Interplay between crystal-size and disorder effects in the high-energy optical response of photonic crystal slabs

Abstract

Experimental reflectance spectra have been obtained for colloidal crystals whose widths ranged from one to several sphere monolayers, and their features in the higher order band energy range have been reproduced theoretically. In order to fit the measured data, optical extinction has been introduced in the theoretical model, which accounts for structure imperfections and disorder, the main sources of losses in an actual measurement. A complex spectrum in the high frequency region is observed even for one ordered monolayer, being this peak structure gradually modified as more layers are piled up. This allowed us to identify which peaks are reminiscent of the optical reflectance features of a single close-packed layer and which are the result of building up a three dimensional periodicity. A clear correlation between the amount of extinction introduced in the fitting and the slab width has been found, which demonstrates that wider real crystals produce less diffusely scattered light. At the same time, we find that the optical response of thinner crystals is more robust against the introduction of extinction than that of thicker ones, for which the effect is dramatic. DOI: 10.1103/PhysRevB.76.245103 PACS number͑s͒: 78.20.Bh, 78.40.Ϫq, 42.70.Qs, 41.20.Jb Improvements in the processes of fabrication of selfassembled three dimensional ͑3D͒ photonic crystals ͑PhCs͒, which are materials with a spatially periodic dielectric function in all three dimensions, have made possible the observation of high quality optical spectra in higher order band frequencies.1-3 Also, the appearance of localized modes inside band gaps in the photonic band structure due to the addition of local defects is a well-known effect, which is analogous to the doping of semiconductors.4 Point, line, or plane defects are created within the crystal by locally adding or removing material in a controlled manner, 5,6 so they are different from intrinsic defects, which are unintentional disruptions of the spatial periodicity of the dielectric function that arise during the fabrication process. Despite new fabrication techniques that have alleviated the effect of disorder in the so-called low-energy range, where the lattice constant is less than the wavelength of light, very recently, it has been demonstrated that extinction due to intrinsic defects in 3D PhCs strongly affects the shape of the experimental spectra in the high-energy range, where the lattice constant is greater than the wavelength.7 Also, calculations of the photonic band structure, performed considering extinction, have shown a clear correlation between the behavior of the imaginary part of the wave vector and the optical features observed in the spectra. This means that disorder, while having a small influence on the measured spectra in the low-energy range, amplifies its effects at higher energies and, consequently, further improvement of the fabrication techniques is required to achieve optical quality at those photon energies. 8 In order to perform a valid comparison between the opt...

Understanding of transmission in the range of high-order photonic bands in thin opal film

“…Similar reflectance bands were earlier experimentally observed and reproduced numerically, 19 but the difference between surface and volume modes was ignored in this analsis.…”

Relation between growth dynamics and the spatial distribution of intrinsic defects in self-assembled colloidal crystal films

“…It should be noted that the amount of disorder present in colloidal crystal films has previously been approximated by assuming an optical extinction factor that accounts for imperfections in the lattice. 18,19 The most remarkable result of these two precedents was that the amount of disorder is smaller for thicker sample. Our study indicates that the thicker regions of a particular film are indeed expected to be less defective since they grow more slowly.…”

Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals

“…Furthermore, only the first six layers are involved in the optical response of the slab because waves have a finite penetration depth into the slab. 16,18 Figure 4 shows the measured ͑solid lines͒ and calculated ͑dashed lines͒ efficiencies of the reflected beams ͑1, 0͒ and ͑1,−1͒, where a good correlation between theory and experiment is obtained. In this case, a shift of the peaks toward higher wavelengths ͑red shift͒ can be appreciated.…”

“…16 Besides, the modeling of disorder via extinction has also shown that sharp resonances are smoothed out more dramatically as a consequence of the diffuse light scattering. 17,18 It has been found that the unintentional imperfections introduced in the fabrication process 19 produce diffusely scattered light which removes energy from the coherent reflected and transmitted beams. 16 This effect has been simulated by adding extinction to the theoretical model of a perfectly ordered lattice of spheres, obtaining fittings of the specular reflectance and forward transmittance experimental data with a degree of accuracy that has no precedent.…”