Three-dimensionally confined modes in micropost microcavities: quality factors and Purcell factors

Abstract

Abstract-We present detailed calculations of the mode structure of distributed-Bragg-reflector micropost microcavities. Two methods are used: a first-principles, finite-difference time-domain model, and an approximate, heuristic model based on the separation of variables. We calculate modal quality factors, as well as enhancement of spontaneous emission rates, from single quantum dots in the microcavities. Both ideal and realistic post shapes are considered. The two methods give similar results, and are capable of accurately predicting experimentally measured values.Index Terms-Cavity quantum electrodynamics, microcavities, photonic bandgaps, quantum dots, spontaneous emission modification.

Micro-Optical Resonators for Microlasers and Integrated Optoelectronics

“…The finite-difference time-domain (FDTD) method (Chu, 1989) has been a main workhorse in modelling and design of optical microresonators (both in 2-D and 3-D) over the past few decades, due to its simplicity and flexibility (Fujita, 2001;Fong, 2003Fong, , 2004Ryu, 2004;Painter, 2001;Pelton, 2002;Hagness, 1997;Vuckovic, 1999;Rosenblit, 2004). However, the FDTD method suffers from relatively large dispersive error, staircasing errors at resonator boundaries, and reduction of accuracy to the first order at material interfaces.…”

“…In micropost and micropillar resonators (Gayral, 1998;Solomon, 2001;Pelton, 2002;Benyoucef, 2004;Santori, 2004), the transverse mode confinement is due to TIR at the semiconductor-air interface, while confinement in the vertical direction is provided by a pair of distributed Bragg reflectors. Thus, these microresonator structures can be seen as 1-D PC defect cavities in a fibre.…”

“…In wavelength-sized microresonator structures, semiconductor material luminescence can be either suppressed or enhanced, and they also enable narrowing of the spectral linewidth of the emitted light (Haroche, 1989;Yokoyama, 1992;Yamamoto, 1993;Vahala, 2003). Since 1946, when it was first proposed that the spontaneous emission from an excited state of an emitter can be significantly altered if it is placed into low-loss wavelength-scale cavity (Purcell, 1946), various microresonator designs for efficient control of spontaneous emission have been explored including microdisk Baba, 1997Baba, , 1999Backes, 1999;Cao, 2000;Fujita, 1999Fujita, , 2001Fujita, , 2002Zhang, 1996), microsphere Shopova, 2004;Rakovich, 2003) and micropost (Pelton, 2002;Reithmaier, 2004;Santori, 2004;Solomon, 2001;Gayral, 1998) resonators as well as PC defect cavities Boroditsky, 1999;Gayral, 1999). Depending on the Q-factors (resonance linewidths) of the modes supported by the microresonator in the spontaneous emission range of the resonator material, the two situations illustrated in Fig.…”

“…QDs of various sizes can now be fabricated by self-assembly, and have been integrated as emitters (so-called artificial atoms) in microdisk (Cao, 2000), PC defect (Yoshie, 2001;Hennesy, 2003), micropost/micropillar (Santori, 2004;Solomon, 2001;Gayral, 1998;Benyoucef, 2004), and microsphere (Shopova, 2004;Rakovich, 2003) resonators. The challenge is then to carefully design and tune the microresonator modal and geometrical properties to manipulate and increase the strength of coupling between the QD and an optical field of the resonator mode (Pelton, 2002;Hennesy, 2003). Figure 8.…”

“…In the micropost and micropillar resonators, emission occurs in a single-lobe pattern (Gayral, 1998;Pelton, 2002), which makes their coupling to fibres relatively straightforward. However, due to a rotational symmetry of the structure, the emission patterns of the WG modes in microspheres or circular microdisks are not unidirectional.…”