Finite-size and disorder-induced modification of light transport and emission in photonic crystals

Abstract

The imperative thought of taming the light transport and spontaneous emission result in the development of photonic crystal structures that possess a spatial variation of refractive index on an optical wavelength scale. The structures inhibit the propagation of certain frequencies of light through it due to the optical Bragg diffraction. These frequencies are reflected back into the incident medium and this forbidden range of frequencies for the structure constitutes the photonic stop gap in the propagation direction. The formation of the photonic stop gap is vulnerable to the direction and polarization of the incident light. When the photonic stop gaps present in all possible directions overlap with each other over a specific frequency range, a photonic band gap is formed which hinders the propagation of light of any state of polarization. The photonic band gap decimates the local density of photon states (LDOS) to zero leading to the complete inhibition of spontaneous emission as followed by the Fermi golden rule. The present thesis deals with finite-size and disorder-induced modification in the light transport and emission using self-assembled photonic crystals. The photonic crystal samples are fabricated through the self-assembly method using polymer colloids of sub- micron diameter. The structural characterization of the photonic crystals is obtained using the scanning electron microscope. We have seen very good long-range ordering of the spheres with the (111) plane of the fcc crystal parallel to the substrate. The reflectivity and the transmittance of light through the photonic crystals are measured to study the photonic stop gaps. The dimensions of the incident light beam used in the reflectivity measurements are 5 mm × 5 mm and therefore, it provides area-averaged reflectivity spectra over hundreds of crystal domains. We discuss the angle- polarization-dependent photonic stop gaps and associated multiple Bragg diffraction at the high-symmetry points in photonic crystals with fcc symmetry. Optical reflectivity measurements show prominent multiple Bragg diffraction at K point for TE polarized light. Contrary, the TM polarized light exhibit quasi-collapse of stop gap at K point till the Brewster angle. Unlike the case of K point, multiple Bragg diffraction is apparent at W point for both TE and TM polarizations. The inherited multiple Bragg diffraction is observed for TE polarization whereas that is suppressed for TM polarization as a consequence of Brewster effect. The measured multiple peaks at the K and W point are assigned to the {111} or {200} family of crystal planes. The polarization anisotropy factor is estimated to enumerate the non-identical stop gap formation at the K and W points. We have observed a significant shift in the on-resonance Brewster angle as compared to the measured and calculated off-resonance values. The estimated polarization anisotropy values are in good agreement with the theoretical calculations for ideal photonic crystals with fcc symmetry. The propagation and emission of light in a synthesized photonic crystal is routinely affected by the intrinsic disorder, and its finite-size. Thus, theoretical calculation based on the notion of a defect free crystal with an infinite thickness is irrational in the real world experiments. Therefore, it is important to study the extent of inhibition in spontaneous emission possible in self-assembled photonic crystals. The single domain reflectivity measurements show the stop gaps with near 100% reflectivity which is in strong agreement with theoretical calculation. This suggests the resemblance of the single domain with its minimal disorder to an ideal crystal with fcc symmetry. We have measured the spontaneous emission intensity and lifetime for an embedded dye molecule at the stop gap wavelength which show strong inhibition in relation to the reference sample. Our results show spatial fluctuation in spontaneous emission suppression that has a linear scaling with crystal size which is also in agreement with the theory. The photonic crystals are fabricated with different levels of disorder to exhibit the consistent interaction of light in a complex photonic structure with spatial random variation in refractive index. Exceptionally, it is found that the disordered structure with short-range order introduces a frequency gap called the gaplike resonance. The gaplike resonance is formed for the photonic structure with short range order composed of clusters made of few spheres coincides with the photonic stop gap for a perfect photonic crystal. We have performed the wavelength-dependent spontaneous emission decay rate measurements to authenticate the gap like resonance. The emission rate is suppressed in a similar way as that of its ordered counterpart.