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.
We experimentally demonstrate full two-dimensional focalization of light beams at visible frequencies by a three-dimensional woodpile photonic crystal. The focalization (the flat lensing) with focal distances of the order of The concept of flat PhC lensing is based on the transformation of the phases of the angular field components. The convex-curved phase shifts of field components accumulated during propagation inside the PhC can be compensated by the usual concave-curved phase shifts during propagation in a homogeneous material, both in front of and behind the PhC, resulting in focusing behind the PhC. The distance between the object and the PhC, l 1 , and between the PhC and the image, l 2 , [ Fig. 1(a)] obey the relation l 1 l 2 f , where f is the focal distance of the flat PhC lens. This is in contrast to the usual focusing by conventional or by Fresnel lenses, where the well-known relation 1∕l 1 1∕l 2 1∕f holds.In this Letter we experimentally demonstrate full two-dimensional (2D) focusing by a polymer-based threedimensional (3D) woodpile PhC. Full 2D flat lens focusing has been experimentally shown for microwaves [7] and for sound waves [8]. Moreover, even 1D focusing/imaging by PhC slabs has thus far been experimentally demonstrated only in the near-IR frequency range [9].PhC lensing is usually considered for modulation periods of the order of wavelength. Flat lensing occurs due to the convex-curved spatial dispersion (or isofrequency) lines in the first, or at most in the second, propagation band. In particular, for PhCs of square symmetry, the corner of the Brillouin zone (BZ) is positioned at λ d 0n (λ is the wavelength,n is the effective refractive index of the PhC, and d 0 is the lattice period). The self-collimation (SC) (the flattening of the spatial dispersion lines) occurs at frequencies below the corner of the BZ, i.e., at λ > d 0n . The flat lensing, which is based on anomalously curved spatial dispersion lines, generally occurs between the frequencies of SC and of the edge of the BZ. The experimental demonstration of flat lensing in the visible range is therefore a difficult task, due to technological limitations of PhC fabrication techniques at this scale. We use an alternative approach based on PhCs with relatively large modulation periods, but searching the flat lensing effects in higher order bands. This, on one hand, simplifies the fabrication of the samples, but on the other hand makes the observation and interpretation of the
We experimentally observe formation of narrow laser beams behind the woodpile photonic crystal, when the beam remains well collimated in free propagation behind the crystal. We show that the collimation depends on the input laser beam's focusing conditions, and we interpret theoretically the observed effect by calculating the spatial dispersion of propagation eigenmodes and by numerical simulation of paraxial propagation model.
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