  The use of an optically thick slab may provide versatile solutions for the
realization of a current injection type laser using photonic crystals. Here, we
show that a transversely higher-order defect mode can be designed to be
confined by a photonic band gap in such a thick slab. Using simulations, we
show that a high-Q of 10^5 is possible from a finely tuned second-order
hexapole mode. Experimentally, we achieve optically pumped pulsed lasing at
1347 nm from the second-order hexapole mode with a peak threshold pump power of
88 uW.
