Optical characterization of lasing in self-assembled photonic crystals

Spontaneous emission, a fundamental radiative relaxation mechanism in an excited medium triggered by vacuum fluctuations, can be controlled by modifying the density of states (DOS) of the corresponding energy transition event. Nanostructures offer a way to control the DOS in a particular frequency range and thus control spontaneous emission. Accordingly, an active area of research interest in nanophotonics is the control of spontaneous emission dynamics of dipole-allowed transitions. The confinement in such structures is achieved by using photonic bandgaps that essentially act as virtual walls for the designed wavelength. Photonic crystals (PhCs) are artificial structures containing a periodically varying refractive index, with a periodicity in the order of the optical wavelength. The periodicity of PhCs results in dispersion diagrams containing a series of allowed and forbidden bands. As a result of this, the propagation of light is prohibited either in certain directions (resulting in a pseudo photonic stopband) or in all directions (providing a complete stopband), depending on the periodicity, index contrast, and crystal structure. The density of electromagnetic modes at a given frequency — the local density of states — is reduced inside the photonic band gap and increased near the band edges. With an active medium present inside a PhC, it is possible to tune the emission characteristics of the active medium cleverly in certain frequency ranges depending on the extent of overlap of the emission band with the photonic stopband. In this work, three-dimensional (3D) PhCs are fabricated using Rhodamine-B doped polystyrene (PS-RhB) colloidal spheres by inward growing self-assembly technique, which is quick and cost-effective. The structural characterization of the PhCs is carried out using scanning electron microscopy (SEM) and atomic force microscopy (AFM). A clear hexagonal arrangement of the colloidal spheres parallel to the surface of the substrate is observed. It represents the (111) plane of the face centered cubic (fcc) crystal orientation. Optical characterization is carried out by measuring the specular reflectance and transmittance at different angles from the PhC. The pseudo stopband properties of the PhCs are analyzed by measuring the spectral characteristics of angle-dependent reflection. For larger index contrast, the PhC is infiltrated with ZnO and inverted. Red shift and blue shift in the wavelength of reflection peak is observed in infiltrated and inverse PhCs respectively, with reference to the direct PhC, due to the change in the effective refractive index. Heterostructure PhC is fabricated by growing a second PhC with a different colloidal diameter on the top of the first PhC. The inevitable disorder in the self-assembled PhCs and the resultant extinction is modeled by comparing the experimentally obtained reflection spectrum with the reflection spectrum calculated using Korringa–Kohn–Rostoker (KKR) method with complex dielectric constant containing a positive imaginary part. The magnitude of the positive imaginary part of the dielectric constant can be used as a measure of the structural disorder in the structure. It is found that the higher order modes are very sensitive to the scattering losses. We estimate the thickness and disorder of the PhCs after a significant amount of fine-tuning in the parameters for a good match with the experimentally obtained reflection spectrum. The disorder in the heterostructure PhCs is estimated and higher extinction values are attributed to the scattering losses near the interfaces of the heterostructure PhC. Spectral distribution of emission is measured in a large angular range (8 deg to 180 deg) around PS-RhB PhC while exciting the crystal at 532 nm under normal-incidence condition. Its comparison with the emission characteristics from the same dye-doped colloids in a liquid suspension provides a better understanding of the anisotropic propagation of light within the structure due to its pseudo-gap properties. Spontaneous emission is suppressed by 40% in the presence of the stopband over a large bandwidth (∼50%) of the first-order bandgap in the [111] direction of the PhC, due to an appropriate choice of the colloidal diameter. Spectral modifications in the spontaneous emission occur with the variation in the detection angle. Reflection and transmission are complementary because of the absence of strong absorptive effects. The emission spectra are given for several angles and compared with the isotropic emission from PS-RhB colloidal suspension in water, establishing the extent of anisotropy in the emission from the ordered crystals. We theoretically study the low-threshold band-edge lasing in 3D opals with an fcc lattice structure, using a complex-valued dielectric constant (with a negative imaginary part to model the gain) in the KKR method. We show that the lasing threshold at the low-frequency band edge is smaller than that at the high-frequency band edge for the first-order stopband of the PhC. A 100-fold reduction in the lasing threshold is observed near the first order stopband edge in the [111] direction due to the reduced group velocity, which enhances the light matter interaction. Much more significant reduction in the threshold is observed for the lasing modes in high energy region as their group velocities are typically smaller than that of the modes at the first order band edge. We also analyze the impact of the number of ordered layers in the PhC on the frequency of band-edge lasing and the lasing threshold near the first-order stopband in the [111] direction. Thus we demonstrate a broad tunability of the lasing frequency with change in the emission collection angle with a relatively small variation in lasing threshold. We found that 25 ordered layers in the opal are sufficient to achieve a significant reduction in lasing threshold and to overcome finite size effects. The calculated value of the lasing wavelength is found to be in close agreement with the experimentally obtained value reported by our group in the recent past. We propose and analyze a PhC-based microcavity composed of a heterostructure, in order to decrease the lasing threshold even further. The design consists of a 3D PhC, grown from colloids containing the gain medium, sandwiched between two identical passive multilayer stacks, which form an equivalent external cavity. When the defect mode of the external cavity becomes resonant with the band edge region of the 3D PhC, the net availability of the DOS for the mode increases in comparison to a stand-alone configuration. The lasing threshold characteristics are calculated using KKR method. The PhC heterostructure cavity suggested in our work has the advantages of low lasing threshold and tunability of the lasing wavelength. The latter is achieved by changing either the number of layers or the periodicity in the sandwiched 3D PhC. We unambiguously demonstrate that the lasing threshold is significantly reduced for the cavity modes near the band edges of the sandwiched 3D PhC, when compared to other cavity modes. A decrease in the lasing threshold by two orders of magnitude is observed as compared to the stand-alone 3D PhC. The dependence of the lasing threshold and the wavelength on the number of layers in the sandwiched 3D PhC and the multilayer stack is also calculated and analyzed. The obtained results show the potency for designing PhC-based, compact on-chip lasers with ultra-low thresholds.Thesis submitted in partial fulfillment of the requirements of the degree of Doctor of Philosophy of the Indian Institute of Technology Bombay, India and Monash University, Australia