of modulation d || > λ (we will use d z to denote the thickness of one layer, two layers comprise one period d || = 2d z ); hence, current fabrication techniques can be applied more easily. Such kind of filtering has been recently demonstrated experimentally in different 3D configurations using PhCs with a square symmetry in transverse space [15,16], as well as photonic structures with axisymmetric rings [17,18]. The gapless filtering has been recently proposed also to clean atomic ensembles on Bose-Einstein condensates [19].…”

“…The fabrication algorithm and the fabrication setup are reported in detail in [15]. PhCs were inscribed layer by layer by relative translation of the focal point inside the bulk of the glass sample.…”

Intrinsic beam shaping mechanism in spatially modulated broad area semiconductor amplifiers

“…Hence, a proper selection of the geometry, satisfying Q % 1, sets angular band-gaps at small angles from the optical axis direction, whereas the on-axis radiation lays in propagation bands. This results in a low-angle-pass filter recently proposed and demonstrated not only in optics [12][13][14][15] but also in acoustics (by so called Sonic Crystals). 16,17 On the other hand, materials with periodically in space modulated gain have recently shown to provide anisotropic amplification profile.…”

Super-collimation by axisymmetric photonic crystals

“…9 The beam manipulation with PhCs in the far field domain get less attention: perhaps the only known effect of PhC action on the spatial frequency spectrum is a spatial (angular) filtering of the beams due to the angular band-gaps. [10][11][12] In spatial filtering, a range of the angular components of a beam can be removed due to the angular band-gaps, i.e., the waves can be reflected in backward direction 10,11 or deflected at large angles in forward direction. 12 In the latter case, the angular distribution of the transmitted field is modified as illustrated in Fig.…”

“…In every second layer, the structure of rings is reciprocal, i.e., the radii with refractive index maxima correspond to radii with index minima in the next layer (next longitudinal half-period). The longitudinal period of the structure was calculated following the spatial filtering theory, 12,13 where the angle of the filtered out components is given (in paraxial approximation) by…”