When a dipole emitter is surrounded by a set of mirrors, its radiative decay rate experiences a significant change. For example, when the emitter is located at the node of a standing-wave [solid curve in Fig. 2(a)], the emission is rigorously forbidden. In the opposite case where the emitter is located at the intensity antinode [dotted curve in Fig. 2(a)], the emission rate is maximized. This phenomenon is now well established and is known as the ‘Purcell effect’ after E. M. Purcell – the renowned American physicist who won the Nobel Prize for physics in 1952.
A photonic crystal is an artificial dielectric material possessing a photonic bandgap – a spectral energy band within which any radiation is rigorously forbidden. As the name ‘crystal’ implies, a notable geometrical feature of a ‘photonic crystal’ is a periodic arrangement of dielectrics – often, it is in the form of periodically drilled air-holes in a dielectric slab. When a dipole emitter's radiative transition energy falls inside the photonic bandgap, the radiation is quenched and the emitter will remain in its excited state forever. In Fig. 2(b), we depict this situation as the exponentially decaying field amplitude on both sides of the dipole emitter.
What would happen if the emitter’s radiative transition energy falls ‘outside’ of the bandgap or the photonic crystal in question does not support any energy bandgap? It is not so difficult to imagine the emitter experiencing a radiative transition. However, the radiative decay rate may still be controlled by setting up mirrors around the imperfect photonic crystal [See Fig. 2(c)], in the similar manner as in the case of Fig. 2(a) – Depending where the emitter is located, its radiative rate can be either suppressed or enhanced.
In our new paper , we theoretically investigate an optically-thick photonic crystal slab [Fig. 1(a)] that does not support a photonic bandgap. More specifically, we consider the effect of a simple boundary termination on the quality (Q) factor of a spatially localized mode [See Fig. 1(b)]. Note that the localized photon state in this case corresponds to the point dipole emitter in Fig. 2. Therefore, we expect a similar modulation of the coupling strength between the localized photon state and the standing wave modes (in-plane Bloch modes), which will be manifested as Q factor modulation as a function of the size of the boundary termination (our mirror) [See Fig. 1(c)]. We find that Q can be increased to over 100,000 even in the absence of a photonic bandgap. This finding will be of practical importance for the design of current-injection photonic crystal nanolasers.
- Kim, S.-H., Homyk, A., Walavalkar, S. & Scherer, A. (2012). High-Q Impurity Photon States Bounded by a Photonic Band Pseudogap in an Optically Thick Photonic Crystal Slab. Physical Review B, 86(24), 245114.